%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW294+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:31:11 PM UTC 2026
% Result : Theorem 33.31s 18.22s
% Output : CNFRefutation 33.60s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_6014)
% Comments :
%------------------------------------------------------------------------------
fof(fact_of__int__num,axiom,
! [X94,X7] :
( class_Rings_Oring__1(X7)
=> ( ( X94 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(c_Int_Oring__1__class_Oof__int(X7),X94) = c_Groups_Ozero__class_Ozero(X7) )
& ( X94 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X7),X94) = hAPP(c_Groups_Ouminus__class_Ouminus(X7),hAPP(c_Int_Oring__1__class_Oof__int(X7),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X94))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X7),X94) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X7),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X7,X7)),tc_fun(tc_Int_Oint,X7)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,X7),X7),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X7,X7)),tc_fun(tc_Int_Oint,X7)),tc_Int_Oint),c_COMBB(tc_fun(X7,X7),X7,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X7,tc_fun(tc_fun(X7,X7),X7),tc_Int_Oint),c_HOL_OLet(X7,X7)),c_Int_Oring__1__class_Oof__int(X7)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X7,X7),tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,X7)),tc_fun(tc_fun(X7,X7),tc_fun(X7,X7)),tc_Int_Oint),c_COMBS(X7,X7,X7)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X7,X7),tc_fun(X7,tc_fun(X7,X7))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,X7)),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_fun(X7,X7))),tc_Int_Oint),c_COMBB(X7,tc_fun(X7,X7),X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),tc_Int_Oint),c_If(X7)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X7,X7,X7),c_Groups_Oplus__class_Oplus(X7)),c_COMBI(X7))))),hAPP(hAPP(c_COMBC(X7,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X7),c_Groups_Oplus__class_Oplus(X7)),hAPP(hAPP(c_COMBS(X7,X7,X7),c_Groups_Oplus__class_Oplus(X7)),c_COMBI(X7)))),c_Groups_Oone__class_Oone(X7))))),c_Divides_Odivmod__int(X94,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__num) ).
fof(fact_not__sum__power2__lt__zero,axiom,
! [X98,X86,X87] :
( class_Rings_Olinordered__idom(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).
fof(fact_power2__less__0,axiom,
! [X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__0) ).
fof(fact_zmod__number__of__Bit1,axiom,
! [X139,X128] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__number__of__Bit1) ).
fof(fact_negDivAlg__eqn__number__of,axiom,
! [X128,X139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139))))
=> c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139))))
=> c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn__number__of) ).
fof(fact_negDivAlg__eqn__1__number__of,axiom,
! [X128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).
fof(fact_posDivAlg__eqn__number__of,axiom,
! [X128,X139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn__number__of) ).
fof(fact_posDivAlg__eqn__1__number__of,axiom,
! [X128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn__1__number__of) ).
fof(fact_negDivAlg__eqn,axiom,
! [X71,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)))
=> c_Divides_OnegDivAlg(X71,X84) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)))
=> c_Divides_OnegDivAlg(X71,X84) = hAPP(c_Divides_Oadjust(X84),c_Divides_OnegDivAlg(X71,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn) ).
fof(fact_posDivAlg__eqn,axiom,
! [X71,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),X84))
=> c_Divides_OposDivAlg(X71,X84) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),X84))
=> c_Divides_OposDivAlg(X71,X84) = hAPP(c_Divides_Oadjust(X84),c_Divides_OposDivAlg(X71,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn) ).
fof(fact_power__number__of__odd__number__of,axiom,
! [X163,X125,X7] :
( class_Int_Onumber__ring(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = hAPP(hAPP(c_HOL_OLet(X7,X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125))),hAPP(hAPP(c_COMBS(X7,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X7),c_Groups_Otimes__class_Otimes(X7)),hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)))),c_COMBI(X7))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = c_Groups_Oone__class_Oone(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__odd__number__of) ).
fof(fact_power__number__of__odd,axiom,
! [X26,X125,X7] :
( class_Int_Onumber__ring(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X7),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = hAPP(hAPP(c_HOL_OLet(X7,X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125))),hAPP(hAPP(c_COMBS(X7,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X7),c_Groups_Otimes__class_Otimes(X7)),hAPP(c_Groups_Otimes__class_Otimes(X7),X26))),c_COMBI(X7))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X7),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = c_Groups_Oone__class_Oone(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__odd) ).
fof(fact_zpower__number__of__odd,axiom,
! [X26,X125] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26))),c_COMBI(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__number__of__odd) ).
fof(fact_irrefl__tranclI,axiom,
! [X6,X172,X7] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X7,X7),X172)),c_Transitive__Closure_Ortrancl(X7,X172)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X6)),c_Transitive__Closure_Otrancl(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).
fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
! [X136,X23,X24,X25] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23,X136)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24))
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23),X25))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X136))
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23),X25))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X23)) )
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X136))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X136),X24)) ) ) ) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23),X136)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__psubset__iff) ).
fof(fact_acyclic__def,axiom,
! [X172,X7] :
( c_Wellfounded_Oacyclic(X7,X172)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),c_Transitive__Closure_Otrancl(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
fof(fact_zdiv__number__of__Bit1,axiom,
! [X139,X128] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X139))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X139))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit1) ).
fof(fact_acyclicI,axiom,
! [X172,X7] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),c_Transitive__Closure_Otrancl(X7,X172)))
=> c_Wellfounded_Oacyclic(X7,X172) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicI) ).
fof(fact_nat__number__of__Bit1,axiom,
! [X125] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Bit1) ).
fof(fact_upt__rec__number__of,axiom,
! [X33,X90] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33)))
=> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33)))
=> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__rec__number__of) ).
fof(fact_iszero__number__of__Bit1,axiom,
! [X128,X87] :
( ( class_Int_Onumber__ring(X87)
& class_Int_Oring__char__0(X87) )
=> ~ c_Int_Oiszero(X87,hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit1(X128))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__number__of__Bit1) ).
fof(fact_not__iszero__Numeral1,axiom,
! [X87] :
( class_Int_Onumber__ring(X87)
=> ~ c_Int_Oiszero(X87,hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__iszero__Numeral1) ).
fof(fact_Suc__nat__number__of__add,axiom,
! [X33,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X139))),X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__number__of__add) ).
fof(fact_upt__Suc,axiom,
! [X113,X114] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> c_List_Oupt(X114,hAPP(c_Nat_OSuc,X113)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X114,X113)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X113),c_List_Olist_ONil(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> c_List_Oupt(X114,hAPP(c_Nat_OSuc,X113)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__Suc) ).
fof(fact_upt__rec,axiom,
! [X113,X114] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> c_List_Oupt(X114,X113) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X114),c_List_Oupt(hAPP(c_Nat_OSuc,X114),X113)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> c_List_Oupt(X114,X113) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__rec) ).
fof(fact_nat__number__of__diff__1,axiom,
! [X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X139)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__diff__1) ).
fof(fact_nat__number__of__add__1,axiom,
! [X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X139)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__add__1) ).
fof(fact_nat__1__add__number__of,axiom,
! [X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X139)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__number__of) ).
fof(fact_Suc__nat__number__of,axiom,
! [X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X139)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__number__of) ).
fof(fact_adjust__def,axiom,
! [X24] : c_Divides_Oadjust(X24) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X24))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X24))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_adjust__def) ).
fof(fact_succ__Bit0,axiom,
! [X96] : c_Int_Osucc(c_Int_OBit0(X96)) = c_Int_OBit1(X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Bit0) ).
fof(fact_Bit0__def,axiom,
! [X96] : c_Int_OBit0(X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_diff__bin__simps_I2_J,axiom,
! [X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),c_Int_OMin) = c_Int_Osucc(X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I2_J) ).
fof(fact_prod__fun__imageE,axiom,
! [X191,X1,X2,X190,X119,X23,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),X23),hAPP(c_Set_Oimage(tc_prod(X119,X190),tc_prod(X7,X105),c_Product__Type_Omap__pair(X119,X7,X190,X105,X2,X1)),X191)))
=> ~ ! [X3,X82] :
( X23 = hAPP(hAPP(c_Product__Type_OPair(X7,X105),hAPP(X2,X3)),hAPP(X1,X82))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X119,X190)),hAPP(hAPP(c_Product__Type_OPair(X119,X190),X3),X82)),X191)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__fun__imageE) ).
fof(fact_divmod__int__pdivmod,axiom,
! [X157,X94] :
( ( X94 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X94,X157) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( X94 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( X157 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X94,X157) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94) )
& ( X157 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X94,X157) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X157))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X157)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X157),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X94,X157)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X157))))),c_Divides_Opdivmod(X94,X157)))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__pdivmod) ).
fof(fact_apsnd__def,axiom,
! [X2,X7,X119,X105] : c_Product__Type_Oapsnd(X105,X119,X7,X2) = c_Product__Type_Omap__pair(X7,X7,X105,X119,c_Fun_Oid(X7),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__def) ).
fof(fact_divmod__int__code,axiom,
! [X157,X94] :
( ( X94 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X94,X157) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( X94 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( X157 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X94,X157) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94) )
& ( X157 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X94,X157) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X157))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X94)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X157))),c_Divides_Opdivmod(X94,X157)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X157))))),c_Divides_Opdivmod(X94,X157)))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__code) ).
fof(fact_Nitpick_Oplus__frac__def,axiom,
! [X172,X153,X7] : c_Nitpick_Oplus__frac(X7,X153,X172) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X7),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X7),X153),hAPP(c_Nitpick_Odenom(X7),X172))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X7),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X7),tc_Int_Oint),c_Nitpick_Ofrac(X7)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X7),X153))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X7),X153))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X7),X172))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X7),X172)))))),c_COMBI(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).
fof(fact_Nitpick_Odenom__def,axiom,
! [X7] : c_Nitpick_Odenom(X7) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X7,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Odenom__def) ).
fof(fact_Nitpick_Onum__def,axiom,
! [X7] : c_Nitpick_Onum(X7) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X7,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Onum__def) ).
fof(fact_reflcl__set__eq,axiom,
! [X127,X6,X172,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X7,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X7,X7)))),c_Product__Type_OPair(X7,X7)))),X172)),c_fequal),X6),X127))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),c_Relation_OId(X7)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__set__eq) ).
fof(fact_rtrancl__empty,axiom,
! [X7] : c_Transitive__Closure_Ortrancl(X7,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))) = c_Relation_OId(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__empty) ).
fof(fact_adjust__eq,axiom,
! [X172,X153,X24] : hAPP(c_Divides_Oadjust(X24),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X153),X172)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X172),X24)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X153)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X153)),X172))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_adjust__eq) ).
fof(fact_trancl__insert,axiom,
! [X172,X6,X127,X7] : c_Transitive__Closure_Otrancl(X7,hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X6)),X172)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X7,X172)),hAPP(c_Set_OCollect(tc_prod(X7,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X7,X7))),hAPP(hAPP(c_COMBC(X7,X7,tc_prod(X7,X7)),c_Product__Type_OPair(X7,X7)),X127))),c_Transitive__Closure_Ortrancl(X7,X172))))),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X7,X7))),hAPP(c_Product__Type_OPair(X7,X7),X6))),c_Transitive__Closure_Ortrancl(X7,X172)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__insert) ).
fof(fact_trancl__unfold__left,axiom,
! [X172,X7] : c_Transitive__Closure_Otrancl(X7,X172) = hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X172),c_Transitive__Closure_Ortrancl(X7,X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).
fof(fact_map__add__map__of__foldr,axiom,
! [X289,X95,X105,X7] : c_Map_Omap__add(X7,X105,X95,c_Map_Omap__of(X7,X105,X289)) = c_List_Ofoldr(tc_prod(X7,X105),tc_fun(X7,tc_Option_Ooption(X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_fun(tc_fun(X7,tc_Option_Ooption(X105)),tc_fun(X7,tc_Option_Ooption(X105)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_Option_Ooption(X105)),tc_fun(X105,tc_fun(tc_fun(X7,tc_Option_Ooption(X105)),tc_fun(X7,tc_Option_Ooption(X105))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X105),tc_fun(tc_fun(X7,tc_Option_Ooption(X105)),tc_fun(X7,tc_Option_Ooption(X105)))),tc_fun(tc_fun(X105,tc_Option_Ooption(X105)),tc_fun(X105,tc_fun(tc_fun(X7,tc_Option_Ooption(X105)),tc_fun(X7,tc_Option_Ooption(X105))))),X7),c_COMBB(tc_Option_Ooption(X105),tc_fun(tc_fun(X7,tc_Option_Ooption(X105)),tc_fun(X7,tc_Option_Ooption(X105))),X105)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_Option_Ooption(X105)),tc_fun(tc_Option_Ooption(X105),tc_fun(X7,tc_Option_Ooption(X105)))),tc_fun(tc_Option_Ooption(X105),tc_fun(tc_fun(X7,tc_Option_Ooption(X105)),tc_fun(X7,tc_Option_Ooption(X105)))),X7),c_COMBC(tc_fun(X7,tc_Option_Ooption(X105)),tc_Option_Ooption(X105),tc_fun(X7,tc_Option_Ooption(X105)))),hAPP(c_COMBC(tc_fun(X7,tc_Option_Ooption(X105)),X7,tc_fun(tc_Option_Ooption(X105),tc_fun(X7,tc_Option_Ooption(X105)))),c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)))))),c_Option_Ooption_OSome(X105))),X289,X95),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__map__of__foldr) ).
fof(fact_foldr__foldl,axiom,
! [X25,X292,X2,X7,X105] : c_List_Ofoldr(X105,X7,X2,X292,X25) = hAPP(c_List_Ofoldl(X7,X105,hAPP(c_COMBC(X105,X7,X7),X2),X25),hAPP(c_List_Orev(X105),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__foldl) ).
fof(fact_sum__power2__le__zero__iff,axiom,
! [X127,X6,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X6),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X127),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X7)))
<=> ( X6 = c_Groups_Ozero__class_Ozero(X7)
& X127 = c_Groups_Ozero__class_Ozero(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).
fof(fact_transpose_Opsimps_I3_J,axiom,
! [X331,X292,X6,X7] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X7)),c_List_Otranspose__rel(X7)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),X331)))
=> c_List_Otranspose(X7,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),X331)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Oconcat(X7,hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_Olist__case(tc_List_Olist(X7),X7,c_List_Olist_ONil(X7),hAPP(hAPP(c_COMBB(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),X7),c_COMBK(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_COMBC(X7,tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_OCons(X7)),c_List_Olist_ONil(X7))))),X331)))),c_List_Otranspose(X7,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X7)),X292),c_List_Oconcat(tc_List_Olist(X7),hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(tc_List_Olist(X7))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X7)),X7,c_List_Olist_ONil(tc_List_Olist(X7)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X7),tc_List_Olist(tc_List_Olist(X7))),X7),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_List_Olist(tc_List_Olist(X7)),tc_List_Olist(tc_List_Olist(X7))),c_List_Olist_OCons(tc_List_Olist(X7))),c_List_Olist_ONil(tc_List_Olist(X7)))))),X331))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I3_J) ).
fof(fact_concat__conv__foldl,axiom,
! [X331,X7] : c_List_Oconcat(X7,X331) = hAPP(c_List_Ofoldl(tc_List_Olist(X7),tc_List_Olist(X7),c_List_Oappend(X7),c_List_Olist_ONil(X7)),X331),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__conv__foldl) ).
fof(fact_transpose_Osimps_I3_J,axiom,
! [X331,X292,X6,X7] : c_List_Otranspose(X7,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),X331)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Oconcat(X7,hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_Olist__case(tc_List_Olist(X7),X7,c_List_Olist_ONil(X7),hAPP(hAPP(c_COMBB(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),X7),c_COMBK(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_COMBC(X7,tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_OCons(X7)),c_List_Olist_ONil(X7))))),X331)))),c_List_Otranspose(X7,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X7)),X292),c_List_Oconcat(tc_List_Olist(X7),hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(tc_List_Olist(X7))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X7)),X7,c_List_Olist_ONil(tc_List_Olist(X7)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X7),tc_List_Olist(tc_List_Olist(X7))),X7),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_List_Olist(tc_List_Olist(X7)),tc_List_Olist(tc_List_Olist(X7))),c_List_Olist_OCons(tc_List_Olist(X7))),c_List_Olist_ONil(tc_List_Olist(X7)))))),X331))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I3_J) ).
fof(fact_odd__power__less__zero,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33)))),c_Groups_Ozero__class_Ozero(X87))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__power__less__zero) ).
fof(fact_rel__compE,axiom,
! [X45,X172,X119,X287,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),X287),hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),X172),X45)))
=> ~ ! [X3,X82,X154] :
( X287 = hAPP(hAPP(c_Product__Type_OPair(X7,X105),X3),X154)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X119)),hAPP(hAPP(c_Product__Type_OPair(X7,X119),X3),X82)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X119,X105)),hAPP(hAPP(c_Product__Type_OPair(X119,X105),X82),X154)),X45)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__compE) ).
fof(fact_odd__0__le__power__imp__0__le,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33)))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).
fof(fact_evaln__elim__cases_I7_J,axiom,
! [X58,X44,X45,X25,X38,X39] :
( c_Natural_Oevaln(c_Com_Ocom_OCall(X39,X38,X25),X45,X44,X58)
=> ~ ! [X62] :
( X58 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X62),hAPP(c_Natural_Ogetlocs,X45))),X39),hAPP(hAPP(c_Natural_Ogetlocs,X62),c_Com_ORes))
=> ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X38),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X45),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X25,X45)),X44,X62) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I7_J) ).
fof(fact_power2__diff,axiom,
! [X98,X86,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X86),X98)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X86)),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__diff) ).
fof(fact_power2__sum,axiom,
! [X98,X86,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X86),X98)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X86)),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__sum) ).
fof(fact_dvd_OgreaterThan__iff,axiom,
! [X94,X107] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X107),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X94)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),X107))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X107),X94)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThan__iff) ).
fof(fact_dvd_OlessThan__iff,axiom,
! [X94,X107] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X107),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X94)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X107),X94))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),X107)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OlessThan__iff) ).
fof(fact_Nitpick_Osetsum_H__def,axiom,
! [X2,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Nitpick_Osetsum_H(X7,X105,X2,X149) = hAPP(c_List_Omonoid__add__class_Olistsum(X105),hAPP(hAPP(c_List_Omap(X7,X105),X2),c_Hilbert__Choice_OEps(tc_List_Olist(X7),hAPP(hAPP(c_COMBS(tc_List_Olist(X7),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X7)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X7)),c_fequal),c_List_Oset(X7))),X149))),c_List_Odistinct(X7))))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Nitpick_Osetsum_H(X7,X105,X2,X149) = c_Groups_Ozero__class_Ozero(X105) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).
fof(fact_sum__power2__gt__zero__iff,axiom,
! [X127,X6,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X6),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X127),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
<=> ( X6 != c_Groups_Ozero__class_Ozero(X7)
| X127 != c_Groups_Ozero__class_Ozero(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
fof(fact_transpose__aux__max,axiom,
! [X331,X105,X292,X7] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292))),c_List_Ofoldr(tc_List_Olist(X105),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X105)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X105))),X331,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)),c_List_Ofoldr(tc_List_Olist(X105),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X105)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X105),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X105)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X105)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X105),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X105)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X105),tc_List_Olist(X105),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X105)))),X331),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__max) ).
fof(fact_sublist__shift__lemma,axiom,
! [X107,X292,X149,X7] : hAPP(hAPP(c_List_Omap(tc_prod(X7,tc_Nat_Onat),X7),c_Product__Type_Ofst(X7,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X7,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X7,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X7,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X7,tc_Nat_Onat))),X149)),hAPP(hAPP(c_List_Ozip(X7,tc_Nat_Onat),X292),c_List_Oupt(X107,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X7,tc_Nat_Onat),X7),c_Product__Type_Ofst(X7,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X7,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X7,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X7,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X7,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X7,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X7,tc_Nat_Onat))),X107))),X149)),hAPP(hAPP(c_List_Ozip(X7,tc_Nat_Onat),X292),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__shift__lemma) ).
fof(fact_sorted__list__of__set__range,axiom,
! [X44,X95] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X44)) = c_List_Oupt(X95,X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__range) ).
fof(fact_Random_Osimps,axiom,
! [X198,X1,X7,X199] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X199),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(X7,X1,X199,X198) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X7)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X199),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(X7,X1,X199,X198) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X1,X198)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X7,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X199),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X198))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7))))),tc_prod(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X7)),hAPP(hAPP(c_COMBB(X7,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X7)),c_Product__Type_Ofst(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Random_Osimps) ).
fof(fact_Suc__div__eq__add3__div__number__of,axiom,
! [X139,X90] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X90)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).
fof(fact_Suc__div__eq__add3__div,axiom,
! [X33,X90] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X90)))),X33) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X90)),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div) ).
fof(fact_New__DSequence_Opos__not__seq__def,axiom,
! [X107,X196] : hAPP(c_New__DSequence_Opos__not__seq(X196),X107) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X196,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X107))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).
fof(fact_mem__splitE,axiom,
! [X161,X23,X119,X105,X26,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X26),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,tc_fun(X7,tc_HOL_Obool)),X23),X161)))
=> ~ ! [X3,X82] :
( X161 = hAPP(hAPP(c_Product__Type_OPair(X105,X119),X3),X82)
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X26),hAPP(hAPP(X23,X3),X82))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitE) ).
fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
! [X163,X149,X6,X26,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),X163))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ~ ! [X82] :
( X163 = hAPP(hAPP(X2,X6),X82)
=> ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,X149),X82)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).
fof(fact_int__of__code,axiom,
! [X96] :
( ( X96 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Code__Numeral_Oint__of,X96) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X96 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X96,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Code__Numeral_Oint__of,X96) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X96),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
& ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X96,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Code__Numeral_Oint__of,X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X96),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__of__code) ).
fof(fact_sum__power2__ge__zero,axiom,
! [X98,X86,X87] :
( class_Rings_Olinordered__idom(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__ge__zero) ).
fof(fact_pigeonhole__infinite,axiom,
! [X2,X105,X149,X7] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(c_Set_Oimage(X7,X105,X2),X149)))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))),hAPP(hAPP(c_COMBC(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X105,tc_fun(X105,tc_HOL_Obool),X7),c_fequal),X2)),hAPP(X2,X3)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole__infinite) ).
fof(fact_concat__injective,axiom,
! [X293,X292,X7] :
( c_List_Oconcat(X7,X292) = c_List_Oconcat(X7,X293)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),X293)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),X3),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X7),tc_List_Olist(X7),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_Nat_Onat),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X7),tc_Nat_Onat),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_List_Olist(X7)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X7))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X7)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X7))))),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),X3)) )
=> X292 = X293 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__injective) ).
fof(fact_concat__eq__concat__iff,axiom,
! [X293,X292,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),X3),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X7),tc_List_Olist(X7),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_Nat_Onat),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X7),tc_Nat_Onat),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_List_Olist(X7)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X7))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X7)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X7))))),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),X3)) )
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),X293)
=> ( c_List_Oconcat(X7,X292) = c_List_Oconcat(X7,X293)
<=> X292 = X293 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__eq__concat__iff) ).
fof(fact_nat__rec__add__eq__if,axiom,
! [X44,X163,X2,X25,X7] : hAPP(c_Nat_Onat_Onat__rec(X7,X25,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),X44)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X7),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X7,X7),hAPP(hAPP(c_COMBC(tc_Int_Oint,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),tc_Int_Oint),c_If(X7)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X7,X25,X2),X44))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X7,X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X7,X7),tc_Int_Oint),X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X44))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Int_Oint),c_Nat_Onat_Onat__rec(X7,X25,X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X44))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__add__eq__if) ).
fof(fact_add__Min__right,axiom,
! [X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Int_OMin) = c_Int_Opred(X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min__right) ).
fof(fact_neg__zmod__mult__2,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X71)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X84),c_Groups_Oone__class_Oone(tc_Int_Oint)),X71))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zmod__mult__2) ).
fof(fact_neg__zdiv__mult__2,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X84))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X71)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X84),c_Groups_Oone__class_Oone(tc_Int_Oint))),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zdiv__mult__2) ).
fof(fact_pos__zdiv__mult__2,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X84))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X71)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zdiv__mult__2) ).
fof(fact_eq__number__of__Suc,axiom,
! [X44,X163] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163) = hAPP(c_Nat_OSuc,X44)
<=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X44))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__Suc) ).
fof(fact_Suc__eq__number__of,axiom,
! [X163,X44] :
( hAPP(c_Nat_OSuc,X44) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)
<=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X44))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__number__of) ).
fof(fact_Nitpick_Ocard_H__def,axiom,
! [X149,X7] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Nitpick_Ocard_H(X7,X149) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),c_Hilbert__Choice_OEps(tc_List_Olist(X7),hAPP(hAPP(c_COMBS(tc_List_Olist(X7),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X7)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X7)),c_fequal),c_List_Oset(X7))),X149))),c_List_Odistinct(X7)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Nitpick_Ocard_H(X7,X149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ocard_H__def) ).
fof(fact_card__less__Suc2,axiom,
! [X107,X210] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X210))
=> hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X210))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X107)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X210))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X107))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less__Suc2) ).
fof(fact_power2__le__imp__le,axiom,
! [X98,X86,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).
fof(fact_power2__less__imp__less,axiom,
! [X98,X86,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).
fof(fact_vimage__if,axiom,
! [X155,X105,X136,X149,X23,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X136),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBC(X105,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X105),c_If(X7)),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X155))),X23)),X136)),X149) = c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X136),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBC(X105,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X105),c_If(X7)),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X155))),X23)),X136)),X149) = X155 ) ) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X136),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBC(X105,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X105),c_If(X7)),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X155))),X23)),X136)),X149) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X105,tc_HOL_Obool)),X155) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X136),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBC(X105,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X105),c_If(X7)),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X155))),X23)),X136)),X149) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__if) ).
fof(fact_pos__zmod__mult__2,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X71)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X71))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmod__mult__2) ).
fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
! [X139,X90] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X90))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X90),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod__number__of) ).
fof(fact_zero__le__even__power_H,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).
fof(fact_Suc__mod__eq__add3__mod,axiom,
! [X33,X90] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X90))),X33) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X90),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod) ).
fof(fact_mod__Suc__eq__mod__add3,axiom,
! [X33,X90] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X33)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__mod__add3) ).
fof(fact_div__Suc__eq__div__add3,axiom,
! [X33,X90] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X33)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__Suc__eq__div__add3) ).
fof(fact_trancl__Int__subset,axiom,
! [X45,X172,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X45))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X7,X172)),X45)),X172)),X45))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X7,X172)),X45)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__Int__subset) ).
fof(fact_setprod__gen__delta,axiom,
! [X23,X24,X25,X209,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),X23)),X209) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(X24,X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X105),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X209)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),X23)),X209) = hAPP(hAPP(c_Power_Opower__class_Opower(X105),X23),hAPP(c_Finite__Set_Ocard(X7),X209)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__gen__delta) ).
fof(fact_setprod__delta,axiom,
! [X24,X25,X209,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),c_Groups_Oone__class_Oone(X105))),X209) = hAPP(X24,X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),c_Groups_Oone__class_Oone(X105))),X209) = c_Groups_Oone__class_Oone(X105) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__delta) ).
fof(fact_setsum__delta,axiom,
! [X24,X25,X209,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),c_Groups_Ozero__class_Ozero(X105))),X209) = hAPP(X24,X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),c_Groups_Ozero__class_Ozero(X105))),X209) = c_Groups_Ozero__class_Ozero(X105) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta) ).
fof(fact_le__Suc__number__of,axiom,
! [X163,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)))
<=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44)),c_Int_Onat))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__number__of) ).
fof(fact_less__Suc__number__of,axiom,
! [X163,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)))
<=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44)),c_Int_Onat))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__number__of) ).
fof(fact_apsnd__apfst__commute,axiom,
! [X161,X1,X190,X2,X7,X105,X119] : hAPP(c_Product__Type_Oapsnd(X119,X105,X7,X2),hAPP(c_Product__Type_Oapfst(X190,X7,X119,X1),X161)) = hAPP(c_Product__Type_Oapfst(X190,X7,X105,X1),hAPP(c_Product__Type_Oapsnd(X119,X105,X190,X2),X161)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__apfst__commute) ).
fof(fact_apfst__def,axiom,
! [X2,X105,X119,X7] : c_Product__Type_Oapfst(X7,X119,X105,X2) = c_Product__Type_Omap__pair(X7,X119,X105,X105,X2,c_Fun_Oid(X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__def) ).
fof(fact_lexord__append__leftD,axiom,
! [X172,X163,X160,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Oappend(X7),X6),X160)),hAPP(hAPP(c_List_Oappend(X7),X6),X163))),c_List_Olexord(X7,X172)))
=> ( ! [X110] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X110),X110)),X172))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X160),X163)),c_List_Olexord(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).
fof(fact_rel__pow__E2,axiom,
! [X191,X44,X26,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)))
=> ( ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X6 != X26 )
=> ~ ! [X82,X116] :
( X44 = hAPP(c_Nat_OSuc,X116)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X82)),X191))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X116),X191))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__E2) ).
fof(fact_map__comp__Some__iff,axiom,
! [X163,X94,X284,X285,X119,X7,X105] :
( c_Map_Omap__comp(X105,X7,X119,X285,X284,X94) = hAPP(c_Option_Ooption_OSome(X7),X163)
<=> ? [X291] :
( hAPP(X284,X94) = hAPP(c_Option_Ooption_OSome(X105),X291)
& hAPP(X285,X291) = hAPP(c_Option_Ooption_OSome(X7),X163) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__Some__iff) ).
fof(fact_map__comp__def,axiom,
! [X94,X1,X2,X119,X7,X105] : c_Map_Omap__comp(X105,X7,X119,X2,X1,X94) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X7),X105,c_Option_Ooption_ONone(X7),X2),hAPP(X1,X94)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__def) ).
fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
! [X24,X25] :
( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25,X24) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff) ).
fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
! [X157,X94] :
( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X94,X157) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),X157))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X157),X94)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff) ).
fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
! [X24,X25] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25,X24)
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff2) ).
fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
! [X157,X94] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X94,X157)
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),X157))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X157),X94)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff2) ).
fof(fact_dvd_Ostrict__monoD,axiom,
! [X127,X6,X2,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X7,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X127),X6)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(X2,X6)),hAPP(X2,X127))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ostrict__monoD) ).
fof(fact_power__odd__eq,axiom,
! [X33,X71,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__odd__eq) ).
fof(fact_evalc__elim__cases_I7_J,axiom,
! [X58,X45,X25,X38,X39] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X39,X38,X25)),X45),X58))
=> ~ ! [X62] :
( X58 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X62),hAPP(c_Natural_Ogetlocs,X45))),X39),hAPP(hAPP(c_Natural_Ogetlocs,X62),c_Com_ORes))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X38)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X45),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X25,X45))),X62)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I7_J) ).
fof(fact_apsnd__compose,axiom,
! [X6,X1,X190,X2,X7,X105,X119] : hAPP(c_Product__Type_Oapsnd(X119,X105,X7,X2),hAPP(c_Product__Type_Oapsnd(X190,X119,X7,X1),X6)) = hAPP(c_Product__Type_Oapsnd(X190,X105,X7,hAPP(c_Fun_Ocomp(X119,X105,X190,X2),X1)),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__compose) ).
fof(fact_apfst__compose,axiom,
! [X6,X1,X190,X2,X105,X7,X119] : hAPP(c_Product__Type_Oapfst(X119,X7,X105,X2),hAPP(c_Product__Type_Oapfst(X190,X119,X105,X1),X6)) = hAPP(c_Product__Type_Oapfst(X190,X7,X105,hAPP(c_Fun_Ocomp(X119,X7,X190,X2),X1)),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__compose) ).
fof(fact_sum__power2__eq__zero__iff,axiom,
! [X127,X6,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X6),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X127),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X7)
<=> ( X6 = c_Groups_Ozero__class_Ozero(X7)
& X127 = c_Groups_Ozero__class_Ozero(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
fof(fact_evaln__elim__cases_I3_J,axiom,
! [X46,X44,X45,X23,X25,X60] :
( c_Natural_Oevaln(c_Com_Ocom_OLocal(X60,X25,X23),X45,X44,X46)
=> ~ ! [X62] :
( X46 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X62),c_Com_Ovname_OLoc(X60)),hAPP(hAPP(c_Natural_Ogetlocs,X45),X60))
=> ~ c_Natural_Oevaln(X23,hAPP(hAPP(hAPP(c_Natural_Oupdate,X45),c_Com_Ovname_OLoc(X60)),hAPP(X25,X45)),X44,X62) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I3_J) ).
fof(fact_transpose__rectangle,axiom,
! [X44,X7,X292] :
( ( X292 = c_List_Olist_ONil(tc_List_Olist(X7))
=> X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> ( ! [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X147),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),X292)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X7)),X292),X147)) = X44 )
=> c_List_Otranspose(X7,X292) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X7)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X7)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X7),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X7)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X7)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X7),hAPP(hAPP(c_COMBB(tc_List_Olist(X7),tc_fun(tc_Nat_Onat,X7),tc_Nat_Onat),c_List_Onth(X7)),hAPP(c_List_Onth(tc_List_Olist(X7)),X292))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),X292)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__rectangle) ).
fof(fact_negDivAlg_Opinduct,axiom,
! [X38,X42,X187] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X42)))
=> ( ! [X110,X188] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X110),X188)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X110),X188)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X188),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> hBOOL(hAPP(hAPP(X38,X110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X188))) )
=> hBOOL(hAPP(hAPP(X38,X110),X188)) ) )
=> hBOOL(hAPP(hAPP(X38,X187),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Opinduct) ).
fof(fact_setprod__delta_H,axiom,
! [X24,X25,X209,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(c_fequal,X25))),X24)),c_Groups_Oone__class_Oone(X105))),X209) = hAPP(X24,X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(c_fequal,X25))),X24)),c_Groups_Oone__class_Oone(X105))),X209) = c_Groups_Oone__class_Oone(X105) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__delta_H) ).
fof(fact_setsum__delta_H,axiom,
! [X24,X25,X209,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(c_fequal,X25))),X24)),c_Groups_Ozero__class_Ozero(X105))),X209) = hAPP(X24,X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(c_fequal,X25))),X24)),c_Groups_Ozero__class_Ozero(X105))),X209) = c_Groups_Ozero__class_Ozero(X105) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta_H) ).
fof(fact_posDivAlg_Opinduct,axiom,
! [X38,X42,X187] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X42)))
=> ( ! [X110,X188] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X110),X188)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X110),X188))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X188),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> hBOOL(hAPP(hAPP(X38,X110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X188))) )
=> hBOOL(hAPP(hAPP(X38,X110),X188)) ) )
=> hBOOL(hAPP(hAPP(X38,X187),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Opinduct) ).
fof(fact_listrel__Cons2,axiom,
! [X172,X293,X127,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X293))),c_List_Olistrel(X7,X172)))
=> ~ ! [X3,X307] :
( X292 = hAPP(hAPP(c_List_Olist_OCons(X7),X3),X307)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X127)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X307),X293)),c_List_Olistrel(X7,X172))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons2) ).
fof(fact_rel__pow__Suc__E2,axiom,
! [X191,X44,X26,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),hAPP(c_Nat_OSuc,X44)),X191)))
=> ~ ! [X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X82)),X191))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__E2) ).
fof(fact_Nitpick_Otimes__frac__def,axiom,
! [X138,X144,X87] : c_Nitpick_Otimes__frac(X87,X144,X138) = hAPP(hAPP(c_Nitpick_Ofrac(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X87),X144)),hAPP(c_Nitpick_Onum(X87),X138))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X87),X144)),hAPP(c_Nitpick_Odenom(X87),X138))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).
fof(fact_rel__pow__E,axiom,
! [X191,X44,X26,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)))
=> ( ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X6 != X26 )
=> ~ ! [X82,X116] :
( X44 = hAPP(c_Nat_OSuc,X116)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X82)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X116),X191)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X26)),X191)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__E) ).
fof(fact_rel__pow__Suc__E,axiom,
! [X191,X44,X26,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),hAPP(c_Nat_OSuc,X44)),X191)))
=> ~ ! [X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X82)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X26)),X191)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__E) ).
fof(fact_negDivAlg_Opsimps,axiom,
! [X24,X25] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X25),X24)))
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),X24)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OnegDivAlg(X25,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),X24)) )
& ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),X24)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OnegDivAlg(X25,X24) = hAPP(c_Divides_Oadjust(X24),c_Divides_OnegDivAlg(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X24))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Opsimps) ).
fof(fact_posDivAlg_Opsimps,axiom,
! [X24,X25] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X25),X24)))
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X24))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OposDivAlg(X25,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25) )
& ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X24))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OposDivAlg(X25,X24) = hAPP(c_Divides_Oadjust(X24),c_Divides_OposDivAlg(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X24))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Opsimps) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
! [X33,X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X33))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).
fof(fact_arith__series__int,axiom,
! [X44,X136,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X136))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X44))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X136)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__int) ).
fof(fact_le__number__of__Suc,axiom,
! [X44,X163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),hAPP(c_Nat_OSuc,X44)))
<=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X44)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of__Suc) ).
fof(fact_less__number__of__Suc,axiom,
! [X44,X163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),hAPP(c_Nat_OSuc,X44)))
<=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X44)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__Suc) ).
fof(fact_of__nat__double,axiom,
! [X86,X87] :
( class_Rings_Osemiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X86))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onat,X86))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onat,X86))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__double) ).
fof(fact_negDivAlg_Osimps,axiom,
! [X84,X71] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OnegDivAlg(X71,X84) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)) )
& ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OnegDivAlg(X71,X84) = hAPP(c_Divides_Oadjust(X84),c_Divides_OnegDivAlg(X71,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Osimps) ).
fof(fact_posDivAlg_Osimps,axiom,
! [X84,X71] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),X84))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OposDivAlg(X71,X84) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71) )
& ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),X84))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OposDivAlg(X71,X84) = hAPP(c_Divides_Oadjust(X84),c_Divides_OposDivAlg(X71,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Osimps) ).
fof(fact_power__minus1__odd,axiom,
! [X33,X87] :
( class_Rings_Oring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Oone__class_Oone(X87))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33))) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Oone__class_Oone(X87)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus1__odd) ).
fof(fact_power__minus__even,axiom,
! [X33,X71,X87] :
( class_Rings_Oring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus__even) ).
fof(fact_power__m1__odd,axiom,
! [X33,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33))) = hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__odd) ).
fof(fact_Suc3__eq__add__3,axiom,
! [X33] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X33))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).
fof(fact_ImageE,axiom,
! [X149,X172,X105,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(c_Relation_OImage(X105,X7,X172),X149)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X3),X24)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(X105),X3),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ImageE) ).
fof(fact_nat__case__add__eq__if,axiom,
! [X44,X163,X2,X25,X7] : c_Nat_Onat_Onat__case(X7,X25,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),X44)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X7),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X7,X7),hAPP(hAPP(c_COMBC(tc_Int_Oint,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),tc_Int_Oint),c_If(X7)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X7,X25,X2,X44))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Int_Oint),X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X44)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__add__eq__if) ).
fof(fact_mod2__gr__0,axiom,
! [X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X95,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X95,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod2__gr__0) ).
fof(fact_apsnd__eq__conv,axiom,
! [X1,X6,X2,X7,X105,X119] :
( hAPP(c_Product__Type_Oapsnd(X119,X105,X7,X2),X6) = hAPP(c_Product__Type_Oapsnd(X119,X105,X7,X1),X6)
<=> hAPP(X2,hAPP(c_Product__Type_Osnd(X7,X119),X6)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X7,X119),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__eq__conv) ).
fof(fact_apfst__eq__conv,axiom,
! [X1,X6,X2,X105,X7,X119] :
( hAPP(c_Product__Type_Oapfst(X119,X7,X105,X2),X6) = hAPP(c_Product__Type_Oapfst(X119,X7,X105,X1),X6)
<=> hAPP(X2,hAPP(c_Product__Type_Ofst(X119,X105),X6)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X119,X105),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__eq__conv) ).
fof(fact_Id__def,axiom,
! [X7] : c_Relation_OId(X7) = hAPP(c_Set_OCollect(tc_prod(X7,X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X7,X7)),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBC(tc_prod(X7,X7),tc_fun(X7,tc_prod(X7,X7)),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_prod(X7,X7)),tc_fun(X7,tc_HOL_Obool)),tc_prod(X7,X7)),c_COMBB(tc_prod(X7,X7),tc_HOL_Obool,X7)),c_fequal)),hAPP(hAPP(c_COMBS(X7,X7,tc_prod(X7,X7)),c_Product__Type_OPair(X7,X7)),c_COMBI(X7))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__def) ).
fof(fact_apsnd__apfst,axiom,
! [X6,X1,X190,X2,X7,X105,X119] : hAPP(c_Product__Type_Oapsnd(X119,X105,X7,X2),hAPP(c_Product__Type_Oapfst(X190,X7,X119,X1),X6)) = hAPP(hAPP(c_Product__Type_OPair(X7,X105),hAPP(X1,hAPP(c_Product__Type_Ofst(X190,X119),X6))),hAPP(X2,hAPP(c_Product__Type_Osnd(X190,X119),X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__apfst) ).
fof(fact_apfst__apsnd,axiom,
! [X6,X1,X190,X2,X105,X7,X119] : hAPP(c_Product__Type_Oapfst(X119,X7,X105,X2),hAPP(c_Product__Type_Oapsnd(X190,X105,X119,X1),X6)) = hAPP(hAPP(c_Product__Type_OPair(X7,X105),hAPP(X2,hAPP(c_Product__Type_Ofst(X119,X190),X6))),hAPP(X1,hAPP(c_Product__Type_Osnd(X119,X190),X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__apsnd) ).
fof(fact_dvd_Ostrict__monoI,axiom,
! [X2,X7] :
( class_Orderings_Oorder(X7)
=> ( ! [X3,X82] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X82))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X82),X3)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(X2,X3)),hAPP(X2,X82))) )
=> c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X7,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ostrict__monoI) ).
fof(fact_half__gt__zero__iff,axiom,
! [X172,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber__ring(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X172),hAPP(c_Int_Onumber__class_Onumber__of(X7),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X172)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).
fof(fact_max__Suc__number__of,axiom,
! [X44,X163] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),hAPP(c_Nat_OSuc,X44)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X44))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X44)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc__number__of) ).
fof(fact_zero__less__power2,axiom,
! [X25,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> X25 != c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power2) ).
fof(fact_min__Suc__number__of,axiom,
! [X44,X163] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),hAPP(c_Nat_OSuc,X44)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X44)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc__number__of) ).
fof(fact_nat__rec__number__of,axiom,
! [X163,X2,X25,X7] : hAPP(c_Nat_Onat_Onat__rec(X7,X25,X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X7),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X7,X7),hAPP(hAPP(c_COMBC(tc_Int_Oint,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),tc_Int_Oint),c_If(X7)),c_Nat__Numeral_Oneg)),X25)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X7,X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X7,X7),tc_Int_Oint),X2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Int_Oint),c_Nat_Onat_Onat__rec(X7,X25,X2)),c_Int_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__number__of) ).
fof(fact_transpose__aux__filter__head,axiom,
! [X331,X7] : c_List_Oconcat(X7,hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_Olist__case(tc_List_Olist(X7),X7,c_List_Olist_ONil(X7),hAPP(hAPP(c_COMBB(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),X7),c_COMBK(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_COMBC(X7,tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_OCons(X7)),c_List_Olist_ONil(X7))))),X331)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),X7),c_List_Ohd(X7)),hAPP(c_List_Ofilter(tc_List_Olist(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X7)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_List_Olist(X7),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X7)))),X331)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__filter__head) ).
fof(fact_transpose__aux__filter__tail,axiom,
! [X331,X7] : c_List_Oconcat(tc_List_Olist(X7),hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(tc_List_Olist(X7))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X7)),X7,c_List_Olist_ONil(tc_List_Olist(X7)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X7),tc_List_Olist(tc_List_Olist(X7))),X7),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_List_Olist(tc_List_Olist(X7)),tc_List_Olist(tc_List_Olist(X7))),c_List_Olist_OCons(tc_List_Olist(X7))),c_List_Olist_ONil(tc_List_Olist(X7)))))),X331)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Otl(X7)),hAPP(c_List_Ofilter(tc_List_Olist(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X7)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_List_Olist(X7),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X7)))),X331)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__filter__tail) ).
fof(fact_rtrancl__Int__subset,axiom,
! [X172,X45,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Relation_OId(X7)),X45))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X7,X172)),X45)),X172)),X45))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X7,X172)),X45)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Int__subset) ).
fof(fact_listrel__Cons1,axiom,
! [X172,X292,X293,X127,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X293)),X292)),c_List_Olistrel(X7,X172)))
=> ~ ! [X82,X306] :
( X292 = hAPP(hAPP(c_List_Olist_OCons(X7),X82),X306)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X82)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X293),X306)),c_List_Olistrel(X7,X172))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons1) ).
fof(fact_power__even__eq,axiom,
! [X33,X71,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__even__eq) ).
fof(fact_sublist__def,axiom,
! [X149,X292,X7] : c_List_Osublist(X7,X292,X149) = hAPP(hAPP(c_List_Omap(tc_prod(X7,tc_Nat_Onat),X7),c_Product__Type_Ofst(X7,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X7,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X7,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X7,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X7,tc_Nat_Onat))),X149)),hAPP(hAPP(c_List_Ozip(X7,tc_Nat_Onat),X292),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__def) ).
fof(fact_fold1Set_Oequations,axiom,
! [X41,X43,X42,X2,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,X2,hAPP(hAPP(c_Set_Oinsert(X7),X42),X43)),X41))
<=> ? [X110,X239] :
( hAPP(hAPP(c_Set_Oinsert(X7),X42),X43) = hAPP(hAPP(c_Set_Oinsert(X7),X110),X239)
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,X2,X110,X239),X41))
& ~ hBOOL(hAPP(hAPP(c_member(X7),X110),X239)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set_Oequations) ).
fof(fact_Nitpick_Ouminus__frac__def,axiom,
! [X144,X87] : c_Nitpick_Ouminus__frac(X87,X144) = c_Nitpick_OAbs__Frac(X87,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(X87),X144))),hAPP(c_Nitpick_Odenom(X87),X144))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).
fof(fact_snd__apsnd,axiom,
! [X6,X2,X119,X7,X105] : hAPP(c_Product__Type_Osnd(X105,X7),hAPP(c_Product__Type_Oapsnd(X119,X7,X105,X2),X6)) = hAPP(X2,hAPP(c_Product__Type_Osnd(X105,X119),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__apsnd) ).
fof(fact_fst__apfst,axiom,
! [X6,X2,X119,X105,X7] : hAPP(c_Product__Type_Ofst(X7,X105),hAPP(c_Product__Type_Oapfst(X119,X7,X105,X2),X6)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X119,X105),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__apfst) ).
fof(fact_fst__apsnd,axiom,
! [X6,X2,X119,X105,X7] : hAPP(c_Product__Type_Ofst(X7,X105),hAPP(c_Product__Type_Oapsnd(X119,X105,X7,X2),X6)) = hAPP(c_Product__Type_Ofst(X7,X119),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__apsnd) ).
fof(fact_snd__apfst,axiom,
! [X6,X2,X119,X7,X105] : hAPP(c_Product__Type_Osnd(X105,X7),hAPP(c_Product__Type_Oapfst(X119,X105,X7,X2),X6)) = hAPP(c_Product__Type_Osnd(X119,X7),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__apfst) ).
fof(fact_small_H_Opinduct,axiom,
! [X38,X43,X42,X187] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X187),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X42),X43))))
=> ( ! [X240,X159,X147] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X240),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X159),X147))))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X159),X147))
=> ( hAPP(X240,X147) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
=> hBOOL(hAPP(hAPP(hAPP(X38,X240),X159),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X147),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
=> hBOOL(hAPP(hAPP(hAPP(X38,X240),X159),X147)) ) )
=> hBOOL(hAPP(hAPP(hAPP(X38,X187),X42),X43)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small_H_Opinduct) ).
fof(fact_nat__case__number__of,axiom,
! [X163,X2,X25,X7] : c_Nat_Onat_Onat__case(X7,X25,X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X7),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X7,X7),hAPP(hAPP(c_COMBC(tc_Int_Oint,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),tc_Int_Oint),c_If(X7)),c_Nat__Numeral_Oneg)),X25)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Int_Oint),X2),c_Int_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__number__of) ).
fof(fact_max__number__of__Suc,axiom,
! [X163,X44] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X44))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X44)),c_Int_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__number__of__Suc) ).
fof(fact_min__number__of__Suc,axiom,
! [X163,X44] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X44)),c_Int_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__number__of__Suc) ).
fof(fact_Suc__n__div__2__gt__zero,axiom,
! [X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__div__2__gt__zero) ).
fof(fact_half__gt__zero,axiom,
! [X138,X87] :
( ( class_Fields_Olinordered__field__inverse__zero(X87)
& class_Int_Onumber__ring(X87) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X138))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X138),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half__gt__zero) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X33,X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_div__2__gt__zero,axiom,
! [X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X33),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__2__gt__zero) ).
fof(fact_power3__eq__cube,axiom,
! [X71,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X71)),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power3__eq__cube) ).
fof(fact_zero__le__power2,axiom,
! [X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power2) ).
fof(fact_power__minus1__even,axiom,
! [X33,X87] :
( class_Rings_Oring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Oone__class_Oone(X87))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33)) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus1__even) ).
fof(fact_power__m1__even,axiom,
! [X33,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33)) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__even) ).
fof(fact_diff__nat__number__of,axiom,
! [X163,X169] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X169),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X169),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X163),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X169)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__nat__number__of) ).
fof(fact_diff__nat__eq__if,axiom,
! [X26,X141] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X141))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X141)) = hAPP(c_Int_Onat,X26) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X141))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X141)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),X141)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__nat__eq__if) ).
fof(fact_fold__graph__permute__diff,axiom,
! [X25,X6,X149,X24,X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,c_Groups_Otimes__class_Otimes(X7),X24,X149),X6))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X24),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,c_Groups_Otimes__class_Otimes(X7),X25,hAPP(hAPP(c_Set_Oinsert(X7),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),X6)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__permute__diff) ).
fof(fact_concat__map__singleton,axiom,
! [X292,X2,X105,X7] : c_List_Oconcat(X7,hAPP(hAPP(c_List_Omap(X105,tc_List_Olist(X7)),hAPP(hAPP(c_COMBC(X105,tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_COMBB(X7,tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),X105),c_List_Olist_OCons(X7)),X2)),c_List_Olist_ONil(X7))),X292)) = hAPP(hAPP(c_List_Omap(X105,X7),X2),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__map__singleton) ).
fof(fact_Nitpick_Oless__eq__frac__def,axiom,
! [X172,X153,X7] :
( c_Nitpick_Oless__eq__frac(X7,X153,X172)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X7),c_Nitpick_Oplus__frac(X7,X153,c_Nitpick_Ouminus__frac(X7,X172)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oless__eq__frac__def) ).
fof(fact_Nitpick_Oless__frac__def,axiom,
! [X172,X153,X7] :
( c_Nitpick_Oless__frac(X7,X153,X172)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X7),c_Nitpick_Oplus__frac(X7,X153,c_Nitpick_Ouminus__frac(X7,X172)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oless__frac__def) ).
fof(fact_power2__eq__imp__eq,axiom,
! [X98,X86,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> X86 = X98 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).
fof(fact_less__2__cases,axiom,
! [X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X33 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__2__cases) ).
fof(fact_div2__Suc__Suc,axiom,
! [X90] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X90))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div2__Suc__Suc) ).
fof(fact_abs__power2,axiom,
! [X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power2) ).
fof(fact_Nitpick_Oof__frac__def,axiom,
! [X144,X87,X7] :
( ( class_Rings_Oinverse(X7)
& class_Rings_Oring__1(X7) )
=> c_Nitpick_Oof__frac(X87,X7,X144) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),hAPP(c_Int_Oring__1__class_Oof__int(X7),hAPP(c_Nitpick_Onum(X87),X144))),hAPP(c_Int_Oring__1__class_Oof__int(X7),hAPP(c_Nitpick_Odenom(X87),X144))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oof__frac__def) ).
fof(fact_converseE,axiom,
! [X172,X279,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),X279),hAPP(c_Relation_Oconverse(X105,X7),X172)))
=> ~ ! [X3,X82] :
( X279 = hAPP(hAPP(c_Product__Type_OPair(X7,X105),X82),X3)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X3),X82)),X172)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseE) ).
fof(fact_setsum__natinterval__difff,axiom,
! [X2,X44,X95,X7] :
( class_Groups_Oab__group__add(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X7)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(X2,X95)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X7)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44)) = c_Groups_Ozero__class_Ozero(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__natinterval__difff) ).
fof(fact_map__upd__upds__conv__if,axiom,
! [X127,X2,X292,X293,X105,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)),X292))))
=> c_Map_Omap__upds(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X2),X6),hAPP(c_Option_Ooption_OSome(X105),X127)),X292,X293) = c_Map_Omap__upds(X7,X105,X2,X292,X293) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)),X292))))
=> c_Map_Omap__upds(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X2),X6),hAPP(c_Option_Ooption_OSome(X105),X127)),X292,X293) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Omap__upds(X7,X105,X2,X292,X293)),X6),hAPP(c_Option_Ooption_OSome(X105),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__upds__conv__if) ).
fof(fact_fold__graph__insert__swap,axiom,
! [X26,X127,X149,X24,X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,c_Groups_Otimes__class_Otimes(X7),X24,X149),X127))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X24),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,c_Groups_Otimes__class_Otimes(X7),X26,hAPP(hAPP(c_Set_Oinsert(X7),X24),X149)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X26),X127))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__insert__swap) ).
fof(fact_fold__graph_OinsertI,axiom,
! [X127,X26,X2,X105,X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,X149),X127))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),hAPP(hAPP(X2,X6),X127))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).
fof(fact_map__comp__None__iff,axiom,
! [X94,X284,X285,X119,X7,X105] :
( c_Map_Omap__comp(X105,X7,X119,X285,X284,X94) = c_Option_Ooption_ONone(X7)
<=> ( hAPP(X284,X94) = c_Option_Ooption_ONone(X105)
| ? [X291] :
( hAPP(X284,X94) = hAPP(c_Option_Ooption_OSome(X105),X291)
& hAPP(X285,X291) = c_Option_Ooption_ONone(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__None__iff) ).
fof(fact_tranclD,axiom,
! [X191,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Otrancl(X7,X191)))
=> ? [X154] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X154)),X191))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X154),X127)),c_Transitive__Closure_Ortrancl(X7,X191))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD) ).
fof(fact_tranclD2,axiom,
! [X191,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Otrancl(X7,X191)))
=> ? [X154] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X154)),c_Transitive__Closure_Ortrancl(X7,X191)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X154),X127)),X191)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD2) ).
fof(fact_apfst__conv,axiom,
! [X127,X6,X2,X105,X7,X119] : hAPP(c_Product__Type_Oapfst(X119,X7,X105,X2),hAPP(hAPP(c_Product__Type_OPair(X119,X105),X6),X127)) = hAPP(hAPP(c_Product__Type_OPair(X7,X105),hAPP(X2,X6)),X127),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__conv) ).
fof(fact_apsnd__conv,axiom,
! [X127,X6,X2,X7,X105,X119] : hAPP(c_Product__Type_Oapsnd(X119,X105,X7,X2),hAPP(hAPP(c_Product__Type_OPair(X7,X119),X6),X127)) = hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),hAPP(X2,X127)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__conv) ).
fof(fact_aset_I10_J,axiom,
! [X46,X149,X192,X136] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),X192))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X149))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X207),X206) ) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X46)))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X192)),X46))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I10_J) ).
fof(fact_bset_I10_J,axiom,
! [X46,X155,X192,X136] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),X192))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X155))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X207),X206) ) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X46)))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X192)),X46))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I10_J) ).
fof(fact_map__upds__twist,axiom,
! [X321,X24,X95,X105,X322,X25,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_List_Oset(X7),X322)))
=> c_Map_Omap__upds(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X95),X25),hAPP(c_Option_Ooption_OSome(X105),X24)),X322,X321) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Omap__upds(X7,X105,X95,X322,X321)),X25),hAPP(c_Option_Ooption_OSome(X105),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__twist) ).
fof(fact_evalc__elim__cases_I3_J,axiom,
! [X46,X45,X23,X25,X60] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X60,X25,X23)),X45),X46))
=> ~ ! [X62] :
( X46 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X62),c_Com_Ovname_OLoc(X60)),hAPP(hAPP(c_Natural_Ogetlocs,X45),X60))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),hAPP(hAPP(hAPP(c_Natural_Oupdate,X45),c_Com_Ovname_OLoc(X60)),hAPP(X25,X45))),X62)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I3_J) ).
fof(fact_transpose__max__length,axiom,
! [X292,X7] : c_List_Ofoldr(tc_List_Olist(X7),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X7)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X7))),c_List_Otranspose(X7,X292),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),hAPP(c_List_Ofilter(tc_List_Olist(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X7)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_List_Olist(X7),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X7)))),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__max__length) ).
fof(fact_zmod__number__of__Bit0,axiom,
! [X128,X139] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__number__of__Bit0) ).
fof(fact_power2__abs,axiom,
! [X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__abs) ).
fof(fact_power2__minus,axiom,
! [X71,X87] :
( class_Rings_Oring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__minus) ).
fof(fact_mod2__Suc__Suc,axiom,
! [X90] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod2__Suc__Suc) ).
fof(fact_finite__subset__induct,axiom,
! [X38,X149,X215,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X215))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X215),X149))
=> ( hBOOL(hAPP(X38,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> ( ! [X110,X241] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X241))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X110),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X110),X241))
=> ( hBOOL(hAPP(X38,X241))
=> hBOOL(hAPP(X38,hAPP(hAPP(c_Set_Oinsert(X7),X110),X241))) ) ) ) )
=> hBOOL(hAPP(X38,X215)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset__induct) ).
fof(fact_mult__2,axiom,
! [X97,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X97) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X97),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2) ).
fof(fact_nat__mult__2,axiom,
! [X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X97) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2) ).
fof(fact_add__2__eq__Suc,axiom,
! [X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X33) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).
fof(fact_folding__image__simple_Oinsert,axiom,
! [X6,X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X105),X6),X149))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X105),X6),X149)) = hAPP(hAPP(X2,hAPP(X1,X6)),hAPP(X215,X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
fof(fact_RangeE,axiom,
! [X172,X105,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(c_Relation_ORange(X105,X7),X172)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X3),X24)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeE) ).
fof(fact_trancl__trans,axiom,
! [X23,X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Otrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X23)),c_Transitive__Closure_Otrancl(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X23)),c_Transitive__Closure_Otrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__trans) ).
fof(fact_trancl__converseI,axiom,
! [X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),hAPP(c_Relation_Oconverse(X7,X7),c_Transitive__Closure_Otrancl(X7,X172))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Otrancl(X7,hAPP(c_Relation_Oconverse(X7,X7),X172)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converseI) ).
fof(fact_trancl__converseD,axiom,
! [X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Otrancl(X7,hAPP(c_Relation_Oconverse(X7,X7),X172))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),hAPP(c_Relation_Oconverse(X7,X7),c_Transitive__Closure_Otrancl(X7,X172)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converseD) ).
fof(fact_restrict__fun__upd,axiom,
! [X127,X95,X105,X192,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X192))
=> c_Map_Orestrict__map(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X95),X6),X127),X192) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Orestrict__map(X7,X105,X95,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X192),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),X6),X127) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X192))
=> c_Map_Orestrict__map(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X95),X6),X127),X192) = c_Map_Orestrict__map(X7,X105,X95,X192) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__fun__upd) ).
fof(fact_fold1Set_Ointros,axiom,
! [X6,X149,X25,X2,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,X2,X25,X149),X6))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,X2,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set_Ointros) ).
fof(fact_power2__eq__1__iff,axiom,
! [X25,X7] :
( class_Rings_Oring__1__no__zero__divisors(X7)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X7)
<=> ( X25 = c_Groups_Oone__class_Oone(X7)
| X25 = hAPP(c_Groups_Ouminus__class_Ouminus(X7),c_Groups_Oone__class_Oone(X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__1__iff) ).
fof(fact_zero__eq__power2,axiom,
! [X25,X7] :
( class_Rings_Oring__1__no__zero__divisors(X7)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X7)
<=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__eq__power2) ).
fof(fact_map__of__zip__upd,axiom,
! [X26,X127,X6,X302,X292,X105,X293,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X293) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X292)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X302) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X292)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X105),X6),hAPP(c_List_Oset(X105),X292)))
=> ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,tc_Option_Ooption(X7)),c_Map_Omap__of(X105,X7,hAPP(hAPP(c_List_Ozip(X105,X7),X292),X293))),X6),hAPP(c_Option_Ooption_OSome(X7),X127)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,tc_Option_Ooption(X7)),c_Map_Omap__of(X105,X7,hAPP(hAPP(c_List_Ozip(X105,X7),X292),X302))),X6),hAPP(c_Option_Ooption_OSome(X7),X26))
=> c_Map_Omap__of(X105,X7,hAPP(hAPP(c_List_Ozip(X105,X7),X292),X293)) = c_Map_Omap__of(X105,X7,hAPP(hAPP(c_List_Ozip(X105,X7),X292),X302)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__upd) ).
fof(fact_rotate__rev,axiom,
! [X300,X33,X87] : hAPP(c_List_Orotate(X87,X33),hAPP(c_List_Orev(X87),X300)) = hAPP(c_List_Orev(X87),hAPP(c_List_Orotate(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__rev) ).
fof(fact_rotate__def,axiom,
! [X44,X7] : c_List_Orotate(X7,X44) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X7),tc_List_Olist(X7)),X44),c_List_Orotate1(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__def) ).
fof(fact_rtrancl__trancl__trancl,axiom,
! [X26,X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X26)),c_Transitive__Closure_Otrancl(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),c_Transitive__Closure_Otrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
fof(fact_trancl__rtrancl__trancl,axiom,
! [X23,X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Otrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X23)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X23)),c_Transitive__Closure_Otrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
fof(fact_trancl__into__trancl2,axiom,
! [X23,X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X23)),c_Transitive__Closure_Otrancl(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X23)),c_Transitive__Closure_Otrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
! [X23,X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Otrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X23)),X172))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X23)),c_Transitive__Closure_Otrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
fof(fact_Collect__conv__if,axiom,
! [X7,X25,X38] :
( ( hBOOL(hAPP(X38,X25))
=> hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X38)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(X38,X25))
=> hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X38)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conv__if) ).
fof(fact_foldr__map,axiom,
! [X25,X292,X2,X119,X1,X7,X105] : c_List_Ofoldr(X105,X7,X1,hAPP(hAPP(c_List_Omap(X119,X105),X2),X292),X25) = c_List_Ofoldr(X119,X7,hAPP(c_Fun_Ocomp(X105,tc_fun(X7,X7),X119,X1),X2),X292,X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__map) ).
fof(fact_trancl__subset__Sigma,axiom,
! [X149,X172,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),hAPP(hAPP(c_Product__Type_OSigma(X7,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),X149))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X7,X172)),hAPP(hAPP(c_Product__Type_OSigma(X7,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),X149)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma) ).
fof(fact_norm__frac_Opsimps,axiom,
! [X24,X25] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X25),X24)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X25,X24) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X25,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( ~ ( X25 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X25,X24) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X25),X24)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Opsimps) ).
fof(fact_foldr__append,axiom,
! [X25,X293,X292,X2,X7,X105] : c_List_Ofoldr(X105,X7,X2,hAPP(hAPP(c_List_Oappend(X105),X292),X293),X25) = c_List_Ofoldr(X105,X7,X2,X292,c_List_Ofoldr(X105,X7,X2,X293,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__append) ).
fof(fact_psubset__insert__iff,axiom,
! [X155,X6,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),X155)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X155)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__insert__iff) ).
fof(fact_lexord__irreflexive,axiom,
! [X127,X172,X7] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X127),X127)),c_List_Olexord(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).
fof(fact_diff__bin__simps_I8_J,axiom,
! [X115,X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X96)),c_Int_OBit1(X115)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X96)),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I8_J) ).
fof(fact_inj__on__insert,axiom,
! [X149,X25,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149))
<=> ( c_Fun_Oinj__on(X7,X105,X2,X149)
& ~ hBOOL(hAPP(hAPP(c_member(X105),hAPP(X2,X25)),hAPP(c_Set_Oimage(X7,X105,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__insert) ).
fof(fact_apfst__id,axiom,
! [X105,X7] : c_Product__Type_Oapfst(X7,X7,X105,c_Fun_Oid(X7)) = c_Fun_Oid(tc_prod(X7,X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__id) ).
fof(fact_apsnd__id,axiom,
! [X7,X105] : c_Product__Type_Oapsnd(X105,X105,X7,c_Fun_Oid(X105)) = c_Fun_Oid(tc_prod(X7,X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__id) ).
fof(fact_trancl__reflcl,axiom,
! [X172,X7] : c_Transitive__Closure_Otrancl(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),c_Relation_OId(X7))) = c_Transitive__Closure_Ortrancl(X7,X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__reflcl) ).
fof(fact_subset__insert__iff,axiom,
! [X155,X6,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),X155)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X155)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert__iff) ).
fof(fact_eq__special_I4_J,axiom,
! [X6,X7] :
( class_Int_Onumber__ring(X7)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X7),X6) = c_Groups_Oone__class_Oone(X7)
<=> c_Int_Oiszero(X7,hAPP(c_Int_Onumber__class_Onumber__of(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I4_J) ).
fof(fact_eq__special_I2_J,axiom,
! [X127,X7] :
( class_Int_Onumber__ring(X7)
=> ( c_Groups_Oone__class_Oone(X7) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X127)
<=> c_Int_Oiszero(X7,hAPP(c_Int_Onumber__class_Onumber__of(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X127)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I2_J) ).
fof(fact_small_H_Opsimps,axiom,
! [X107,X136,X2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X136),X107))))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),X107))
=> c_Smallcheck_Osmall_H(X2,X136,X107) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),X107))
=> c_Smallcheck_Osmall_H(X2,X136,X107) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X2,X136,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X107)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small_H_Opsimps) ).
fof(fact_norm__frac_Osimps,axiom,
! [X25,X24] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X25,X24) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X25,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( ~ ( X25 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X25,X24) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X25),X24)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Osimps) ).
fof(fact_rtrancl__into__trancl2,axiom,
! [X23,X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X23)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X23)),c_Transitive__Closure_Otrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
fof(fact_rtrancl__into__trancl1,axiom,
! [X23,X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X23)),X172))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X23)),c_Transitive__Closure_Otrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
fof(fact_power2__eq__square__number__of,axiom,
! [X128,X7] :
( ( class_Groups_Omonoid__mult(X7)
& class_Int_Onumber(X7) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X128)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).
fof(fact_r__r__into__trancl,axiom,
! [X23,X191,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X191))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X23)),X191))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X23)),c_Transitive__Closure_Otrancl(X7,X191))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
fof(fact_DomainE,axiom,
! [X172,X105,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Relation_ODomain(X7,X105),X172)))
=> ~ ! [X82] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X82)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainE) ).
fof(fact_add__self__div__2,axiom,
! [X90] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X90,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__self__div__2) ).
fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
! [X136,X23,X24,X25] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23,X136)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24))
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23),X25))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X136)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__subset__iff) ).
fof(fact_mult__2__right,axiom,
! [X97,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X97),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2__right) ).
fof(fact_power2__eq__square,axiom,
! [X71,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__square) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X86) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_INF2__E,axiom,
! [X25,X23,X24,X155,X149,X119,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_fun(X119,tc_HOL_Obool))),X149),X155),X24),X23))
=> ( ~ hBOOL(hAPP(hAPP(hAPP(X155,X25),X24),X23))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__E) ).
fof(fact_nat__mult__2__right,axiom,
! [X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).
fof(fact_add__2__eq__Suc_H,axiom,
! [X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).
fof(fact_one__power2,axiom,
! [X87] :
( class_Rings_Osemiring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),c_Groups_Oone__class_Oone(X87)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__power2) ).
fof(fact_zero__power2,axiom,
! [X87] :
( class_Rings_Osemiring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__power2) ).
fof(fact_trancl__mono,axiom,
! [X45,X172,X161,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),c_Transitive__Closure_Otrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X45))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),c_Transitive__Closure_Otrancl(X7,X45))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__mono) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [X98,X86,X87] :
( class_Rings_Olinordered__ring(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X98),X98))),c_Groups_Ozero__class_Ozero(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_trancl__subset__Field2,axiom,
! [X172,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X7,X172)),hAPP(hAPP(c_Product__Type_OSigma(X7,X7),hAPP(c_Relation_OField(X7),X172)),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),hAPP(c_Relation_OField(X7),X172))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Field2) ).
fof(fact_sup2E,axiom,
! [X127,X6,X155,X149,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X149),X155),X6),X127))
=> ( ~ hBOOL(hAPP(hAPP(X149,X6),X127))
=> hBOOL(hAPP(hAPP(X155,X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2E) ).
fof(fact_rtrancl__eq__or__trancl,axiom,
! [X191,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,X191)))
<=> ( X6 = X127
| ( X6 != X127
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Otrancl(X7,X191))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
fof(fact_trancl__into__rtrancl,axiom,
! [X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Otrancl(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Ortrancl(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
fof(fact_inf2E,axiom,
! [X127,X6,X155,X149,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X149),X155),X6),X127))
=> ~ ( hBOOL(hAPP(hAPP(X149,X6),X127))
=> ~ hBOOL(hAPP(hAPP(X155,X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2E) ).
fof(fact_rel__simps_I34_J,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X94)),c_Int_OBit1(X157)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).
fof(fact_less__eq__int__code_I16_J,axiom,
! [X170,X171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X171)),c_Int_OBit1(X170)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X171),X170)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).
fof(fact_rel__simps_I17_J,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X94)),c_Int_OBit1(X157)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).
fof(fact_less__int__code_I16_J,axiom,
! [X170,X171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X171)),c_Int_OBit1(X170)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X171),X170)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).
fof(fact_length__transpose,axiom,
! [X292,X7] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),c_List_Otranspose(X7,X292)) = c_List_Ofoldr(tc_List_Olist(X7),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X7)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X7))),X292,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__transpose) ).
fof(fact_trancl__power,axiom,
! [X191,X161,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),c_Transitive__Closure_Otrancl(X7,X191)))
<=> ? [X70] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X70))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X70),X191))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__power) ).
fof(fact_concat__append,axiom,
! [X301,X300,X87] : c_List_Oconcat(X87,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X87)),X300),X301)) = hAPP(hAPP(c_List_Oappend(X87),c_List_Oconcat(X87,X300)),c_List_Oconcat(X87,X301)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__append) ).
fof(fact_distinct__list__update,axiom,
! [X107,X25,X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X292)),hAPP(hAPP(c_Set_Oinsert(X7),hAPP(hAPP(c_List_Onth(X7),X292),X107)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))
=> hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Olist__update(X7,X292),X107),X25))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__list__update) ).
fof(fact_pigeonhole,axiom,
! [X149,X2,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),hAPP(c_Set_Oimage(X105,X7,X2),X149))),hAPP(c_Finite__Set_Ocard(X105),X149)))
=> ~ c_Fun_Oinj__on(X105,X7,X2,X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
fof(fact_rtranclD,axiom,
! [X191,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Ortrancl(X7,X191)))
=> ( X25 = X24
| ( X25 != X24
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Otrancl(X7,X191))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclD) ).
fof(fact_trancl_Or__into__trancl,axiom,
! [X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Otrancl(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
fof(fact_divide__le__eq__number__of,axiom,
! [X125,X23,X24,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).
fof(fact_divide__less__eq__number__of,axiom,
! [X125,X23,X24,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).
fof(fact_le__divide__eq__number__of,axiom,
! [X23,X24,X125,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).
fof(fact_less__divide__eq__number__of,axiom,
! [X23,X24,X125,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).
fof(fact_Collect__conv__if2,axiom,
! [X7,X25,X38] :
( ( hBOOL(hAPP(X38,X25))
=> hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(c_fequal,X25))),X38)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(X38,X25))
=> hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(c_fequal,X25))),X38)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conv__if2) ).
fof(fact_rotate__drop__take,axiom,
! [X300,X33,X87] : hAPP(c_List_Orotate(X87,X33),X300) = hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Odrop(X87),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300))),X300)),hAPP(hAPP(c_List_Otake(X87),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300))),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__drop__take) ).
fof(fact_in__set__zipE,axiom,
! [X293,X292,X127,X6,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),hAPP(c_List_Oset(tc_prod(X7,X105)),hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293))))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> ~ hBOOL(hAPP(hAPP(c_member(X105),X127),hAPP(c_List_Oset(X105),X293))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__zipE) ).
fof(fact_map__add__upd__left,axiom,
! [X276,X277,X278,X105,X95,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X95),c_Map_Odom(X7,X105,X278)))
=> c_Map_Omap__add(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X277),X95),hAPP(c_Option_Ooption_OSome(X105),X276)),X278) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Omap__add(X7,X105,X277,X278)),X95),hAPP(c_Option_Ooption_OSome(X105),X276)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__upd__left) ).
fof(fact_acyclic__insert,axiom,
! [X172,X6,X127,X7] :
( c_Wellfounded_Oacyclic(X7,hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X6)),X172))
<=> ( c_Wellfounded_Oacyclic(X7,X172)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__insert) ).
fof(fact_wf__insert,axiom,
! [X172,X6,X127,X7] :
( c_Wellfounded_Owf(X7,hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X6)),X172))
<=> ( c_Wellfounded_Owf(X7,X172)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__insert) ).
fof(fact_trancl__unfold,axiom,
! [X172,X7] : c_Transitive__Closure_Otrancl(X7,X172) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),c_Transitive__Closure_Otrancl(X7,X172)),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold) ).
fof(fact_wf__eq__minimal,axiom,
! [X172,X7] :
( c_Wellfounded_Owf(X7,X172)
<=> ! [X274] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X7),X3),X274))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X274))
& ! [X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X3)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X82),X274)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
fof(fact_rel__simps_I33_J,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X94)),c_Int_OBit0(X157)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).
fof(fact_less__eq__int__code_I15_J,axiom,
! [X170,X171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X171)),c_Int_OBit0(X170)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X171),X170)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).
fof(fact_less__int__code_I15_J,axiom,
! [X170,X171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X171)),c_Int_OBit0(X170)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X171),X170)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).
fof(fact_rel__simps_I16_J,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X94)),c_Int_OBit0(X157)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).
fof(fact_fun__upd__None__restrict,axiom,
! [X95,X105,X192,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X192))
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Orestrict__map(X7,X105,X95,X192)),X6),c_Option_Ooption_ONone(X105)) = c_Map_Orestrict__map(X7,X105,X95,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X192),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X192))
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Orestrict__map(X7,X105,X95,X192)),X6),c_Option_Ooption_ONone(X105)) = c_Map_Orestrict__map(X7,X105,X95,X192) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__None__restrict) ).
fof(fact_Nitpick_Oint__lcm__def,axiom,
! [X98,X86] : c_Nitpick_Oint__lcm(X86,X98) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X86)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X98)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oint__lcm__def) ).
fof(fact_Nitpick_Onat__lcm__def,axiom,
! [X98,X86] : c_Nitpick_Onat__lcm(X86,X98) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X98)),c_Nitpick_Onat__gcd(X86,X98)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Onat__lcm__def) ).
fof(fact_foldr_Osimps_I2_J,axiom,
! [X25,X292,X6,X2,X7,X105] : c_List_Ofoldr(X105,X7,X2,hAPP(hAPP(c_List_Olist_OCons(X105),X6),X292),X25) = hAPP(hAPP(X2,X6),c_List_Ofoldr(X105,X7,X2,X292,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr_Osimps_I2_J) ).
fof(fact_wf__not__sym,axiom,
! [X6,X25,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X6)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X25)),X172)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__sym) ).
fof(fact_wf__asym,axiom,
! [X6,X25,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X6)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X25)),X172)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__asym) ).
fof(fact_divmod__nat__rel__def,axiom,
! [X195,X44,X95] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X95,X44),X195))
<=> ( X95 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X195)),X44)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X195))
& ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X195) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X44 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X195)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X195)),X44)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X195)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X195)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__def) ).
fof(fact_divide__le__eq__number__of1,axiom,
! [X25,X125,X24,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X25))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).
fof(fact_divide__less__eq__number__of1,axiom,
! [X25,X125,X24,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X25))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).
fof(fact_minus__Bit1,axiom,
! [X96] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X96)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Bit1) ).
fof(fact_evaln__WHILE__case,axiom,
! [X46,X44,X45,X23,X24] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X45,X44,X46)
=> ( ( X46 = X45
=> hBOOL(hAPP(X24,X45)) )
=> ~ ( hBOOL(hAPP(X24,X45))
=> ! [X62] :
( c_Natural_Oevaln(X23,X45,X44,X62)
=> ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X62,X44,X46) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__WHILE__case) ).
fof(fact_evaln_Oequations_I8_J,axiom,
! [X72,X47,X43,X41,X42] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X42,X41),X43,X47,X72)
<=> ( ( X72 = X43
& ~ hBOOL(hAPP(X42,X43)) )
| ( hBOOL(hAPP(X42,X43))
& ? [X62] :
( c_Natural_Oevaln(X41,X43,X47,X62)
& c_Natural_Oevaln(c_Com_Ocom_OWhile(X42,X41),X62,X47,X72) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I8_J) ).
fof(fact_evaln__elim__cases_I4_J,axiom,
! [X35,X33,X9,X48,X49] :
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X49,X48),X9,X33,X35)
=> ~ ! [X62] :
( c_Natural_Oevaln(X49,X9,X33,X62)
=> ~ c_Natural_Oevaln(X48,X62,X33,X35) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I4_J) ).
fof(fact_less__eq,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X95),X44)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq) ).
fof(fact_quotientE,axiom,
! [X172,X149,X39,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X39),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> ~ ! [X3] :
( X39 = hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X3),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X3),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientE) ).
fof(fact_divmod__nat__if,axiom,
! [X95,X44] :
( ( ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) )
=> c_Divides_Odivmod__nat(X95,X44) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X95) )
& ( ~ ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) )
=> c_Divides_Odivmod__nat(X95,X44) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X44),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__if) ).
fof(fact_divmod__nat__def,axiom,
! [X44,X95] : c_Divides_Odivmod__nat(X95,X44) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X95,X44)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__def) ).
fof(fact_bin__less__0__simps_I4_J,axiom,
! [X125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X125)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).
fof(fact_append__eq__append__conv__if,axiom,
! [X326,X327,X328,X329,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X329),X328) = hAPP(hAPP(c_List_Oappend(X7),X327),X326)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X329)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X327)))
=> ( X329 = hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X329)),X327)
& X328 = hAPP(hAPP(c_List_Oappend(X7),hAPP(hAPP(c_List_Odrop(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X329)),X327)),X326) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X329)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X327)))
=> ( hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X327)),X329) = X327
& hAPP(hAPP(c_List_Oappend(X7),hAPP(hAPP(c_List_Odrop(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X327)),X329)),X328) = X326 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv__if) ).
fof(fact_rel__simps_I30_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X94)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I30_J) ).
fof(fact_rel__simps_I29_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X94)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).
fof(fact_rel__simps_I12_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X94)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).
fof(fact_rel__simps_I13_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X94)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I13_J) ).
fof(fact_neg__number__of__Bit1,axiom,
! [X125] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X125))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Bit1) ).
fof(fact_le__special_I2_J,axiom,
! [X127,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Rings_Olinordered__idom(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Oone__class_Oone(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I2_J) ).
fof(fact_less__special_I2_J,axiom,
! [X127,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Rings_Olinordered__idom(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Oone__class_Oone(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I2_J) ).
fof(fact_le__divide__eq__number__of1,axiom,
! [X125,X24,X25,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).
fof(fact_less__divide__eq__number__of1,axiom,
! [X125,X24,X25,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).
fof(fact_sup2CI,axiom,
! [X105,X7,X149,X127,X6,X155] :
( ( ~ hBOOL(hAPP(hAPP(X155,X6),X127))
=> hBOOL(hAPP(hAPP(X149,X6),X127)) )
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X149),X155),X6),X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2CI) ).
fof(fact_not__acc__down,axiom,
! [X191,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),c_Wellfounded_Oacc(X7,X191)))
=> ~ ! [X154] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X154),X6)),X191))
=> hBOOL(hAPP(hAPP(c_member(X7),X154),c_Wellfounded_Oacc(X7,X191))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
fof(fact_flat__lub__def,axiom,
! [X24,X149,X7] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(X7,X24,X149) = X24 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(X7,X24,X149) = c_HOL_OThe(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_flat__lub__def) ).
fof(fact_evalc__WHILE__case,axiom,
! [X46,X45,X23,X24] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X45),X46))
=> ( ( X46 = X45
=> hBOOL(hAPP(X24,X45)) )
=> ~ ( hBOOL(hAPP(X24,X45))
=> ! [X62] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X45),X62))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X62),X46)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__WHILE__case) ).
fof(fact_evalc_Oequations_I8_J,axiom,
! [X61,X43,X41,X42] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X42,X41)),X43),X61))
<=> ( ( X61 = X43
& ~ hBOOL(hAPP(X42,X43)) )
| ( hBOOL(hAPP(X42,X43))
& ? [X62] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X41),X43),X62))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X42,X41)),X62),X61)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I8_J) ).
fof(fact_not__Nil__listrel1,axiom,
! [X172,X292,X7] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_ONil(X7)),X292)),c_List_Olistrel1(X7,X172))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).
fof(fact_Nil__notin__lex,axiom,
! [X172,X293,X7] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_ONil(X7)),X293)),c_List_Olex(X7,X172))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__notin__lex) ).
fof(fact_fun__upd__image,axiom,
! [X127,X2,X105,X149,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Set_Oimage(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X127)),X149) = hAPP(hAPP(c_Set_Oinsert(X105),X127),hAPP(c_Set_Oimage(X7,X105,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Set_Oimage(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X127)),X149) = hAPP(c_Set_Oimage(X7,X105,X2),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__image) ).
fof(fact_not__listrel1__Nil,axiom,
! [X172,X292,X7] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),c_List_Olist_ONil(X7))),c_List_Olistrel1(X7,X172))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).
fof(fact_lexord__Nil__right,axiom,
! [X172,X6,X7] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),c_List_Olist_ONil(X7))),c_List_Olexord(X7,X172))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).
fof(fact_Nil2__notin__lex,axiom,
! [X172,X292,X7] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),c_List_Olist_ONil(X7))),c_List_Olex(X7,X172))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil2__notin__lex) ).
fof(fact_foldl__foldr1__lemma,axiom,
! [X292,X25,X7] :
( class_Groups_Omonoid__add(X7)
=> hAPP(c_List_Ofoldl(X7,X7,c_Groups_Oplus__class_Oplus(X7),X25),X292) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),c_List_Ofoldr(X7,X7,c_Groups_Oplus__class_Oplus(X7),X292,c_Groups_Ozero__class_Ozero(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr1__lemma) ).
fof(fact_pair__in__Id__conv,axiom,
! [X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Relation_OId(X7)))
<=> X25 = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).
fof(fact_map__of__eq__None__iff,axiom,
! [X6,X288,X7,X105] :
( hAPP(c_Map_Omap__of(X105,X7,X288),X6) = c_Option_Ooption_ONone(X7)
<=> ~ hBOOL(hAPP(hAPP(c_member(X105),X6),hAPP(c_Set_Oimage(tc_prod(X105,X7),X105,c_Product__Type_Ofst(X105,X7)),hAPP(c_List_Oset(tc_prod(X105,X7)),X288)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__eq__None__iff) ).
fof(fact_one__add__one__is__two,axiom,
! [X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Oone__class_Oone(X87)),c_Groups_Oone__class_Oone(X87)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).
fof(fact_map__upds__apply__nontin,axiom,
! [X293,X2,X105,X292,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hAPP(c_Map_Omap__upds(X7,X105,X2,X292,X293),X6) = hAPP(X2,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__apply__nontin) ).
fof(fact_override__on__def,axiom,
! [X1,X2,X105,X149,X25,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(c_Fun_Ooverride__on(X7,X105,X2,X1,X149),X25) = hAPP(X1,X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(c_Fun_Ooverride__on(X7,X105,X2,X1,X149),X25) = hAPP(X2,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__def) ).
fof(fact_divmod__nat__step,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> c_Divides_Odivmod__nat(X90,X33) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),X33))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__step) ).
fof(fact_evalc__elim__cases_I4_J,axiom,
! [X35,X9,X48,X49] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X49,X48)),X9),X35))
=> ~ ! [X62] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X49),X9),X62))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X48),X62),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I4_J) ).
fof(fact_foldl__foldr,axiom,
! [X292,X25,X2,X105,X7] : hAPP(c_List_Ofoldl(X7,X105,X2,X25),X292) = c_List_Ofoldr(X105,X7,hAPP(c_COMBC(X7,X105,X7),X2),hAPP(c_List_Orev(X105),X292),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr) ).
fof(fact_override__on__apply__notin,axiom,
! [X1,X2,X105,X149,X25,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(c_Fun_Ooverride__on(X7,X105,X2,X1,X149),X25) = hAPP(X2,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__apply__notin) ).
fof(fact_comm__monoid__big_OF__eq,axiom,
! [X1,X149,X215,X26,X2,X105,X7] :
( c_Big__Operators_Ocomm__monoid__big(X7,X105,X2,X26,X215)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> hAPP(hAPP(X215,X1),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X105,X2),X1),X26),X149) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> hAPP(hAPP(X215,X1),X149) = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
fof(fact_in__measure,axiom,
! [X2,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),hAPP(c_Wellfounded_Omeasure(X7),X2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X6)),hAPP(X2,X127))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
fof(fact_measure__def,axiom,
! [X7] : c_Wellfounded_Omeasure(X7) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X7),c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measure__def) ).
fof(fact_SigmaE2,axiom,
! [X155,X149,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ~ hBOOL(hAPP(hAPP(c_member(X105),X24),hAPP(X155,X25))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE2) ).
fof(fact_map__concat,axiom,
! [X292,X2,X7,X105] : hAPP(hAPP(c_List_Omap(X105,X7),X2),c_List_Oconcat(X105,X292)) = c_List_Oconcat(X7,hAPP(hAPP(c_List_Omap(tc_List_Olist(X105),tc_List_Olist(X7)),hAPP(c_List_Omap(X105,X7),X2)),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__concat) ).
fof(fact_diff__bin__simps_I9_J,axiom,
! [X115,X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X96)),c_Int_OBit0(X115)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).
fof(fact_add__Bit1__Bit0,axiom,
! [X115,X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X96)),c_Int_OBit0(X115)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).
fof(fact_insort__insert__insort__key,axiom,
! [X292,X105,X6,X2,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X6)),hAPP(c_Set_Oimage(X105,X7,X2),hAPP(c_List_Oset(X105),X292))))
=> c_List_Olinorder__class_Oinsort__insert__key(X105,X7,X2,X6,X292) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),X292) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__insort__key) ).
fof(fact_total__on__diff__Id,axiom,
! [X172,X149,X7] :
( c_Relation_Ototal__on(X7,X149,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),c_Relation_OId(X7)))
<=> c_Relation_Ototal__on(X7,X149,X172) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__diff__Id) ).
fof(fact_Suc__diff__eq__diff__pred,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X33))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X33) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).
fof(fact_mult__Bit1,axiom,
! [X115,X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X96)),X115) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X96),X115))),X115),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit1) ).
fof(fact_number__of1,axiom,
! [X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X33))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X33)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of1) ).
fof(fact_add__Bit1__Bit1,axiom,
! [X115,X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X96)),c_Int_OBit1(X115)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Int_Osucc(X115))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit1) ).
fof(fact_less__eq__int__code_I14_J,axiom,
! [X170,X171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X171)),c_Int_OBit1(X170)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X171),X170)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).
fof(fact_rel__simps_I32_J,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X94)),c_Int_OBit1(X157)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).
fof(fact_rel__simps_I15_J,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X94)),c_Int_OBit1(X157)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).
fof(fact_less__int__code_I14_J,axiom,
! [X170,X171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X171)),c_Int_OBit1(X170)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X171),X170)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).
fof(fact_finite__trancl,axiom,
! [X172,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X7)),c_Transitive__Closure_Otrancl(X7,X172)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X7)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__trancl) ).
fof(fact_card__Diff__insert,axiom,
! [X155,X25,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X155))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__insert) ).
fof(fact_rev__concat,axiom,
! [X292,X7] : hAPP(c_List_Orev(X7),c_List_Oconcat(X7,X292)) = c_List_Oconcat(X7,hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Orev(X7)),hAPP(c_List_Orev(tc_List_Olist(X7)),X292))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__concat) ).
fof(fact_fold__image__insert,axiom,
! [X26,X1,X25,X149,X7,X105] :
( class_Groups_Oab__semigroup__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),X26),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(X1,X25)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),X26),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__insert) ).
fof(fact_filter__concat,axiom,
! [X292,X161,X7] : hAPP(c_List_Ofilter(X7,X161),c_List_Oconcat(X7,X292)) = c_List_Oconcat(X7,hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Ofilter(X7,X161)),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__concat) ).
fof(fact_divide__le__eq,axiom,
! [X25,X23,X24,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),X25))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq) ).
fof(fact_divide__less__eq,axiom,
! [X25,X23,X24,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),X25))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq) ).
fof(fact_distinct__rotate,axiom,
! [X292,X44,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(c_List_Orotate(X7,X44),X292)))
<=> hBOOL(hAPP(c_List_Odistinct(X7),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__rotate) ).
fof(fact_Not__Domain__rtrancl,axiom,
! [X127,X191,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_Relation_ODomain(X7,X7),X191)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,X191)))
<=> X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(fact_add__Bit0__Bit1,axiom,
! [X115,X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X96)),c_Int_OBit1(X115)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).
fof(fact_comm__monoid__big_Oinfinite,axiom,
! [X1,X149,X215,X26,X2,X105,X7] :
( c_Big__Operators_Ocomm__monoid__big(X7,X105,X2,X26,X215)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> hAPP(hAPP(X215,X1),X149) = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).
fof(fact_diff__special_I2_J,axiom,
! [X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),c_Groups_Oone__class_Oone(X87)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__special_I2_J) ).
fof(fact_distinct__insort,axiom,
! [X292,X6,X2,X7,X105] :
( class_Orderings_Olinorder(X105)
=> ( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X105,X2),X6),X292)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
& hBOOL(hAPP(c_List_Odistinct(X7),X292)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__insort) ).
fof(fact_diff__special_I1_J,axiom,
! [X128,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),c_Groups_Oone__class_Oone(X87)),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__special_I1_J) ).
fof(fact_r__into__trancl_H,axiom,
! [X172,X161,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),X172))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),c_Transitive__Closure_Otrancl(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
fof(fact_concat_Osimps_I2_J,axiom,
! [X300,X86,X87] : c_List_Oconcat(X87,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X87)),X86),X300)) = hAPP(hAPP(c_List_Oappend(X87),X86),c_List_Oconcat(X87,X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat_Osimps_I2_J) ).
fof(fact_add__special_I2_J,axiom,
! [X128,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Oone__class_Oone(X87)),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I2_J) ).
fof(fact_atLeastatMost__psubset__iff,axiom,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X23,X136)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X23),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),X136))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),X25))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),X136)) ) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X23),X136)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__psubset__iff) ).
fof(fact_insert__partition,axiom,
! [X215,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X6),X215))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),X6),X215)))
=> ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X206),hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),X6),X215)))
=> ( X3 != X206
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3),X206) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X6),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X215)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__partition) ).
fof(fact_reflcl__trancl,axiom,
! [X172,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X7,X172)),c_Relation_OId(X7)) = c_Transitive__Closure_Ortrancl(X7,X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__trancl) ).
fof(fact_list__update__append,axiom,
! [X86,X301,X300,X87,X33] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Olist__update(X87,hAPP(hAPP(c_List_Oappend(X87),X300),X301)),X33),X86) = hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Olist__update(X87,X300),X33),X86)),X301) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Olist__update(X87,hAPP(hAPP(c_List_Oappend(X87),X300),X301)),X33),X86) = hAPP(hAPP(c_List_Oappend(X87),X300),hAPP(hAPP(c_List_Olist__update(X87,X301),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300))),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__append) ).
fof(fact_le__divide__eq,axiom,
! [X23,X24,X25,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq) ).
fof(fact_less__divide__eq,axiom,
! [X23,X24,X25,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq) ).
fof(fact_mult__numeral__1,axiom,
! [X71,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit1(c_Int_OPls))),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1) ).
fof(fact_rotate__add,axiom,
! [X44,X95,X7] : c_List_Orotate(X7,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X44)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X7),tc_List_Olist(X7),tc_List_Olist(X7),c_List_Orotate(X7,X95)),c_List_Orotate(X7,X44)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__add) ).
fof(fact_atLeastatMost__subset__iff,axiom,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X23,X136)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X23),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),X136)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__subset__iff) ).
fof(fact_le__special_I4_J,axiom,
! [X6,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Rings_Olinordered__idom(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X6)),c_Groups_Oone__class_Oone(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Int_OBit1(c_Int_OPls))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I4_J) ).
fof(fact_less__special_I4_J,axiom,
! [X6,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Rings_Olinordered__idom(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X6)),c_Groups_Oone__class_Oone(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),c_Int_OBit1(c_Int_OPls))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I4_J) ).
fof(fact_IdE,axiom,
! [X161,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),c_Relation_OId(X7)))
=> ~ ! [X3] : X161 != hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdE) ).
fof(fact_evalc_Oequations_I6_J,axiom,
! [X47,X43,X41,X61,X42] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X42,X61,X41)),X43),X47))
<=> ( ( hBOOL(hAPP(X42,X43))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X61),X43),X47)) )
| ( ~ hBOOL(hAPP(X42,X43))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X41),X43),X47)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I6_J) ).
fof(fact_evalc_Oequations_I5_J,axiom,
! [X47,X43,X61,X41,X42] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X42,X41,X61)),X43),X47))
<=> ( ( hBOOL(hAPP(X42,X43))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X41),X43),X47)) )
| ( ~ hBOOL(hAPP(X42,X43))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X61),X43),X47)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I5_J) ).
fof(fact_evalc__elim__cases_I5_J,axiom,
! [X46,X45,X56,X57,X24] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X24,X57,X56)),X45),X46))
=> ( ( hBOOL(hAPP(X24,X45))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X57),X45),X46)) )
=> ~ ( ~ hBOOL(hAPP(X24,X45))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X56),X45),X46)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I5_J) ).
fof(fact_diff__bin__simps_I4_J,axiom,
! [X115] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X115)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I4_J) ).
fof(fact_IdI,axiom,
! [X25,X7] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X25)),c_Relation_OId(X7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdI) ).
fof(fact_foldl__conv__concat,axiom,
! [X331,X292,X7] : hAPP(c_List_Ofoldl(tc_List_Olist(X7),tc_List_Olist(X7),c_List_Oappend(X7),X292),X331) = hAPP(hAPP(c_List_Oappend(X7),X292),c_List_Oconcat(X7,X331)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__conv__concat) ).
fof(fact_diff__bin__simps_I10_J,axiom,
! [X115,X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X96)),c_Int_OBit1(X115)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).
fof(fact_insort__insert__insort,axiom,
! [X292,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> c_List_Olinorder__class_Oinsort__insert__key(X7,X7,c_COMBI(X7),X6,X292) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7)),X6),X292) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__insort) ).
fof(fact_irrefl__def,axiom,
! [X172,X7] :
( c_Relation_Oirrefl(X7,X172)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
fof(fact_wf__not__refl,axiom,
! [X25,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X25)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__refl) ).
fof(fact_wf__irrefl,axiom,
! [X25,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X25)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__irrefl) ).
fof(fact_rtrancl__unfold,axiom,
! [X172,X7] : c_Transitive__Closure_Ortrancl(X7,X172) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Relation_OId(X7)),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),c_Transitive__Closure_Ortrancl(X7,X172)),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__unfold) ).
fof(fact_INT__E,axiom,
! [X25,X155,X149,X105,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(X155,X25)))
=> ~ hBOOL(hAPP(hAPP(c_member(X105),X25),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__E) ).
fof(fact_rel__simps_I22_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).
fof(fact_rel__simps_I5_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).
fof(fact_rel__simps_I26_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I26_J) ).
fof(fact_rel__simps_I9_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I9_J) ).
fof(fact_power__number__of__even__number__of,axiom,
! [X125,X163,X7] :
( class_Int_Onumber__ring(X7)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X125))) = hAPP(hAPP(c_HOL_OLet(X7,X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125))),hAPP(hAPP(c_COMBS(X7,X7,X7),c_Groups_Otimes__class_Otimes(X7)),c_COMBI(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__even__number__of) ).
fof(fact_inj__on__fun__updI,axiom,
! [X6,X127,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X105),X127),hAPP(c_Set_Oimage(X7,X105,X2),X149)))
=> c_Fun_Oinj__on(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X127),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).
fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
! [X6,X127,X23] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X127))
=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6),X127)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X23)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X127),X23)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X127))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X127))
=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6),X127)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X127))
=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6),X127)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).
fof(fact_foldl__foldr1,axiom,
! [X292,X7] :
( class_Groups_Omonoid__add(X7)
=> hAPP(c_List_Ofoldl(X7,X7,c_Groups_Oplus__class_Oplus(X7),c_Groups_Ozero__class_Ozero(X7)),X292) = c_List_Ofoldr(X7,X7,c_Groups_Oplus__class_Oplus(X7),X292,c_Groups_Ozero__class_Ozero(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr1) ).
fof(fact_nth__map__upt,axiom,
! [X2,X7,X95,X44,X107] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),X95)))
=> hAPP(hAPP(c_List_Onth(X7),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X7),X2),c_List_Oupt(X95,X44))),X107) = hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X107)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__map__upt) ).
fof(fact_rotate__rotate,axiom,
! [X300,X33,X90,X87] : hAPP(c_List_Orotate(X87,X90),hAPP(c_List_Orotate(X87,X33),X300)) = hAPP(c_List_Orotate(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33)),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__rotate) ).
fof(fact_foldr__conv__foldl,axiom,
! [X25,X292,X7] :
( class_Groups_Oab__semigroup__add(X7)
=> c_List_Ofoldr(X7,X7,c_Groups_Oplus__class_Oplus(X7),X292,X25) = hAPP(c_List_Ofoldl(X7,X7,c_Groups_Oplus__class_Oplus(X7),X25),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__conv__foldl) ).
fof(fact_map__of__zip__map,axiom,
! [X2,X105,X292,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hAPP(c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Ozip(X7,X105),X292),hAPP(hAPP(c_List_Omap(X7,X105),X2),X292))),X6) = hAPP(c_Option_Ooption_OSome(X105),hAPP(X2,X6)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hAPP(c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Ozip(X7,X105),X292),hAPP(hAPP(c_List_Omap(X7,X105),X2),X292))),X6) = c_Option_Ooption_ONone(X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__map) ).
fof(fact_rotate__conv__mod,axiom,
! [X300,X33,X87] : hAPP(c_List_Orotate(X87,X33),X300) = hAPP(c_List_Orotate(X87,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300))),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__conv__mod) ).
fof(fact_image__map__upd,axiom,
! [X127,X95,X105,X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Set_Oimage(X7,tc_Option_Ooption(X105),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X95),X6),hAPP(c_Option_Ooption_OSome(X105),X127))),X149) = hAPP(c_Set_Oimage(X7,tc_Option_Ooption(X105),X95),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__map__upd) ).
fof(fact_pred__Bit0,axiom,
! [X96] : c_Int_Opred(c_Int_OBit0(X96)) = c_Int_OBit1(c_Int_Opred(X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Bit0) ).
fof(fact_setprod__diff1,axiom,
! [X25,X2,X149,X7,X105] :
( class_Fields_Ofield(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hAPP(X2,X25) != c_Groups_Ozero__class_Ozero(X105)
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149)),hAPP(X2,X25)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__diff1) ).
fof(fact_refl__reflcl,axiom,
! [X172,X7] : c_Relation_Orefl__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),c_Relation_OId(X7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__reflcl) ).
fof(fact_setsum__diff1,axiom,
! [X2,X25,X149,X7,X105] :
( class_Groups_Oab__group__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149)),hAPP(X2,X25)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1) ).
fof(fact_set__concat,axiom,
! [X292,X7] : hAPP(c_List_Oset(X7),c_List_Oconcat(X7,X292)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X7),tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X7)),X292)),c_List_Oset(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__concat) ).
fof(fact_length__concat,axiom,
! [X331,X7] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),c_List_Oconcat(X7,X331)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X7))),X331)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__concat) ).
fof(fact_INF1__E,axiom,
! [X25,X24,X155,X149,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155),X24))
=> ( ~ hBOOL(hAPP(hAPP(X155,X25),X24))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__E) ).
fof(fact_foldr__max__sorted,axiom,
! [X127,X292,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(c_List_Orev(X7),X292))
=> ( ( X292 = c_List_Olist_ONil(X7)
=> c_List_Ofoldr(X7,X7,c_Orderings_Oord__class_Omax(X7),X292,X127) = X127 )
& ( X292 != c_List_Olist_ONil(X7)
=> c_List_Ofoldr(X7,X7,c_Orderings_Oord__class_Omax(X7),X292,X127) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_List_Onth(X7),X292),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X127) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__max__sorted) ).
fof(fact_length__filter__less,axiom,
! [X38,X292,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> ( ~ hBOOL(hAPP(X38,X6))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(c_List_Ofilter(X7,X38),X292))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__less) ).
fof(fact_rtrancl__reflcl,axiom,
! [X191,X7] : c_Transitive__Closure_Ortrancl(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X191),c_Relation_OId(X7))) = c_Transitive__Closure_Ortrancl(X7,X191),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl) ).
fof(fact_rtrancl__r__diff__Id,axiom,
! [X172,X7] : c_Transitive__Closure_Ortrancl(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),c_Relation_OId(X7))) = c_Transitive__Closure_Ortrancl(X7,X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__r__diff__Id) ).
fof(fact_irrefl__diff__Id,axiom,
! [X172,X7] : c_Relation_Oirrefl(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),c_Relation_OId(X7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__diff__Id) ).
fof(fact_divmod__int__relI,axiom,
! [X138,X144,X84,X71] :
( X71 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X144)),X138)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X138))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X138),X84)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X138))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X138),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),X138))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__relI) ).
fof(fact_diff__bin__simps_I5_J,axiom,
! [X115] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X115)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I5_J) ).
fof(fact_setsum__diff1__nat,axiom,
! [X2,X149,X25,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X149)),hAPP(X2,X25)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1__nat) ).
fof(fact_wf__converse__trancl,axiom,
! [X172,X7] :
( c_Wellfounded_Owf(X7,hAPP(c_Relation_Oconverse(X7,X7),X172))
=> c_Wellfounded_Owf(X7,hAPP(c_Relation_Oconverse(X7,X7),c_Transitive__Closure_Otrancl(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__converse__trancl) ).
fof(fact_small_H_Osimps,axiom,
! [X2,X107,X136] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),X107))
=> c_Smallcheck_Osmall_H(X2,X136,X107) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),X107))
=> c_Smallcheck_Osmall_H(X2,X136,X107) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X2,X136,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X107)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small_H_Osimps) ).
fof(fact_concat__eq__Nil__conv,axiom,
! [X331,X7] :
( c_List_Oconcat(X7,X331) = c_List_Olist_ONil(X7)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X3),hAPP(c_List_Oset(tc_List_Olist(X7)),X331)))
=> X3 = c_List_Olist_ONil(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__eq__Nil__conv) ).
fof(fact_Nil__eq__concat__conv,axiom,
! [X331,X7] :
( c_List_Olist_ONil(X7) = c_List_Oconcat(X7,X331)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X3),hAPP(c_List_Oset(tc_List_Olist(X7)),X331)))
=> X3 = c_List_Olist_ONil(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__eq__concat__conv) ).
fof(fact_upt__add__eq__append,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> c_List_Oupt(X114,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X96)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X114,X113)),c_List_Oupt(X113,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X96))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__add__eq__append) ).
fof(fact_setsum__cl__ivl__Suc,axiom,
! [X2,X95,X44,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X95))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(c_Nat_OSuc,X44))) = c_Groups_Ozero__class_Ozero(X7) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X95))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(c_Nat_OSuc,X44))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44))),hAPP(X2,hAPP(c_Nat_OSuc,X44))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cl__ivl__Suc) ).
fof(fact_UnE,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnE) ).
fof(fact_folding_Oinsert,axiom,
! [X6,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,X149)),hAPP(X2,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert) ).
fof(fact_succ__Bit1,axiom,
! [X96] : c_Int_Osucc(c_Int_OBit1(X96)) = c_Int_OBit0(c_Int_Osucc(X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Bit1) ).
fof(fact_evaln__elim__cases_I6_J,axiom,
! [X51,X33,X9,X79] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X79),X9,X33,X51)
=> ~ ! [X70] :
( X33 = hAPP(c_Nat_OSuc,X70)
=> ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X79)),X9,X70,X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I6_J) ).
fof(fact_power__number__of__even,axiom,
! [X125,X26,X7] :
( class_Int_Onumber__ring(X7)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X7),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X125))) = hAPP(hAPP(c_HOL_OLet(X7,X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125))),hAPP(hAPP(c_COMBS(X7,X7,X7),c_Groups_Otimes__class_Otimes(X7)),c_COMBI(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__even) ).
fof(fact_Diff__iff,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
& ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__iff) ).
fof(fact_DiffD2,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD2) ).
fof(fact_card__Suc__eq,axiom,
! [X94,X149,X7] :
( hAPP(c_Finite__Set_Ocard(X7),X149) = hAPP(c_Nat_OSuc,X94)
<=> ? [X188,X221] :
( X149 = hAPP(hAPP(c_Set_Oinsert(X7),X188),X221)
& ~ hBOOL(hAPP(hAPP(c_member(X7),X188),X221))
& hAPP(c_Finite__Set_Ocard(X7),X221) = X94
& ( X94 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X221 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__eq) ).
fof(fact_take__upt,axiom,
! [X33,X90,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X90)),X33))
=> hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X90),c_List_Oupt(X114,X33)) = c_List_Oupt(X114,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__upt) ).
fof(fact_rotate__map,axiom,
! [X292,X2,X105,X44,X7] : hAPP(c_List_Orotate(X7,X44),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)) = hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(c_List_Orotate(X105,X44),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__map) ).
fof(fact_trancl__converse,axiom,
! [X172,X7] : c_Transitive__Closure_Otrancl(X7,hAPP(c_Relation_Oconverse(X7,X7),X172)) = hAPP(c_Relation_Oconverse(X7,X7),c_Transitive__Closure_Otrancl(X7,X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converse) ).
fof(fact_insort__key_Osimps_I2_J,axiom,
! [X293,X105,X127,X6,X2,X7] :
( class_Orderings_Olinorder(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X2,X6)),hAPP(X2,X127)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),hAPP(hAPP(c_List_Olist_OCons(X105),X127),X293)) = hAPP(hAPP(c_List_Olist_OCons(X105),X6),hAPP(hAPP(c_List_Olist_OCons(X105),X127),X293)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X2,X6)),hAPP(X2,X127)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),hAPP(hAPP(c_List_Olist_OCons(X105),X127),X293)) = hAPP(hAPP(c_List_Olist_OCons(X105),X127),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),X293)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key_Osimps_I2_J) ).
fof(fact_upto__rec__number__of,axiom,
! [X33,X90] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33)))
=> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33)))
=> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto__rec__number__of) ).
fof(fact_subset__insert,axiom,
! [X155,X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),X155)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
fof(fact_IntE,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntE) ).
fof(fact_upto_Opsimps,axiom,
! [X158,X107] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X158)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X107),X158))
=> c_List_Oupto(X107,X158) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X107),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint)),X158)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X107),X158))
=> c_List_Oupto(X107,X158) = c_List_Olist_ONil(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto_Opsimps) ).
fof(fact_fun__left__comm_Ofold__insert,axiom,
! [X26,X6,X149,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(X2,X6),hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).
fof(fact_evalc_OIfFalse,axiom,
! [X59,X58,X57,X45,X24] :
( ~ hBOOL(hAPP(X24,X45))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X57),X45),X58))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X24,X59,X57)),X45),X58)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OIfFalse) ).
fof(fact_map__of__zip__is__None,axiom,
! [X6,X293,X105,X292,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)
=> ( hAPP(c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293)),X6) = c_Option_Ooption_ONone(X105)
<=> ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__is__None) ).
fof(fact_map__fun__upd,axiom,
! [X163,X2,X105,X292,X127,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X127),hAPP(c_List_Oset(X7),X292)))
=> hAPP(hAPP(c_List_Omap(X7,X105),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X127),X163)),X292) = hAPP(hAPP(c_List_Omap(X7,X105),X2),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__fun__upd) ).
fof(fact_notin__set__sublistI,axiom,
! [X211,X292,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),c_List_Osublist(X7,X292,X211)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__set__sublistI) ).
fof(fact_notin__set__remove1,axiom,
! [X127,X292,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),c_List_Oremove1(X7,X127,X292)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__set__remove1) ).
fof(fact_nth__upt,axiom,
! [X113,X96,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X96)),X113))
=> hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X114,X113)),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X96) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__upt) ).
fof(fact_zpower__number__of__even,axiom,
! [X125,X26] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X125))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__number__of__even) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X7,X105] :
( class_Orderings_Oord(X105)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,X105)),X2),X1))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X105)),X2),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X105)),X1),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_pick_Osimps,axiom,
! [X300,X86,X87,X114] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X114),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X87),X86)))
=> hAPP(c_Random_Opick(X87,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X87)),X86),X300)),X114) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X87),X86) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X114),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X87),X86)))
=> hAPP(c_Random_Opick(X87,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X87)),X86),X300)),X114) = hAPP(c_Random_Opick(X87,X300),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X114),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X87),X86))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick_Osimps) ).
fof(fact_UnionE,axiom,
! [X193,X149,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X149),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X193)))
=> ~ ! [X273] :
( hBOOL(hAPP(hAPP(c_member(X7),X149),X273))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X273),X193)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionE) ).
fof(fact_less__eq__int__code_I13_J,axiom,
! [X170,X171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X171)),c_Int_OBit0(X170)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X171),X170)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).
fof(fact_rel__simps_I31_J,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X94)),c_Int_OBit0(X157)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).
fof(fact_less__int__code_I13_J,axiom,
! [X170,X171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X171)),c_Int_OBit0(X170)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X171),X170)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).
fof(fact_rel__simps_I14_J,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X94)),c_Int_OBit0(X157)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).
fof(fact_card__Diff__singleton__if,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X7),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton__if) ).
fof(fact_add__special_I3_J,axiom,
! [X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),c_Groups_Oone__class_Oone(X87)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I3_J) ).
fof(fact_le__number__of__eq__not__less,axiom,
! [X125,X163,X7] :
( ( class_Int_Onumber(X7)
& class_Orderings_Olinorder(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).
fof(fact_bot2E,axiom,
! [X127,X6,X105,X7] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X6),X127)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).
fof(fact_evaln_Oequations_I6_J,axiom,
! [X61,X47,X43,X41,X72,X42] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X42,X72,X41),X43,X47,X61)
<=> ( ( hBOOL(hAPP(X42,X43))
& c_Natural_Oevaln(X72,X43,X47,X61) )
| ( ~ hBOOL(hAPP(X42,X43))
& c_Natural_Oevaln(X41,X43,X47,X61) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I6_J) ).
fof(fact_evaln_Oequations_I5_J,axiom,
! [X61,X47,X43,X72,X41,X42] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X42,X41,X72),X43,X47,X61)
<=> ( ( hBOOL(hAPP(X42,X43))
& c_Natural_Oevaln(X41,X43,X47,X61) )
| ( ~ hBOOL(hAPP(X42,X43))
& c_Natural_Oevaln(X72,X43,X47,X61) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I5_J) ).
fof(fact_evaln__elim__cases_I5_J,axiom,
! [X46,X44,X45,X56,X57,X24] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X24,X57,X56),X45,X44,X46)
=> ( ( hBOOL(hAPP(X24,X45))
=> ~ c_Natural_Oevaln(X57,X45,X44,X46) )
=> ~ ( ~ hBOOL(hAPP(X24,X45))
=> ~ c_Natural_Oevaln(X56,X45,X44,X46) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I5_J) ).
fof(fact_divmod__int__rel__mod__eq,axiom,
! [X98,X150,X151,X120] :
( X120 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X151),X150)),X98)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X151))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X151)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X151))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X151),X98))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> ( X151 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X120,X151) = X98 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).
fof(fact_foldr_Osimps_I1_J,axiom,
! [X25,X2,X7,X105] : c_List_Ofoldr(X105,X7,X2,c_List_Olist_ONil(X105),X25) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr_Osimps_I1_J) ).
fof(fact_divmod__int__rel__div__eq,axiom,
! [X152,X98,X151,X120] :
( X120 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X151),X98)),X152)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X151))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X152))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X152),X151)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X151))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X151),X152))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X152),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> ( X151 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X120),X151) = X98 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).
fof(fact_rotate__Suc,axiom,
! [X300,X33,X87] : hAPP(c_List_Orotate(X87,hAPP(c_Nat_OSuc,X33)),X300) = hAPP(c_List_Orotate1(X87),hAPP(c_List_Orotate(X87,X33),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__Suc) ).
fof(fact_fun__left__comm_Ofold__insert2,axiom,
! [X26,X6,X149,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),hAPP(hAPP(X2,X6),X26)),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).
fof(fact_upt__eq__Cons__conv,axiom,
! [X292,X6,X158,X107] :
( c_List_Oupt(X107,X158) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X6),X292)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),X158))
& X107 = X6
& c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X158) = X292 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__eq__Cons__conv) ).
fof(fact_setsum__op__ivl__Suc,axiom,
! [X2,X95,X44,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X95))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X44))) = c_Groups_Ozero__class_Ozero(X7) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X95))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X44))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X44))),hAPP(X2,X44)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).
fof(fact_sup1E,axiom,
! [X6,X155,X149,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155),X6))
=> ( ~ hBOOL(hAPP(X149,X6))
=> hBOOL(hAPP(X155,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
fof(fact_pred__Bit1,axiom,
! [X96] : c_Int_Opred(c_Int_OBit1(X96)) = c_Int_OBit0(X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Bit1) ).
fof(fact_nat__number__of__add__left,axiom,
! [X96,X165,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),X96) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),X165))),X96) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__add__left) ).
fof(fact_trancl__empty,axiom,
! [X7] : c_Transitive__Closure_Otrancl(X7,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__empty) ).
fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
! [X44,X95,X2,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X95,X44))) = hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X7),X2),c_List_Oupt(X95,X44))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).
fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
! [X44,X95,X2,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X7),X2),c_List_Oupt(X95,X44))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X95,X44))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).
fof(fact_inf1E,axiom,
! [X6,X155,X149,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155),X6))
=> ~ ( hBOOL(hAPP(X149,X6))
=> ~ hBOOL(hAPP(X155,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
fof(fact_rotate1__rotate__swap,axiom,
! [X300,X33,X87] : hAPP(c_List_Orotate1(X87),hAPP(c_List_Orotate(X87,X33),X300)) = hAPP(c_List_Orotate(X87,X33),hAPP(c_List_Orotate1(X87),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__rotate__swap) ).
fof(fact_number__of__Bit1,axiom,
! [X128,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit1(X128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Oone__class_Oone(X87)),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128))),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit1) ).
fof(fact_DiffI,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X155))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffI) ).
fof(fact_code__numeral_Orecs_I2_J,axiom,
! [X176,X21,X22,X7] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X7,X22,X21,c_Code__Numeral_OSuc__code__numeral(X176)) = hAPP(hAPP(X21,X176),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X7,X22,X21,X176)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).
fof(fact_Suc__code__numeral__def,axiom,
! [X96] : c_Code__Numeral_OSuc__code__numeral(X96) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X96))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__code__numeral__def) ).
fof(fact_card__def,axiom,
! [X149,X7] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ocard(X7),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X7),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X149) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ocard(X7),X149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def) ).
fof(fact_Id__O__R,axiom,
! [X191,X105,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X105),c_Relation_OId(X7)),X191) = X191,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__O__R) ).
fof(fact_divide__numeral__1,axiom,
! [X71,X87] :
( ( class_Fields_Ofield(X87)
& class_Int_Onumber__ring(X87) )
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit1(c_Int_OPls))) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__numeral__1) ).
fof(fact_divide__Numeral1,axiom,
! [X86,X87] :
( ( class_Fields_Ofield(X87)
& class_Int_Onumber__ring(X87) )
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit1(c_Int_OPls))) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral1) ).
fof(fact_le__supE,axiom,
! [X86,X84,X71,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84)),X86))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X86))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supE) ).
fof(fact_min__max_Ole__supE,axiom,
! [X86,X84,X71,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84)),X86))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X86))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supE) ).
fof(fact_mult__numeral__1__right,axiom,
! [X71,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit1(c_Int_OPls))) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
fof(fact_hd__rotate__conv__nth,axiom,
! [X33,X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> hAPP(c_List_Ohd(X87),hAPP(c_List_Orotate(X87,X33),X300)) = hAPP(hAPP(c_List_Onth(X87),X300),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__rotate__conv__nth) ).
fof(fact_nat__number__of__mult__left,axiom,
! [X96,X165,X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X139),X165))),X96) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).
fof(fact_rotate__length01,axiom,
! [X33,X300,X87] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
=> hAPP(c_List_Orotate(X87,X33),X300) = X300 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__length01) ).
fof(fact_Int__insert__left,axiom,
! [X155,X193,X25,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X193))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)),X193) = hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X193))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)),X193) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left) ).
fof(fact_UnCI,axiom,
! [X149,X155,X23,X7] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X155))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),X149)) )
=> hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnCI) ).
fof(fact_map__add__dom__app__simps_I2_J,axiom,
! [X281,X280,X105,X95,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X95),c_Map_Odom(X7,X105,X280)))
=> hAPP(c_Map_Omap__add(X7,X105,X280,X281),X95) = hAPP(X281,X95) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I2_J) ).
fof(fact_map__add__dom__app__simps_I3_J,axiom,
! [X280,X281,X105,X95,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X95),c_Map_Odom(X7,X105,X281)))
=> hAPP(c_Map_Omap__add(X7,X105,X280,X281),X95) = hAPP(X280,X95) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I3_J) ).
fof(fact_not__square__less__zero,axiom,
! [X71,X87] :
( class_Rings_Olinordered__ring(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X71)),c_Groups_Ozero__class_Ozero(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_bin__less__0__simps_I3_J,axiom,
! [X125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X125)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).
fof(fact_zdiv__number__of__Bit0,axiom,
! [X128,X139] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X139))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit0) ).
fof(fact_add__leE,axiom,
! [X33,X96,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X96)),X33))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_rel__simps_I27_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X94)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).
fof(fact_rel__simps_I28_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X94)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I28_J) ).
fof(fact_rel__simps_I11_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X94)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I11_J) ).
fof(fact_rel__simps_I10_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X94)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).
fof(fact_neg__number__of__Bit0,axiom,
! [X125] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X125))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Bit0) ).
fof(fact_Image__Id,axiom,
! [X149,X7] : hAPP(c_Relation_OImage(X7,X7,c_Relation_OId(X7)),X149) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id) ).
fof(fact_insert__Diff__if,axiom,
! [X149,X155,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),X155) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),X155) = hAPP(hAPP(c_Set_Oinsert(X7),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__if) ).
fof(fact_map__comp__empty_I2_J,axiom,
! [X6,X95,X119,X7,X105] : c_Map_Omap__comp(X105,X7,X119,hAPP(c_COMBK(tc_Option_Ooption(X7),X105),c_Option_Ooption_ONone(X7)),X95,X6) = c_Option_Ooption_ONone(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__empty_I2_J) ).
fof(fact_map__comp__empty_I1_J,axiom,
! [X6,X95,X119,X7,X105] : c_Map_Omap__comp(X105,X7,X119,X95,hAPP(c_COMBK(tc_Option_Ooption(X105),X119),c_Option_Ooption_ONone(X105)),X6) = c_Option_Ooption_ONone(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__empty_I1_J) ).
fof(fact_le__iff__pred__less,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),X157))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X94)),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__pred__less) ).
fof(fact_diff__bin__simps_I6_J,axiom,
! [X115] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X115)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I6_J) ).
fof(fact_evaln_OIfFalse,axiom,
! [X59,X58,X44,X57,X45,X24] :
( ~ hBOOL(hAPP(X24,X45))
=> ( c_Natural_Oevaln(X57,X45,X44,X58)
=> c_Natural_Oevaln(c_Com_Ocom_OCond(X24,X59,X57),X45,X44,X58) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OIfFalse) ).
fof(fact_div__if,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__if) ).
fof(fact_div__geq,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__geq) ).
fof(fact_not__zle__0__negative,axiom,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X33))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__zle__0__negative) ).
fof(fact_rtrancl__reflcl__absorb,axiom,
! [X191,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X7,X191)),c_Relation_OId(X7)) = c_Transitive__Closure_Ortrancl(X7,X191),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl__absorb) ).
fof(fact_upt__Suc__append,axiom,
! [X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> c_List_Oupt(X114,hAPP(c_Nat_OSuc,X113)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X114,X113)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X113),c_List_Olist_ONil(tc_Nat_Onat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__Suc__append) ).
fof(fact_Int__insert__right,axiom,
! [X155,X149,X25,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right) ).
fof(fact_setprod_OF__eq,axiom,
! [X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),c_Groups_Oone__class_Oone(X105)),X149) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149) = c_Groups_Oone__class_Oone(X105) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_OF__eq) ).
fof(fact_setsum_OF__eq,axiom,
! [X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Oplus__class_Oplus(X105)),X1),c_Groups_Ozero__class_Ozero(X105)),X149) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149) = c_Groups_Ozero__class_Ozero(X105) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_OF__eq) ).
fof(fact_nth__append,axiom,
! [X301,X300,X87,X33] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)),X33) = hAPP(hAPP(c_List_Onth(X87),X300),X33) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)),X33) = hAPP(hAPP(c_List_Onth(X87),X301),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append) ).
fof(fact_ComplE,axiom,
! [X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplE) ).
fof(fact_ComplD,axiom,
! [X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplD) ).
fof(fact_Compl__iff,axiom,
! [X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)))
<=> ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__iff) ).
fof(fact_nat__number__of__Bit0,axiom,
! [X125] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X125)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Bit0) ).
fof(fact_max__number__of,axiom,
! [X139,X63,X7] :
( ( class_Int_Onumber(X7)
& class_Orderings_Oord(X7) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X139) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X63) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__number__of) ).
fof(fact_min__number__of,axiom,
! [X139,X63,X7] :
( ( class_Int_Onumber(X7)
& class_Orderings_Oord(X7) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X63) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X139) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__number__of) ).
fof(fact_not__add__less1,axiom,
! [X113,X114] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X113)),X114)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X114,X113] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X114)),X114)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_remove1__append,axiom,
! [X293,X292,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> c_List_Oremove1(X7,X6,hAPP(hAPP(c_List_Oappend(X7),X292),X293)) = hAPP(hAPP(c_List_Oappend(X7),c_List_Oremove1(X7,X6,X292)),X293) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> c_List_Oremove1(X7,X6,hAPP(hAPP(c_List_Oappend(X7),X292),X293)) = hAPP(hAPP(c_List_Oappend(X7),X292),c_List_Oremove1(X7,X6,X293)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__append) ).
fof(fact_neg__number__of__pred__iff__0,axiom,
! [X163] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X163))))
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__pred__iff__0) ).
fof(fact_empty__fold1SetE,axiom,
! [X6,X2,X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,X2,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold1SetE) ).
fof(fact_rel__simps_I51_J,axiom,
! [X157,X94] :
( c_Int_OBit1(X94) = c_Int_OBit1(X157)
<=> X94 = X157 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).
fof(fact_restrict__map__def,axiom,
! [X95,X105,X149,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Map_Orestrict__map(X7,X105,X95,X149),X6) = hAPP(X95,X6) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Map_Orestrict__map(X7,X105,X95,X149),X6) = c_Option_Ooption_ONone(X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__def) ).
fof(fact_nat__diff__split__asm,axiom,
! [X24,X25,X38] :
( hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X24)))
<=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X24))
& ~ hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X159] :
( X25 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X159)
& ~ hBOOL(hAPP(X38,X159)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_distinct_Osimps_I2_J,axiom,
! [X292,X6,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
& hBOOL(hAPP(c_List_Odistinct(X7),X292)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I2_J) ).
fof(fact_finite__map__freshness,axiom,
! [X2,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Map_Odom(X7,X105,X2)))
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))
=> ? [X3] : hAPP(X2,X3) = c_Option_Ooption_ONone(X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__map__freshness) ).
fof(fact_length__rotate,axiom,
! [X300,X33,X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),hAPP(c_List_Orotate(X87,X33),X300)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rotate) ).
fof(fact_Diff__insert__absorb,axiom,
! [X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).
fof(fact_setprod_Oinsert,axiom,
! [X1,X6,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(X1,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinsert) ).
fof(fact_setprod__insert,axiom,
! [X2,X25,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(X2,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__insert) ).
fof(fact_setsum_Oinsert,axiom,
! [X1,X6,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(X1,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinsert) ).
fof(fact_setsum__insert,axiom,
! [X2,X25,X215,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X215))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X215))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Set_Oinsert(X7),X25),X215)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(X2,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X215)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__insert) ).
fof(fact_drop__upt,axiom,
! [X113,X114,X90] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X90),c_List_Oupt(X114,X113)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X90),X113),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__upt) ).
fof(fact_filter__empty__conv,axiom,
! [X292,X38,X7] :
( hAPP(c_List_Ofilter(X7,X38),X292) = c_List_Olist_ONil(X7)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X292)))
=> ~ hBOOL(hAPP(X38,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__empty__conv) ).
fof(fact_not__int__zless__negative,axiom,
! [X90,X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).
fof(fact_set__rotate,axiom,
! [X292,X44,X7] : hAPP(c_List_Oset(X7),hAPP(c_List_Orotate(X7,X44),X292)) = hAPP(c_List_Oset(X7),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rotate) ).
fof(fact_sup1CI,axiom,
! [X7,X149,X6,X155] :
( ( ~ hBOOL(hAPP(X155,X6))
=> hBOOL(hAPP(X149,X6)) )
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).
fof(fact_partition__P,axiom,
! [X332,X333,X292,X38,X7] :
( c_List_Opartition(X7,X38,X292) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X333),X332)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X333)))
=> hBOOL(hAPP(X38,X3)) )
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X332)))
=> ~ hBOOL(hAPP(X38,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__P) ).
fof(fact_trancl__domain,axiom,
! [X172,X7] : hAPP(c_Relation_ODomain(X7,X7),c_Transitive__Closure_Otrancl(X7,X172)) = hAPP(c_Relation_ODomain(X7,X7),X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__domain) ).
fof(fact_trancl__range,axiom,
! [X172,X7] : hAPP(c_Relation_ORange(X7,X7),c_Transitive__Closure_Otrancl(X7,X172)) = hAPP(c_Relation_ORange(X7,X7),X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__range) ).
fof(fact_le__nat__number__of,axiom,
! [X169,X163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X163),X169))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X163),c_Int_OPls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__nat__number__of) ).
fof(fact_dvd_Oless__trans,axiom,
! [X97,X98,X86] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X86)) )
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X97))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X98)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X97))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
fof(fact_diff__bin__simps_I7_J,axiom,
! [X115,X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X96)),c_Int_OBit0(X115)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).
fof(fact_add__Bit0__Bit0,axiom,
! [X115,X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X96)),c_Int_OBit0(X115)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).
fof(fact_folding__one_Oeq__fold_H,axiom,
! [X6,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,X2),X6),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold_H) ).
fof(fact_Abs__Integ__cases,axiom,
! [X6] :
~ ! [X82] :
( X6 = hAPP(c_Int_OAbs__Integ,X82)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X82),c_Int_OInteg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__cases) ).
fof(fact_upt__conv__Cons,axiom,
! [X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> c_List_Oupt(X114,X113) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X114),c_List_Oupt(hAPP(c_Nat_OSuc,X114),X113)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__conv__Cons) ).
fof(fact_map__comp__simps_I2_J,axiom,
! [X285,X105,X119,X290,X7,X94,X284] :
( hAPP(X284,X94) = hAPP(c_Option_Ooption_OSome(X7),X290)
=> c_Map_Omap__comp(X7,X119,X105,X285,X284,X94) = hAPP(X285,X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__simps_I2_J) ).
fof(fact_filter__insort__triv,axiom,
! [X292,X2,X7,X6,X38,X105] :
( class_Orderings_Olinorder(X105)
=> ( ~ hBOOL(hAPP(X38,X6))
=> hAPP(c_List_Ofilter(X7,X38),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X105,X2),X6),X292)) = hAPP(c_List_Ofilter(X7,X38),X292) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__insort__triv) ).
fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omin(X7)),X6),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).
fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omax(X7)),X6),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold_H) ).
fof(fact_nat__dvd__iff,axiom,
! [X95,X26] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),X95))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
=> X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__iff) ).
fof(fact_not__psubset__empty,axiom,
! [X149,X7] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
fof(fact_restrict__out,axiom,
! [X95,X105,X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Map_Orestrict__map(X7,X105,X95,X149),X6) = c_Option_Ooption_ONone(X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__out) ).
fof(fact_fold1__eq__fold,axiom,
! [X25,X149,X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Groups_Otimes__class_Otimes(X7)),X25),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__eq__fold) ).
fof(fact_number__of__Bit0,axiom,
! [X128,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit0(X128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128))),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit0) ).
fof(fact_map__nth,axiom,
! [X292,X7] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X7),hAPP(c_List_Onth(X7),X292)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292))) = X292,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__nth) ).
fof(fact_le__infE,axiom,
! [X84,X71,X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84)))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X71))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infE) ).
fof(fact_min__max_Ole__infE,axiom,
! [X84,X71,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84)))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X71))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infE) ).
fof(fact_length__remove1,axiom,
! [X292,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),c_List_Oremove1(X7,X6,X292)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),c_List_Oremove1(X7,X6,X292)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remove1) ).
fof(fact_Int__insert__left__if0,axiom,
! [X155,X193,X25,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X193))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)),X193) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).
fof(fact_nat__of__aux__code,axiom,
! [X33,X114] :
( ( X114 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> c_Code__Numeral_Onat__of__aux(X114,X33) = X33 )
& ( X114 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> c_Code__Numeral_Onat__of__aux(X114,X33) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X114),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__aux__code) ).
fof(fact_nat__of__aux__def,axiom,
! [X33,X114] : c_Code__Numeral_Onat__of__aux(X114,X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X114)),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__aux__def) ).
fof(fact_wf__trancl,axiom,
! [X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> c_Wellfounded_Owf(X7,c_Transitive__Closure_Otrancl(X7,X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__trancl) ).
fof(fact_R__O__Id,axiom,
! [X191,X105,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X105,X105),X191),c_Relation_OId(X105)) = X191,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_R__O__Id) ).
fof(fact_map__comp__simps_I1_J,axiom,
! [X285,X105,X119,X7,X94,X284] :
( hAPP(X284,X94) = c_Option_Ooption_ONone(X7)
=> c_Map_Omap__comp(X7,X119,X105,X285,X284,X94) = c_Option_Ooption_ONone(X119) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__simps_I1_J) ).
fof(fact_trancl__unfold__right,axiom,
! [X172,X7] : c_Transitive__Closure_Otrancl(X7,X172) = hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),c_Transitive__Closure_Ortrancl(X7,X172)),X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold__right) ).
fof(fact_trancl__rtrancl__absorb,axiom,
! [X191,X7] : c_Transitive__Closure_Ortrancl(X7,c_Transitive__Closure_Otrancl(X7,X191)) = c_Transitive__Closure_Ortrancl(X7,X191),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
fof(fact_concat_Osimps_I1_J,axiom,
! [X87] : c_List_Oconcat(X87,c_List_Olist_ONil(tc_List_Olist(X87))) = c_List_Olist_ONil(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat_Osimps_I1_J) ).
fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
! [X24,X25] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff) ).
fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
! [X24,X25] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24)
<=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff2) ).
fof(fact_Inf__fin_Oeq__fold_H,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),X6),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).
fof(fact_Min_Oeq__fold_H,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omin(X7)),X6),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oeq__fold_H) ).
fof(fact_Max_Oeq__fold_H,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omax(X7)),X6),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oeq__fold_H) ).
fof(fact_Sup__fin_Oeq__fold_H,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7)),X6),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).
fof(fact_eq__nat__number__of,axiom,
! [X169,X163] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)
<=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X163)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X163)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X163) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
=> X163 = X169 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).
fof(fact_abs__number__of,axiom,
! [X86,X87] :
( ( class_Int_Onumber__ring(X87)
& class_Rings_Olinordered__idom(X87) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X86)),c_Groups_Ozero__class_Ozero(X87)))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X86)) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X86)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X86)),c_Groups_Ozero__class_Ozero(X87)))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X86)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),X86) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__number__of) ).
fof(fact_converse__Id,axiom,
! [X7] : hAPP(c_Relation_Oconverse(X7,X7),c_Relation_OId(X7)) = c_Relation_OId(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Id) ).
fof(fact_mod__nat__number__of,axiom,
! [X165,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__nat__number__of) ).
fof(fact_min__max_OInf__fin_Oinsert,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).
fof(fact_min__max_OSup__fin_Oinsert,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).
fof(fact_mult__Bit0,axiom,
! [X115,X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X96)),X115) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X96),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit0) ).
fof(fact_dvd_Ole__less__trans,axiom,
! [X97,X98,X86] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X97))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X98)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X97))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
fof(fact_dvd_Oless__le__trans,axiom,
! [X97,X98,X86] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X86)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X97))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X97))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
fof(fact_power__nat__number__of__number__of,axiom,
! [X128,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__nat__number__of__number__of) ).
fof(fact_div__nat__number__of,axiom,
! [X165,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nat__number__of) ).
fof(fact_fold1__insert,axiom,
! [X6,X149,X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__insert) ).
fof(fact_dvd_OatLeastatMost__empty,axiom,
! [X25,X24] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X25))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24)) )
=> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty) ).
fof(fact_Suc__diff__number__of,axiom,
! [X90,X139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X139))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X139))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__number__of) ).
fof(fact_ex__least__nat__less,axiom,
! [X44,X38] :
( ~ hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X38,X44))
=> ? [X118] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X118),X44))
& ! [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X147),X118))
=> ~ hBOOL(hAPP(X38,X147)) )
& hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X118),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_greaterThanAtMost__upt,axiom,
! [X95,X44] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X44,X95) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X44),hAPP(c_Nat_OSuc,X95))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__upt) ).
fof(fact_rel__simps_I21_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).
fof(fact_rel__simps_I4_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).
fof(fact_rel__simps_I25_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I25_J) ).
fof(fact_rel__simps_I8_J,axiom,
! [X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I8_J) ).
fof(fact_Int__insert__right__if0,axiom,
! [X155,X149,X25,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).
fof(fact_rotate__id,axiom,
! [X300,X87,X33] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Orotate(X87,X33),X300) = X300 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__id) ).
fof(fact_rotate__is__Nil__conv,axiom,
! [X292,X44,X7] :
( hAPP(c_List_Orotate(X7,X44),X292) = c_List_Olist_ONil(X7)
<=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__is__Nil__conv) ).
fof(fact_simp__from__to,axiom,
! [X107,X158] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X158),X107))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X107,X158) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X158),X107))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X107,X158) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X107),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint)),X158)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_simp__from__to) ).
fof(fact_double__number__of__Bit0,axiom,
! [X128,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Oone__class_Oone(X87)),c_Groups_Oone__class_Oone(X87))),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit0(X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).
fof(fact_insertCI,axiom,
! [X24,X155,X25,X7] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X155))
=> X25 = X24 )
=> hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(hAPP(c_Set_Oinsert(X7),X24),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
fof(fact_Bit1__def,axiom,
! [X96] : c_Int_OBit1(X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X96)),X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(fact_internal__split__conv,axiom,
! [X24,X25,X23,X7,X119,X105] : hAPP(hAPP(c_Product__Type_Ointernal__split(X105,X119,X7),X23),hAPP(hAPP(c_Product__Type_OPair(X105,X119),X25),X24)) = hAPP(hAPP(X23,X25),X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__conv) ).
fof(fact_internal__split__def,axiom,
! [X119,X105,X7] : c_Product__Type_Ointernal__split(X7,X105,X119) = c_Product__Type_Oprod_Oprod__case(X7,X105,X119),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__def) ).
fof(fact_ComplI,axiom,
! [X149,X23,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplI) ).
fof(fact_vimage__const,axiom,
! [X105,X149,X23,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(c_COMBK(X7,X105),X23)),X149) = c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(c_COMBK(X7,X105),X23)),X149) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__const) ).
fof(fact_folding__one_Oinsert,axiom,
! [X6,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(X2,X6),hAPP(X215,X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert) ).
fof(fact_zdvd__not__zless,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X33))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X33),X90)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
fof(fact_nat__dvd__not__less,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X90)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
fof(fact_map__Suc__upt,axiom,
! [X44,X95] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X95,X44)) = c_List_Oupt(hAPP(c_Nat_OSuc,X95),hAPP(c_Nat_OSuc,X44)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__Suc__upt) ).
fof(fact_divmod__int__def,axiom,
! [X84,X71] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> c_Divides_Odivmod__int(X71,X84) = c_Divides_OposDivAlg(X71,X84) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( ( X71 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X71,X84) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( X71 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X71,X84) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84))) ) ) ) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> c_Divides_Odivmod__int(X71,X84) = c_Divides_OnegDivAlg(X71,X84) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> c_Divides_Odivmod__int(X71,X84) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__def) ).
fof(fact_refl__Id,axiom,
! [X7] : c_Relation_Orefl__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),c_Relation_OId(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__Id) ).
fof(fact_numeral__1__eq__1,axiom,
! [X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).
fof(fact_semiring__norm_I110_J,axiom,
! [X87] :
( class_Int_Onumber__ring(X87)
=> c_Groups_Oone__class_Oone(X87) = hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit1(c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).
fof(fact_not__less__eq__eq,axiom,
! [X44,X95] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_abs__not__less__zero,axiom,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),c_Groups_Ozero__class_Ozero(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
fof(fact_of__nat__less__0__iff,axiom,
! [X90,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X90)),c_Groups_Ozero__class_Ozero(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).
fof(fact_iszero__number__of__Bit0,axiom,
! [X125,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Int_Oring__char__0(X7) )
=> ( c_Int_Oiszero(X7,hAPP(c_Int_Onumber__class_Onumber__of(X7),c_Int_OBit0(X125)))
<=> c_Int_Oiszero(X7,hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__number__of__Bit0) ).
fof(fact_add__nat__number__of,axiom,
! [X165,X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X165),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X165),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),X165)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nat__number__of) ).
fof(fact_power__nat__number__of,axiom,
! [X33,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),X33) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),X33) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__nat__number__of) ).
fof(fact_diff__bin__simps_I3_J,axiom,
! [X115] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X115)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).
fof(fact_minus__shift__def,axiom,
! [X138,X115,X96] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X115))
=> c_Random_Ominus__shift(X138,X96,X115) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X138),X96)),X115) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X115))
=> c_Random_Ominus__shift(X138,X96,X115) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X96),X115) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__shift__def) ).
fof(fact_split__zmod,axiom,
! [X94,X44,X38] :
( hBOOL(hAPP(X38,c_Divides_Odiv__class_Omod(tc_Int_Oint,X44,X94)))
<=> ( ( X94 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X38,X44)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
=> ! [X147,X117] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X117))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X117),X94))
& X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X147)),X117) )
=> hBOOL(hAPP(X38,X117)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X147,X117] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X117))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X117),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X147)),X117) )
=> hBOOL(hAPP(X38,X117)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zmod) ).
fof(fact_upto_Osimps,axiom,
! [X113,X114] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X114),X113))
=> c_List_Oupto(X114,X113) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X114),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X114),c_Groups_Oone__class_Oone(tc_Int_Oint)),X113)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X114),X113))
=> c_List_Oupto(X114,X113) = c_List_Olist_ONil(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto_Osimps) ).
fof(fact_rel__simps_I49_J,axiom,
! [X115,X96] : c_Int_OBit0(X96) != c_Int_OBit1(X115),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).
fof(fact_rel__simps_I50_J,axiom,
! [X115,X96] : c_Int_OBit1(X96) != c_Int_OBit0(X115),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).
fof(fact_divmod__nat__div__mod,axiom,
! [X33,X90] : c_Divides_Odivmod__nat(X90,X33) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__div__mod) ).
fof(fact_code__numeral_Osimps_I5_J,axiom,
! [X176,X21,X22,X7] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X7,X22,X21,c_Code__Numeral_OSuc__code__numeral(X176)) = hAPP(X21,X176),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I5_J) ).
fof(fact_greaterThanLessThan__upt,axiom,
! [X95,X44] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X44,X95) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X44),X95)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__upt) ).
fof(fact_of__int__of__nat,axiom,
! [X96,X87] :
( class_Rings_Oring__1(X87)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),X96) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),X96) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onat,X96)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__of__nat) ).
fof(fact_WTs__elim__cases_I5_J,axiom,
! [X56,X57,X24] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X24,X57,X56)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X57))
=> ~ hBOOL(hAPP(c_Com_OWT,X56)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I5_J) ).
fof(fact_Domain__Id,axiom,
! [X7] : hAPP(c_Relation_ODomain(X7,X7),c_Relation_OId(X7)) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id) ).
fof(fact_Range__Id,axiom,
! [X7] : hAPP(c_Relation_ORange(X7,X7),c_Relation_OId(X7)) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id) ).
fof(fact_Inf__fin_Oinsert,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X6),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert) ).
fof(fact_Min_Oinsert,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olinorder__class_OMin(X7,X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oinsert) ).
fof(fact_Max_Oinsert,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olinorder__class_OMax(X7,X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oinsert) ).
fof(fact_Sup__fin_Oinsert,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert) ).
fof(fact_rtrancl__trancl__absorb,axiom,
! [X191,X7] : c_Transitive__Closure_Otrancl(X7,c_Transitive__Closure_Ortrancl(X7,X191)) = c_Transitive__Closure_Ortrancl(X7,X191),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
fof(fact_sublist__singleton,axiom,
! [X6,X7,X149] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X149))
=> c_List_Osublist(X7,hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7)),X149) = hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X149))
=> c_List_Osublist(X7,hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7)),X149) = c_List_Olist_ONil(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__singleton) ).
fof(fact_one__mod__nat__number__of,axiom,
! [X165] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__mod__nat__number__of) ).
fof(fact_single__valued__Id,axiom,
! [X7] : c_Relation_Osingle__valued(X7,X7,c_Relation_OId(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id) ).
fof(fact_less__le__not__le,axiom,
! [X127,X6,X7] :
( class_Orderings_Opreorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_card_Oinsert,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X7),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert) ).
fof(fact_split__zdiv,axiom,
! [X94,X44,X38] :
( hBOOL(hAPP(X38,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X44),X94)))
<=> ( ( X94 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
=> ! [X147] :
( ? [X117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X117))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X117),X94))
& X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X147)),X117) )
=> hBOOL(hAPP(X38,X147)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X147] :
( ? [X117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X117))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X117),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X147)),X117) )
=> hBOOL(hAPP(X38,X147)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zdiv) ).
fof(fact_insert__ident,axiom,
! [X155,X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
=> ( hAPP(hAPP(c_Set_Oinsert(X7),X6),X149) = hAPP(hAPP(c_Set_Oinsert(X7),X6),X155)
<=> X149 = X155 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
fof(fact_card__insert__if,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(c_Finite__Set_Ocard(X7),X149) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X7),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).
fof(fact_last__upt,axiom,
! [X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> c_List_Olast(tc_Nat_Onat,c_List_Oupt(X114,X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X113),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__upt) ).
fof(fact_Suc__code__numeral__minus__one,axiom,
! [X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X33)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__code__numeral__minus__one) ).
fof(fact_not__less__eq,axiom,
! [X44,X95] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X95))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_distinct__upt,axiom,
! [X113,X114] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X114,X113))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__upt) ).
fof(fact_relpow_Osimps_I1_J,axiom,
! [X191,X7] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X191) = c_Relation_OId(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_relpow_Osimps_I1_J) ).
fof(fact_int__less__0__conv,axiom,
! [X96] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X96)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__less__0__conv) ).
fof(fact_rel__simps_I43_J,axiom,
! [X157] :
( c_Int_OMin = c_Int_OBit1(X157)
<=> c_Int_OMin = X157 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).
fof(fact_rel__simps_I47_J,axiom,
! [X94] :
( c_Int_OBit1(X94) = c_Int_OMin
<=> X94 = c_Int_OMin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).
fof(fact_rel__simps_I46_J,axiom,
! [X96] : c_Int_OBit1(X96) != c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
fof(fact_rel__simps_I39_J,axiom,
! [X115] : c_Int_OPls != c_Int_OBit1(X115),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
fof(fact_of__nat__number__of__lemma,axiom,
! [X139,X87] :
( class_Int_Onumber__ring(X87)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),X139) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = c_Groups_Ozero__class_Ozero(X87) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__number__of__lemma) ).
fof(fact_card__insert__disjoint,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X7),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
<=> X6 = X127 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_infinite__UNIV__listI,axiom,
! [X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X7)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X7),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__listI) ).
fof(fact_evalc_OWhileFalse,axiom,
! [X23,X45,X24] :
( ~ hBOOL(hAPP(X24,X45))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X45),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileFalse) ).
fof(fact_order__less__asym_H,axiom,
! [X84,X71,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X71)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_order__less__asym,axiom,
! [X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_linorder__not__le,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X127),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_leD,axiom,
! [X86,X98,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__less,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X127),X6))
| X6 = X127 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_xt1_I9_J,axiom,
! [X71,X84,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X71))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_mult__nat__number__of,axiom,
! [X165,X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X139),X165)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).
fof(fact_hd__upt,axiom,
! [X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X114,X113)) = X114 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__upt) ).
fof(fact_empty__iff,axiom,
! [X23,X7] : ~ hBOOL(hAPP(hAPP(c_member(X7),X23),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
fof(fact_emptyE,axiom,
! [X25,X7] : ~ hBOOL(hAPP(hAPP(c_member(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
fof(fact_le__SucE,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,X33)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> X90 = hAPP(c_Nat_OSuc,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_atLeastAtMost__upt,axiom,
! [X95,X44] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X44,X95) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X44,hAPP(c_Nat_OSuc,X95))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__upt) ).
fof(fact_atLeastLessThanSuc,axiom,
! [X44,X95] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X44)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X44),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X44)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X44)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc) ).
fof(fact_filter_Osimps_I2_J,axiom,
! [X292,X7,X6,X38] :
( ( hBOOL(hAPP(X38,X6))
=> hAPP(c_List_Ofilter(X7,X38),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)) = hAPP(hAPP(c_List_Olist_OCons(X7),X6),hAPP(c_List_Ofilter(X7,X38),X292)) )
& ( ~ hBOOL(hAPP(X38,X6))
=> hAPP(c_List_Ofilter(X7,X38),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)) = hAPP(c_List_Ofilter(X7,X38),X292) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter_Osimps_I2_J) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X95,X44] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X95)))
<=> X44 = X95 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [X90,X33] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_OSuc,X90)))
=> X90 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucE,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,X33)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> X90 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_divmod__nat__rel__divmod__nat,axiom,
! [X33,X90] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X90,X33),c_Divides_Odivmod__nat(X90,X33))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).
fof(fact_code__numeral_Osize_I4_J,axiom,
! [X174] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X174)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X174)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osize_I4_J) ).
fof(fact_atMost__upto,axiom,
! [X44] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X44) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__upto) ).
fof(fact_number__of__pred,axiom,
! [X128,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_Opred(X128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Oone__class_Oone(X87))),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__pred) ).
fof(fact_evaln_OWhileFalse,axiom,
! [X44,X23,X45,X24] :
( ~ hBOOL(hAPP(X24,X45))
=> c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X45,X44,X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileFalse) ).
fof(fact_greaterThanAtMost__empty__iff2,axiom,
! [X157,X94,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X94,X157)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X94),X157)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).
fof(fact_atLeastatMost__empty__iff2,axiom,
! [X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff2) ).
fof(fact_greaterThanAtMost__empty__iff,axiom,
! [X157,X94,X7] :
( class_Orderings_Oorder(X7)
=> ( c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X94,X157) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X94),X157)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).
fof(fact_atLeastatMost__empty__iff,axiom,
! [X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff) ).
fof(fact_dvd_Ole__less,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
<=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X127),X6)) )
| X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
fof(fact_dvd_Oless__le,axiom,
! [X127,X6] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X127),X6)) )
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
& X6 != X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
fof(fact_dvd_Oneq__le__trans,axiom,
! [X84,X71] :
( X71 != X84
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X71),X84))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X71)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
fof(fact_dvd_Ole__imp__less__or__eq,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X86)) )
| X86 = X98 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
fof(fact_dvd_Ole__neq__trans,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X71),X84))
=> ( X71 != X84
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X71),X84))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X71)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
fof(fact_divmod__nat__base,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> c_Divides_Odivmod__nat(X90,X33) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__base) ).
fof(fact_equalityE,axiom,
! [X7,X155,X149] :
( X149 = X155
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_z3div__def,axiom,
! [X96,X115] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115))
=> c_SMT_Oz3div(X96,X115) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),X115) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115))
=> c_SMT_Oz3div(X96,X115) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X115))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z3div__def) ).
fof(fact_mod__if,axiom,
! [X33,X90] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33) = X90 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33),X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__if) ).
fof(fact_mod__geq,axiom,
! [X33,X90] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__geq) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
<=> X6 = X127 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_atLeastLessThan__empty__iff,axiom,
! [X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X25),X24) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
fof(fact_atLeastLessThan__empty__iff2,axiom,
! [X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X25),X24)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
fof(conj_0,conjecture,
! [X231,X232] :
( v_P(X231,X232)
=> ! [X233] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),X232,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X233)
=> v_Q(X231,X233) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_code__numeral_Oinject,axiom,
! [X175,X176] :
( c_Code__Numeral_OSuc__code__numeral(X176) = c_Code__Numeral_OSuc__code__numeral(X175)
<=> X176 = X175 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Oinject) ).
fof(fact_code__numeral_Osize_I2_J,axiom,
! [X174] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X174)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X174)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osize_I2_J) ).
fof(fact_minus__Bit0,axiom,
! [X96] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X96)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Bit0) ).
fof(fact_all__not__in__conv,axiom,
! [X149,X7] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
<=> X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_remove1__idem,axiom,
! [X292,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> c_List_Oremove1(X7,X6,X292) = X292 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__idem) ).
fof(fact_length__upt,axiom,
! [X113,X114] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X114,X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X113),X114),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__upt) ).
fof(fact_sgn__if,axiom,
! [X86,X87] :
( class_Groups_Osgn__if(X87)
=> ( ( X86 = c_Groups_Ozero__class_Ozero(X87)
=> c_Groups_Osgn__class_Osgn(X87,X86) = c_Groups_Ozero__class_Ozero(X87) )
& ( X86 != c_Groups_Ozero__class_Ozero(X87)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> c_Groups_Osgn__class_Osgn(X87,X86) = c_Groups_Oone__class_Oone(X87) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> c_Groups_Osgn__class_Osgn(X87,X86) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Oone__class_Oone(X87)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__if) ).
fof(fact_upt__eq__Nil__conv,axiom,
! [X158,X107] :
( c_List_Oupt(X107,X158) = c_List_Olist_ONil(tc_Nat_Onat)
<=> ( X158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X158),X107)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__eq__Nil__conv) ).
fof(fact_upt__conv__Nil,axiom,
! [X114,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X113),X114))
=> c_List_Oupt(X114,X113) = c_List_Olist_ONil(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__conv__Nil) ).
fof(fact_z3mod__def,axiom,
! [X96,X115] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115))
=> c_SMT_Oz3mod(X96,X115) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X115) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115))
=> c_SMT_Oz3mod(X96,X115) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X115)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z3mod__def) ).
fof(fact_abs__if,axiom,
! [X71,X87] :
( class_Groups_Oabs__if(X87)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),X71) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),X71) = X71 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__if) ).
fof(fact_not__one__le__zero,axiom,
! [X87] :
( class_Rings_Olinordered__semidom(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Oone__class_Oone(X87)),c_Groups_Ozero__class_Ozero(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_not__one__less__zero,axiom,
! [X87] :
( class_Rings_Olinordered__semidom(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),c_Groups_Ozero__class_Ozero(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_add__diff__inverse,axiom,
! [X33,X90] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)) = X90 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_atLeast__upt,axiom,
! [X44] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X44) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__upt) ).
fof(fact_linorder__neqE,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( X86 != X98
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X6,X127,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X127),X6))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
<=> X6 = X127 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__cases,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> ( X86 != X98
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X98,X86,X87] :
( class_Rings_Olinordered__idom(X87)
=> ( X86 != X98
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__le__cases,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_leI,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_not__leE,axiom,
! [X86,X98,X87] :
( class_Orderings_Olinorder(X87)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_set__upt,axiom,
! [X158,X107] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X107,X158)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X107),X158),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__upt) ).
fof(fact_atLeastLessThan__upt,axiom,
! [X158,X107] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X107),X158) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X107,X158)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__upt) ).
fof(fact_succ__pred,axiom,
! [X86] : c_Int_Osucc(c_Int_Opred(X86)) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__pred) ).
fof(fact_number__of__succ,axiom,
! [X96,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_Osucc(X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Oone__class_Oone(X87)),hAPP(c_Int_Onumber__class_Onumber__of(X87),X96)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__succ) ).
fof(fact_equals0D,axiom,
! [X25,X7,X149] :
( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
fof(fact_not__neg__eq__ge__0,axiom,
! [X6] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X6))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__eq__ge__0) ).
fof(fact_nat__eq__iff,axiom,
! [X95,X125] :
( hAPP(c_Int_Onat,X125) = X95
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X125))
=> X125 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X125))
=> X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff) ).
fof(fact_nat__eq__iff2,axiom,
! [X125,X95] :
( X95 = hAPP(c_Int_Onat,X125)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X125))
=> X125 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X125))
=> X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).
fof(fact_int__nat__eq,axiom,
! [X97] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X97)) = X97 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X97)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__nat__eq) ).
fof(fact_tsub__def,axiom,
! [X86,X98] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X86))
=> c_Nat__Transfer_Otsub(X86,X98) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X86),X98) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X86))
=> c_Nat__Transfer_Otsub(X86,X98) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__def) ).
fof(fact_of__nat__number__of__eq,axiom,
! [X139,X87] :
( class_Int_Onumber__ring(X87)
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = c_Groups_Ozero__class_Ozero(X87) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),X139) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__number__of__eq) ).
fof(fact_mod__nat__def,axiom,
! [X33,X90] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X90,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__nat__def) ).
fof(fact_remove1__filter__not,axiom,
! [X292,X7,X6,X38] :
( ~ hBOOL(hAPP(X38,X6))
=> c_List_Oremove1(X7,X6,hAPP(c_List_Ofilter(X7,X38),X292)) = hAPP(c_List_Ofilter(X7,X38),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__filter__not) ).
fof(fact_div__nat__def,axiom,
! [X33,X90] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X90,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nat__def) ).
fof(fact_int__nat__number__of,axiom,
! [X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__nat__number__of) ).
fof(fact_zabs__def,axiom,
! [X114] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X114),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X114) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X114) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X114),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X114) = X114 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__def) ).
fof(fact_linorder__neqE__nat,axiom,
! [X98,X86] :
( X86 != X98
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_divmod__nat__eq,axiom,
! [X180,X33,X90] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X90,X33),X180))
=> c_Divides_Odivmod__nat(X90,X33) = X180 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).
fof(fact_zsgn__def,axiom,
! [X114] :
( ( X114 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X114 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X114))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X114))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zsgn__def) ).
fof(fact_sorted__upt,axiom,
! [X113,X114] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X114,X113)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__upt) ).
fof(fact_wf__measure,axiom,
! [X2,X7] : c_Wellfounded_Owf(X7,hAPP(c_Wellfounded_Omeasure(X7),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measure) ).
fof(fact_order__less__irrefl,axiom,
! [X86,X87] :
( class_Orderings_Opreorder(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_beyond__def,axiom,
! [X115,X96] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X115))
=> c_Quickcheck_Obeyond(X96,X115) = X115 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X115))
=> c_Quickcheck_Obeyond(X96,X115) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_beyond__def) ).
fof(fact_rotate0,axiom,
! [X7] : c_List_Orotate(X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate0) ).
fof(fact_less__nat__zero__code,axiom,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_not__less0,axiom,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__zeroE,axiom,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_WTs__elim__cases_I4_J,axiom,
! [X48,X49] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X49,X48)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X49))
=> ~ hBOOL(hAPP(c_Com_OWT,X48)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I4_J) ).
fof(fact_divmod__nat__zero,axiom,
! [X90] : c_Divides_Odivmod__nat(X90,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__zero) ).
fof(fact_less__irrefl__nat,axiom,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_rel__simps_I48_J,axiom,
! [X157,X94] :
( c_Int_OBit0(X94) = c_Int_OBit0(X157)
<=> X94 = X157 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).
fof(fact_setprod__infinite,axiom,
! [X2,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149) = c_Groups_Oone__class_Oone(X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__infinite) ).
fof(fact_setprod_Oinfinite,axiom,
! [X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149) = c_Groups_Oone__class_Oone(X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinfinite) ).
fof(fact_setsum__infinite,axiom,
! [X2,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149) = c_Groups_Ozero__class_Ozero(X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__infinite) ).
fof(fact_setsum_Oinfinite,axiom,
! [X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149) = c_Groups_Ozero__class_Ozero(X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinfinite) ).
fof(fact_not__neg__int,axiom,
! [X33] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__int) ).
fof(fact_code__numeral_Osimps_I3_J,axiom,
! [X178] : c_Code__Numeral_OSuc__code__numeral(X178) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I3_J) ).
fof(fact_code__numeral_Osimps_I2_J,axiom,
! [X177] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).
fof(help_c__fimplies__3,axiom,
! [X194,X38] :
( ~ hBOOL(hAPP(hAPP(c_fimplies,X38),X194))
| ~ hBOOL(X38)
| hBOOL(X194) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__3) ).
fof(fact_card__eq__0__iff,axiom,
! [X149,X7] :
( hAPP(c_Finite__Set_Ocard(X7),X149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).
fof(help_c__fdisj__3,axiom,
! [X194,X38] :
( ~ hBOOL(hAPP(hAPP(c_fdisj,X38),X194))
| hBOOL(X38)
| hBOOL(X194) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__3) ).
fof(help_c__fconj__2,axiom,
! [X194,X38] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X38),X194))
| hBOOL(X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [X194,X38] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X38),X194))
| hBOOL(X194) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__3) ).
fof(fact_empty__Collect__eq,axiom,
! [X38,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7),X38)
<=> ! [X3] : ~ hBOOL(hAPP(X38,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).
fof(fact_Collect__empty__eq,axiom,
! [X38,X7] :
( hAPP(c_Set_OCollect(X7),X38) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X38,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(help_c__fequal__1,axiom,
! [X127,X6] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X6),X127))
| X6 = X127 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_nat__of__code,axiom,
! [X114] : hAPP(c_Code__Numeral_Onat__of,X114) = c_Code__Numeral_Onat__of__aux(X114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__code) ).
fof(fact_succ__def,axiom,
! [X96] : c_Int_Osucc(X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__def) ).
fof(fact_pred__def,axiom,
! [X96] : c_Int_Opred(X96) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__def) ).
fof(fact_upt__0,axiom,
! [X114] : c_List_Oupt(X114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__0) ).
fof(help_c__fconj__1,axiom,
! [X194,X38] :
( ~ hBOOL(X38)
| ~ hBOOL(X194)
| hBOOL(hAPP(hAPP(c_fconj,X38),X194)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__1) ).
fof(fact_add__Min,axiom,
! [X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X96) = c_Int_Opred(X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min) ).
fof(fact_nonzero__number__of__Min,axiom,
! [X87] :
( class_Int_Onumber__ring(X87)
=> ~ c_Int_Oiszero(X87,hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__number__of__Min) ).
fof(help_c__fdisj__1,axiom,
! [X194,X38] :
( ~ hBOOL(X38)
| hBOOL(hAPP(hAPP(c_fdisj,X38),X194)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__1) ).
fof(help_c__fdisj__2,axiom,
! [X38,X194] :
( ~ hBOOL(X194)
| hBOOL(hAPP(hAPP(c_fdisj,X38),X194)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__2) ).
fof(help_c__fimplies__2,axiom,
! [X38,X194] :
( ~ hBOOL(X194)
| hBOOL(hAPP(hAPP(c_fimplies,X38),X194)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__2) ).
fof(fact_is__none__code_I2_J,axiom,
! [X86,X7] : ~ c_Option_Ois__none(X7,hAPP(c_Option_Ooption_OSome(X7),X86)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__none__code_I2_J) ).
fof(fact_rel__simps_I38_J,axiom,
! [X157] :
( c_Int_OPls = c_Int_OBit0(X157)
<=> c_Int_OPls = X157 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).
fof(fact_rel__simps_I44_J,axiom,
! [X94] :
( c_Int_OBit0(X94) = c_Int_OPls
<=> X94 = c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
fof(fact_rel__simps_I45_J,axiom,
! [X96] : c_Int_OBit0(X96) != c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).
fof(fact_rel__simps_I42_J,axiom,
! [X115] : c_Int_OMin != c_Int_OBit0(X115),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).
fof(fact_not__neg__nat,axiom,
! [X97] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X97))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X97)) = X97 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__nat) ).
fof(fact_card__infinite,axiom,
! [X149,X7] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ocard(X7),X149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
fof(help_c__fNot__1,axiom,
! [X38] :
( ~ hBOOL(hAPP(c_fNot,X38))
| ~ hBOOL(X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_not__iszero__1,axiom,
! [X87] :
( class_Rings_Osemiring__1(X87)
=> ~ c_Int_Oiszero(X87,c_Groups_Oone__class_Oone(X87)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__iszero__1) ).
fof(help_c__fNot__2,axiom,
! [X38] :
( ~ ~ hBOOL(X38)
| hBOOL(hAPP(c_fNot,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(fact_UN__equiv__class__type2,axiom,
! [X155,X257,X258,X2,X119,X248,X249,X105,X250,X251,X7] :
( c_Equiv__Relations_Oequiv(X7,X251,X250)
=> ( c_Equiv__Relations_Oequiv(X105,X249,X248)
=> ( c_Equiv__Relations_Ocongruent2(X7,X105,tc_fun(X119,tc_HOL_Obool),X250,X248,X2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X258),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X251),X250)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X105,tc_HOL_Obool)),X257),hAPP(hAPP(c_Equiv__Relations_Oquotient(X105),X249),X248)))
=> ( ! [X142] :
( hBOOL(hAPP(hAPP(c_member(X7),X142),X251))
=> ! [X259] :
( hBOOL(hAPP(hAPP(c_member(X105),X259),X249))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X119,tc_HOL_Obool)),hAPP(hAPP(X2,X142),X259)),X155)) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X119,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X119,tc_HOL_Obool)),X258),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(X119,tc_HOL_Obool)),tc_fun(X119,tc_HOL_Obool),X7),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X119,tc_HOL_Obool)),X257)),X2))),X155)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__type2) ).
fof(fact_com_Orecs_I5_J,axiom,
! [X54,X55,X13,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OCond(X13,X55,X54)) = hAPP(hAPP(hAPP(hAPP(hAPP(X18,X13),X55),X54),c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,X55)),c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,X54)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I5_J) ).
fof(fact_com_Orecs_I4_J,axiom,
! [X54,X55,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OSemi(X55,X54)) = hAPP(hAPP(hAPP(hAPP(X19,X55),X54),c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,X55)),c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,X54)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I4_J) ).
fof(fact_setsum__mult__setsum__if__inj,axiom,
! [X155,X149,X1,X2,X105,X7,X119] :
( class_Rings_Osemiring__0(X119)
=> ( c_Fun_Oinj__on(tc_prod(X7,X105),X119,hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,X119),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,X119),tc_fun(X105,X119)),hAPP(hAPP(c_COMBB(tc_fun(X119,X119),tc_fun(tc_fun(X105,X119),tc_fun(X105,X119)),X7),c_COMBB(X119,X119,X105)),hAPP(hAPP(c_COMBB(X119,tc_fun(X119,X119),X7),c_Groups_Otimes__class_Otimes(X119)),X2))),X1)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X155)))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X119),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X119),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X119),X1),X155)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X119,X119),c_Fun_Oid(X119)),hAPP(c_Set_OCollect(X119),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X119),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X105,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X119),hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X105))),hAPP(hAPP(c_COMBC(X119,tc_fun(X7,tc_fun(X105,tc_HOL_Obool)),tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool))),tc_fun(tc_fun(X7,tc_fun(X105,tc_HOL_Obool)),tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X119),c_COMBS(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X105,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X7,tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool))),X119),hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBS(X105,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X105,tc_HOL_Obool)),tc_fun(X7,tc_fun(X105,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X119),hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X105),c_fconj))),hAPP(hAPP(c_COMBC(X119,tc_fun(X7,tc_fun(X105,X119)),tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X105,X119),tc_fun(X105,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_fun(X105,X119)),tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X119),c_COMBB(tc_fun(X105,X119),tc_fun(X105,tc_HOL_Obool),X7)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_HOL_Obool),tc_fun(tc_fun(X105,X119),tc_fun(X105,tc_HOL_Obool)),X119),c_COMBB(X119,tc_HOL_Obool,X105)),c_fequal))),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,X119),tc_fun(X105,X119)),hAPP(hAPP(c_COMBB(tc_fun(X119,X119),tc_fun(tc_fun(X105,X119),tc_fun(X105,X119)),X7),c_COMBB(X119,X119,X105)),hAPP(hAPP(c_COMBB(X119,tc_fun(X119,X119),X7),c_Groups_Otimes__class_Otimes(X119)),X2))),X1)))))),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)))),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X155))))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).
fof(fact_rel__comp__def,axiom,
! [X45,X172,X105,X119,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),X172),X45) = hAPP(c_Set_OCollect(tc_prod(X7,X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(X119,tc_HOL_Obool)),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBB(tc_fun(X119,tc_HOL_Obool),tc_HOL_Obool,X105),c_HOL_OEx(X119))),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_fun(X119,tc_HOL_Obool)),tc_fun(X105,tc_fun(X119,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X119,tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),tc_fun(tc_fun(X105,tc_fun(X119,tc_HOL_Obool)),tc_fun(X105,tc_fun(X119,tc_HOL_Obool))),X7),c_COMBB(tc_fun(X119,tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool),X105)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X119,tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),X7),c_COMBS(X119,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_HOL_Obool),tc_fun(X119,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X119),c_fconj)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X119),tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_fun(tc_fun(tc_prod(X7,X119),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X119),tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),X7),c_COMBC(X119,tc_fun(tc_prod(X7,X119),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_prod(X7,X119)),tc_fun(X119,tc_fun(tc_fun(tc_prod(X7,X119),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X119),tc_fun(tc_fun(tc_prod(X7,X119),tc_HOL_Obool),tc_HOL_Obool),X119),c_member(tc_prod(X7,X119)))),c_Product__Type_OPair(X7,X119)))),X172))))),hAPP(hAPP(c_COMBC(X105,tc_fun(tc_prod(X119,X105),tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_fun(tc_fun(tc_prod(X119,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X119,X105),tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),X105),c_COMBC(X119,tc_fun(tc_prod(X119,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_prod(X119,X105)),tc_fun(X119,tc_fun(tc_fun(tc_prod(X119,X105),tc_HOL_Obool),tc_HOL_Obool)),X105),hAPP(c_COMBB(tc_prod(X119,X105),tc_fun(tc_fun(tc_prod(X119,X105),tc_HOL_Obool),tc_HOL_Obool),X119),c_member(tc_prod(X119,X105)))),hAPP(c_COMBC(X119,X105,tc_prod(X119,X105)),c_Product__Type_OPair(X119,X105))))),X45))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__def) ).
fof(fact_min__max_Osup__Inf2__distrib,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X155)) = c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X7),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),tc_fun(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),X7),c_COMBS(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),X7),hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X7),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_fun(X7,X7)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_fun(X7,X7)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),X7),c_COMBB(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool),X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X7)),c_fequal))),c_Orderings_Oord__class_Omax(X7)))))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155))))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).
fof(fact_min__max_Oinf__Sup2__distrib,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X155)) = c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X7),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),tc_fun(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),X7),c_COMBS(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),X7),hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X7),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_fun(X7,X7)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_fun(X7,X7)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),X7),c_COMBB(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool),X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X7)),c_fequal))),c_Orderings_Oord__class_Omin(X7)))))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155))))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).
fof(fact_inf__Sup2__distrib,axiom,
! [X155,X149,X7] :
( class_Lattices_Odistrib__lattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)),c_Big__Operators_Olattice__class_OSup__fin(X7,X155)) = c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X7),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),tc_fun(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),X7),c_COMBS(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),X7),hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X7),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_fun(X7,X7)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_fun(X7,X7)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),X7),c_COMBB(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool),X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X7)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X7)))))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155))))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup2__distrib) ).
fof(fact_sup__Inf2__distrib,axiom,
! [X155,X149,X7] :
( class_Lattices_Odistrib__lattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)),c_Big__Operators_Olattice__class_OInf__fin(X7,X155)) = c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X7),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),tc_fun(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),X7),c_COMBS(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),X7),hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X7),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_fun(X7,X7)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_fun(X7,X7)),tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),X7),c_COMBB(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool),X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X7)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X7)))))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155))))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf2__distrib) ).
fof(fact_com_Orecs_I3_J,axiom,
! [X66,X13,X67,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OLocal(X67,X13,X66)) = hAPP(hAPP(hAPP(hAPP(X20,X67),X13),X66),c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,X66)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I3_J) ).
fof(fact_com_Orecs_I6_J,axiom,
! [X66,X13,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OWhile(X13,X66)) = hAPP(hAPP(hAPP(X17,X13),X66),c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,X66)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I6_J) ).
fof(fact_set__Cons__def,axiom,
! [X237,X149,X7] : c_List_Oset__Cons(X7,X149,X237) = hAPP(c_Set_OCollect(tc_List_Olist(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X7)),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),tc_List_Olist(X7)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(tc_List_Olist(X7)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool))),tc_fun(tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_HOL_Obool))),tc_List_Olist(X7)),c_COMBS(X7,tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X7,tc_fun(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool))),tc_List_Olist(X7)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),X7),c_COMBS(tc_List_Olist(X7),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X7)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X7)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_List_Olist(X7))),tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_List_Olist(X7))),tc_fun(X7,tc_fun(tc_List_Olist(X7),tc_HOL_Obool))),tc_List_Olist(X7)),c_COMBB(tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),tc_fun(tc_List_Olist(X7),tc_HOL_Obool),X7)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_List_Olist(X7)),c_COMBB(tc_List_Olist(X7),tc_HOL_Obool,tc_List_Olist(X7))),c_fequal))),c_List_Olist_OCons(X7)))))),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X7))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X7))),X237)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__Cons__def) ).
fof(fact_hoare__derivs_OCall,axiom,
! [X25,X39,X222,X194,X40,X38,X216,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X38),hAPP(c_Com_Ocom_OBODY,X40)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X7),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X194)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,X222)))),X39)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),X7),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,X222)))),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X7),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X38)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),X25)))),c_Com_Ocom_OCall(X39,X40,X25)),X194)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OCall) ).
fof(fact_image__INT,axiom,
! [X158,X155,X149,X119,X193,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X193)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X119),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(X155,X3)),X193)) )
=> ( hBOOL(hAPP(hAPP(c_member(X119),X158),X149))
=> hAPP(c_Set_Oimage(X7,X105,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X119),c_Set_Oimage(X7,X105,X2)),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__INT) ).
fof(fact_com_Orecs_I8_J,axiom,
! [X13,X5,X14,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OCall(X14,X5,X13)) = hAPP(hAPP(hAPP(X15,X14),X5),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I8_J) ).
fof(fact_com_Osimps_I66_J,axiom,
! [X66,X13,X67,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__case(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OLocal(X67,X13,X66)) = hAPP(hAPP(hAPP(X20,X67),X13),X66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I66_J) ).
fof(fact_com_Osimps_I68_J,axiom,
! [X54,X55,X13,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__case(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OCond(X13,X55,X54)) = hAPP(hAPP(hAPP(X18,X13),X55),X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I68_J) ).
fof(fact_com_Osimps_I71_J,axiom,
! [X13,X5,X14,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__case(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OCall(X14,X5,X13)) = hAPP(hAPP(hAPP(X15,X14),X5),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I71_J) ).
fof(fact_com_Orecs_I2_J,axiom,
! [X13,X14,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OAss(X14,X13)) = hAPP(hAPP(X21,X14),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I2_J) ).
fof(fact_com_Osimps_I69_J,axiom,
! [X66,X13,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__case(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OWhile(X13,X66)) = hAPP(hAPP(X17,X13),X66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I69_J) ).
fof(fact_com_Osimps_I67_J,axiom,
! [X54,X55,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__case(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OSemi(X55,X54)) = hAPP(hAPP(X19,X55),X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I67_J) ).
fof(fact_com_Osimps_I65_J,axiom,
! [X13,X14,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__case(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OAss(X14,X13)) = hAPP(hAPP(X21,X14),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I65_J) ).
fof(fact_com_Orecs_I7_J,axiom,
! [X5,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,hAPP(c_Com_Ocom_OBODY,X5)) = hAPP(X16,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I7_J) ).
fof(fact_com_Osimps_I70_J,axiom,
! [X5,X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__case(X7,X22,X21,X20,X19,X18,X17,X16,X15,hAPP(c_Com_Ocom_OBODY,X5)) = hAPP(X16,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I70_J) ).
fof(fact_com_Orecs_I1_J,axiom,
! [X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__rec(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OSKIP) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I1_J) ).
fof(fact_com_Osimps_I64_J,axiom,
! [X15,X16,X17,X18,X19,X20,X21,X22,X7] : c_Com_Ocom_Ocom__case(X7,X22,X21,X20,X19,X18,X17,X16,X15,c_Com_Ocom_OSKIP) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I64_J) ).
fof(fact_inf__Int__eq2,axiom,
! [X127,X6,X209,X191,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),X191)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),X209)),X6),X127))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X191),X209))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
fof(fact_sup__Un__eq2,axiom,
! [X127,X6,X209,X191,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),X191)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),X209)),X6),X127))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X191),X209))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq2) ).
fof(fact_lenlex__conv,axiom,
! [X172,X7] : c_List_Olenlex(X7,X172) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X7),tc_List_Olist(X7),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_List_Olist(X7)),c_COMBS(tc_List_Olist(X7),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X7)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X7)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_Nat_Onat),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X7),tc_Nat_Onat),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_List_Olist(X7)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X7))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X7)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X7))))),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_List_Olist(X7)),c_COMBS(tc_List_Olist(X7),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X7)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X7)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_Nat_Onat),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X7),tc_Nat_Onat),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_List_Olist(X7)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X7))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X7)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X7))))),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_fun(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_List_Olist(X7)),c_COMBC(tc_List_Olist(X7),tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),tc_fun(tc_List_Olist(X7),tc_fun(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X7)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X7)),c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))))),c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7))))),c_List_Olex(X7,X172)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lenlex__conv) ).
fof(fact_INF__INT__eq2,axiom,
! [X127,X6,X172,X119,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_fun(X119,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_fun(X105,tc_fun(X119,tc_HOL_Obool)),X7),hAPP(c_COMBC(X105,tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),X105),c_COMBC(X119,tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_prod(X105,X119)),tc_fun(X119,tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool)),X105),hAPP(c_COMBB(tc_prod(X105,X119),tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool),X119),c_member(tc_prod(X105,X119)))),c_Product__Type_OPair(X105,X119))))),X172)),X6),X127))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X119)),hAPP(hAPP(c_Product__Type_OPair(X105,X119),X6),X127)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(tc_prod(X105,X119),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq2) ).
fof(fact_SUP__UN__eq2,axiom,
! [X127,X6,X172,X119,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_fun(X119,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_fun(X105,tc_fun(X119,tc_HOL_Obool)),X7),hAPP(c_COMBC(X105,tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),X105),c_COMBC(X119,tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_prod(X105,X119)),tc_fun(X119,tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool)),X105),hAPP(c_COMBB(tc_prod(X105,X119),tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool),X119),c_member(tc_prod(X105,X119)))),c_Product__Type_OPair(X105,X119))))),X172)),X6),X127))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X119)),hAPP(hAPP(c_Product__Type_OPair(X105,X119),X6),X127)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(tc_prod(X105,X119),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq2) ).
fof(fact_UN__equiv__class__inject,axiom,
! [X60,X39,X2,X105,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( c_Equiv__Relations_Ocongruent(X7,tc_fun(X105,tc_HOL_Obool),X172,X2)
=> ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X39),X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X60),X2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X39),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X60),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> ! [X82] :
( hBOOL(hAPP(hAPP(c_member(X7),X82),X149))
=> ( hAPP(X2,X3) = hAPP(X2,X82)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X82)),X172)) ) ) )
=> X39 = X60 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__inject) ).
fof(fact_hoare__derivs_OBody,axiom,
! [X230,X194,X38,X216,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)),X216),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X7),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X7))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X7))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X7)),X38)),c_Com_Ocom_OBODY)),X194)),X230)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X7),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X7))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X7))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X7)),X38)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X194)),X230))
=> c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X7),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X7))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X7,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X7))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X7)),X38)),c_Com_Ocom_OBODY)),X194)),X230)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OBody) ).
fof(fact_finite__image__set,axiom,
! [X2,X105,X38,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),X38)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(c_Set_OCollect(X105),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X105),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBC(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X105),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj)),hAPP(hAPP(c_COMBC(X105,tc_fun(X7,X105),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X7,X105),tc_fun(X7,tc_HOL_Obool)),X105),c_COMBB(X105,tc_HOL_Obool,X7)),c_fequal)),X2)))),X38))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__image__set) ).
fof(fact_setsum__reindex__cong,axiom,
! [X200,X1,X155,X149,X2,X105,X7,X119] :
( class_Groups_Ocomm__monoid__add(X119)
=> ( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( X155 = hAPP(c_Set_Oimage(X7,X105,X2),X149)
=> ( ! [X110] :
( hBOOL(hAPP(hAPP(c_member(X7),X110),X149))
=> hAPP(X1,X110) = hAPP(X200,hAPP(X2,X110)) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X119),X200),X155) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X119),X1),X149) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__cong) ).
fof(fact_hoare__derivs_OLocal,axiom,
! [X25,X222,X39,X194,X23,X38,X216,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X38),X23),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X7),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X194)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(X39))),hAPP(hAPP(c_Natural_Ogetlocs,X222),X39))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),X7),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,X222)))),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X7),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X38)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(X39))),X25)))),c_Com_Ocom_OLocal(X39,X25,X23)),X194)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OLocal) ).
fof(fact_strong__setprod__reindex__cong,axiom,
! [X200,X1,X155,X149,X2,X105,X7,X119] :
( class_Groups_Ocomm__monoid__mult(X119)
=> ( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( X155 = hAPP(c_Set_Oimage(X7,X105,X2),X149)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hAPP(X1,X3) = hAPP(hAPP(c_Fun_Ocomp(X105,X119,X7,X200),X2),X3) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X119),X200),X155) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X119),X1),X149) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strong__setprod__reindex__cong) ).
fof(fact_setsum__ivl__cong,axiom,
! [X1,X2,X136,X24,X23,X25,X7,X105] :
( ( class_Groups_Ocomm__monoid__add(X105)
& class_Orderings_Oord(X7) )
=> ( X25 = X23
=> ( X24 = X136
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X23),X3))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X3),X136))
=> hAPP(X2,X3) = hAPP(X1,X3) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X25),X24)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X23),X136)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__ivl__cong) ).
fof(fact_minus__int__def,axiom,
! [X26] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X26)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__int__def) ).
fof(fact_exE__realizer,axiom,
! [X119,X2,X194,X161,X7,X105,X38] :
( hBOOL(hAPP(hAPP(X38,hAPP(c_Product__Type_Osnd(X105,X7),X161)),hAPP(c_Product__Type_Ofst(X105,X7),X161)))
=> ( ! [X3,X82] :
( hBOOL(hAPP(hAPP(X38,X82),X3))
=> hBOOL(hAPP(X194,hAPP(hAPP(X2,X3),X82))) )
=> hBOOL(hAPP(X194,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X7,X119),X2),X161))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exE__realizer) ).
fof(fact_rp__inv__image__def,axiom,
! [X105,X7] : c_FunDef_Orp__inv__image(X7,X105) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X105,X7),tc_prod(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_prod(X105,X105),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X105,X7),tc_fun(tc_prod(X105,X105),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X105,X7),tc_prod(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_prod(X105,X105),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X105,X7),tc_fun(tc_prod(X105,X105),tc_HOL_Obool)),tc_fun(tc_fun(X105,X7),tc_prod(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_prod(X105,X105),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X105,X7),tc_fun(tc_prod(X105,X105),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X105,X7),tc_prod(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_prod(X105,X105),tc_HOL_Obool))))),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X105,X7),tc_fun(tc_prod(X105,X105),tc_HOL_Obool)),tc_fun(tc_fun(X105,X7),tc_prod(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_prod(X105,X105),tc_HOL_Obool))),tc_fun(tc_prod(X7,X7),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X105,X7),tc_fun(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_prod(X105,X105),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X105,X7),tc_fun(tc_prod(X105,X105),tc_HOL_Obool)),tc_fun(tc_fun(X105,X7),tc_prod(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_prod(X105,X105),tc_HOL_Obool)))),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_COMBS(tc_fun(X105,X7),tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_prod(X105,X105),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X105,X7),tc_fun(tc_prod(X105,X105),tc_HOL_Obool)),tc_fun(tc_fun(X105,X7),tc_fun(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_prod(X105,X105),tc_HOL_Obool)))),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_prod(X105,X105),tc_HOL_Obool))),tc_fun(X105,X7)),c_Product__Type_OPair(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(tc_prod(X105,X105),tc_HOL_Obool)))),c_Relation_Oinv__image(X7,X105))))),c_Relation_Oinv__image(X7,X105))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__def) ).
fof(fact_inv__image__def,axiom,
! [X2,X172,X7,X105] : hAPP(hAPP(c_Relation_Oinv__image(X105,X7),X172),X2) = hAPP(c_Set_OCollect(tc_prod(X7,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBC(X7,tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X105,X105)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X105,X105),tc_fun(tc_fun(tc_prod(X105,X105),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X105,X105)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,X105),tc_fun(X7,tc_prod(X105,X105))),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X105,X105)),tc_fun(tc_fun(X7,X105),tc_fun(X7,tc_prod(X105,X105))),X7),c_COMBB(X105,tc_prod(X105,X105),X7)),hAPP(hAPP(c_COMBB(X105,tc_fun(X105,tc_prod(X105,X105)),X7),c_Product__Type_OPair(X105,X105)),X2))),X2)))),X172))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__def) ).
fof(fact_set__zip,axiom,
! [X293,X292,X105,X7] : hAPP(c_List_Oset(tc_prod(X7,X105)),hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293)) = hAPP(c_Set_OCollect(tc_prod(X7,X105)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X7,X105)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X7,X105),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X7,X105)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X7,X105)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X7,X105),tc_fun(tc_Nat_Onat,tc_prod(X7,X105)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X7,X105)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X7,X105)),c_COMBB(tc_prod(X7,X105),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X105,tc_prod(X7,X105)),hAPP(hAPP(c_COMBB(X7,tc_fun(X105,tc_prod(X7,X105)),tc_Nat_Onat),c_Product__Type_OPair(X7,X105)),hAPP(c_List_Onth(X7),X292))),hAPP(c_List_Onth(X105),X293)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip) ).
fof(fact_pred__subset__eq2,axiom,
! [X209,X191,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),X191)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),X209)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X191),X209)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact_Pow__Compl,axiom,
! [X149,X7] : hAPP(c_Set_OPow(X7),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)) = hAPP(c_Set_OCollect(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X7,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),c_COMBS(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X7,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X7,tc_HOL_Obool)),hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X149)),c_Set_OPow(X7))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__Compl) ).
fof(fact_map__upds__fold__map__upd,axiom,
! [X323,X297,X95,X105,X7] : c_Map_Omap__upds(X7,X105,X95,X297,X323) = hAPP(c_List_Ofoldl(tc_fun(X7,tc_Option_Ooption(X105)),tc_prod(X7,X105),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X105,tc_fun(X7,tc_Option_Ooption(X105)))),tc_fun(tc_prod(X7,X105),tc_fun(X7,tc_Option_Ooption(X105))),tc_fun(X7,tc_Option_Ooption(X105))),c_Product__Type_Oprod_Oprod__case(X7,X105,tc_fun(X7,tc_Option_Ooption(X105)))),hAPP(hAPP(c_COMBC(tc_fun(X7,tc_Option_Ooption(X105)),tc_fun(X105,tc_Option_Ooption(X105)),tc_fun(X7,tc_fun(X105,tc_fun(X7,tc_Option_Ooption(X105))))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(X105,tc_Option_Ooption(X105)),tc_fun(X105,tc_fun(X7,tc_Option_Ooption(X105))))),tc_fun(tc_fun(X105,tc_Option_Ooption(X105)),tc_fun(X7,tc_fun(X105,tc_fun(X7,tc_Option_Ooption(X105))))),tc_fun(X7,tc_Option_Ooption(X105))),c_COMBC(X7,tc_fun(X105,tc_Option_Ooption(X105)),tc_fun(X105,tc_fun(X7,tc_Option_Ooption(X105))))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_Option_Ooption(X105),tc_fun(X7,tc_Option_Ooption(X105)))),tc_fun(X7,tc_fun(tc_fun(X105,tc_Option_Ooption(X105)),tc_fun(X105,tc_fun(X7,tc_Option_Ooption(X105))))),tc_fun(X7,tc_Option_Ooption(X105))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X105),tc_fun(X7,tc_Option_Ooption(X105))),tc_fun(tc_fun(X105,tc_Option_Ooption(X105)),tc_fun(X105,tc_fun(X7,tc_Option_Ooption(X105)))),X7),c_COMBB(tc_Option_Ooption(X105),tc_fun(X7,tc_Option_Ooption(X105)),X105))),c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105))))),c_Option_Ooption_OSome(X105))),X95),hAPP(hAPP(c_List_Ozip(X7,X105),X297),X323)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__fold__map__upd) ).
fof(fact_UN__equiv__class__type,axiom,
! [X155,X39,X2,X105,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( c_Equiv__Relations_Ocongruent(X7,tc_fun(X105,tc_HOL_Obool),X172,X2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X39),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X105,tc_HOL_Obool)),hAPP(X2,X3)),X155)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X39),X2)),X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__type) ).
fof(fact_INF2__iff,axiom,
! [X23,X24,X155,X149,X119,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_fun(X119,tc_HOL_Obool))),X149),X155),X24),X23))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(hAPP(X155,X3),X24),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__iff) ).
fof(fact_min__max_Osup__Inf1__distrib,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)) = c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X7)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X7),X6))))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).
fof(fact_min__max_Oinf__Sup1__distrib,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)) = c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X7)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X7),X6))))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).
fof(fact_inf__Sup1__distrib,axiom,
! [X6,X149,X7] :
( class_Lattices_Odistrib__lattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X6),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)) = c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X7)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X6))))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup1__distrib) ).
fof(fact_sup__Inf1__distrib,axiom,
! [X6,X149,X7] :
( class_Lattices_Odistrib__lattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)) = c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X7)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6))))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf1__distrib) ).
fof(fact_add__Min__commute,axiom,
! [X94,X214,X7] :
( class_Groups_Olinordered__ab__semigroup__add(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> ( X214 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X94),c_Big__Operators_Olinorder__class_OMin(X7,X214)) = c_Big__Operators_Olinorder__class_OMin(X7,hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X7)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X7),X94))))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X214))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min__commute) ).
fof(fact_add__Max__commute,axiom,
! [X94,X214,X7] :
( class_Groups_Olinordered__ab__semigroup__add(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> ( X214 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X94),c_Big__Operators_Olinorder__class_OMax(X7,X214)) = c_Big__Operators_Olinorder__class_OMax(X7,hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X7)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X7),X94))))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X214))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Max__commute) ).
fof(fact_anamorph_Osimps,axiom,
! [X6,X2,X7,X105,X94] :
( ( X94 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Lazy__Sequence_Oanamorph(X105,X7,X2,X94),X6) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),X105),c_List_Olist_ONil(X7)),X6) )
& ( X94 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Lazy__Sequence_Oanamorph(X105,X7,X2,X94),X6) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X7),X105),tc_prod(X7,X105),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),X105),c_List_Olist_ONil(X7)),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_prod(tc_List_Olist(X7),X105)),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_prod(tc_List_Olist(X7),X105)),tc_fun(X105,tc_prod(tc_List_Olist(X7),X105))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X7),X105),tc_prod(tc_List_Olist(X7),X105)),tc_fun(tc_fun(X105,tc_prod(tc_List_Olist(X7),X105)),tc_fun(X105,tc_prod(tc_List_Olist(X7),X105))),X7),c_COMBB(tc_prod(tc_List_Olist(X7),X105),tc_prod(tc_List_Olist(X7),X105),X105)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_fun(X105,tc_prod(tc_List_Olist(X7),X105))),tc_fun(tc_prod(tc_List_Olist(X7),X105),tc_prod(tc_List_Olist(X7),X105)),X7),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X7),X105,tc_prod(tc_List_Olist(X7),X105))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),tc_fun(tc_List_Olist(X7),tc_fun(X105,tc_prod(tc_List_Olist(X7),X105))),X7),hAPP(c_COMBB(tc_List_Olist(X7),tc_fun(X105,tc_prod(tc_List_Olist(X7),X105)),tc_List_Olist(X7)),c_Product__Type_OPair(tc_List_Olist(X7),X105))),c_List_Olist_OCons(X7))))),c_Lazy__Sequence_Oanamorph(X105,X7,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X94),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X2,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_anamorph_Osimps) ).
fof(fact_listrel__iff__zip,axiom,
! [X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel(X7,X172)))
<=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X293)
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X3),hAPP(c_List_Oset(tc_prod(X7,X7)),hAPP(hAPP(c_List_Ozip(X7,X7),X292),X293))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X7,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X7,X7)))),c_Product__Type_OPair(X7,X7)))),X172)),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__iff__zip) ).
fof(fact_DomainP__Domain__eq,axiom,
! [X6,X172,X105,X7] :
( hBOOL(hAPP(c_Predicate_ODomainP(X7,X105,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),X172)),X6))
<=> hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_Relation_ODomain(X7,X105),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(fact_RangeP__Range__eq,axiom,
! [X6,X172,X105,X7] :
( hBOOL(hAPP(c_Predicate_ORangeP(X7,X105,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),X172)),X6))
<=> hBOOL(hAPP(hAPP(c_member(X105),X6),hAPP(c_Relation_ORange(X7,X105),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_accp__acc__eq,axiom,
! [X6,X172,X7] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X7,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X7,X7)))),c_Product__Type_OPair(X7,X7)))),X172)),X6))
<=> hBOOL(hAPP(hAPP(c_member(X7),X6),c_Wellfounded_Oacc(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
fof(fact_fold__graph_H_Oequations_I2_J,axiom,
! [X61,X42,X43,X47,X41,X105,X7] :
( c_Nitpick_Ofold__graph_H(X7,X105,X41,X47,X43,hAPP(hAPP(X41,X42),X61))
<=> ( ( X43 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
& hAPP(hAPP(X41,X42),X61) = X47 )
| ? [X3,X82] :
( hAPP(hAPP(X41,X42),X61) = hAPP(hAPP(X41,X3),X82)
& hBOOL(hAPP(hAPP(c_member(X7),X3),X43))
& c_Nitpick_Ofold__graph_H(X7,X105,X41,X47,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X43),hAPP(hAPP(c_Set_Oinsert(X7),X3),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X82) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
fof(fact_SUP2__iff,axiom,
! [X23,X24,X155,X149,X119,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_fun(X119,tc_HOL_Obool))),X149),X155),X24),X23))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& hBOOL(hAPP(hAPP(hAPP(X155,X3),X24),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__iff) ).
fof(fact_partition_Osimps_I2_J,axiom,
! [X292,X6,X38,X7] : c_List_Opartition(X7,X38,hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X7),tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_COMBS(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),tc_fun(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)))),tc_fun(tc_fun(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),tc_fun(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)))),tc_List_Olist(X7)),c_COMBS(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),tc_fun(tc_List_Olist(X7),tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)))),tc_List_Olist(X7)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),tc_List_Olist(X7)),hAPP(c_If(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(X38,X6)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),tc_List_Olist(X7)),c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(c_List_Olist_OCons(X7),X6))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),tc_fun(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),tc_fun(tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),tc_fun(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)))),tc_List_Olist(X7)),c_COMBB(tc_List_Olist(X7),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_List_Olist(X7))),c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)))),hAPP(c_List_Olist_OCons(X7),X6)))),c_List_Opartition(X7,X38,X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).
fof(fact_Ass,axiom,
! [X25,X39,X38,X216,X7] : c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X7),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X38)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X39)),X25))),c_Com_Ocom_OAss(X39,X25)),X38)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ass) ).
fof(fact_hoare__derivs_Oequations_I8_J,axiom,
! [X47,X41,X43,X42,X7] : c_Hoare__Mirabelle_Ohoare__derivs(X7,X42,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X7),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X43)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X41)),X47))),c_Com_Ocom_OAss(X41,X47)),X43)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I8_J) ).
fof(fact_lexn_Osimps_I2_J,axiom,
! [X44,X172,X7] : hAPP(c_List_Olexn(X7,X172),hAPP(c_Nat_OSuc,X44)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X7,tc_List_Olist(X7)),tc_prod(X7,tc_List_Olist(X7))),tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),c_Product__Type_Omap__pair(tc_prod(X7,tc_List_Olist(X7)),tc_List_Olist(X7),tc_prod(X7,tc_List_Olist(X7)),tc_List_Olist(X7),hAPP(c_Product__Type_Oprod_Oprod__case(X7,tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_OCons(X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_OCons(X7)))),c_Wellfounded_Olex__prod(X7,tc_List_Olist(X7),X172,hAPP(c_List_Olexn(X7,X172),X44)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X7),tc_List_Olist(X7),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),tc_List_Olist(X7)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X7))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X7)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X7)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),hAPP(c_Nat_OSuc,X44))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X7)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),hAPP(c_Nat_OSuc,X44)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn_Osimps_I2_J) ).
fof(fact_set__sublist,axiom,
! [X211,X292,X7] : hAPP(c_List_Oset(X7),c_List_Osublist(X7,X292,X211)) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X7),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_Nat_Onat,X7),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X7),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X7),X292))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X211))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sublist) ).
fof(fact_pred__comp__rel__comp__eq,axiom,
! [X127,X6,X45,X172,X119,X105,X7] :
( c_Predicate_Opred__comp(X7,X105,X119,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),X172),hAPP(hAPP(c_COMBC(X105,tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),X105),c_COMBC(X119,tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_prod(X105,X119)),tc_fun(X119,tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool)),X105),hAPP(c_COMBB(tc_prod(X105,X119),tc_fun(tc_fun(tc_prod(X105,X119),tc_HOL_Obool),tc_HOL_Obool),X119),c_member(tc_prod(X105,X119)))),c_Product__Type_OPair(X105,X119)))),X45),X6,X127)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X119)),hAPP(hAPP(c_Product__Type_OPair(X7,X119),X6),X127)),hAPP(hAPP(c_Relation_Orel__comp(X7,X105,X119),X172),X45))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp__rel__comp__eq) ).
fof(fact_setsum__multicount__gen,axiom,
! [X94,X191,X46,X105,X45,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X45))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X46))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X46))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X45))),hAPP(hAPP(c_COMBC(X7,X105,tc_HOL_Obool),X191),X3)))) = hAPP(X94,X3) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_Nat_Onat,X7),c_Finite__Set_Ocard(X105)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),c_Set_OCollect(X105)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBS(X105,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X105),c_fconj),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X46)))),X191)))),X45) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,tc_Nat_Onat),X94),X46) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__multicount__gen) ).
fof(fact_set__conv__nth,axiom,
! [X292,X7] : hAPP(c_List_Oset(X7),X292) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X7),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_Nat_Onat,X7),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X7),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X7),X292))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__conv__nth) ).
fof(fact_Sigma__def,axiom,
! [X155,X149,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBS(X7,tc_fun(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool))),X155)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(tc_prod(X7,X105),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool))),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(tc_prod(X7,X105),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(tc_prod(X7,X105),tc_HOL_Obool))),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X105),c_Set_Oinsert(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X105),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__def) ).
fof(fact_setsum__multicount,axiom,
! [X94,X191,X238,X105,X209,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X238))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X238))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X209))),hAPP(hAPP(c_COMBC(X7,X105,tc_HOL_Obool),X191),X3)))) = X94 )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_Nat_Onat,X7),c_Finite__Set_Ocard(X105)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),c_Set_OCollect(X105)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBS(X105,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X105),c_fconj),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X238)))),X191)))),X209) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),hAPP(c_Finite__Set_Ocard(X105),X238)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__multicount) ).
fof(fact_setsum__setsum__restrict,axiom,
! [X191,X2,X238,X105,X209,X7,X119] :
( class_Groups_Ocomm__monoid__add(X119)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X238))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X119),hAPP(hAPP(c_COMBS(X7,tc_fun(X105,tc_HOL_Obool),X119),hAPP(hAPP(c_COMBB(tc_fun(X105,X119),tc_fun(tc_fun(X105,tc_HOL_Obool),X119),X7),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X119)),X2)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),c_Set_OCollect(X105)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBS(X105,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X105),c_fconj),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X238)))),X191)))),X209) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X119),hAPP(hAPP(c_COMBS(X105,tc_fun(X7,tc_HOL_Obool),X119),hAPP(hAPP(c_COMBB(tc_fun(X7,X119),tc_fun(tc_fun(X7,tc_HOL_Obool),X119),X105),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X119)),hAPP(c_COMBC(X7,X105,X119),X2))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),c_Set_OCollect(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X209)))),hAPP(c_COMBC(X7,X105,tc_HOL_Obool),X191))))),X238) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__setsum__restrict) ).
fof(fact_sequence__trans,axiom,
! [X94,X107,X172,X2,X7] :
( ! [X147] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),hAPP(X2,hAPP(c_Nat_OSuc,X147))),hAPP(X2,X147))),c_Transitive__Closure_Ortrancl(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),X94))),hAPP(X2,X107))),c_Transitive__Closure_Ortrancl(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sequence__trans) ).
fof(fact_divmod__int__rel__def,axiom,
! [X24,X25] : c_Divides_Odivmod__int__rel(X25,X24) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X25))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X24))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__def) ).
fof(fact_setsum__product,axiom,
! [X155,X1,X119,X149,X2,X105,X7] :
( class_Rings_Osemiring__0(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X119,X7),X1),X155)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBC(X105,tc_fun(X119,tc_HOL_Obool),X7),hAPP(hAPP(c_COMBB(tc_fun(X119,X7),tc_fun(tc_fun(X119,tc_HOL_Obool),X7),X105),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X119,X7)),hAPP(hAPP(c_COMBC(X105,tc_fun(X119,X7),tc_fun(X119,X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,X7),tc_fun(tc_fun(X119,X7),tc_fun(X119,X7)),X105),c_COMBB(X7,X7,X119)),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),c_Groups_Otimes__class_Otimes(X7)),X2))),X1))),X155)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__product) ).
fof(fact_fold__image__Sigma,axiom,
! [X1,X155,X105,X149,X7,X119] :
( class_Groups_Ocomm__monoid__mult(X119)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(X155,X3))) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X119,X7,c_Groups_Otimes__class_Otimes(X119)),hAPP(hAPP(c_COMBS(X7,tc_fun(X105,tc_HOL_Obool),X119),hAPP(hAPP(c_COMBC(X7,X119,tc_fun(tc_fun(X105,tc_HOL_Obool),X119)),hAPP(hAPP(c_COMBB(tc_fun(X105,X119),tc_fun(X119,tc_fun(tc_fun(X105,tc_HOL_Obool),X119)),X7),c_Finite__Set_Ofold__image(X119,X105,c_Groups_Otimes__class_Otimes(X119))),X1)),c_Groups_Oone__class_Oone(X119))),X155)),c_Groups_Oone__class_Oone(X119)),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X119,tc_prod(X7,X105),c_Groups_Otimes__class_Otimes(X119)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,X119),X1)),c_Groups_Oone__class_Oone(X119)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Sigma) ).
fof(fact_finite__lists__length__le,axiom,
! [X44,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X7)),hAPP(c_Set_OCollect(tc_List_Olist(X7)),hAPP(hAPP(c_COMBS(tc_List_Olist(X7),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X7)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X7)),c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool))),c_List_Oset(X7))),X149))),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X7)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),X44))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lists__length__le) ).
fof(fact_finite__lists__length__eq,axiom,
! [X44,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X7)),hAPP(c_Set_OCollect(tc_List_Olist(X7)),hAPP(hAPP(c_COMBS(tc_List_Olist(X7),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X7)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X7)),c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool))),c_List_Oset(X7))),X149))),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X7)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),X44))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lists__length__eq) ).
fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
! [X155,X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149),X155)))
=> hAPP(X1,X3) = X26 )
=> hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(X2,hAPP(X215,X149)),hAPP(X215,X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).
fof(fact_nat__def,axiom,
! [X26] : hAPP(c_Int_Onat,X26) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X26)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__def) ).
fof(fact_evaln_Oequations_I10_J,axiom,
! [X61,X47,X43,X41,X42,X72] :
( c_Natural_Oevaln(c_Com_Ocom_OCall(X72,X42,X41),X43,X47,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X61),hAPP(c_Natural_Ogetlocs,X43))),X72),hAPP(hAPP(c_Natural_Ogetlocs,X61),c_Com_ORes)))
<=> ? [X62] :
( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X61),hAPP(c_Natural_Ogetlocs,X43))),X72),hAPP(hAPP(c_Natural_Ogetlocs,X61),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X62),hAPP(c_Natural_Ogetlocs,X43))),X72),hAPP(hAPP(c_Natural_Ogetlocs,X62),c_Com_ORes))
& c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X42),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X43),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X41,X43)),X47,X62) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I10_J) ).
fof(fact_nat__intermed__int__val,axiom,
! [X94,X2,X44,X95] :
( ! [X147] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X147))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X147),X44)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X147),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X147)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X95)),X94))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),hAPP(X2,X44)))
=> ? [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X147))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X147),X44))
& hAPP(X2,X147) = X94 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__intermed__int__val) ).
fof(fact_Sigma__mono,axiom,
! [X192,X155,X105,X193,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X193))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(X155,X3)),hAPP(X192,X3))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X193),X192))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__mono) ).
fof(fact_setprod__dvd__setprod__subset2,axiom,
! [X1,X2,X149,X155,X7,X105] :
( class_Rings_Ocomm__semiring__1(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X105),hAPP(X2,X3)),hAPP(X1,X3))) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X155))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__dvd__setprod__subset2) ).
fof(fact_mem__splitI2,axiom,
! [X23,X26,X119,X105,X7,X161] :
( ! [X110,X188] :
( X161 = hAPP(hAPP(c_Product__Type_OPair(X7,X105),X110),X188)
=> hBOOL(hAPP(hAPP(c_member(X119),X26),hAPP(hAPP(X23,X110),X188))) )
=> hBOOL(hAPP(hAPP(c_member(X119),X26),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_fun(X119,tc_HOL_Obool)),X23),X161))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI2) ).
fof(fact_converse__def,axiom,
! [X172,X7,X105] : hAPP(c_Relation_Oconverse(X105,X7),X172) = hAPP(c_Set_OCollect(tc_prod(X7,X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X105,X7),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X105,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X105,X7),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X105,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X105,X7)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X105,X7),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X105,X7),tc_fun(tc_fun(tc_prod(X105,X7),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X105,X7)))),hAPP(c_COMBC(X105,X7,tc_prod(X105,X7)),c_Product__Type_OPair(X105,X7))))),X172))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__def) ).
fof(fact_card__less__Suc,axiom,
! [X107,X210] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X210))
=> hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X210))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X107))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X210))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X107))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less__Suc) ).
fof(fact_setsum__image__gen,axiom,
! [X2,X119,X1,X209,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X209) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X119,X105),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),X105,X119),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X119),c_Set_OCollect(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X119),hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X209)))),hAPP(c_COMBC(X7,X119,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X119,tc_fun(X119,tc_HOL_Obool),X7),c_fequal),X2)))))),hAPP(c_Set_Oimage(X7,X119,X2),X209)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__image__gen) ).
fof(fact_refl__on__def_H,axiom,
! [X172,X149,X7] :
( c_Relation_Orefl__on(X7,X149,X172)
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X3),X172))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))),X3)) )
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),X172)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def_H) ).
fof(fact_zip__Cons,axiom,
! [X293,X127,X292,X105,X7] : hAPP(hAPP(c_List_Ozip(X7,X105),X292),hAPP(hAPP(c_List_Olist_OCons(X105),X127),X293)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X7,X105)),X7,c_List_Olist_ONil(tc_prod(X7,X105)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_List_Olist(X7),tc_List_Olist(tc_prod(X7,X105))),tc_fun(tc_List_Olist(X7),tc_List_Olist(tc_prod(X7,X105)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X7,X105)),tc_List_Olist(tc_prod(X7,X105))),tc_fun(tc_fun(tc_List_Olist(X7),tc_List_Olist(tc_prod(X7,X105))),tc_fun(tc_List_Olist(X7),tc_List_Olist(tc_prod(X7,X105)))),X7),c_COMBB(tc_List_Olist(tc_prod(X7,X105)),tc_List_Olist(tc_prod(X7,X105)),tc_List_Olist(X7))),hAPP(hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_List_Olist(tc_prod(X7,X105)),tc_List_Olist(tc_prod(X7,X105))),X7),c_List_Olist_OCons(tc_prod(X7,X105))),hAPP(hAPP(c_COMBC(X7,X105,tc_prod(X7,X105)),c_Product__Type_OPair(X7,X105)),X127)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_List_Olist(X105),tc_List_Olist(tc_prod(X7,X105))),c_List_Ozip(X7,X105)),X293))),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons) ).
fof(fact_max__extp__max__ext__eq,axiom,
! [X235,X6,X191,X7] :
( c_Wellfounded_Omax__extp(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X7,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X7,X7)))),c_Product__Type_OPair(X7,X7)))),X191),X6,X235)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X6),X235)),c_Wellfounded_Omax__ext(X7,X191))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).
fof(fact_listrelp__listrel__eq,axiom,
! [X235,X6,X172,X7] :
( c_List_Olistrelp(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X7,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X7,X7)))),c_Product__Type_OPair(X7,X7)))),X172),X6,X235)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),X235)),c_List_Olistrel(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp__listrel__eq) ).
fof(fact_UN__Times__distrib,axiom,
! [X215,X261,X155,X149,X105,X7,X190,X119] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X119,X190),tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X119,X190),X149),hAPP(c_COMBK(tc_fun(X190,tc_HOL_Obool),X119),X155))),hAPP(c_Product__Type_Oprod_Oprod__case(X119,X190,tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X119,tc_fun(X190,tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),tc_fun(X190,tc_fun(tc_prod(X7,X105),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_fun(X105,tc_HOL_Obool)),tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),tc_fun(tc_fun(X190,tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),tc_fun(X190,tc_fun(tc_prod(X7,X105),tc_HOL_Obool))),X119),c_COMBB(tc_fun(X7,tc_fun(X105,tc_HOL_Obool)),tc_fun(tc_prod(X7,X105),tc_HOL_Obool),X190)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_fun(X105,tc_HOL_Obool)),tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X119),c_Product__Type_OSigma(X7,X105)),X261))),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_fun(X105,tc_HOL_Obool)),X190),c_COMBK(tc_fun(X105,tc_HOL_Obool),X7)),X215)))) = hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),X149),X261)),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X190,tc_fun(X105,tc_HOL_Obool)),X155),X215))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Times__distrib) ).
fof(fact_equivp__equiv,axiom,
! [X149,X7] :
( c_Equiv__Relations_Oequiv(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),X149)
<=> c_Equiv__Relations_Oequivp(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X7,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X7,X7)))),c_Product__Type_OPair(X7,X7)))),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__equiv) ).
fof(fact_wfP__wf__eq,axiom,
! [X172,X7] :
( c_Wellfounded_OwfP(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X7,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X7,X7)))),c_Product__Type_OPair(X7,X7)))),X172))
<=> c_Wellfounded_Owf(X7,X172) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__wf__eq) ).
fof(fact_pred__equals__eq2,axiom,
! [X209,X191,X105,X7] :
( hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),X191) = hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBC(X105,tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_HOL_Obool),X105),c_member(tc_prod(X7,X105)))),c_Product__Type_OPair(X7,X105)))),X209)
<=> X191 = X209 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_map__zip__map2,axiom,
! [X293,X1,X190,X292,X2,X7,X119,X105] : hAPP(hAPP(c_List_Omap(tc_prod(X105,X119),X7),X2),hAPP(hAPP(c_List_Ozip(X105,X119),X292),hAPP(hAPP(c_List_Omap(X190,X119),X1),X293))) = hAPP(hAPP(c_List_Omap(tc_prod(X105,X190),X7),hAPP(c_Product__Type_Oprod_Oprod__case(X105,X190,X7),hAPP(hAPP(c_COMBB(tc_fun(X190,tc_prod(X105,X119)),tc_fun(X190,X7),X105),hAPP(c_COMBB(tc_prod(X105,X119),X7,X190),X2)),hAPP(hAPP(c_COMBC(X105,tc_fun(X190,X119),tc_fun(X190,tc_prod(X105,X119))),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_prod(X105,X119)),tc_fun(tc_fun(X190,X119),tc_fun(X190,tc_prod(X105,X119))),X105),c_COMBB(X119,tc_prod(X105,X119),X190)),c_Product__Type_OPair(X105,X119))),X1)))),hAPP(hAPP(c_List_Ozip(X105,X190),X292),X293)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__zip__map2) ).
fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
! [X25,X127,X149,X26,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,X149),X127))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ? [X268] :
( X127 = hAPP(hAPP(X2,X25),X268)
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X268)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).
fof(fact_map__of__map,axiom,
! [X292,X2,X119,X105,X7] : c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Omap(tc_prod(X7,X119),tc_prod(X7,X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X119,tc_prod(X7,X105)),hAPP(hAPP(c_COMBC(X7,tc_fun(X119,X105),tc_fun(X119,tc_prod(X7,X105))),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(tc_fun(X119,X105),tc_fun(X119,tc_prod(X7,X105))),X7),c_COMBB(X105,tc_prod(X7,X105),X119)),c_Product__Type_OPair(X7,X105))),X2))),X292)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(X119),tc_Option_Ooption(X105),X7,hAPP(c_Option_Omap(X119,X105),X2)),c_Map_Omap__of(X7,X119,X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__map) ).
fof(fact_zip__Cons1,axiom,
! [X293,X292,X6,X105,X7] : hAPP(hAPP(c_List_Ozip(X7,X105),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),X293) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X7,X105)),X105,c_List_Olist_ONil(tc_prod(X7,X105)),hAPP(hAPP(c_COMBC(X105,tc_fun(tc_List_Olist(X105),tc_List_Olist(tc_prod(X7,X105))),tc_fun(tc_List_Olist(X105),tc_List_Olist(tc_prod(X7,X105)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X7,X105)),tc_List_Olist(tc_prod(X7,X105))),tc_fun(tc_fun(tc_List_Olist(X105),tc_List_Olist(tc_prod(X7,X105))),tc_fun(tc_List_Olist(X105),tc_List_Olist(tc_prod(X7,X105)))),X105),c_COMBB(tc_List_Olist(tc_prod(X7,X105)),tc_List_Olist(tc_prod(X7,X105)),tc_List_Olist(X105))),hAPP(hAPP(c_COMBB(tc_prod(X7,X105),tc_fun(tc_List_Olist(tc_prod(X7,X105)),tc_List_Olist(tc_prod(X7,X105))),X105),c_List_Olist_OCons(tc_prod(X7,X105))),hAPP(c_Product__Type_OPair(X7,X105),X6)))),hAPP(c_List_Ozip(X7,X105),X292))),X293),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons1) ).
fof(fact_wf__if__measure,axiom,
! [X7,X1,X2,X38] :
( ! [X3] :
( hBOOL(hAPP(X38,X3))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,hAPP(X1,X3))),hAPP(X2,X3))) )
=> c_Wellfounded_Owf(X7,hAPP(c_Set_OCollect(tc_prod(X7,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X7),hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),X38))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X7)),c_fequal)),X1))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__if__measure) ).
fof(fact_max__ext__compat,axiom,
! [X209,X191,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X191),X209)),X191))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X7,X191)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X7,X209)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X7,X191))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__compat) ).
fof(fact_min__ext__compat,axiom,
! [X209,X191,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X191),X209)),X191))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X7,X191)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X7,X209)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X7,X191))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__compat) ).
fof(fact_hoare__derivs_OIf,axiom,
! [X136,X194,X23,X24,X38,X216,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),c_Hoare__Mirabelle_Opeek__and(X7,X38,X24)),X23),X194)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),c_Hoare__Mirabelle_Opeek__and(X7,X38,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X24))),X136),X194)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X38),c_Com_Ocom_OCond(X24,X23,X136)),X194)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OIf) ).
fof(fact_setsum__restrict__set_H,axiom,
! [X155,X2,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155))),X2)),c_Groups_Ozero__class_Ozero(X105))),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__restrict__set_H) ).
fof(fact_zip__map__map,axiom,
! [X293,X1,X190,X292,X2,X119,X105,X7] : hAPP(hAPP(c_List_Ozip(X7,X105),hAPP(hAPP(c_List_Omap(X119,X7),X2),X292)),hAPP(hAPP(c_List_Omap(X190,X105),X1),X293)) = hAPP(hAPP(c_List_Omap(tc_prod(X119,X190),tc_prod(X7,X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X119,X190,tc_prod(X7,X105)),hAPP(hAPP(c_COMBC(X119,tc_fun(X190,X105),tc_fun(X190,tc_prod(X7,X105))),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(tc_fun(X190,X105),tc_fun(X190,tc_prod(X7,X105))),X119),c_COMBB(X105,tc_prod(X7,X105),X190)),hAPP(hAPP(c_COMBB(X7,tc_fun(X105,tc_prod(X7,X105)),X119),c_Product__Type_OPair(X7,X105)),X2))),X1))),hAPP(hAPP(c_List_Ozip(X119,X190),X292),X293)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map__map) ).
fof(fact_finite__psubset__def,axiom,
! [X7] : c_Wellfounded_Ofinite__psubset(X7) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),c_COMBS(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X7)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__psubset__def) ).
fof(fact_map__pair__imageI,axiom,
! [X1,X2,X190,X119,X191,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),X191))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X119,X190)),hAPP(hAPP(c_Product__Type_OPair(X119,X190),hAPP(X2,X25)),hAPP(X1,X24))),hAPP(c_Set_Oimage(tc_prod(X7,X105),tc_prod(X119,X190),c_Product__Type_Omap__pair(X7,X119,X105,X190,X2,X1)),X191))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__imageI) ).
fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
! [X197,X198,X199,X2,X191,X7,X105] : c_New__Random__Sequence_Oneg__decr__bind(X105,X7,X191,X2,X199,X198,X197) = c_New__DSequence_Oneg__decr__bind(X105,X7,hAPP(hAPP(hAPP(X191,X199),X198),X197),hAPP(hAPP(c_COMBC(X105,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X7)))),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X7))))),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X7)))))),X2),X199)),X198)),X197)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).
fof(fact_INTER__def,axiom,
! [X155,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OAll(X105)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBS(X105,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X105),c_fimplies),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X149)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X105)),c_member(X7))),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__def) ).
fof(fact_congruent__def,axiom,
! [X2,X172,X105,X7] :
( c_Equiv__Relations_Ocongruent(X7,X105,X172,X2)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X3),X172))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,X105),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X7,X105),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(X105,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(X105,tc_fun(X105,tc_HOL_Obool),X7),c_fequal),X2))),X2)),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent__def) ).
fof(fact_finite__Collect__bounded__ex,axiom,
! [X194,X105,X38,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),X38)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(c_Set_OCollect(X105),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X105),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),X38))),X194)))))
<=> ! [X82] :
( hBOOL(hAPP(X38,X82))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(c_Set_OCollect(X105),hAPP(hAPP(c_COMBC(X105,X7,tc_HOL_Obool),X194),X82)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__bounded__ex) ).
fof(fact_setprod__Sigma,axiom,
! [X2,X155,X105,X149,X7,X119] :
( class_Groups_Ocomm__monoid__mult(X119)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(X155,X3))) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X119),hAPP(hAPP(c_COMBS(X7,tc_fun(X105,tc_HOL_Obool),X119),hAPP(hAPP(c_COMBB(tc_fun(X105,X119),tc_fun(tc_fun(X105,tc_HOL_Obool),X119),X7),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X119)),X2)),X155)),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X7,X105),X119),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,X119),X2)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Sigma) ).
fof(fact_setsum__Sigma,axiom,
! [X2,X155,X105,X149,X7,X119] :
( class_Groups_Ocomm__monoid__add(X119)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(X155,X3))) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X119),hAPP(hAPP(c_COMBS(X7,tc_fun(X105,tc_HOL_Obool),X119),hAPP(hAPP(c_COMBB(tc_fun(X105,X119),tc_fun(tc_fun(X105,tc_HOL_Obool),X119),X7),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X119)),X2)),X155)),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X7,X105),X119),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,X119),X2)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Sigma) ).
fof(fact_setsum__restrict__set,axiom,
! [X155,X2,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155))),X2)),c_Groups_Ozero__class_Ozero(X105))),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__restrict__set) ).
fof(fact_UN__finite2__subset,axiom,
! [X155,X94,X149,X7] :
( ! [X70] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X70)),X149)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X70),X94))),X155)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X149)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__subset) ).
fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
! [X197,X198,X199,X2,X191,X7,X105] : c_New__Random__Sequence_Opos__decr__bind(X105,X7,X191,X2,X199,X198,X197) = c_New__DSequence_Opos__decr__bind(X105,X7,hAPP(hAPP(hAPP(X191,X199),X198),X197),hAPP(hAPP(c_COMBC(X105,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X7))),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X7)))),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X7))))),X2),X199)),X198)),X197)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).
fof(fact_image__split__eq__Sigma,axiom,
! [X149,X1,X2,X105,X7,X119] : hAPP(c_Set_Oimage(X119,tc_prod(X7,X105),hAPP(hAPP(c_COMBS(X119,X105,tc_prod(X7,X105)),hAPP(hAPP(c_COMBB(X7,tc_fun(X105,tc_prod(X7,X105)),X119),c_Product__Type_OPair(X7,X105)),X2)),X1)),X149) = hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(c_Set_Oimage(X119,X7,X2),X149)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),c_Set_Oimage(X119,X105,X1)),hAPP(hAPP(c_COMBC(X7,tc_fun(X119,tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_HOL_Obool),tc_fun(tc_fun(X119,tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X119,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X119,tc_HOL_Obool),X7),c_Set_Ovimage(X119,X7,X2)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),X149))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__split__eq__Sigma) ).
fof(fact_Sup__Inf,axiom,
! [X149,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OSup__class_OSup(X7,X149) = c_Complete__Lattice_OInf__class_OInf(X7,hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OAll(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X7),hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fimplies),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)))),hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X7)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__Inf) ).
fof(fact_setsum__nonneg__leq__bound,axiom,
! [X107,X155,X2,X45,X7,X105] :
( class_Groups_Oordered__ab__group__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X45))
=> ( ! [X147] :
( hBOOL(hAPP(hAPP(c_member(X7),X147),X45))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),c_Groups_Ozero__class_Ozero(X105)),hAPP(X2,X147))) )
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X45) = X155
=> ( hBOOL(hAPP(hAPP(c_member(X7),X107),X45))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(X2,X107)),X155)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__nonneg__leq__bound) ).
fof(fact_Inf__Sup,axiom,
! [X149,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OInf__class_OInf(X7,X149) = c_Complete__Lattice_OSup__class_OSup(X7,hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OAll(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X7),hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fimplies),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)))),c_Orderings_Oord__class_Oless__eq(X7))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__Sup) ).
fof(fact_Int__UN__distrib2,axiom,
! [X155,X252,X119,X149,X211,X105,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X211),X149)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),X252),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X211),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),X252)),hAPP(hAPP(c_COMBC(X105,tc_fun(X119,tc_fun(X7,tc_HOL_Obool)),tc_fun(X119,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_fun(X119,tc_fun(X7,tc_HOL_Obool)),tc_fun(X119,tc_fun(X7,tc_HOL_Obool))),X105),c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X119)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool))),X149))),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib2) ).
fof(fact_Un__INT__distrib2,axiom,
! [X155,X252,X119,X149,X211,X105,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X211),X149)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X7,tc_HOL_Obool)),X252),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X211),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X7,tc_HOL_Obool)),X252)),hAPP(hAPP(c_COMBC(X105,tc_fun(X119,tc_fun(X7,tc_HOL_Obool)),tc_fun(X119,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_fun(X119,tc_fun(X7,tc_HOL_Obool)),tc_fun(X119,tc_fun(X7,tc_HOL_Obool))),X105),c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X119)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool))),X149))),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib2) ).
fof(fact_neg__bind__def,axiom,
! [X197,X198,X199,X2,X191,X7,X105] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X105,X7,X191,X2),X199),X198),X197) = c_New__DSequence_Oneg__bind(X105,X7,hAPP(hAPP(hAPP(X191,X199),X198),X197),hAPP(hAPP(c_COMBC(X105,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X7)))),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X7))))),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X7)))))),X2),X199)),X198)),X197)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__bind__def) ).
fof(fact_Inter__eq,axiom,
! [X149,X7] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X149) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OAll(tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),X7),hAPP(c_COMBS(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X7,tc_HOL_Obool))),X149)))),c_member(X7)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__eq) ).
fof(fact_rtrancl__Un__separatorE,axiom,
! [X194,X38,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Ortrancl(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X38),X194))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X3)),c_Transitive__Closure_Ortrancl(X7,X38)))
=> ! [X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X82)),X194))
=> X3 = X82 ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Ortrancl(X7,X38))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).
fof(fact_rtrancl__Un__separator__converseE,axiom,
! [X194,X38,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Ortrancl(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X38),X194))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X24)),c_Transitive__Closure_Ortrancl(X7,X38)))
=> ! [X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X3)),X194))
=> X82 = X3 ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Ortrancl(X7,X38))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
fof(fact_zip__map2,axiom,
! [X293,X2,X119,X292,X105,X7] : hAPP(hAPP(c_List_Ozip(X7,X105),X292),hAPP(hAPP(c_List_Omap(X119,X105),X2),X293)) = hAPP(hAPP(c_List_Omap(tc_prod(X7,X119),tc_prod(X7,X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X119,tc_prod(X7,X105)),hAPP(hAPP(c_COMBC(X7,tc_fun(X119,X105),tc_fun(X119,tc_prod(X7,X105))),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(tc_fun(X119,X105),tc_fun(X119,tc_prod(X7,X105))),X7),c_COMBB(X105,tc_prod(X7,X105),X119)),c_Product__Type_OPair(X7,X105))),X2))),hAPP(hAPP(c_List_Ozip(X7,X119),X292),X293)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map2) ).
fof(fact_nat0__intermed__int__val,axiom,
! [X94,X2,X44] :
( ! [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X147),X44))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X147),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X147)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X94))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),hAPP(X2,X44)))
=> ? [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X147),X44))
& hAPP(X2,X147) = X94 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat0__intermed__int__val) ).
fof(fact_int__val__lemma,axiom,
! [X94,X2,X44] :
( ! [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X147),X44))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X147),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X147)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X94))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),hAPP(X2,X44)))
=> ? [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X147),X44))
& hAPP(X2,X147) = X94 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__val__lemma) ).
fof(fact_small__prod__def,axiom,
! [X136,X2,X7,X105] :
( ( class_Smallcheck_Osmall(X105)
& class_Smallcheck_Osmall(X7) )
=> hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X7,X105)),X2),X136) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X7),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X7),c_Smallcheck_Osmall__class_Osmall(X105)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X105),X2)),c_Product__Type_OPair(X7,X105)))),X136)),X136) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__prod__def) ).
fof(fact_inj__vimage__singleton,axiom,
! [X25,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(hAPP(c_Set_Oinsert(X105),X25),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X7),c_HOL_OThe(X7,hAPP(hAPP(c_COMBC(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X105,tc_fun(X105,tc_HOL_Obool),X7),c_fequal),X2)),X25))),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__vimage__singleton) ).
fof(fact_pos__bind__def,axiom,
! [X197,X198,X199,X2,X191,X7,X105] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X105,X7,X191,X2),X199),X198),X197) = c_New__DSequence_Opos__bind(X105,X7,hAPP(hAPP(hAPP(X191,X199),X198),X197),hAPP(hAPP(c_COMBC(X105,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X7))),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X7)))),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X7))))),X2),X199)),X198)),X197)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__bind__def) ).
fof(fact_evalc_Oequations_I10_J,axiom,
! [X47,X43,X41,X42,X61] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X61,X42,X41)),X43),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X47),hAPP(c_Natural_Ogetlocs,X43))),X61),hAPP(hAPP(c_Natural_Ogetlocs,X47),c_Com_ORes))))
<=> ? [X62] :
( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X47),hAPP(c_Natural_Ogetlocs,X43))),X61),hAPP(hAPP(c_Natural_Ogetlocs,X47),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X62),hAPP(c_Natural_Ogetlocs,X43))),X61),hAPP(hAPP(c_Natural_Ogetlocs,X62),c_Com_ORes))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X42)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X43),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X41,X43))),X62)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I10_J) ).
fof(fact_Nitpick_Oprod__def,axiom,
! [X155,X149,X105,X7] : c_Nitpick_Oprod(X7,X105,X149,X155) = hAPP(c_Set_OCollect(tc_prod(X7,X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)))),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oprod__def) ).
fof(fact_dvd_Ostrict__mono__mono,axiom,
! [X2,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X7,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
=> c_Orderings_Oorder_Omono(tc_Nat_Onat,X7,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ostrict__mono__mono) ).
fof(fact_map__pair_Ocompositionality,axiom,
! [X262,X107,X200,X201,X189,X1,X2,X105,X190,X7,X119] : hAPP(c_Product__Type_Omap__pair(X119,X7,X190,X105,X2,X1),hAPP(c_Product__Type_Omap__pair(X189,X119,X201,X190,X200,X107),X262)) = hAPP(c_Product__Type_Omap__pair(X189,X7,X201,X105,hAPP(c_Fun_Ocomp(X119,X7,X189,X2),X200),hAPP(c_Fun_Ocomp(X190,X105,X201,X1),X107)),X262),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Ocompositionality) ).
fof(fact_le,axiom,
! [X163,X160,X127,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X127)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X160),X163)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X163)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X160),X127))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le) ).
fof(fact_less,axiom,
! [X163,X160,X127,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X127)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X160),X163)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X163)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X160),X127))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less) ).
fof(fact_setsum__reindex__nonzero,axiom,
! [X105,X200,X2,X209,X7,X119] :
( class_Groups_Ocomm__monoid__add(X119)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X209))
=> ! [X82] :
( hBOOL(hAPP(hAPP(c_member(X7),X82),X209))
=> ( X3 != X82
=> ( hAPP(X2,X3) = hAPP(X2,X82)
=> hAPP(X200,hAPP(X2,X3)) = c_Groups_Ozero__class_Ozero(X119) ) ) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X119),X200),hAPP(c_Set_Oimage(X7,X105,X2),X209)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X119),hAPP(c_Fun_Ocomp(X105,X119,X7,X200),X2)),X209) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__nonzero) ).
fof(fact_if__image__distrib,axiom,
! [X209,X1,X2,X38,X7,X105] : hAPP(c_Set_Oimage(X105,X7,hAPP(hAPP(c_COMBS(X105,X7,X7),hAPP(hAPP(c_COMBS(X105,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X105),c_If(X7)),X38)),X2)),X1)),X209) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X7,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X209),hAPP(c_Set_OCollect(X105),X38)))),hAPP(c_Set_Oimage(X105,X7,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X209),hAPP(c_Set_OCollect(X105),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X105),c_fNot),X38))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_if__image__distrib) ).
fof(fact_mult,axiom,
! [X163,X160,X127,X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X127)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X160),X163)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X160)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X127),X163))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X163)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X127),X160)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult) ).
fof(fact_evaln_Oequations_I3_J,axiom,
! [X72,X61,X43,X42,X47,X41] :
( c_Natural_Oevaln(c_Com_Ocom_OLocal(X41,X47,X42),X43,X61,hAPP(hAPP(hAPP(c_Natural_Oupdate,X72),c_Com_Ovname_OLoc(X41)),hAPP(hAPP(c_Natural_Ogetlocs,X43),X41)))
<=> ? [X62] :
( hAPP(hAPP(hAPP(c_Natural_Oupdate,X72),c_Com_Ovname_OLoc(X41)),hAPP(hAPP(c_Natural_Ogetlocs,X43),X41)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,X62),c_Com_Ovname_OLoc(X41)),hAPP(hAPP(c_Natural_Ogetlocs,X43),X41))
& c_Natural_Oevaln(X42,hAPP(hAPP(hAPP(c_Natural_Oupdate,X43),c_Com_Ovname_OLoc(X41)),hAPP(X47,X43)),X61,X62) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I3_J) ).
fof(fact_fold__image__cong,axiom,
! [X26,X200,X1,X149,X7,X105] :
( class_Groups_Oab__semigroup__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hAPP(X1,X3) = hAPP(X200,X3) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),X26),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X200),X26),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__cong) ).
fof(fact_pred__comp_Oequations,axiom,
! [X41,X42,X45,X172,X119,X105,X7] :
( c_Predicate_Opred__comp(X7,X105,X119,X172,X45,X42,X41)
<=> ? [X188] :
( hBOOL(hAPP(hAPP(X172,X42),X188))
& hBOOL(hAPP(hAPP(X45,X188),X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
fof(fact_wf__map__pair__image,axiom,
! [X2,X105,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> c_Wellfounded_Owf(X105,hAPP(c_Set_Oimage(tc_prod(X7,X7),tc_prod(X105,X105),c_Product__Type_Omap__pair(X7,X105,X7,X105,X2,X2)),X172)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__map__pair__image) ).
fof(fact_inj__on__INTER,axiom,
! [X149,X2,X119,X105,X7,X211] :
( X211 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ! [X147] :
( hBOOL(hAPP(hAPP(c_member(X7),X147),X211))
=> c_Fun_Oinj__on(X105,X119,X2,hAPP(X149,X147)) )
=> c_Fun_Oinj__on(X105,X119,X2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X211),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__INTER) ).
fof(fact_listsum__mono,axiom,
! [X1,X2,X292,X7,X105] :
( ( class_Groups_Omonoid__add(X105)
& class_Groups_Oordered__ab__semigroup__add(X105) )
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X292)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(X2,X3)),hAPP(X1,X3))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(c_List_Omonoid__add__class_Olistsum(X105),hAPP(hAPP(c_List_Omap(X7,X105),X2),X292))),hAPP(c_List_Omonoid__add__class_Olistsum(X105),hAPP(hAPP(c_List_Omap(X7,X105),X1),X292)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__mono) ).
fof(fact_setsum__strict__mono,axiom,
! [X1,X2,X149,X7,X105] :
( ( class_Groups_Ocomm__monoid__add(X105)
& class_Groups_Oordered__cancel__ab__semigroup__add(X105) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X105),hAPP(X2,X3)),hAPP(X1,X3))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__strict__mono) ).
fof(fact_setsum__cases,axiom,
! [X1,X2,X38,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBS(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),X38)),X2)),X1)),X149) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Set_OCollect(X7),X38)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7),X38))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cases) ).
fof(fact_folding__one__idem_Ohom__commute,axiom,
! [X214,X200,X215,X2,X7] :
( c_Finite__Set_Ofolding__one__idem(X7,X2,X215)
=> ( ! [X3,X82] : hAPP(X200,hAPP(hAPP(X2,X3),X82)) = hAPP(hAPP(X2,hAPP(X200,X3)),hAPP(X200,X82))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> ( X214 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X200,hAPP(X215,X214)) = hAPP(X215,hAPP(c_Set_Oimage(X7,X7,X200),X214)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
fof(fact_map__pair_Ocomp,axiom,
! [X107,X200,X1,X2,X105,X7,X190,X119,X201,X189] : hAPP(c_Fun_Ocomp(tc_prod(X189,X201),tc_prod(X119,X190),tc_prod(X7,X105),c_Product__Type_Omap__pair(X189,X119,X201,X190,X2,X1)),c_Product__Type_Omap__pair(X7,X189,X105,X201,X200,X107)) = c_Product__Type_Omap__pair(X7,X119,X105,X190,hAPP(c_Fun_Ocomp(X189,X119,X7,X2),X200),hAPP(c_Fun_Ocomp(X201,X190,X105,X1),X107)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Ocomp) ).
fof(fact_map__pair__compose,axiom,
! [X202,X203,X201,X21,X22,X189,X190,X105,X119,X7] : c_Product__Type_Omap__pair(X7,X119,X105,X190,hAPP(c_Fun_Ocomp(X189,X119,X7,X22),X21),hAPP(c_Fun_Ocomp(X201,X190,X105,X203),X202)) = hAPP(c_Fun_Ocomp(tc_prod(X189,X201),tc_prod(X119,X190),tc_prod(X7,X105),c_Product__Type_Omap__pair(X189,X119,X201,X190,X22,X203)),c_Product__Type_Omap__pair(X7,X189,X105,X201,X21,X202)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__compose) ).
fof(fact_listrel__iff__nth,axiom,
! [X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel(X7,X172)))
<=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X293)
& ! [X70] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),hAPP(hAPP(c_List_Onth(X7),X292),X70)),hAPP(hAPP(c_List_Onth(X7),X293),X70))),X172)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__iff__nth) ).
fof(fact_rel__pow__Suc__D2,axiom,
! [X191,X44,X26,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),hAPP(c_Nat_OSuc,X44)),X191)))
=> ? [X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X82)),X191))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__D2) ).
fof(fact_quotient__def,axiom,
! [X172,X149,X7] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X7),c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X7),c_Relation_OImage(X7,X7,X172)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__def) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(fact_Image__iff,axiom,
! [X149,X172,X105,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(c_Relation_OImage(X105,X7,X172),X149)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X3),X24)),X172)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__iff) ).
fof(fact_set__map__of__compr,axiom,
! [X292,X105,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X7),c_Product__Type_Ofst(X7,X105)),X292)))
=> hAPP(c_List_Oset(tc_prod(X7,X105)),X292) = hAPP(c_Set_OCollect(tc_prod(X7,X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_Option_Ooption(X105)),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X105),tc_HOL_Obool),tc_fun(tc_fun(X105,tc_Option_Ooption(X105)),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBB(tc_Option_Ooption(X105),tc_HOL_Obool,X105)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X105),tc_fun(tc_Option_Ooption(X105),tc_HOL_Obool),X7),c_fequal),c_Map_Omap__of(X7,X105,X292)))),c_Option_Ooption_OSome(X105)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__map__of__compr) ).
fof(fact_folding__one_Oclosed,axiom,
! [X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ! [X3,X82] : hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(X2,X3),X82)),hAPP(hAPP(c_Set_Oinsert(X7),X3),hAPP(hAPP(c_Set_Oinsert(X7),X82),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(X215,X149)),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oclosed) ).
fof(fact_quotient__diff1,axiom,
! [X25,X149,X172,X7] :
( c_Fun_Oinj__on(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X7),c_Equiv__Relations_Oquotient(X7)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X172),X149)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X172) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X172)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__diff1) ).
fof(fact_Collect__ball__eq,axiom,
! [X38,X149,X105,X7] : hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OAll(X105)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBS(X105,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X105),c_fimplies),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X149)))),X38))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),c_Set_OCollect(X7)),hAPP(c_COMBC(X7,X105,tc_HOL_Obool),X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__ball__eq) ).
fof(fact_sublist__append,axiom,
! [X149,X320,X157,X7] : c_List_Osublist(X7,hAPP(hAPP(c_List_Oappend(X7),X157),X320),X149) = hAPP(hAPP(c_List_Oappend(X7),c_List_Osublist(X7,X157,X149)),c_List_Osublist(X7,X320,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X157)))),X149)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__append) ).
fof(fact_map__filter__map__filter,axiom,
! [X292,X38,X2,X7,X105] : hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(c_List_Ofilter(X105,X38),X292)) = c_List_Omap__filter(X105,X7,hAPP(hAPP(c_COMBC(X105,tc_Option_Ooption(X7),tc_Option_Ooption(X7)),hAPP(hAPP(c_COMBS(X105,tc_Option_Ooption(X7),tc_fun(tc_Option_Ooption(X7),tc_Option_Ooption(X7))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X7),tc_fun(tc_Option_Ooption(X7),tc_Option_Ooption(X7))),X105),c_If(tc_Option_Ooption(X7))),X38)),hAPP(hAPP(c_COMBB(X7,tc_Option_Ooption(X7),X105),c_Option_Ooption_OSome(X7)),X2))),c_Option_Ooption_ONone(X7)),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__filter__map__filter) ).
fof(fact_card__quotient__disjoint,axiom,
! [X172,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( c_Fun_Oinj__on(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X7),c_Equiv__Relations_Oquotient(X7)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X172),X149)
=> hAPP(c_Finite__Set_Ocard(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)) = hAPP(c_Finite__Set_Ocard(X7),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__quotient__disjoint) ).
fof(fact_dom__if,axiom,
! [X1,X2,X38,X105,X7] : c_Map_Odom(X7,X105,hAPP(hAPP(c_COMBS(X7,tc_Option_Ooption(X105),tc_Option_Ooption(X105)),hAPP(hAPP(c_COMBS(X7,tc_Option_Ooption(X105),tc_fun(tc_Option_Ooption(X105),tc_Option_Ooption(X105))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X105),tc_fun(tc_Option_Ooption(X105),tc_Option_Ooption(X105))),X7),c_If(tc_Option_Ooption(X105))),X38)),X2)),X1)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Map_Odom(X7,X105,X2)),hAPP(c_Set_OCollect(X7),X38))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Map_Odom(X7,X105,X1)),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),X38)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__if) ).
fof(fact_map__filter__def,axiom,
! [X292,X2,X7,X105] : c_List_Omap__filter(X105,X7,X2,X292) = hAPP(hAPP(c_List_Omap(X105,X7),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X7),X7,X105,c_Option_Othe(X7)),X2)),hAPP(c_List_Ofilter(X105,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X105),c_fNot),hAPP(hAPP(c_COMBC(X105,tc_Option_Ooption(X7),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X7),tc_fun(tc_Option_Ooption(X7),tc_HOL_Obool),X105),c_fequal),X2)),c_Option_Ooption_ONone(X7)))),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__filter__def) ).
fof(fact_arith__series__general,axiom,
! [X44,X136,X25,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),c_Groups_Oone__class_Oone(X7)),c_Groups_Oone__class_Oone(X7))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(hAPP(c_COMBB(X7,X7,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X7),X25)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X7)),c_Nat_Osemiring__1__class_Oof__nat(X7))),X136))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X44))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X44)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X136)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__general) ).
fof(fact_dvd_OatLeastLessThan__empty,axiom,
! [X25,X24] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X25))
=> c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25,X24) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty) ).
fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
! [X94,X157] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X157),X94))
=> c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X94,X157) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty) ).
fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
! [X94,X157] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X157),X94))
=> c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X94,X157) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanLessThan__empty) ).
fof(fact_reduction__pair__def,axiom,
! [X38,X7] :
( c_FunDef_Oreduction__pair(X7,X38)
<=> ( c_Wellfounded_Owf(X7,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X38))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X38)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X38))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X38))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pair__def) ).
fof(fact_UN__subset__iff,axiom,
! [X155,X149,X211,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X211),X149)),X155))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X211))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(X149,X3)),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__subset__iff) ).
fof(fact_setsum__bounded,axiom,
! [X220,X2,X149,X7,X105] :
( ( class_Groups_Oordered__ab__semigroup__add(X105)
& class_Rings_Osemiring__1(X105) )
=> ( ! [X147] :
( hBOOL(hAPP(hAPP(c_member(X7),X147),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(X2,X147)),X220)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X105),hAPP(c_Finite__Set_Ocard(X7),X149))),X220))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__bounded) ).
fof(fact_map__pair__def,axiom,
! [X1,X2,X190,X105,X119,X7] : c_Product__Type_Omap__pair(X7,X119,X105,X190,X2,X1) = hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_prod(X119,X190)),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,X190),tc_fun(X105,tc_prod(X119,X190))),hAPP(hAPP(c_COMBB(tc_fun(X190,tc_prod(X119,X190)),tc_fun(tc_fun(X105,X190),tc_fun(X105,tc_prod(X119,X190))),X7),c_COMBB(X190,tc_prod(X119,X190),X105)),hAPP(hAPP(c_COMBB(X119,tc_fun(X190,tc_prod(X119,X190)),X7),c_Product__Type_OPair(X119,X190)),X2))),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__def) ).
fof(fact_decr__lemma,axiom,
! [X97,X86,X106] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X106))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X86),X97))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X106))),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decr__lemma) ).
fof(fact_SUP__le__iff,axiom,
! [X160,X210,X149,X105,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,X7),X149),X210)),X160))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X210,X3)),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__le__iff) ).
fof(fact_transfer__int__nat__numerals_I4_J,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).
fof(fact_transfer__nat__int__numerals_I4_J,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I4_J) ).
fof(fact_lexord__take__index__conv,axiom,
! [X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),X127)),c_List_Olexord(X7,X172)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X6)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X127)))
& hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X6)),X127) = X6 )
| ? [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X147),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X6)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X127))))
& hAPP(hAPP(c_List_Otake(X7),X147),X6) = hAPP(hAPP(c_List_Otake(X7),X147),X127)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),hAPP(hAPP(c_List_Onth(X7),X6),X147)),hAPP(hAPP(c_List_Onth(X7),X127),X147))),X172)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__take__index__conv) ).
fof(fact_pred__comp_Ointros,axiom,
! [X119,X105,X7,X23,X45,X24,X25,X172] :
( hBOOL(hAPP(hAPP(X172,X25),X24))
=> ( hBOOL(hAPP(hAPP(X45,X24),X23))
=> c_Predicate_Opred__comp(X7,X105,X119,X172,X45,X25,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
fof(fact_SetCompr__Sigma__eq,axiom,
! [X194,X38,X105,X7] : hAPP(c_Set_OCollect(tc_prod(X7,X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),X38))),X194))) = hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(c_Set_OCollect(X7),X38)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),c_Set_OCollect(X105)),X194)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetCompr__Sigma__eq) ).
fof(fact_card__less,axiom,
! [X107,X210] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X210))
=> hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X210))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X107))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less) ).
fof(fact_Eps__split__eq,axiom,
! [X127,X6,X105,X7] : c_Hilbert__Choice_OEps(tc_prod(X7,X105),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(c_fequal,X6)))),hAPP(c_fequal,X127)))) = hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Eps__split__eq) ).
fof(fact_The__split__eq,axiom,
! [X127,X6,X105,X7] : c_HOL_OThe(tc_prod(X7,X105),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(c_fequal,X6)))),hAPP(c_fequal,X127)))) = hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_The__split__eq) ).
fof(fact_setsum__commute,axiom,
! [X149,X155,X2,X119,X105,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBC(X105,tc_fun(X119,tc_HOL_Obool),X7),hAPP(hAPP(c_COMBB(tc_fun(X119,X7),tc_fun(tc_fun(X119,tc_HOL_Obool),X7),X105),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X119,X7)),X2)),X155)),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X119,X7),hAPP(hAPP(c_COMBC(X119,tc_fun(X105,tc_HOL_Obool),X7),hAPP(hAPP(c_COMBB(tc_fun(X105,X7),tc_fun(tc_fun(X105,tc_HOL_Obool),X7),X119),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7)),hAPP(c_COMBC(X105,X119,X7),X2))),X149)),X155) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__commute) ).
fof(fact_Collect__split,axiom,
! [X194,X38,X105,X7] : hAPP(c_Set_OCollect(tc_prod(X7,X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),X38))),X194))) = hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(c_Set_OCollect(X7),X38)),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Set_OCollect(X105),X194))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__split) ).
fof(fact_image__eq__fold__image,axiom,
! [X2,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Set_Oimage(X7,X105,X2),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X105,tc_HOL_Obool),X7,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X105,tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Set_Oinsert(X105)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__fold__image) ).
fof(fact_card__Diff2__less,axiom,
! [X127,X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X127),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X7),X127),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X7),X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff2__less) ).
fof(fact_Id__on__def_H,axiom,
! [X149,X7] : c_Relation_OId__on(X7,X149) = hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X7,tc_HOL_Obool)),X7),c_COMBC(X7,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj)),c_fequal))),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__def_H) ).
fof(fact_int__ge__less__than__def,axiom,
! [X136] : c_Int_Oint__ge__less__than(X136) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X136)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__ge__less__than__def) ).
fof(fact_scomp__scomp,axiom,
! [X200,X1,X2,X201,X189,X105,X190,X119,X7] : hAPP(hAPP(c_Product__Type_Oscomp(X7,X119,X190,X105),hAPP(hAPP(c_Product__Type_Oscomp(X7,X189,X201,tc_prod(X119,X190)),X2),X1)),X200) = hAPP(hAPP(c_Product__Type_Oscomp(X7,X189,X201,X105),X2),hAPP(hAPP(c_COMBC(X189,tc_fun(X119,tc_fun(X190,X105)),tc_fun(X201,X105)),hAPP(hAPP(c_COMBB(tc_fun(X201,tc_prod(X119,X190)),tc_fun(tc_fun(X119,tc_fun(X190,X105)),tc_fun(X201,X105)),X189),c_Product__Type_Oscomp(X201,X119,X190,X105)),X1)),X200)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__scomp) ).
fof(fact_wmax__insertI,axiom,
! [X237,X6,X236,X127] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X127),X236))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X127)),c_FunDef_Opair__leq))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X237),X236)),c_FunDef_Omax__weak))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X237)),X236)),c_FunDef_Omax__weak)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmax__insertI) ).
fof(fact_smax__insertI,axiom,
! [X39,X6,X60,X127] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X127),X60))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X127)),c_FunDef_Opair__less))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X39),X60)),c_FunDef_Omax__strict))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X39)),X60)),c_FunDef_Omax__strict)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__insertI) ).
fof(fact_sorted__map__same,axiom,
! [X292,X1,X2,X105,X7] :
( class_Orderings_Olinorder(X7)
=> c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(c_List_Ofilter(X105,hAPP(hAPP(c_COMBC(X105,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,tc_HOL_Obool),X105),c_fequal),X2)),hAPP(X1,X292))),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__map__same) ).
fof(fact_Loop,axiom,
! [X23,X24,X38,X216,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),c_Hoare__Mirabelle_Opeek__and(X7,X38,X24)),X23),X38)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X38),c_Com_Ocom_OWhile(X24,X23)),c_Hoare__Mirabelle_Opeek__and(X7,X38,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X24)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Loop) ).
fof(fact_max__ext_Osimps,axiom,
! [X191,X43,X42,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X42),X43)),c_Wellfounded_Omax__ext(X7,X191)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X42))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X43))
& X43 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X42))
=> ? [X206] :
( hBOOL(hAPP(hAPP(c_member(X7),X206),X43))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X206)),X191)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).
fof(fact_wf__union__merge,axiom,
! [X209,X191,X7] :
( c_Wellfounded_Owf(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X191),X209))
<=> c_Wellfounded_Owf(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X191),X191)),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X209),X191))),X209)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__union__merge) ).
fof(fact_map__pair__surj__on,axiom,
! [X263,X155,X1,X119,X190,X246,X149,X2,X7,X105] :
( hAPP(c_Set_Oimage(X105,X7,X2),X149) = X246
=> ( hAPP(c_Set_Oimage(X190,X119,X1),X155) = X263
=> hAPP(c_Set_Oimage(tc_prod(X105,X190),tc_prod(X7,X119),c_Product__Type_Omap__pair(X105,X7,X190,X119,X2,X1)),hAPP(hAPP(c_Product__Type_OSigma(X105,X190),X149),hAPP(c_COMBK(tc_fun(X190,tc_HOL_Obool),X105),X155))) = hAPP(hAPP(c_Product__Type_OSigma(X7,X119),X246),hAPP(c_COMBK(tc_fun(X119,tc_HOL_Obool),X7),X263)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__surj__on) ).
fof(fact_wmin__insertI,axiom,
! [X236,X127,X237,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X237))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X127)),c_FunDef_Opair__leq))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X237),X236)),c_FunDef_Omin__weak))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X237),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X127),X236))),c_FunDef_Omin__weak)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmin__insertI) ).
fof(fact_smin__insertI,axiom,
! [X236,X127,X237,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X237))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X127)),c_FunDef_Opair__less))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X237),X236)),c_FunDef_Omin__strict))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X237),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X127),X236))),c_FunDef_Omin__strict)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__insertI) ).
fof(fact_insert__fold1SetE,axiom,
! [X6,X39,X25,X2,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,X2,hAPP(hAPP(c_Set_Oinsert(X7),X25),X39)),X6))
=> ~ ! [X110,X239] :
( hAPP(hAPP(c_Set_Oinsert(X7),X25),X39) = hAPP(hAPP(c_Set_Oinsert(X7),X110),X239)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,X2,X110,X239),X6))
=> hBOOL(hAPP(hAPP(c_member(X7),X110),X239)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__fold1SetE) ).
fof(fact_listrel1__iff__update,axiom,
! [X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel1(X7,X172)))
<=> ? [X82,X70] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),hAPP(hAPP(c_List_Onth(X7),X292),X70)),X82)),X172))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
& X293 = hAPP(hAPP(c_List_Olist__update(X7,X292),X70),X82) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__iff__update) ).
fof(fact_map__pair__surj,axiom,
! [X1,X119,X190,X2,X7,X105] :
( hAPP(c_Set_Oimage(X105,X7,X2),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))
=> ( hAPP(c_Set_Oimage(X190,X119,X1),c_Orderings_Otop__class_Otop(tc_fun(X190,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X119,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(X105,X190),tc_prod(X7,X119),c_Product__Type_Omap__pair(X105,X7,X190,X119,X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X105,X190),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X7,X119),tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__surj) ).
fof(fact_minus__fold__remove,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X155),X149) = hAPP(hAPP(c_Finite__Set_Ofold(X7,tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X155),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__fold__remove) ).
fof(fact_map__of__mapk__SomeI,axiom,
! [X6,X94,X46,X119,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> ( hAPP(c_Map_Omap__of(X7,X119,X46),X94) = hAPP(c_Option_Ooption_OSome(X119),X6)
=> hAPP(c_Map_Omap__of(X105,X119,hAPP(hAPP(c_List_Omap(tc_prod(X7,X119),tc_prod(X105,X119)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X119,tc_prod(X105,X119)),hAPP(hAPP(c_COMBB(X105,tc_fun(X119,tc_prod(X105,X119)),X7),c_Product__Type_OPair(X105,X119)),X2))),X46)),hAPP(X2,X94)) = hAPP(c_Option_Ooption_OSome(X119),X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__mapk__SomeI) ).
fof(fact_fst__map__pair,axiom,
! [X6,X1,X2,X190,X119,X105,X7] : hAPP(c_Product__Type_Ofst(X7,X105),hAPP(c_Product__Type_Omap__pair(X119,X7,X190,X105,X2,X1),X6)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X119,X190),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__map__pair) ).
fof(fact_snd__prod__fun,axiom,
! [X6,X1,X2,X190,X119,X7,X105] : hAPP(c_Product__Type_Osnd(X105,X7),hAPP(c_Product__Type_Omap__pair(X119,X105,X190,X7,X2,X1),X6)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X119,X190),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__prod__fun) ).
fof(fact_lexord__linear,axiom,
! [X127,X6,X172,X7] :
( ! [X110,X188] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X110),X188)),X172))
| X110 = X188
| hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X188),X110)),X172)) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),X127)),c_List_Olexord(X7,X172)))
| X6 = X127
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X127),X6)),c_List_Olexord(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__linear) ).
fof(fact_add,axiom,
! [X163,X160,X127,X6] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X127)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X160),X163)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X160)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X127),X163))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add) ).
fof(fact_Id__on__def,axiom,
! [X149,X7] : c_Relation_OId__on(X7,X149) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X7),c_Set_Oinsert(tc_prod(X7,X7))),hAPP(hAPP(c_COMBS(X7,X7,tc_prod(X7,X7)),c_Product__Type_OPair(X7,X7)),c_COMBI(X7)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__def) ).
fof(fact_map__zip__map,axiom,
! [X293,X292,X1,X190,X2,X7,X119,X105] : hAPP(hAPP(c_List_Omap(tc_prod(X105,X119),X7),X2),hAPP(hAPP(c_List_Ozip(X105,X119),hAPP(hAPP(c_List_Omap(X190,X105),X1),X292)),X293)) = hAPP(hAPP(c_List_Omap(tc_prod(X190,X119),X7),hAPP(c_Product__Type_Oprod_Oprod__case(X190,X119,X7),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_prod(X105,X119)),tc_fun(X119,X7),X190),hAPP(c_COMBB(tc_prod(X105,X119),X7,X119),X2)),hAPP(hAPP(c_COMBB(X105,tc_fun(X119,tc_prod(X105,X119)),X190),c_Product__Type_OPair(X105,X119)),X1)))),hAPP(hAPP(c_List_Ozip(X190,X119),X292),X293)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__zip__map) ).
fof(fact_sublist__Cons,axiom,
! [X149,X157,X6,X7] : c_List_Osublist(X7,hAPP(hAPP(c_List_Olist_OCons(X7),X6),X157),X149) = hAPP(hAPP(c_List_Oappend(X7),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X7)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X149)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7))),c_List_Olist_ONil(X7))),c_List_Osublist(X7,X157,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X149)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__Cons) ).
fof(fact_dom__override__on,axiom,
! [X149,X1,X2,X105,X7] : c_Map_Odom(X7,X105,c_Fun_Ooverride__on(X7,tc_Option_Ooption(X105),X2,X1,X149)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),c_Map_Odom(X7,X105,X2)),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),c_Map_Odom(X7,X105,X1)))))),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),c_Map_Odom(X7,X105,X1))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__override__on) ).
fof(fact_nth__nth__transpose__sorted,axiom,
! [X158,X107,X292,X7] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X7))),X292)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),c_List_Otranspose(X7,X292))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X158),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),hAPP(c_List_Ofilter(tc_List_Olist(X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X7)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107)),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),X292))))
=> hAPP(hAPP(c_List_Onth(X7),hAPP(hAPP(c_List_Onth(tc_List_Olist(X7)),c_List_Otranspose(X7,X292)),X107)),X158) = hAPP(hAPP(c_List_Onth(X7),hAPP(hAPP(c_List_Onth(tc_List_Olist(X7)),X292),X158)),X107) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__nth__transpose__sorted) ).
fof(fact_INF__less__iff,axiom,
! [X25,X2,X149,X105,X7] :
( ( class_Complete__Lattice_Ocomplete__lattice(X7)
& class_Orderings_Olinorder(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,X7),X149),X2)),X25))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(X2,X3)),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__less__iff) ).
fof(fact_ball__UN,axiom,
! [X38,X155,X149,X105,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> hBOOL(hAPP(X38,X3)) )
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
=> ! [X206] :
( hBOOL(hAPP(hAPP(c_member(X7),X206),hAPP(X155,X3)))
=> hBOOL(hAPP(X38,X206)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__UN) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J) ).
fof(fact_max__ext__additive,axiom,
! [X192,X193,X191,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X149),X155)),c_Wellfounded_Omax__ext(X7,X191)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X193),X192)),c_Wellfounded_Omax__ext(X7,X191)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X193)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X192))),c_Wellfounded_Omax__ext(X7,X191))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__additive) ).
fof(fact_SigmaE,axiom,
! [X155,X149,X23,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),X23),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> ! [X82] :
( hBOOL(hAPP(hAPP(c_member(X105),X82),hAPP(X155,X3)))
=> X23 != hAPP(hAPP(c_Product__Type_OPair(X7,X105),X3),X82) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE) ).
fof(fact_foldl__map,axiom,
! [X292,X2,X119,X25,X1,X105,X7] : hAPP(c_List_Ofoldl(X7,X105,X1,X25),hAPP(hAPP(c_List_Omap(X119,X105),X2),X292)) = hAPP(c_List_Ofoldl(X7,X119,hAPP(hAPP(c_COMBC(X7,tc_fun(X119,X105),tc_fun(X119,X7)),hAPP(hAPP(c_COMBB(tc_fun(X105,X7),tc_fun(tc_fun(X119,X105),tc_fun(X119,X7)),X7),c_COMBB(X105,X7,X119)),X1)),X2),X25),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__map) ).
fof(fact_rel__comp__UNION__distrib2,axiom,
! [X45,X172,X211,X190,X105,X119,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X190,tc_fun(tc_prod(X7,X119),tc_HOL_Obool)),X211),X172)),X45) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X190,tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X211),hAPP(hAPP(c_COMBC(X190,tc_fun(tc_prod(X119,X105),tc_HOL_Obool),tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X7,X119),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X119,X105),tc_HOL_Obool),tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X190),c_Relation_Orel__comp(X7,X119,X105)),X172)),X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib2) ).
fof(fact_finite__Collect__disjI,axiom,
! [X194,X38,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fdisj),X38)),X194))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),X38)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),X194))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__disjI) ).
fof(fact_UN__equiv__class2,axiom,
! [X43,X42,X2,X119,X248,X249,X105,X250,X251,X7] :
( c_Equiv__Relations_Oequiv(X7,X251,X250)
=> ( c_Equiv__Relations_Oequiv(X105,X249,X248)
=> ( c_Equiv__Relations_Ocongruent2(X7,X105,tc_fun(X119,tc_HOL_Obool),X250,X248,X2)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X42),X251))
=> ( hBOOL(hAPP(hAPP(c_member(X105),X43),X249))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X119,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X250),hAPP(hAPP(c_Set_Oinsert(X7),X42),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(X119,tc_HOL_Obool)),tc_fun(X119,tc_HOL_Obool),X7),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X119,tc_HOL_Obool)),hAPP(c_Relation_OImage(X105,X105,X248),hAPP(hAPP(c_Set_Oinsert(X105),X43),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)))))),X2)) = hAPP(hAPP(X2,X42),X43) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class2) ).
fof(fact_length__sublist,axiom,
! [X211,X292,X7] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),c_List_Osublist(X7,X292,X211)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X211)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__sublist) ).
fof(fact_length__filter__conv__card,axiom,
! [X292,X161,X7] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(c_List_Ofilter(X7,X161),X292)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))),hAPP(hAPP(c_COMBB(X7,tc_HOL_Obool,tc_Nat_Onat),X161),hAPP(c_List_Onth(X7),X292))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__conv__card) ).
fof(fact_fold__image__distrib,axiom,
! [X200,X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),hAPP(hAPP(c_COMBS(X7,X105,X105),hAPP(hAPP(c_COMBB(X105,tc_fun(X105,X105),X7),c_Groups_Otimes__class_Otimes(X105)),X1)),X200)),c_Groups_Oone__class_Oone(X105)),X149) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),c_Groups_Oone__class_Oone(X105)),X149)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X200),c_Groups_Oone__class_Oone(X105)),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__distrib) ).
fof(fact_snoc__listrel1__snoc__iff,axiom,
! [X172,X127,X293,X6,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Oappend(X7),X292),hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7)))),hAPP(hAPP(c_List_Oappend(X7),X293),hAPP(hAPP(c_List_Olist_OCons(X7),X127),c_List_Olist_ONil(X7))))),c_List_Olistrel1(X7,X172)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel1(X7,X172)))
& X6 = X127 )
| ( X292 = X293
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
fof(fact_UN__finite2__eq,axiom,
! [X155,X94,X149,X7] :
( ! [X70] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X70)),X149) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X70),X94))),X155)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X149) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X155) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__eq) ).
fof(fact_max__ext_Ointros,axiom,
! [X191,X60,X39,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X39))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X60))
=> ( X60 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X39))
=> ? [X206] :
( hBOOL(hAPP(hAPP(c_member(X7),X206),X60))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X206)),X191)) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X39),X60)),c_Wellfounded_Omax__ext(X7,X191))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).
fof(fact_ran__def,axiom,
! [X95,X7,X105] : c_Map_Oran(X105,X7,X95) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X105)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X7),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBC(X105,tc_Option_Ooption(X7),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X7),tc_fun(tc_Option_Ooption(X7),tc_HOL_Obool),X105),c_fequal),X95))),c_Option_Ooption_OSome(X7)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__def) ).
fof(fact_wf__no__infinite__down__chainE,axiom,
! [X2,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ~ ! [X118] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),hAPP(X2,hAPP(c_Nat_OSuc,X118))),hAPP(X2,X118))),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__no__infinite__down__chainE) ).
fof(fact_wf__iff__no__infinite__down__chain,axiom,
! [X172,X7] :
( c_Wellfounded_Owf(X7,X172)
<=> ~ ? [X240] :
! [X147] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),hAPP(X240,hAPP(c_Nat_OSuc,X147))),hAPP(X240,X147))),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).
fof(fact_congruent2__implies__congruent__UN,axiom,
! [X25,X2,X119,X248,X249,X105,X250,X251,X7] :
( c_Equiv__Relations_Oequiv(X7,X251,X250)
=> ( c_Equiv__Relations_Oequiv(X105,X249,X248)
=> ( c_Equiv__Relations_Ocongruent2(X7,X105,tc_fun(X119,tc_HOL_Obool),X250,X248,X2)
=> ( hBOOL(hAPP(hAPP(c_member(X105),X25),X249))
=> c_Equiv__Relations_Ocongruent(X7,tc_fun(X119,tc_HOL_Obool),X250,hAPP(hAPP(c_COMBB(tc_fun(X105,tc_fun(X119,tc_HOL_Obool)),tc_fun(X119,tc_HOL_Obool),X7),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X119,tc_HOL_Obool)),hAPP(c_Relation_OImage(X105,X105,X248),hAPP(hAPP(c_Set_Oinsert(X105),X25),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)))))),X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2__implies__congruent__UN) ).
fof(fact_Diff1__fold__graph,axiom,
! [X127,X6,X149,X26,X2,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X127))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,X149),hAPP(hAPP(X2,X6),X127))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff1__fold__graph) ).
fof(fact_setsum__mono3,axiom,
! [X2,X149,X155,X7,X105] :
( ( class_Groups_Ocomm__monoid__add(X105)
& class_Groups_Oordered__ab__semigroup__add(X105) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X155),X149)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),c_Groups_Ozero__class_Ozero(X105)),hAPP(X2,X3))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X155))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono3) ).
fof(fact_setsum__mono2,axiom,
! [X2,X149,X155,X7,X105] :
( class_Groups_Oordered__comm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( ! [X188] :
( hBOOL(hAPP(hAPP(c_member(X7),X188),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X155),X149)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),c_Groups_Ozero__class_Ozero(X105)),hAPP(X2,X188))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X155))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono2) ).
fof(fact_INF__INT__eq,axiom,
! [X6,X172,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105))),X172)),X6))
<=> hBOOL(hAPP(hAPP(c_member(X105),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq) ).
fof(fact_SUP__UN__eq,axiom,
! [X6,X172,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105))),X172)),X6))
<=> hBOOL(hAPP(hAPP(c_member(X105),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq) ).
fof(fact_le__add__iff1,axiom,
! [X136,X24,X23,X156,X25,X7] :
( class_Rings_Oordered__ring(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X156)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X156)),X136)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X25),X24)),X156)),X23)),X136)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff1) ).
fof(fact_less__add__iff1,axiom,
! [X136,X24,X23,X156,X25,X7] :
( class_Rings_Oordered__ring(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X156)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X156)),X136)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X25),X24)),X156)),X23)),X136)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff1) ).
fof(fact_fold__graph_H_Ointros_I2_J,axiom,
! [X127,X26,X2,X105,X149,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( c_Nitpick_Ofold__graph_H(X7,X105,X2,X26,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X127)
=> c_Nitpick_Ofold__graph_H(X7,X105,X2,X26,X149,hAPP(hAPP(X2,X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
fof(fact_INT__subset__iff,axiom,
! [X149,X211,X105,X155,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X211),X149)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X211))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(X149,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__subset__iff) ).
fof(fact_zminus1__lemma,axiom,
! [X172,X153,X24,X25] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X24),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X153),X172)))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),X24),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X172),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X153)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X153)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X172),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24),X172))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus1__lemma) ).
fof(fact_INT__iff,axiom,
! [X155,X149,X105,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(X155,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__iff) ).
fof(fact_vimage__Times,axiom,
! [X155,X149,X2,X119,X105,X7] : hAPP(c_Set_Ovimage(X7,tc_prod(X105,X119),X2),hAPP(hAPP(c_Product__Type_OSigma(X105,X119),X149),hAPP(c_COMBK(tc_fun(X119,tc_HOL_Obool),X105),X155))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7,X105,hAPP(c_Fun_Ocomp(tc_prod(X105,X119),X105,X7,c_Product__Type_Ofst(X105,X119)),X2)),X149)),hAPP(c_Set_Ovimage(X7,X119,hAPP(c_Fun_Ocomp(tc_prod(X105,X119),X119,X7,c_Product__Type_Osnd(X105,X119)),X2)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Times) ).
fof(fact_in__lex__prod,axiom,
! [X45,X172,X112,X89,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X105),tc_prod(X7,X105))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X105),tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X89),X112))),c_Wellfounded_Olex__prod(X7,X105,X172,X45)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X89)),X172))
| ( X25 = X89
& hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X105)),hAPP(hAPP(c_Product__Type_OPair(X105,X105),X24),X112)),X45)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact_INF1__iff,axiom,
! [X24,X155,X149,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155),X24))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(X155,X3),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__iff) ).
fof(fact_finite__M__bounded__by__nat,axiom,
! [X107,X38] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),X38)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X107))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__M__bounded__by__nat) ).
fof(fact_incr__lemma,axiom,
! [X86,X97,X106] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X106))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X97),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X86),X97))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X106)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incr__lemma) ).
fof(fact_le__INF__iff,axiom,
! [X210,X149,X105,X160,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X160),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,X7),X149),X210)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X160),hAPP(X210,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__INF__iff) ).
fof(fact_setsum__nonneg__0,axiom,
! [X107,X2,X45,X7,X105] :
( class_Groups_Oordered__ab__group__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X45))
=> ( ! [X147] :
( hBOOL(hAPP(hAPP(c_member(X7),X147),X45))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),c_Groups_Ozero__class_Ozero(X105)),hAPP(X2,X147))) )
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X45) = c_Groups_Ozero__class_Ozero(X105)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X107),X45))
=> hAPP(X2,X107) = c_Groups_Ozero__class_Ozero(X105) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__nonneg__0) ).
fof(fact_the__inv__into__def,axiom,
! [X6,X2,X149,X105,X7] : hAPP(c_Fun_Othe__inv__into(X7,X105,X149,X2),X6) = c_HOL_OThe(X7,hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))),hAPP(hAPP(c_COMBC(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X105,tc_fun(X105,tc_HOL_Obool),X7),c_fequal),X2)),X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__def) ).
fof(fact_listrel1E,axiom,
! [X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel1(X7,X172)))
=> ~ ! [X3,X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X82)),X172))
=> ! [X319,X325] :
( X292 = hAPP(hAPP(c_List_Oappend(X7),X319),hAPP(hAPP(c_List_Olist_OCons(X7),X3),X325))
=> X293 != hAPP(hAPP(c_List_Oappend(X7),X319),hAPP(hAPP(c_List_Olist_OCons(X7),X82),X325)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1E) ).
fof(fact_setsum__Plus,axiom,
! [X2,X155,X105,X149,X7,X119] :
( class_Groups_Ocomm__monoid__add(X119)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(X7,X105),X119),X2),c_Sum__Type_OPlus(X7,X105,X149,X155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X119),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X119),hAPP(c_Fun_Ocomp(tc_sum(X7,X105),X119,X7,X2),c_Sum__Type_OInl(X7,X105))),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X119),hAPP(c_Fun_Ocomp(tc_sum(X7,X105),X119,X105,X2),c_Sum__Type_OInr(X105,X7))),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Plus) ).
fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
! [X127,X6,X149,X26,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,X149),X6))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,X149),X127))
=> X127 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).
fof(fact_listsum__subtractf,axiom,
! [X292,X1,X2,X105,X7] :
( class_Groups_Oab__group__add(X7)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),hAPP(hAPP(c_COMBS(X105,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),c_Groups_Ominus__class_Ominus(X7)),X2)),X1)),X292)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292))),hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),X1),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__subtractf) ).
fof(fact_listsum__addf,axiom,
! [X292,X1,X2,X105,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),hAPP(hAPP(c_COMBS(X105,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),c_Groups_Oplus__class_Oplus(X7)),X2)),X1)),X292)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292))),hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),X1),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__addf) ).
fof(fact_UN__Pow__subset,axiom,
! [X155,X149,X105,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),X105),c_Set_OPow(X7)),X155))),hAPP(c_Set_OPow(X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Pow__subset) ).
fof(fact_nat__le__add__iff1,axiom,
! [X44,X95,X160,X107,X158] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X158),X107))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X160)),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X158),X160)),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X107),X158)),X160)),X95)),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_nat__less__add__iff1,axiom,
! [X44,X95,X160,X107,X158] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X158),X107))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X160)),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X158),X160)),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X107),X158)),X160)),X95)),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_listsum__mult__const,axiom,
! [X292,X23,X2,X105,X7] :
( class_Rings_Osemiring__0(X7)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),hAPP(hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),c_Groups_Otimes__class_Otimes(X7)),X2)),X23)),X292)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292))),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__mult__const) ).
fof(fact_int__ge__less__than2__def,axiom,
! [X136] : c_Int_Oint__ge__less__than2(X136) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X136)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__ge__less__than2__def) ).
fof(fact_fold__image__Un__one,axiom,
! [X2,X238,X209,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X238))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X209),X238)))
=> hAPP(X2,X3) = c_Groups_Oone__class_Oone(X105) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X2),c_Groups_Oone__class_Oone(X105)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X209),X238)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X2),c_Groups_Oone__class_Oone(X105)),X209)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X2),c_Groups_Oone__class_Oone(X105)),X238)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__one) ).
fof(fact_inf__Int__eq,axiom,
! [X6,X209,X191,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X191)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X209)),X6))
<=> hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X191),X209))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
fof(fact_sup__Un__eq,axiom,
! [X6,X209,X191,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X191)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X209)),X6))
<=> hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X191),X209))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq) ).
fof(fact_insert__Collect,axiom,
! [X38,X25,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(c_Set_OCollect(X7),X38)) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25)))),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Collect) ).
fof(fact_equiv__class__nondisjoint,axiom,
! [X24,X25,X6,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__nondisjoint) ).
fof(fact_divmod__nat__rel__add1__eq,axiom,
! [X183,X184,X84,X185,X186,X10,X71] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X71,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X186),X185)))
=> ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X84,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X184),X183)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))
=> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X71),X84),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X186),X184)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X185),X183)),X10))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X185),X183),X10)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).
fof(fact_Random__Sequence_Omap__def,axiom,
! [X38,X2,X7,X105] : c_Random__Sequence_Omap(X105,X7,X2,X38) = c_Random__Sequence_Obind(X105,X7,X38,hAPP(c_Fun_Ocomp(X7,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X105,c_Random__Sequence_Osingle(X7)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Random__Sequence_Omap__def) ).
fof(fact_setprod__Un,axiom,
! [X2,X155,X149,X7,X105] :
( class_Fields_Ofield(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> hAPP(X2,X3) != c_Groups_Ozero__class_Ozero(X105) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X155))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un) ).
fof(fact_zadd1__lemma,axiom,
! [X183,X184,X84,X185,X186,X10,X71] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X186),X185)))
=> ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X184),X183)))
=> ( X10 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X186),X184)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X185),X183)),X10))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X185),X183),X10)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd1__lemma) ).
fof(fact_setprod__cartesian__product,axiom,
! [X149,X155,X2,X119,X105,X7] :
( class_Groups_Ocomm__monoid__mult(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X7),hAPP(hAPP(c_COMBC(X105,tc_fun(X119,tc_HOL_Obool),X7),hAPP(hAPP(c_COMBB(tc_fun(X119,X7),tc_fun(tc_fun(X119,tc_HOL_Obool),X7),X105),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X119,X7)),X2)),X155)),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X105,X119),X7),hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,X7),X2)),hAPP(hAPP(c_Product__Type_OSigma(X105,X119),X149),hAPP(c_COMBK(tc_fun(X119,tc_HOL_Obool),X105),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__cartesian__product) ).
fof(fact_setsum__cartesian__product,axiom,
! [X149,X155,X2,X119,X105,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBC(X105,tc_fun(X119,tc_HOL_Obool),X7),hAPP(hAPP(c_COMBB(tc_fun(X119,X7),tc_fun(tc_fun(X119,tc_HOL_Obool),X7),X105),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X119,X7)),X2)),X155)),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X105,X119),X7),hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,X7),X2)),hAPP(hAPP(c_Product__Type_OSigma(X105,X119),X149),hAPP(c_COMBK(tc_fun(X119,tc_HOL_Obool),X105),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cartesian__product) ).
fof(fact_map__pair__inj__on,axiom,
! [X155,X1,X190,X119,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( c_Fun_Oinj__on(X119,X190,X1,X155)
=> c_Fun_Oinj__on(tc_prod(X7,X119),tc_prod(X105,X190),c_Product__Type_Omap__pair(X7,X105,X119,X190,X2,X1),hAPP(hAPP(c_Product__Type_OSigma(X7,X119),X149),hAPP(c_COMBK(tc_fun(X119,tc_HOL_Obool),X7),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__inj__on) ).
fof(fact_divmod__nat__rel__mult1__eq,axiom,
! [X71,X138,X144,X10,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X84,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X144),X138)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))
=> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X71),X84),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X71),X144)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X71),X138)),X10))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X71),X138),X10)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).
fof(fact_lift__Suc__mono__less__iff,axiom,
! [X95,X44,X2,X7] :
( class_Orderings_Oorder(X7)
=> ( ! [X70] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(X2,X70)),hAPP(X2,hAPP(c_Nat_OSuc,X70))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(X2,X44)),hAPP(X2,X95)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X95)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lift__Suc__mono__less__iff) ).
fof(fact_lift__Suc__mono__less,axiom,
! [X126,X44,X2,X7] :
( class_Orderings_Oorder(X7)
=> ( ! [X70] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(X2,X70)),hAPP(X2,hAPP(c_Nat_OSuc,X70))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X126))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(X2,X44)),hAPP(X2,X126))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lift__Suc__mono__less) ).
fof(fact_ran__restrictD,axiom,
! [X149,X95,X105,X127,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X127),c_Map_Oran(X105,X7,c_Map_Orestrict__map(X105,X7,X95,X149))))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
& hAPP(X95,X3) = hAPP(c_Option_Ooption_OSome(X7),X127) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__restrictD) ).
fof(fact_zmult1__lemma,axiom,
! [X71,X138,X144,X10,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),X138)))
=> ( X10 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X84),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X144)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X138)),X10))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X138),X10)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult1__lemma) ).
fof(fact_Ex__inj__on__UNION__Sigma,axiom,
! [X149,X211,X105,X7] :
? [X240] :
( c_Fun_Oinj__on(X7,tc_prod(X105,X7),X240,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X211),X149))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X105,X7),tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,tc_prod(X105,X7),X240),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X211),X149))),hAPP(hAPP(c_Product__Type_OSigma(X105,X7),X211),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).
fof(fact_sublist__shift__lemma__Suc,axiom,
! [X335,X292,X38,X7] : hAPP(hAPP(c_List_Omap(tc_prod(X7,tc_Nat_Onat),X7),c_Product__Type_Ofst(X7,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X7,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X7,tc_Nat_Onat)),X38),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X7,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X7,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X7,tc_Nat_Onat),X292),X335))) = hAPP(hAPP(c_List_Omap(tc_prod(X7,tc_Nat_Onat),X7),c_Product__Type_Ofst(X7,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X7,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X7,tc_Nat_Onat)),X38),c_Product__Type_Osnd(X7,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X7,tc_Nat_Onat),X292),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X335)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__shift__lemma__Suc) ).
fof(fact_fst__comp__map__pair,axiom,
! [X1,X2,X105,X7,X190,X119] : hAPP(c_Fun_Ocomp(tc_prod(X119,X190),X119,tc_prod(X7,X105),c_Product__Type_Ofst(X119,X190)),c_Product__Type_Omap__pair(X7,X119,X105,X190,X2,X1)) = hAPP(c_Fun_Ocomp(X7,X119,tc_prod(X7,X105),X2),c_Product__Type_Ofst(X7,X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__comp__map__pair) ).
fof(fact_snd__comp__map__pair,axiom,
! [X1,X2,X105,X7,X119,X190] : hAPP(c_Fun_Ocomp(tc_prod(X190,X119),X119,tc_prod(X7,X105),c_Product__Type_Osnd(X190,X119)),c_Product__Type_Omap__pair(X7,X190,X105,X119,X2,X1)) = hAPP(c_Fun_Ocomp(X105,X119,tc_prod(X7,X105),X1),c_Product__Type_Osnd(X7,X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__comp__map__pair) ).
fof(fact_INT__extend__simps_I9_J,axiom,
! [X193,X155,X119,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(X105,tc_fun(X119,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_HOL_Obool),tc_fun(tc_fun(X119,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),X105),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X7,tc_HOL_Obool))),X155)),X193)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X119,tc_HOL_Obool)),X149),X155)),X193),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I9_J) ).
fof(fact_UN__extend__simps_I9_J,axiom,
! [X193,X155,X119,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(X105,tc_fun(X119,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X119,tc_HOL_Obool),tc_fun(tc_fun(X119,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),X105),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool))),X155)),X193)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X119,tc_HOL_Obool)),X149),X155)),X193),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I9_J) ).
fof(fact_INT__simps_I9_J,axiom,
! [X193,X155,X149,X119,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X105,tc_HOL_Obool)),X149),X155)),X193) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(X119,tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),X119),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool))),X155)),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I9_J) ).
fof(fact_UN__UN__flatten,axiom,
! [X193,X155,X149,X119,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X105,tc_HOL_Obool)),X149),X155)),X193) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(X119,tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),X119),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool))),X155)),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__flatten) ).
fof(fact_UN__simps_I9_J,axiom,
! [X193,X155,X149,X119,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X105,tc_HOL_Obool)),X149),X155)),X193) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(X119,tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),X119),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool))),X155)),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I9_J) ).
fof(fact_congruent2D,axiom,
! [X253,X254,X255,X256,X2,X248,X250,X119,X105,X7] :
( c_Equiv__Relations_Ocongruent2(X7,X105,X119,X250,X248,X2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X256),X255)),X250))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X105)),hAPP(hAPP(c_Product__Type_OPair(X105,X105),X254),X253)),X248))
=> hAPP(hAPP(X2,X256),X254) = hAPP(hAPP(X2,X255),X253) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2D) ).
fof(fact_Int__Collect__mono,axiom,
! [X194,X38,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> ( hBOOL(hAPP(X38,X3))
=> hBOOL(hAPP(X194,X3)) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Set_OCollect(X7),X38))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(c_Set_OCollect(X7),X194)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect__mono) ).
fof(fact_map__upds__append1,axiom,
! [X6,X95,X293,X105,X292,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)))
=> c_Map_Omap__upds(X7,X105,X95,hAPP(hAPP(c_List_Oappend(X7),X292),hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7))),X293) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Omap__upds(X7,X105,X95,X292,X293)),X6),hAPP(c_Option_Ooption_OSome(X105),hAPP(hAPP(c_List_Onth(X105),X293),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__append1) ).
fof(fact_UN__finite__subset,axiom,
! [X193,X149,X7] :
( ! [X70] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X70)),X149)),X193))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X149)),X193)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite__subset) ).
fof(fact_set__diff__eq,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__diff__eq) ).
fof(fact_finite__Collect__conjI,axiom,
! [X194,X38,X7] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),X38)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),X194))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),X38)),X194)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__conjI) ).
fof(fact_evalc_Oequations_I3_J,axiom,
! [X61,X43,X42,X47,X41] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X41,X47,X42)),X43),hAPP(hAPP(hAPP(c_Natural_Oupdate,X61),c_Com_Ovname_OLoc(X41)),hAPP(hAPP(c_Natural_Ogetlocs,X43),X41))))
<=> ? [X62] :
( hAPP(hAPP(hAPP(c_Natural_Oupdate,X61),c_Com_Ovname_OLoc(X41)),hAPP(hAPP(c_Natural_Ogetlocs,X43),X41)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,X62),c_Com_Ovname_OLoc(X41)),hAPP(hAPP(c_Natural_Ogetlocs,X43),X41))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X42),hAPP(hAPP(hAPP(c_Natural_Oupdate,X43),c_Com_Ovname_OLoc(X41)),hAPP(X47,X43))),X62)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I3_J) ).
fof(fact_UN__UN__finite__eq,axiom,
! [X149,X7] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X149)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__finite__eq) ).
fof(fact_map__pair__simp,axiom,
! [X24,X25,X1,X2,X105,X190,X7,X119] : hAPP(c_Product__Type_Omap__pair(X119,X7,X190,X105,X2,X1),hAPP(hAPP(c_Product__Type_OPair(X119,X190),X25),X24)) = hAPP(hAPP(c_Product__Type_OPair(X7,X105),hAPP(X2,X25)),hAPP(X1,X24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__simp) ).
fof(fact_map__pair__ident,axiom,
! [X26,X105,X7] : hAPP(c_Product__Type_Omap__pair(X7,X7,X105,X105,c_COMBI(X7),c_COMBI(X105)),X26) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__ident) ).
fof(fact_aset_I9_J,axiom,
! [X46,X149,X192,X136] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),X192))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X149))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X207),X206) ) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X46)))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X192)),X46))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I9_J) ).
fof(fact_bset_I9_J,axiom,
! [X46,X155,X192,X136] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),X192))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X155))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X207),X206) ) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X46)))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X192)),X46))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I9_J) ).
fof(fact_folding__image__simple_Ounion__inter,axiom,
! [X155,X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155))
=> hAPP(hAPP(X2,hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),X155))),hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(X2,hAPP(X215,X149)),hAPP(X215,X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).
fof(fact_setprod__Un__one,axiom,
! [X2,X238,X209,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X238))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X209),X238)))
=> hAPP(X2,X3) = c_Groups_Oone__class_Oone(X105) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X209),X238)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X209)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X238)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__one) ).
fof(fact_setprod_Ounion__inter__neutral,axiom,
! [X1,X155,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> hAPP(X1,X3) = c_Groups_Oone__class_Oone(X105) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).
fof(fact_setsum_Ounion__inter__neutral,axiom,
! [X1,X155,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> hAPP(X1,X3) = c_Groups_Ozero__class_Ozero(X105) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).
fof(fact_setsum__Un__zero,axiom,
! [X2,X238,X209,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X238))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X209),X238)))
=> hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X105) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X209),X238)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X209)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X238)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__zero) ).
fof(fact_Image__singleton,axiom,
! [X25,X172,X7,X105] : hAPP(c_Relation_OImage(X105,X7,X172),hAPP(hAPP(c_Set_Oinsert(X105),X25),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X105,X7),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X105,X7),tc_fun(tc_fun(tc_prod(X105,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X105,X7))),hAPP(c_Product__Type_OPair(X105,X7),X25))),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton) ).
fof(fact_folding__image__simple_Oremove,axiom,
! [X6,X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X105),X6),X149))
=> hAPP(X215,X149) = hAPP(hAPP(X2,hAPP(X1,X6)),hAPP(X215,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X105),X6),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oremove) ).
fof(fact_subset__image__iff,axiom,
! [X149,X2,X105,X155,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(c_Set_Oimage(X105,X7,X2),X149)))
<=> ? [X208] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),X208),X149))
& X155 = hAPP(c_Set_Oimage(X105,X7,X2),X208) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_UN__iff,axiom,
! [X155,X149,X105,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
& hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(X155,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__iff) ).
fof(fact_folding__image__simple_Oinsert__remove,axiom,
! [X6,X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X105),X6),X149)) = hAPP(hAPP(X2,hAPP(X1,X6)),hAPP(X215,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X105),X6),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).
fof(fact_the__inv__into__comp,axiom,
! [X6,X149,X1,X119,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,hAPP(c_Set_Oimage(X119,X7,X1),X149))
=> ( c_Fun_Oinj__on(X119,X7,X1,X149)
=> ( hBOOL(hAPP(hAPP(c_member(X105),X6),hAPP(c_Set_Oimage(X7,X105,X2),hAPP(c_Set_Oimage(X119,X7,X1),X149))))
=> hAPP(c_Fun_Othe__inv__into(X119,X105,X149,hAPP(c_Fun_Ocomp(X7,X105,X119,X2),X1)),X6) = hAPP(hAPP(c_Fun_Ocomp(X7,X119,X105,c_Fun_Othe__inv__into(X119,X7,X149,X1)),c_Fun_Othe__inv__into(X7,X105,hAPP(c_Set_Oimage(X119,X7,X1),X149),X2)),X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__comp) ).
fof(fact_setprod__mono__one__right,axiom,
! [X2,X209,X238,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X238))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X209),X238))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X238),X209)))
=> hAPP(X2,X3) = c_Groups_Oone__class_Oone(X105) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X238) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X209) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__mono__one__right) ).
fof(fact_setprod__mono__one__left,axiom,
! [X2,X209,X238,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X238))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X209),X238))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X238),X209)))
=> hAPP(X2,X3) = c_Groups_Oone__class_Oone(X105) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X209) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X238) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__mono__one__left) ).
fof(fact_setsum__mono__zero__left,axiom,
! [X2,X209,X238,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X238))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X209),X238))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X238),X209)))
=> hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X105) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X209) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X238) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono__zero__left) ).
fof(fact_setsum__mono__zero__right,axiom,
! [X2,X209,X238,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X238))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X209),X238))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X238),X209)))
=> hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X105) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X238) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X209) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono__zero__right) ).
fof(fact_SUP1__iff,axiom,
! [X24,X155,X149,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155),X24))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& hBOOL(hAPP(hAPP(X155,X3),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__iff) ).
fof(fact_rtrancl__imp__UN__rel__pow,axiom,
! [X191,X161,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),c_Transitive__Closure_Ortrancl(X7,X191)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool)),X191)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).
fof(fact_Int__Inter__image,axiom,
! [X155,X149,X193,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBS(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_Oimage(X105,tc_fun(X7,tc_HOL_Obool),X149),X193))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_Oimage(X105,tc_fun(X7,tc_HOL_Obool),X155),X193))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Inter__image) ).
fof(fact_Un__Union__image,axiom,
! [X155,X149,X193,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBS(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_Oimage(X105,tc_fun(X7,tc_HOL_Obool),X149),X193))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_Oimage(X105,tc_fun(X7,tc_HOL_Obool),X155),X193))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Union__image) ).
fof(fact_lexord__append__left__rightI,axiom,
! [X127,X6,X160,X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Oappend(X7),X160),hAPP(hAPP(c_List_Olist_OCons(X7),X25),X6))),hAPP(hAPP(c_List_Oappend(X7),X160),hAPP(hAPP(c_List_Olist_OCons(X7),X24),X127)))),c_List_Olexord(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).
fof(fact_intrel__iff,axiom,
! [X163,X160,X127,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X127)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X160),X163))),c_Int_Ointrel))
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X163) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X160),X127) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_intrel__iff) ).
fof(fact_same__fstI,axiom,
! [X7,X191,X127,X234,X105,X6,X38] :
( hBOOL(hAPP(X38,X6))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X105)),hAPP(hAPP(c_Product__Type_OPair(X105,X105),X234),X127)),hAPP(X191,X6)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X105),tc_prod(X7,X105))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X105),tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X234)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127))),c_Recdef_Osame__fst(X7,X105,X38,X191))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_less__SUP__iff,axiom,
! [X2,X149,X105,X25,X7] :
( ( class_Complete__Lattice_Ocomplete__lattice(X7)
& class_Orderings_Olinorder(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,X7),X149),X2)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),hAPP(X2,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SUP__iff) ).
fof(fact_split__twice,axiom,
! [X161,X1,X189,X190,X2,X7,X119,X105] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,X7),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X190,X189,tc_prod(X105,X119)),X1),X161)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X190,X189,X7),hAPP(hAPP(c_COMBB(tc_fun(X189,tc_prod(X105,X119)),tc_fun(X189,X7),X190),hAPP(c_COMBB(tc_prod(X105,X119),X7,X189),hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,X7),X2))),X1)),X161),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__twice) ).
fof(fact_list__size__pointwise,axiom,
! [X1,X2,X292,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X292)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X3)),hAPP(X1,X3))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X7,X2,X292)),c_List_Olist_Olist__size(X7,X1,X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__pointwise) ).
fof(fact_inj__graph,axiom,
! [X105,X7] : c_Fun_Oinj__on(tc_fun(X7,X105),tc_fun(tc_prod(X7,X105),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X7,X105)),c_Set_OCollect(tc_prod(X7,X105))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X105,tc_HOL_Obool)),tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X7,X105)),c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool)),hAPP(c_COMBB(X105,tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBC(X105,X105,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X7,X105),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__graph) ).
fof(fact_numeral__3__eq__3,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(fact_max__extp_Oequations,axiom,
! [X43,X42,X191,X7] :
( c_Wellfounded_Omax__extp(X7,X191,X42,X43)
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X42))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X43))
& X43 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X42))
=> ? [X206] :
( hBOOL(hAPP(hAPP(c_member(X7),X206),X43))
& hBOOL(hAPP(hAPP(X191,X3),X206)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).
fof(fact_Int__def,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__def) ).
fof(fact_Un__def,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fdisj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__def) ).
fof(fact_folding__image__simple_Ounion__disjoint,axiom,
! [X155,X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))
=> hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(X2,hAPP(X215,X149)),hAPP(X215,X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).
fof(fact_fun__upd__restrict__conv,axiom,
! [X127,X95,X105,X192,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X192))
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Orestrict__map(X7,X105,X95,X192)),X6),X127) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Orestrict__map(X7,X105,X95,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X192),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),X6),X127) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__restrict__conv) ).
fof(fact_le__add__iff2,axiom,
! [X136,X24,X23,X156,X25,X7] :
( class_Rings_Oordered__ring(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X156)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X156)),X136)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X24),X25)),X156)),X136))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff2) ).
fof(fact_less__add__iff2,axiom,
! [X136,X24,X23,X156,X25,X7] :
( class_Rings_Oordered__ring(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X156)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X156)),X136)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X24),X25)),X156)),X136))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(fact_Image__INT__subset,axiom,
! [X155,X149,X119,X172,X105,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X105,X7,X172),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X105,tc_HOL_Obool)),X149),X155))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X119),c_Relation_OImage(X105,X7,X172)),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__INT__subset) ).
fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
! [X155,X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple__idem(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(X2,hAPP(X215,X155)),hAPP(X215,X149)) = hAPP(X215,X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X7,X105] :
( class_Orderings_Oord(X105)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X105)),X2),X1))
<=> ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(X2,X3)),hAPP(X1,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_fun__upd__restrict,axiom,
! [X127,X6,X192,X95,X105,X7] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Orestrict__map(X7,X105,X95,X192)),X6),X127) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Orestrict__map(X7,X105,X95,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X192),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),X6),X127),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__restrict) ).
fof(fact_folding__image__simple_Oeq__fold__g,axiom,
! [X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> hAPP(X215,X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X105,X2),X1),X26),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
fof(fact_map__eq__conv,axiom,
! [X1,X292,X2,X7,X105] :
( hAPP(hAPP(c_List_Omap(X105,X7),X2),X292) = hAPP(hAPP(c_List_Omap(X105,X7),X1),X292)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),hAPP(c_List_Oset(X105),X292)))
=> hAPP(X2,X3) = hAPP(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__eq__conv) ).
fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
! [X155,X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple__idem(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155))
=> hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(X2,hAPP(X215,X149)),hAPP(X215,X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).
fof(fact_congruent2__implies__congruent,axiom,
! [X25,X2,X248,X119,X105,X250,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X250)
=> ( c_Equiv__Relations_Ocongruent2(X7,X105,X119,X250,X248,X2)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> c_Equiv__Relations_Ocongruent(X105,X119,X248,hAPP(X2,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2__implies__congruent) ).
fof(fact_append__eq__append__conv2,axiom,
! [X223,X302,X293,X292,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X292),X293) = hAPP(hAPP(c_List_Oappend(X7),X302),X223)
<=> ? [X319] :
( ( X292 = hAPP(hAPP(c_List_Oappend(X7),X302),X319)
& hAPP(hAPP(c_List_Oappend(X7),X319),X293) = X223 )
| ( hAPP(hAPP(c_List_Oappend(X7),X292),X319) = X302
& X293 = hAPP(hAPP(c_List_Oappend(X7),X319),X223) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
fof(fact_inj__on__iff__card__le,axiom,
! [X155,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155))
=> ( ? [X240] :
( c_Fun_Oinj__on(X7,X105,X240,X149)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X240),X149)),X155)) )
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X105),X155))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
fof(fact_folding__image__simple__idem_Oin__idem,axiom,
! [X6,X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple__idem(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X105),X6),X149))
=> hAPP(hAPP(X2,hAPP(X1,X6)),hAPP(X215,X149)) = hAPP(X215,X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
! [X6,X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple__idem(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X105),X6),X149)) = hAPP(hAPP(X2,hAPP(X1,X6)),hAPP(X215,X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
fof(fact_INT__Int__distrib,axiom,
! [X155,X149,X211,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X211),hAPP(hAPP(c_COMBS(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X211),X149)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X211),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Int__distrib) ).
fof(fact_UN__Un__distrib,axiom,
! [X155,X149,X211,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X211),hAPP(hAPP(c_COMBS(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X211),X149)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X211),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un__distrib) ).
fof(fact_folding__image__simple_Oempty,axiom,
! [X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple(X7,X105,X2,X26,X1,X215)
=> hAPP(X215,c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oempty) ).
fof(fact_folding__image__simple__idem_Oidem,axiom,
! [X6,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple__idem(X7,X105,X2,X26,X1,X215)
=> hAPP(hAPP(X2,X6),X6) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
fof(fact_smax__emptyI,axiom,
! [X60] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X60))
=> ( X60 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X60)),c_FunDef_Omax__strict)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__emptyI) ).
fof(fact_set__filter,axiom,
! [X292,X38,X7] : hAPP(c_List_Oset(X7),hAPP(c_List_Ofilter(X7,X38),X292)) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),hAPP(c_List_Oset(X7),X292)))),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__filter) ).
fof(fact_sum__diff__distrib,axiom,
! [X44,X38,X194] :
( ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X194,X3)),hAPP(X38,X3)))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X38),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X44))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X194),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X44))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X38)),X194)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__diff__distrib) ).
fof(fact_inj__on__iff__surj,axiom,
! [X246,X105,X7,X149] :
( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ? [X240] :
( c_Fun_Oinj__on(X7,X105,X240,X149)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X240),X149)),X246)) )
<=> ? [X260] : hAPP(c_Set_Oimage(X105,X7,X260),X246) = X149 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).
fof(fact_Range__iff,axiom,
! [X172,X105,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Relation_ORange(X105,X7),X172)))
<=> ? [X82] : hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X82),X25)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__iff) ).
fof(fact_wmax__emptyI,axiom,
! [X39] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X39))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X39)),c_FunDef_Omax__weak)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmax__emptyI) ).
fof(fact_INT__simps_I1_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) = c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)) )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),X149)),X155) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I1_J) ).
fof(fact_INT__simps_I3_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) = c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)) )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),X149)),X155) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I3_J) ).
fof(fact_UN__simps_I2_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X149)),X155) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I2_J) ).
fof(fact_INT__extend__simps_I1_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),X149)),X155) = X155 )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),X149)),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I1_J) ).
fof(fact_UN__extend__simps_I2_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X149)),X155) = X155 )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X149)),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I2_J) ).
fof(fact_INT__extend__simps_I3_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),X149)),X155) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))),X155) )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),X149)),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I3_J) ).
fof(fact_INT__simps_I6_J,axiom,
! [X155,X149,X193,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),X149)),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I6_J) ).
fof(fact_UN__simps_I4_J,axiom,
! [X155,X149,X193,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),X149)),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I4_J) ).
fof(fact_UN__simps_I6_J,axiom,
! [X155,X149,X193,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),X149)),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I6_J) ).
fof(fact_UN__extend__simps_I4_J,axiom,
! [X155,X149,X193,X105,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),X149)),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool))),X149)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I4_J) ).
fof(fact_INT__extend__simps_I6_J,axiom,
! [X155,X149,X193,X105,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),X149)),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool))),X149)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I6_J) ).
fof(fact_UN__extend__simps_I6_J,axiom,
! [X155,X149,X193,X105,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),X149)),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBC(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool))),X149)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I6_J) ).
fof(fact_rel__comp__subset__Sigma,axiom,
! [X193,X45,X119,X155,X149,X172,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X172),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X155))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X105,X119),tc_HOL_Obool)),X45),hAPP(hAPP(c_Product__Type_OSigma(X105,X119),X155),hAPP(c_COMBK(tc_fun(X119,tc_HOL_Obool),X105),X193))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X119),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X105,X119),X172),X45)),hAPP(hAPP(c_Product__Type_OSigma(X7,X119),X149),hAPP(c_COMBK(tc_fun(X119,tc_HOL_Obool),X7),X193)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__subset__Sigma) ).
fof(fact_Cons__listrel1__Cons,axiom,
! [X172,X293,X127,X292,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X293))),c_List_Olistrel1(X7,X172)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172))
& X292 = X293 )
| ( X6 = X127
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel1(X7,X172))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).
fof(fact_lexord__cons__cons,axiom,
! [X172,X127,X24,X6,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X25),X6)),hAPP(hAPP(c_List_Olist_OCons(X7),X24),X127))),c_List_Olexord(X7,X172)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172))
| ( X25 = X24
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),X127)),c_List_Olexord(X7,X172))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).
fof(fact_Cons__in__lex,axiom,
! [X172,X293,X127,X292,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X293))),c_List_Olex(X7,X172)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172))
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X293) )
| ( X6 = X127
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olex(X7,X172))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__in__lex) ).
fof(fact_Sigma__Int__distrib2,axiom,
! [X155,X149,X211,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),hAPP(hAPP(c_COMBS(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),X149)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).
fof(fact_Sigma__Un__distrib2,axiom,
! [X155,X149,X211,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),hAPP(hAPP(c_COMBS(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),X149)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).
fof(fact_Sigma__Diff__distrib2,axiom,
! [X155,X149,X211,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),hAPP(hAPP(c_COMBS(X7,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),X7),c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool))),X149)),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),X149)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib2) ).
fof(fact_abs__diff__triangle__ineq,axiom,
! [X106,X10,X84,X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X106)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X10))),hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X84),X106))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).
fof(fact_nat__le__add__iff2,axiom,
! [X44,X95,X160,X158,X107] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X158))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X160)),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X158),X160)),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X158),X107)),X160)),X44))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_nat__less__add__iff2,axiom,
! [X44,X95,X160,X158,X107] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X158))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X160)),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X158),X160)),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X158),X107)),X160)),X44))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
fof(fact_folding__image_Odistrib,axiom,
! [X200,X1,X149,X215,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image(X7,X105,X2,X26,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> hAPP(hAPP(X215,hAPP(hAPP(c_COMBS(X105,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),X2),X1)),X200)),X149) = hAPP(hAPP(X2,hAPP(hAPP(X215,X1),X149)),hAPP(hAPP(X215,X200),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Odistrib) ).
fof(fact_fold__image__Un__Int,axiom,
! [X1,X155,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),c_Groups_Oone__class_Oone(X105)),X149)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),c_Groups_Oone__class_Oone(X105)),X155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),c_Groups_Oone__class_Oone(X105)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),c_Groups_Oone__class_Oone(X105)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__Int) ).
fof(fact_arith__series__nat,axiom,
! [X44,X136,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X136))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X44))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X136)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__nat) ).
fof(fact_Un__Int__crazy,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X193),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X193))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X193),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).
fof(fact_evalc_OCall,axiom,
! [X39,X58,X25,X77,X40] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X40)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X77),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X25,X77))),X58))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X39,X40,X25)),X77),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X58),hAPP(c_Natural_Ogetlocs,X77))),X39),hAPP(hAPP(c_Natural_Ogetlocs,X58),c_Com_ORes)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OCall) ).
fof(fact_rtrancl__listrel1__ConsI2,axiom,
! [X293,X292,X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X7),c_List_Olistrel1(X7,X172))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X293))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X7),c_List_Olistrel1(X7,X172)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
fof(fact_image__diff__subset,axiom,
! [X155,X149,X2,X105,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X7,X2),X149)),hAPP(c_Set_Oimage(X105,X7,X2),X155))),hAPP(c_Set_Oimage(X105,X7,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),X149),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__diff__subset) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
! [X38] : hAPP(c_Set_OCollect(tc_Nat_Onat),X38) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X38),c_Int_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).
fof(fact_lenlex__def,axiom,
! [X172,X7] : c_List_Olenlex(X7,X172) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X7)),tc_List_Olist(X7)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X7),c_Wellfounded_Oless__than,c_List_Olex(X7,X172))),hAPP(hAPP(c_COMBS(tc_List_Olist(X7),tc_List_Olist(X7),tc_prod(tc_Nat_Onat,tc_List_Olist(X7))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X7),tc_prod(tc_Nat_Onat,tc_List_Olist(X7))),tc_List_Olist(X7)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X7))),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),c_COMBI(tc_List_Olist(X7)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lenlex__def) ).
fof(fact_refl__onI,axiom,
! [X149,X172,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),hAPP(hAPP(c_Product__Type_OSigma(X7,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),X149))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),X172)) )
=> c_Relation_Orefl__on(X7,X149,X172) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onI) ).
fof(fact_refl__on__def,axiom,
! [X172,X149,X7] :
( c_Relation_Orefl__on(X7,X149,X172)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),hAPP(hAPP(c_Product__Type_OSigma(X7,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),X149))))
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),X172)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def) ).
fof(fact_map__of__map__keys,axiom,
! [X95,X105,X292,X7] :
( hAPP(c_List_Oset(X7),X292) = c_Map_Odom(X7,X105,X95)
=> c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Omap(X7,tc_prod(X7,X105)),hAPP(hAPP(c_COMBS(X7,X105,tc_prod(X7,X105)),c_Product__Type_OPair(X7,X105)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X105),X105,X7),c_Option_Othe(X105)),X95))),X292)) = X95 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__map__keys) ).
fof(fact_insert__compr__raw,axiom,
! [X155,X25,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X25),X155) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fdisj),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__compr__raw) ).
fof(fact_insert__compr,axiom,
! [X155,X25,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X25),X155) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fdisj),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__compr) ).
fof(fact_listrel_OCons,axiom,
! [X293,X292,X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X293))),c_List_Olistrel(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel_OCons) ).
fof(fact_dom__def,axiom,
! [X95,X105,X7] : c_Map_Odom(X7,X105,X95) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),hAPP(hAPP(c_COMBC(X7,tc_Option_Ooption(X105),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X105),tc_fun(tc_Option_Ooption(X105),tc_HOL_Obool),X7),c_fequal),X95)),c_Option_Ooption_ONone(X105)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__def) ).
fof(fact_smin__emptyI,axiom,
! [X39] :
( X39 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X39),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__emptyI) ).
fof(fact_minus,axiom,
! [X127,X6] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X127)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X127),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus) ).
fof(fact_wmin__emptyI,axiom,
! [X39] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X39),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmin__emptyI) ).
fof(fact_fun__left__comm_Ofold__equality,axiom,
! [X127,X149,X26,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,X149),X127))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),X149) = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).
fof(fact_empty__fold__graphE,axiom,
! [X6,X26,X2,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X6))
=> X6 = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold__graphE) ).
fof(fact_subset__equiv__class,axiom,
! [X25,X24,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X24),X149))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__equiv__class) ).
fof(fact_ord_OatLeastLessThan__iff,axiom,
! [X160,X157,X219,X218,X107,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X107),c_SetInterval_Oord_OatLeastLessThan(X7,X218,X219,X157,X160)))
<=> ( hBOOL(hAPP(hAPP(X218,X157),X107))
& hBOOL(hAPP(hAPP(X219,X107),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
fof(fact_ord_OgreaterThanAtMost__iff,axiom,
! [X160,X157,X219,X218,X107,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X107),c_SetInterval_Oord_OgreaterThanAtMost(X7,X218,X219,X157,X160)))
<=> ( hBOOL(hAPP(hAPP(X219,X157),X107))
& hBOOL(hAPP(hAPP(X218,X107),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
! [X1,X2,X155,X149,X7] :
( ( class_Groups_Ocomm__monoid__add(X7)
& class_Groups_Ocomm__monoid__mult(X7) )
=> ( X149 = X155
=> ( c_Nat__Transfer_Onat__set(X155)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
=> hAPP(X2,X3) = hAPP(X1,X3) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X7),X2),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X7),X1),X155) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).
fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
! [X1,X2,X155,X149,X7] :
( ( class_Groups_Ocomm__monoid__add(X7)
& class_Groups_Ocomm__monoid__mult(X7) )
=> ( X149 = X155
=> ( c_Nat__Transfer_Onat__set(X155)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
=> hAPP(X2,X3) = hAPP(X1,X3) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X7),X2),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X7),X1),X155) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I1_J) ).
fof(fact_select__weigth__drop__zero,axiom,
! [X292,X7] : c_Random_Oselect__weight(X7,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X7),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X7)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X292)) = c_Random_Oselect__weight(X7,X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weigth__drop__zero) ).
fof(fact_pick__drop__zero,axiom,
! [X292,X7] : c_Random_Opick(X7,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X7),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X7)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X292)) = c_Random_Opick(X7,X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick__drop__zero) ).
fof(fact_transfer__int__nat__numerals_I3_J,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I3_J) ).
fof(fact_transfer__nat__int__numerals_I3_J,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I3_J) ).
fof(fact_finite__range__map__of__map__add,axiom,
! [X157,X2,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X7)),hAPP(c_Set_Oimage(X105,tc_Option_Ooption(X7),X2),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X7)),hAPP(c_Set_Oimage(X105,tc_Option_Ooption(X7),c_Map_Omap__add(X105,X7,X2,c_Map_Omap__of(X105,X7,X157))),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__map__of__map__add) ).
fof(fact_Domain__Int__subset,axiom,
! [X155,X149,X105,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X7,X105),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X149),X155))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X7,X105),X149)),hAPP(c_Relation_ODomain(X7,X105),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
fof(fact_Range__Int__subset,axiom,
! [X155,X149,X105,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_ORange(X105,X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X105,X7),tc_HOL_Obool)),X149),X155))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_ORange(X105,X7),X149)),hAPP(c_Relation_ORange(X105,X7),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
fof(fact_setprod__dividef,axiom,
! [X1,X2,X149,X7,X105] :
( class_Fields_Ofield__inverse__zero(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBS(X7,X105,X105),hAPP(hAPP(c_COMBB(X105,tc_fun(X105,X105),X7),c_Rings_Oinverse__class_Odivide(X105)),X2)),X1)),X149) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__dividef) ).
fof(fact_setprod_Odistrib,axiom,
! [X200,X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBS(X7,X105,X105),hAPP(hAPP(c_COMBB(X105,tc_fun(X105,X105),X7),c_Groups_Otimes__class_Otimes(X105)),X1)),X200)),X149) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X200),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Odistrib) ).
fof(fact_setsum_Odistrib,axiom,
! [X200,X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBS(X7,X105,X105),hAPP(hAPP(c_COMBB(X105,tc_fun(X105,X105),X7),c_Groups_Oplus__class_Oplus(X105)),X1)),X200)),X149) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X200),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Odistrib) ).
fof(fact_fold__graph__imp__finite,axiom,
! [X6,X149,X26,X2,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,X149),X6))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).
fof(fact_rotate1__def,axiom,
! [X292,X7] : hAPP(c_List_Orotate1(X7),X292) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X7),X7,c_List_Olist_ONil(X7),hAPP(hAPP(c_COMBB(tc_List_Olist(X7),tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),X7),hAPP(c_COMBC(tc_List_Olist(X7),tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Oappend(X7))),hAPP(hAPP(c_COMBC(X7,tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_OCons(X7)),c_List_Olist_ONil(X7)))),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__def) ).
fof(fact_setprod__timesf,axiom,
! [X149,X1,X2,X105,X7] :
( class_Groups_Ocomm__monoid__mult(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X7),hAPP(hAPP(c_COMBS(X105,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),c_Groups_Otimes__class_Otimes(X7)),X2)),X1)),X149) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X7),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X7),X1),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__timesf) ).
fof(fact_setsum__subtractf,axiom,
! [X149,X1,X2,X105,X7] :
( class_Groups_Oab__group__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBS(X105,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),c_Groups_Ominus__class_Ominus(X7)),X2)),X1)),X149) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X1),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__subtractf) ).
fof(fact_setsum__addf,axiom,
! [X149,X1,X2,X105,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBS(X105,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),c_Groups_Oplus__class_Oplus(X7)),X2)),X1)),X149) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X1),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__addf) ).
fof(fact_divmod__nat__rel__mult2__eq,axiom,
! [X10,X138,X144,X84,X71] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X71,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X144),X138)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))
=> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X71,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X10)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X144),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X144,X10))),X138)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).
fof(fact_select__weight__def,axiom,
! [X292,X7] : c_Random_Oselect__weight(X7,X292) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X7),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X7)),X292)))),hAPP(hAPP(c_COMBB(X7,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X7,X292))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__def) ).
fof(fact_insert__times__insert,axiom,
! [X155,X24,X149,X25,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),hAPP(hAPP(c_Set_Oinsert(X105),X24),X155))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),hAPP(hAPP(c_Set_Oinsert(X105),X24),X155)))),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__times__insert) ).
fof(fact_setsum__divide__distrib,axiom,
! [X172,X149,X2,X105,X7] :
( class_Fields_Ofield(X7)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X2),X149)),X172) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),c_Rings_Oinverse__class_Odivide(X7)),X2)),X172)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__divide__distrib) ).
fof(fact_setsum__left__distrib,axiom,
! [X172,X149,X2,X105,X7] :
( class_Rings_Osemiring__0(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X2),X149)),X172) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),c_Groups_Otimes__class_Otimes(X7)),X2)),X172)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__left__distrib) ).
fof(fact_zmult2__lemma,axiom,
! [X10,X138,X144,X84,X71] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),X138)))
=> ( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X10)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X144),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,X144,X10))),X138)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma) ).
fof(fact_listrel__rtrancl__trans,axiom,
! [X302,X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel(X7,c_Transitive__Closure_Ortrancl(X7,X172))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X293),X302)),c_List_Olistrel(X7,c_Transitive__Closure_Ortrancl(X7,X172))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X302)),c_List_Olistrel(X7,c_Transitive__Closure_Ortrancl(X7,X172)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).
fof(fact_pred__subset__eq,axiom,
! [X209,X191,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X191)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X209)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X191),X209)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_reduction__pair__lemma,axiom,
! [X209,X191,X38,X7] :
( c_FunDef_Oreduction__pair(X7,X38)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X191),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X38)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X209),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X38)))
=> ( c_Wellfounded_Owf(X7,X209)
=> c_Wellfounded_Owf(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X191),X209)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pair__lemma) ).
fof(fact_Union__Int__subset,axiom,
! [X155,X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X149),X155))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X149)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Int__subset) ).
fof(fact_Image__subset__eq,axiom,
! [X155,X149,X172,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X105,X7,X172),X149)),X155))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X105,hAPP(c_Relation_Oconverse(X105,X7),X172)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X155))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__subset__eq) ).
fof(fact_image__eq__UN,axiom,
! [X149,X2,X7,X105] : hAPP(c_Set_Oimage(X105,X7,X2),X149) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(X105,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X105),c_Set_Oinsert(X7)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__UN) ).
fof(fact_option__map__o__sum__case,axiom,
! [X200,X1,X2,X105,X7,X119,X190] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X190),tc_Option_Ooption(X119),tc_sum(X7,X105),hAPP(c_Option_Omap(X190,X119),X2)),c_Sum__Type_Osum_Osum__case(X7,tc_Option_Ooption(X190),X105,X1,X200)) = c_Sum__Type_Osum_Osum__case(X7,tc_Option_Ooption(X119),X105,hAPP(c_Fun_Ocomp(tc_Option_Ooption(X190),tc_Option_Ooption(X119),X7,hAPP(c_Option_Omap(X190,X119),X2)),X1),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X190),tc_Option_Ooption(X119),X105,hAPP(c_Option_Omap(X190,X119),X2)),X200)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__o__sum__case) ).
fof(fact_rtrancl__listrel1__ConsI1,axiom,
! [X6,X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X7),c_List_Olistrel1(X7,X172))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X293))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X7),c_List_Olistrel1(X7,X172)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).
fof(fact_option__map__o__map__upd,axiom,
! [X24,X25,X95,X2,X7,X105,X119] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X119),tc_Option_Ooption(X105),X7,hAPP(c_Option_Omap(X119,X105),X2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X119)),X95),X25),hAPP(c_Option_Ooption_OSome(X119),X24))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X119),tc_Option_Ooption(X105),X7,hAPP(c_Option_Omap(X119,X105),X2)),X95)),X25),hAPP(c_Option_Ooption_OSome(X105),hAPP(X2,X24))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__o__map__upd) ).
fof(fact_pair__leqI2,axiom,
! [X46,X45,X24,X25] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X46))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X25),X45)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24),X46))),c_FunDef_Opair__leq)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leqI2) ).
fof(fact_pair__lessI2,axiom,
! [X46,X45,X24,X25] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X46))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X25),X45)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24),X46))),c_FunDef_Opair__less)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI2) ).
fof(fact_rtrancl__Un__subset,axiom,
! [X209,X191,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X7,X191)),c_Transitive__Closure_Ortrancl(X7,X209))),c_Transitive__Closure_Ortrancl(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X191),X209)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).
fof(fact_Image__Int__subset,axiom,
! [X155,X149,X191,X105,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X105,X7,X191),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149),X155))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X105,X7,X191),X149)),hAPP(c_Relation_OImage(X105,X7,X191),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__subset) ).
fof(fact_image__Int__subset,axiom,
! [X155,X149,X2,X105,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X7,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149),X155))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X7,X2),X149)),hAPP(c_Set_Oimage(X105,X7,X2),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int__subset) ).
fof(fact_transfer__nat__int__set__cong,axiom,
! [X275,X38] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
=> ( hBOOL(hAPP(X38,X3))
<=> hBOOL(hAPP(X275,X3)) ) )
=> hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X38)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X275)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__cong) ).
fof(fact_pair__leqI1,axiom,
! [X46,X45,X24,X25] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X24))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X25),X45)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24),X46))),c_FunDef_Opair__leq)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leqI1) ).
fof(fact_pair__lessI1,axiom,
! [X46,X45,X24,X25] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X24))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X25),X45)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24),X46))),c_FunDef_Opair__less)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI1) ).
fof(fact_lists__eq__set,axiom,
! [X149,X7] : c_List_Olists(X7,X149) = hAPP(c_Set_OCollect(tc_List_Olist(X7)),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X7)),c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool))),c_List_Oset(X7))),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__eq__set) ).
fof(fact_append__listrel1I,axiom,
! [X323,X324,X172,X293,X292,X7] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel1(X7,X172)))
& X324 = X323 )
| ( X292 = X293
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X324),X323)),c_List_Olistrel1(X7,X172))) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Oappend(X7),X292),X324)),hAPP(hAPP(c_List_Oappend(X7),X293),X323))),c_List_Olistrel1(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__listrel1I) ).
fof(fact_lexord__append__leftI,axiom,
! [X6,X172,X163,X160,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X160),X163)),c_List_Olexord(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Oappend(X7),X6),X160)),hAPP(hAPP(c_List_Oappend(X7),X6),X163))),c_List_Olexord(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).
fof(fact_listrel1I2,axiom,
! [X6,X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel1(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X293))),c_List_Olistrel1(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I2) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
! [X38] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).
fof(fact_finite__range__updI,axiom,
! [X24,X25,X2,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X7)),hAPP(c_Set_Oimage(X105,tc_Option_Ooption(X7),X2),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X7)),hAPP(c_Set_Oimage(X105,tc_Option_Ooption(X7),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,tc_Option_Ooption(X7)),X2),X25),hAPP(c_Option_Ooption_OSome(X7),X24))),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__updI) ).
fof(fact_zip__map1,axiom,
! [X293,X292,X2,X119,X105,X7] : hAPP(hAPP(c_List_Ozip(X7,X105),hAPP(hAPP(c_List_Omap(X119,X7),X2),X292)),X293) = hAPP(hAPP(c_List_Omap(tc_prod(X119,X105),tc_prod(X7,X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X119,X105,tc_prod(X7,X105)),hAPP(hAPP(c_COMBB(X7,tc_fun(X105,tc_prod(X7,X105)),X119),c_Product__Type_OPair(X7,X105)),X2))),hAPP(hAPP(c_List_Ozip(X119,X105),X292),X293)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map1) ).
fof(fact_mlex__prod__def,axiom,
! [X191,X2,X7] : c_Wellfounded_Omlex__prod(X7,X2,X191) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X7),X7),c_Wellfounded_Olex__prod(tc_Nat_Onat,X7,c_Wellfounded_Oless__than,X191)),hAPP(hAPP(c_COMBS(X7,X7,tc_prod(tc_Nat_Onat,X7)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X7,tc_prod(tc_Nat_Onat,X7)),X7),c_Product__Type_OPair(tc_Nat_Onat,X7)),X2)),c_COMBI(X7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__prod__def) ).
fof(fact_finite__empty__induct,axiom,
! [X38,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(X38,X149))
=> ( ! [X110,X239] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X239))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X110),X239))
=> ( hBOOL(hAPP(X38,X239))
=> hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X239),hAPP(hAPP(c_Set_Oinsert(X7),X110),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) )
=> hBOOL(hAPP(X38,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__empty__induct) ).
fof(fact_Times__subset__cancel2,axiom,
! [X155,X149,X105,X193,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X193))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X105,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X105,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X105),X193))),hAPP(hAPP(c_Product__Type_OSigma(X105,X7),X155),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X105),X193))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),X149),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).
fof(fact_rel__pow__Suc__I2,axiom,
! [X44,X26,X191,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X191))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),hAPP(c_Nat_OSuc,X44)),X191))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__I2) ).
fof(fact_rel__pow__Suc__I,axiom,
! [X26,X191,X44,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X26)),X191))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),hAPP(c_Nat_OSuc,X44)),X191))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__I) ).
fof(fact_image__Pow__mono,axiom,
! [X155,X149,X2,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X7,X2),X149)),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X105,X7,X2)),hAPP(c_Set_OPow(X105),X149))),hAPP(c_Set_OPow(X7),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__mono) ).
fof(fact_select__weight__member,axiom,
! [X45,X292,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X7),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X7)),X292))))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Product__Type_Ofst(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X7,X292),X45))),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X7),X7),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X7)),X292)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__member) ).
fof(fact_setsum__abs,axiom,
! [X149,X2,X105,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Groups_Oabs__class_Oabs(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X2),X149))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBB(X7,X7,X105),c_Groups_Oabs__class_Oabs(X7)),X2)),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__abs) ).
fof(fact_set__minus__filter__out,axiom,
! [X127,X292,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X292)),hAPP(hAPP(c_Set_Oinsert(X7),X127),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(c_List_Oset(X7),hAPP(c_List_Ofilter(X7,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X127))),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__minus__filter__out) ).
fof(fact_filter__filter,axiom,
! [X292,X194,X38,X7] : hAPP(c_List_Ofilter(X7,X38),hAPP(c_List_Ofilter(X7,X194),X292)) = hAPP(c_List_Ofilter(X7,hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),X194)),X38)),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__filter) ).
fof(fact_Domain__Diff__subset,axiom,
! [X155,X149,X105,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X7,X105),X149)),hAPP(c_Relation_ODomain(X7,X105),X155))),hAPP(c_Relation_ODomain(X7,X105),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X149),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).
fof(fact_Range__Diff__subset,axiom,
! [X155,X149,X105,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_ORange(X105,X7),X149)),hAPP(c_Relation_ORange(X105,X7),X155))),hAPP(c_Relation_ORange(X105,X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X105,X7),tc_HOL_Obool)),X149),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).
fof(fact_fun__left__comm__idem__remove,axiom,
! [X7] : c_Finite__Set_Ofun__left__comm__idem(X7,tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__remove) ).
fof(fact_card__Diff1__less,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X7),X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__less) ).
fof(fact_split__comp__eq,axiom,
! [X1,X2,X190,X119,X105,X7] : hAPP(hAPP(c_COMBS(tc_prod(X7,X105),X105,X119),hAPP(hAPP(c_COMBB(X190,tc_fun(X105,X119),tc_prod(X7,X105)),X2),hAPP(hAPP(c_COMBB(X7,X190,tc_prod(X7,X105)),X1),c_Product__Type_Ofst(X7,X105)))),c_Product__Type_Osnd(X7,X105)) = hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,X119),hAPP(hAPP(c_COMBB(X190,tc_fun(X105,X119),X7),X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__comp__eq) ).
fof(fact_insort__key__remove1,axiom,
! [X2,X292,X25,X7,X105] :
( class_Orderings_Olinorder(X105)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_List_Oset(X7),X292)))
=> ( c_List_Olinorder__class_Osorted(X105,hAPP(hAPP(c_List_Omap(X7,X105),X2),X292))
=> ( hAPP(c_List_Ohd(X7),hAPP(c_List_Ofilter(X7,hAPP(hAPP(c_COMBB(X105,tc_HOL_Obool,X7),hAPP(c_fequal,hAPP(X2,X25))),X2)),X292)) = X25
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X105,X2),X25),c_List_Oremove1(X7,X25,X292)) = X292 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key__remove1) ).
fof(fact_sum_Orecs_I1_J,axiom,
! [X25,X21,X22,X119,X7,X105] : c_Sum__Type_Osum_Osum__rec(X105,X7,X119,X22,X21,hAPP(c_Sum__Type_OInl(X105,X119),X25)) = hAPP(X22,X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Orecs_I1_J) ).
fof(fact_sum_Orecs_I2_J,axiom,
! [X24,X21,X22,X119,X7,X105] : c_Sum__Type_Osum_Osum__rec(X105,X7,X119,X22,X21,hAPP(c_Sum__Type_OInr(X119,X105),X24)) = hAPP(X21,X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Orecs_I2_J) ).
fof(fact_equiv__intrel__iff,axiom,
! [X127,X6] :
( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X127),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X127)),c_Int_Ointrel)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__intrel__iff) ).
fof(fact_fold__graph_H_Ointros_I1_J,axiom,
! [X26,X2,X105,X7] : c_Nitpick_Ofold__graph_H(X7,X105,X2,X26,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).
fof(fact_fold__graph_H_Oequations_I1_J,axiom,
! [X43,X42,X105,X7] : c_Nitpick_Ofold__graph_H(X7,X105,X42,X43,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
fof(fact_map__pair_Oid,axiom,
! [X105,X7] : c_Product__Type_Omap__pair(X7,X7,X105,X105,c_Fun_Oid(X7),c_Fun_Oid(X105)) = c_Fun_Oid(tc_prod(X7,X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Oid) ).
fof(fact_map__pair_Oidentity,axiom,
! [X105,X7] : c_Product__Type_Omap__pair(X7,X7,X105,X105,c_COMBI(X7),c_COMBI(X105)) = c_Fun_Oid(tc_prod(X7,X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Oidentity) ).
fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
! [X26,X149,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,X149),hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).
fof(fact_negateSnd__def,axiom,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negateSnd__def) ).
fof(fact_card__Diff1__le,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X7),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__le) ).
fof(fact_rel__comp__mono,axiom,
! [X45,X222,X119,X172,X247,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X247),X172))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X105,X119),tc_HOL_Obool)),X222),X45))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X119),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X105,X119),X247),X222)),hAPP(hAPP(c_Relation_Orel__comp(X7,X105,X119),X172),X45))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__mono) ).
fof(fact_equiv__class__subset,axiom,
! [X24,X25,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__subset) ).
fof(fact_the__inv__into__into,axiom,
! [X155,X6,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( hBOOL(hAPP(hAPP(c_member(X105),X6),hAPP(c_Set_Oimage(X7,X105,X2),X149)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Fun_Othe__inv__into(X7,X105,X149,X2),X6)),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__into) ).
fof(fact_finite__range__imageI,axiom,
! [X2,X119,X1,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_Oimage(X105,X7,X1),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X119),hAPP(c_Set_Oimage(X105,X119,hAPP(hAPP(c_COMBB(X7,X119,X105),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
fof(fact_Inter__Un__subset,axiom,
! [X155,X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X149)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X155))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X149),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__subset) ).
fof(fact_listrel__subset,axiom,
! [X149,X172,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),hAPP(hAPP(c_Product__Type_OSigma(X7,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),X149))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool)),c_List_Olistrel(X7,X172)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olists(X7,X149)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X7),tc_HOL_Obool),tc_List_Olist(X7)),c_List_Olists(X7,X149))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__subset) ).
fof(fact_fold__image__reindex,axiom,
! [X26,X1,X200,X105,X149,X7,X119] :
( class_Groups_Oab__semigroup__mult(X119)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( c_Fun_Oinj__on(X7,X105,X200,X149)
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X119,X105,c_Groups_Otimes__class_Otimes(X119)),X1),X26),hAPP(c_Set_Oimage(X7,X105,X200),X149)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X119,X7,c_Groups_Otimes__class_Otimes(X119)),hAPP(c_Fun_Ocomp(X105,X119,X7,X1),X200)),X26),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__reindex) ).
fof(fact_zmult2__lemma__aux4,axiom,
! [X144,X84,X138,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X138))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X138),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,X144,X10))),X138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).
fof(fact_restrict__map__upds,axiom,
! [X95,X192,X293,X105,X292,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X292)),X192))
=> c_Map_Orestrict__map(X7,X105,c_Map_Omap__upds(X7,X105,X95,X292,X293),X192) = c_Map_Omap__upds(X7,X105,c_Map_Orestrict__map(X7,X105,X95,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X192),hAPP(c_List_Oset(X7),X292))),X292,X293) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__upds) ).
fof(fact_fold__sup__le__sup,axiom,
! [X23,X24,X149,X7] :
( class_Lattices_Osemilattice__sup(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X3),X24)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7)),X23),X149)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X24),X23))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__sup__le__sup) ).
fof(fact_min__max_Ofold__sup__le__sup,axiom,
! [X23,X24,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X3),X24)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omax(X7)),X23),X149)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X24),X23))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).
fof(fact_listrel1I1,axiom,
! [X292,X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X292))),c_List_Olistrel1(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I1) ).
fof(fact_transpose__column,axiom,
! [X107,X292,X7] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X7))),X292)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),X292)))
=> hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),X7),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_Nat_Onat,X7),c_List_Onth(X7)),X107)),hAPP(c_List_Ofilter(tc_List_Olist(X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X7)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107)),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),c_List_Otranspose(X7,X292))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X7)),X292),X107) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__column) ).
fof(fact_split__paired__Eps,axiom,
! [X38,X105,X7] : c_Hilbert__Choice_OEps(tc_prod(X7,X105),X38) = c_Hilbert__Choice_OEps(tc_prod(X7,X105),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_HOL_Obool,X105),X38)),c_Product__Type_OPair(X7,X105)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__Eps) ).
fof(fact_split__paired__The,axiom,
! [X38,X105,X7] : c_HOL_OThe(tc_prod(X7,X105),X38) = c_HOL_OThe(tc_prod(X7,X105),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_COMBB(tc_prod(X7,X105),tc_HOL_Obool,X105),X38)),c_Product__Type_OPair(X7,X105)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__The) ).
fof(fact_Comp,axiom,
! [X191,X136,X194,X23,X38,X216,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X38),X23),X194)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X194),X136),X191)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X38),c_Com_Ocom_OSemi(X23,X136)),X191)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Comp) ).
fof(fact_total__on__def,axiom,
! [X172,X149,X7] :
( c_Relation_Ototal__on(X7,X149,X172)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> ! [X206] :
( hBOOL(hAPP(hAPP(c_member(X7),X206),X149))
=> ( X3 != X206
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X206)),X172))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X206),X3)),X172)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).
fof(fact_mod__lemma,axiom,
! [X144,X84,X138,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X138),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X144,X10))),X138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__lemma) ).
fof(fact_single__valued__confluent,axiom,
! [X26,X127,X6,X172,X7] :
( c_Relation_Osingle__valued(X7,X7,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X26)),c_Transitive__Closure_Ortrancl(X7,X172)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X127)),c_Transitive__Closure_Ortrancl(X7,X172))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
fof(fact_reduction__pairI,axiom,
! [X209,X191,X7] :
( c_Wellfounded_Owf(X7,X191)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X191),X209)),X191))
=> c_FunDef_Oreduction__pair(X7,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X191),X209)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pairI) ).
fof(fact_zmult2__lemma__aux2,axiom,
! [X144,X138,X84,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X138))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X138),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,X144,X10))),X138)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).
fof(fact_select__def,axiom,
! [X292,X7] : c_Random_Oselect(X7,X292) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))),hAPP(hAPP(c_COMBB(X7,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X7),X292)),c_Code__Numeral_Onat__of))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__def) ).
fof(fact_of__int,axiom,
! [X158,X107,X7] :
( class_Rings_Oring__1(X7)
=> hAPP(c_Int_Oring__1__class_Oof__int(X7),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X107),X158)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X107)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X158)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int) ).
fof(fact_dom__option__map,axiom,
! [X95,X2,X119,X105,X7] : c_Map_Odom(X7,X105,hAPP(hAPP(c_COMBS(X7,tc_Option_Ooption(X119),tc_Option_Ooption(X105)),hAPP(hAPP(c_COMBB(tc_fun(X119,X105),tc_fun(tc_Option_Ooption(X119),tc_Option_Ooption(X105)),X7),c_Option_Omap(X119,X105)),X2)),X95)) = c_Map_Odom(X7,X119,X95),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__option__map) ).
fof(fact_diff__single__insert,axiom,
! [X155,X6,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X155))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__single__insert) ).
fof(fact_nat,axiom,
! [X127,X6] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X127)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X127),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat) ).
fof(fact_inj__on__Un,axiom,
! [X155,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))
<=> ( c_Fun_Oinj__on(X7,X105,X2,X149)
& c_Fun_Oinj__on(X7,X105,X2,X155)
& hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155))),hAPP(c_Set_Oimage(X7,X105,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X155),X149))) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un) ).
fof(fact_in__finite__psubset,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X149),X155)),c_Wellfounded_Ofinite__psubset(X7)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
fof(fact_Domain__iff,axiom,
! [X172,X105,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Relation_ODomain(X7,X105),X172)))
<=> ? [X82] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X82)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__iff) ).
fof(fact_Un__Pow__subset,axiom,
! [X155,X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X7),X149)),hAPP(c_Set_OPow(X7),X155))),hAPP(c_Set_OPow(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Pow__subset) ).
fof(fact_nat__diff__add__eq1,axiom,
! [X33,X90,X63,X114,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X113),X114))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X114),X63)),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X113),X63)),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X114),X113)),X63)),X90)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_pick__member,axiom,
! [X292,X7,X107] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X107),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X7),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X7)),X292))))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Random_Opick(X7,X292),X107)),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X7),X7),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X7)),X292)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick__member) ).
fof(fact_rel__compI,axiom,
! [X45,X23,X119,X172,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),X172))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X119)),hAPP(hAPP(c_Product__Type_OPair(X105,X119),X24),X23)),X45))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X119)),hAPP(hAPP(c_Product__Type_OPair(X7,X119),X25),X23)),hAPP(hAPP(c_Relation_Orel__comp(X7,X105,X119),X172),X45))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__compI) ).
fof(fact_sorted__insort__insert__key,axiom,
! [X6,X292,X2,X105,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),X292))
=> c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),c_List_Olinorder__class_Oinsort__insert__key(X105,X7,X2,X6,X292))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__insert__key) ).
fof(fact_bex__Un,axiom,
! [X38,X155,X149,X7] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
& hBOOL(hAPP(X38,X3)) )
<=> ( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& hBOOL(hAPP(X38,X3)) )
| ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X155))
& hBOOL(hAPP(X38,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__Un) ).
fof(fact_ball__Un,axiom,
! [X38,X155,X149,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> hBOOL(hAPP(X38,X3)) )
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(X38,X3)) )
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X155))
=> hBOOL(hAPP(X38,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__Un) ).
fof(fact_INF2__D,axiom,
! [X25,X23,X24,X155,X149,X119,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_fun(X119,tc_HOL_Obool))),X149),X155),X24),X23))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(hAPP(X155,X25),X24),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__D) ).
fof(fact_nat__2,axiom,
hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__2) ).
fof(fact_fun__upd__comp,axiom,
! [X127,X6,X1,X2,X7,X105,X119] : hAPP(c_Fun_Ocomp(X119,X105,X7,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X119),X1),X6),X127)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),hAPP(c_Fun_Ocomp(X119,X105,X7,X2),X1)),X6),hAPP(X2,X127)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__comp) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J) ).
fof(fact_vimage__def,axiom,
! [X155,X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),X155) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBC(X7,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X105,tc_fun(tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),X7),c_member(X105)),X2)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__def) ).
fof(fact_zip__append2,axiom,
! [X299,X301,X300,X7,X87] : hAPP(hAPP(c_List_Ozip(X87,X7),X300),hAPP(hAPP(c_List_Oappend(X7),X301),X299)) = hAPP(hAPP(c_List_Oappend(tc_prod(X87,X7)),hAPP(hAPP(c_List_Ozip(X87,X7),hAPP(hAPP(c_List_Otake(X87),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X301)),X300)),X301)),hAPP(hAPP(c_List_Ozip(X87,X7),hAPP(hAPP(c_List_Odrop(X87),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X301)),X300)),X299)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append2) ).
fof(fact_in__listrel1__converse,axiom,
! [X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),X127)),c_List_Olistrel1(X7,hAPP(c_Relation_Oconverse(X7,X7),X172))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),X127)),hAPP(c_Relation_Oconverse(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olistrel1(X7,X172)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__listrel1__converse) ).
fof(fact_map__filter__simps_I1_J,axiom,
! [X292,X6,X2,X7,X105] : c_List_Omap__filter(X105,X7,X2,hAPP(hAPP(c_List_Olist_OCons(X105),X6),X292)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X7),X7,c_List_Omap__filter(X105,X7,X2,X292),hAPP(hAPP(c_COMBC(X7,tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_OCons(X7)),c_List_Omap__filter(X105,X7,X2,X292))),hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__filter__simps_I1_J) ).
fof(fact_Cons__eq__append__conv,axiom,
! [X302,X293,X292,X6,X7] :
( hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292) = hAPP(hAPP(c_List_Oappend(X7),X293),X302)
<=> ( ( X293 = c_List_Olist_ONil(X7)
& hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292) = X302 )
| ? [X317] :
( hAPP(hAPP(c_List_Olist_OCons(X7),X6),X317) = X293
& X292 = hAPP(hAPP(c_List_Oappend(X7),X317),X302) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).
fof(fact_append__eq__Cons__conv,axiom,
! [X292,X6,X302,X293,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X293),X302) = hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)
<=> ( ( X293 = c_List_Olist_ONil(X7)
& X302 = hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292) )
| ? [X317] :
( X293 = hAPP(hAPP(c_List_Olist_OCons(X7),X6),X317)
& hAPP(hAPP(c_List_Oappend(X7),X317),X302) = X292 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).
fof(fact_min__max_OInf__fin_Oclosed,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ! [X3,X82] : hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X3),X82)),hAPP(hAPP(c_Set_Oinsert(X7),X3),hAPP(hAPP(c_Set_Oinsert(X7),X82),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X7),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).
fof(fact_min__max_OSup__fin_Oclosed,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ! [X3,X82] : hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X3),X82)),hAPP(hAPP(c_Set_Oinsert(X7),X3),hAPP(hAPP(c_Set_Oinsert(X7),X82),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X7),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).
fof(fact_triple__valid__def2,axiom,
! [X194,X23,X38,X44,X7] :
( c_Hoare__Mirabelle_Otriple__valid(X7,X44,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X38),X23),X194))
<=> ! [X231,X232] :
( hBOOL(hAPP(hAPP(X38,X231),X232))
=> ! [X233] :
( c_Natural_Oevaln(X23,X232,X44,X233)
=> hBOOL(hAPP(hAPP(X194,X231),X233)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple__valid__def2) ).
fof(fact_map__of__map__restrict,axiom,
! [X297,X2,X105,X7] : c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Omap(X7,tc_prod(X7,X105)),hAPP(hAPP(c_COMBS(X7,X105,tc_prod(X7,X105)),c_Product__Type_OPair(X7,X105)),X2)),X297)) = c_Map_Orestrict__map(X7,X105,hAPP(c_Fun_Ocomp(X105,tc_Option_Ooption(X105),X7,c_Option_Ooption_OSome(X105)),X2),hAPP(c_List_Oset(X7),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__map__restrict) ).
fof(fact_card__SigmaI,axiom,
! [X155,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(X155,X3))) )
=> hAPP(c_Finite__Set_Ocard(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_Nat_Onat,X7),c_Finite__Set_Ocard(X105)),X155)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__SigmaI) ).
fof(fact_fold__graph_Oequations_I1_J,axiom,
! [X26,X2,X105,X7] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).
fof(fact_fold__graph_OemptyI,axiom,
! [X26,X2,X105,X7] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OemptyI) ).
fof(fact_wf__union__compatible,axiom,
! [X209,X191,X7] :
( c_Wellfounded_Owf(X7,X191)
=> ( c_Wellfounded_Owf(X7,X209)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X191),X209)),X191))
=> c_Wellfounded_Owf(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X191),X209)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__union__compatible) ).
fof(fact_fold1__in,axiom,
! [X149,X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ! [X3,X82] : hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X3),X82)),hAPP(hAPP(c_Set_Oinsert(X7),X3),hAPP(hAPP(c_Set_Oinsert(X7),X82),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),X149)),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__in) ).
fof(fact_unique__quotient__lemma,axiom,
! [X138,X144,X145,X146,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X146)),X145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X144)),X138)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X145))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X145),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X138),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X146),X144)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [X138,X144,X145,X146,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X146)),X145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X144)),X138)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X138),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X138))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X145))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X144),X146)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_distinct__insort__insert,axiom,
! [X6,X2,X292,X7,X105] :
( class_Orderings_Olinorder(X105)
=> ( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> hBOOL(hAPP(c_List_Odistinct(X7),c_List_Olinorder__class_Oinsort__insert__key(X7,X105,X2,X6,X292))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__insort__insert) ).
fof(fact_nth__transpose,axiom,
! [X292,X7,X107] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),c_List_Otranspose(X7,X292))))
=> hAPP(hAPP(c_List_Onth(tc_List_Olist(X7)),c_List_Otranspose(X7,X292)),X107) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),X7),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_Nat_Onat,X7),c_List_Onth(X7)),X107)),hAPP(c_List_Ofilter(tc_List_Olist(X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X7)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107)),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__transpose) ).
fof(fact_Powp__Pow__eq,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Predicate_OPowp(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)),X6))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X6),hAPP(c_Set_OPow(X7),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__Pow__eq) ).
fof(fact_card__bij__eq,axiom,
! [X1,X155,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),X149)),X155))
=> ( c_Fun_Oinj__on(X105,X7,X1,X155)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X7,X1),X155)),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155))
=> hAPP(c_Finite__Set_Ocard(X7),X149) = hAPP(c_Finite__Set_Ocard(X105),X155) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
fof(fact_Eps__split,axiom,
! [X38,X105,X7] : c_Hilbert__Choice_OEps(tc_prod(X7,X105),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),X38)) = c_Hilbert__Choice_OEps(tc_prod(X7,X105),hAPP(hAPP(c_COMBS(tc_prod(X7,X105),X105,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X7,tc_fun(X105,tc_HOL_Obool),tc_prod(X7,X105)),X38),c_Product__Type_Ofst(X7,X105))),c_Product__Type_Osnd(X7,X105))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Eps__split) ).
fof(fact_The__split,axiom,
! [X38,X105,X7] : c_HOL_OThe(tc_prod(X7,X105),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),X38)) = c_HOL_OThe(tc_prod(X7,X105),hAPP(hAPP(c_COMBS(tc_prod(X7,X105),X105,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X7,tc_fun(X105,tc_HOL_Obool),tc_prod(X7,X105)),X38),c_Product__Type_Ofst(X7,X105))),c_Product__Type_Osnd(X7,X105))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_The__split) ).
fof(fact_inf__period_I3_J,axiom,
! [X46,X192,X136,X7] :
( ( class_Rings_Ocomm__ring(X7)
& class_Rings_Odvd(X7) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X136),X192))
=> ! [X3,X118] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X3),X46)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X118),X192))),X46))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_inf__period_I4_J,axiom,
! [X46,X192,X136,X7] :
( ( class_Rings_Ocomm__ring(X7)
& class_Rings_Odvd(X7) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X136),X192))
=> ! [X3,X118] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X3),X46)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X118),X192))),X46))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
fof(fact_div__mod__equality,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84)),X84)),c_Divides_Odiv__class_Omod(X87,X71,X84))),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality) ).
fof(fact_fold__Un__disjoint,axiom,
! [X1,X155,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),c_Groups_Oone__class_Oone(X105)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),c_Groups_Oone__class_Oone(X105)),X149)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),c_Groups_Oone__class_Oone(X105)),X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__Un__disjoint) ).
fof(fact_uminus__listsum__map,axiom,
! [X292,X2,X105,X7] :
( class_Groups_Oab__group__add(X7)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X7),hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292))) = hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),hAPP(c_Fun_Ocomp(X7,X7,X105,c_Groups_Ouminus__class_Ouminus(X7)),X2)),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__listsum__map) ).
fof(fact_neg__map__def,axiom,
! [X38,X2,X7,X105] : c_New__Random__Sequence_Oneg__map(X105,X7,X2,X38) = c_New__Random__Sequence_Oneg__bind(X105,X7,X38,hAPP(c_Fun_Ocomp(X7,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X7)))))),X105,c_New__Random__Sequence_Oneg__single(X7)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__map__def) ).
fof(fact_setsum__abs__ge__zero,axiom,
! [X149,X2,X105,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBB(X7,X7,X105),c_Groups_Oabs__class_Oabs(X7)),X2)),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__abs__ge__zero) ).
fof(fact_finite__Collect__subsets,axiom,
! [X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool))),X149)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__subsets) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [X127,X6,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X127),X127))),c_Groups_Ozero__class_Ozero(X7)))
<=> ( X6 = c_Groups_Ozero__class_Ozero(X7)
& X127 = c_Groups_Ozero__class_Ozero(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_Inf__fin_Oclosed,axiom,
! [X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ! [X3,X82] : hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X3),X82)),hAPP(hAPP(c_Set_Oinsert(X7),X3),hAPP(hAPP(c_Set_Oinsert(X7),X82),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X7),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oclosed) ).
fof(fact_Min_Oclosed,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ! [X3,X82] : hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X3),X82)),hAPP(hAPP(c_Set_Oinsert(X7),X3),hAPP(hAPP(c_Set_Oinsert(X7),X82),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X7),c_Big__Operators_Olinorder__class_OMin(X7,X149)),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oclosed) ).
fof(fact_Max_Oclosed,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ! [X3,X82] : hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X3),X82)),hAPP(hAPP(c_Set_Oinsert(X7),X3),hAPP(hAPP(c_Set_Oinsert(X7),X82),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X7),c_Big__Operators_Olinorder__class_OMax(X7,X149)),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oclosed) ).
fof(fact_Sup__fin_Oclosed,axiom,
! [X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ! [X3,X82] : hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X3),X82)),hAPP(hAPP(c_Set_Oinsert(X7),X3),hAPP(hAPP(c_Set_Oinsert(X7),X82),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X7),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oclosed) ).
fof(fact_folding__image_Oreindex,axiom,
! [X1,X200,X149,X215,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image(X7,X105,X2,X26,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> ( c_Fun_Oinj__on(X105,X105,X200,X149)
=> hAPP(hAPP(X215,X1),hAPP(c_Set_Oimage(X105,X105,X200),X149)) = hAPP(hAPP(X215,hAPP(c_Fun_Ocomp(X105,X7,X105,X1),X200)),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oreindex) ).
fof(fact_transpose__column__length,axiom,
! [X107,X292,X7] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X7))),X292)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),X292)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),hAPP(c_List_Ofilter(tc_List_Olist(X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X7)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107)),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),c_List_Otranspose(X7,X292))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X7)),X292),X107)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__column__length) ).
fof(fact_pair__imageI,axiom,
! [X2,X119,X149,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),X149))
=> hBOOL(hAPP(hAPP(c_member(X119),hAPP(hAPP(X2,X25),X24)),hAPP(c_Set_Oimage(tc_prod(X7,X105),X119,hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,X119),X2)),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__imageI) ).
fof(fact_weak__map__of__SomeI,axiom,
! [X157,X6,X94,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X94),X6)),hAPP(c_List_Oset(tc_prod(X7,X105)),X157)))
=> ? [X3] : hAPP(c_Map_Omap__of(X7,X105,X157),X94) = hAPP(c_Option_Ooption_OSome(X105),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weak__map__of__SomeI) ).
fof(fact_length__filter__map,axiom,
! [X292,X2,X105,X38,X7] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(c_List_Ofilter(X7,X38),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),hAPP(c_List_Ofilter(X105,hAPP(c_Fun_Ocomp(X7,tc_HOL_Obool,X105,X38),X2)),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__map) ).
fof(fact_trancl__subset__Sigma__aux,axiom,
! [X149,X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),hAPP(hAPP(c_Product__Type_OSigma(X7,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),X149))))
=> ( X25 = X24
| hBOOL(hAPP(hAPP(c_member(X7),X25),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
fof(fact_sum__length__filter__compl,axiom,
! [X292,X38,X7] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(c_List_Ofilter(X7,X38),X292))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(c_List_Ofilter(X7,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),X38)),X292))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__length__filter__compl) ).
fof(fact_rtrancl__trans,axiom,
! [X23,X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X23)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X23)),c_Transitive__Closure_Ortrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_zdiv__zadd1__eq,axiom,
! [X10,X84,X71] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X10)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X10)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X10))),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).
fof(fact_div__add1__eq,axiom,
! [X10,X84,X71] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X71),X84)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X71),X10)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X84),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X71,X10)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X84,X10))),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add1__eq) ).
fof(fact_inf2D1,axiom,
! [X127,X6,X155,X149,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X149),X155),X6),X127))
=> hBOOL(hAPP(hAPP(X149,X6),X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D1) ).
fof(fact_inf2D2,axiom,
! [X127,X6,X155,X149,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X149),X155),X6),X127))
=> hBOOL(hAPP(hAPP(X155,X6),X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D2) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [X23,X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X23)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X23)),c_Transitive__Closure_Ortrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [X23,X172,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X23)),X172))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X23)),c_Transitive__Closure_Ortrancl(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_rtrancl__listrel1__if__listrel,axiom,
! [X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X7),c_List_Olistrel1(X7,X172)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
fof(fact_folding_Ocommute__comps_I1_J,axiom,
! [X200,X1,X201,X2,X119,X190,X189,X215,X85,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X85,X215)
=> hAPP(c_Fun_Ocomp(X189,X190,X119,X2),hAPP(c_Fun_Ocomp(X201,X189,X119,X1),X200)) = hAPP(c_Fun_Ocomp(X201,X190,X119,hAPP(c_Fun_Ocomp(X189,X190,X201,X2),X1)),X200) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [X145,X146,X124,X138,X144,X84] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X144)),X138) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X124),X146)),X145)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X124),X146)),X145)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X138),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X145))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X124))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X124),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X146),X144)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
! [X38] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X38)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X38),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).
fof(fact_listrel__reflcl__if__listrel1,axiom,
! [X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel1(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel(X7,c_Transitive__Closure_Ortrancl(X7,X172)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
fof(fact_lexord__lex,axiom,
! [X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),X127)),c_List_Olex(X7,X172)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),X127)),c_List_Olexord(X7,X172)))
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X6) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X127) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__lex) ).
fof(fact_filter__map,axiom,
! [X292,X2,X105,X38,X7] : hAPP(c_List_Ofilter(X7,X38),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)) = hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(c_List_Ofilter(X105,hAPP(c_Fun_Ocomp(X7,tc_HOL_Obool,X105,X38),X2)),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__map) ).
fof(fact_wfP__SUP,axiom,
! [X7,X172,X105] :
( ! [X147] : c_Wellfounded_OwfP(X105,hAPP(X172,X147))
=> ( ! [X147,X117] :
( hAPP(X172,X147) != hAPP(X172,X117)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),c_Predicate_ODomainP(X105,X105,hAPP(X172,X147))),c_Predicate_ORangeP(X105,X105,hAPP(X172,X117))) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) )
=> c_Wellfounded_OwfP(X105,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_fun(X105,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),X172)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__SUP) ).
fof(fact_partition__filter__conv,axiom,
! [X292,X2,X7] : c_List_Opartition(X7,X2,X292) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(c_List_Ofilter(X7,X2),X292)),hAPP(c_List_Ofilter(X7,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X7,c_fNot),X2)),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter__conv) ).
fof(fact_upto_Opinduct,axiom,
! [X38,X42,X187] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X42)))
=> ( ! [X147,X117] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X147),X117)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X147),X117))
=> hBOOL(hAPP(hAPP(X38,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X147),c_Groups_Oone__class_Oone(tc_Int_Oint))),X117)) )
=> hBOOL(hAPP(hAPP(X38,X147),X117)) ) )
=> hBOOL(hAPP(hAPP(X38,X187),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto_Opinduct) ).
fof(fact_map__add__upds,axiom,
! [X293,X292,X284,X285,X105,X7] : c_Map_Omap__add(X7,X105,X285,c_Map_Omap__upds(X7,X105,X284,X292,X293)) = c_Map_Omap__upds(X7,X105,c_Map_Omap__add(X7,X105,X285,X284),X292,X293),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__upds) ).
fof(fact_Ints__odd__less__0,axiom,
! [X25,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Int_Oring__1__class_OInts(X7)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),c_Groups_Oone__class_Oone(X7)),X25)),X25)),c_Groups_Ozero__class_Ozero(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).
fof(fact_zdiv__zmod__equality2,axiom,
! [X96,X84,X71] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84)),X84)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84))),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).
fof(fact_zdvd__period,axiom,
! [X23,X46,X6,X136,X25] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X25),X136))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X46)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X136))),X46))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__period) ).
fof(fact_dom__map__upds,axiom,
! [X293,X292,X95,X105,X7] : c_Map_Odom(X7,X105,c_Map_Omap__upds(X7,X105,X95,X292,X293)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)),X292))),c_Map_Odom(X7,X105,X95)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__map__upds) ).
fof(fact_INFI__set__fold,axiom,
! [X2,X292,X105,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,X7),hAPP(c_List_Oset(X105),X292)),X2) = hAPP(c_List_Ofoldl(X7,X105,hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),c_Lattices_Osemilattice__inf__class_Oinf(X7)),X2)),c_Orderings_Otop__class_Otop(X7)),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__set__fold) ).
fof(fact_SUPR__set__fold,axiom,
! [X2,X292,X105,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,X7),hAPP(c_List_Oset(X105),X292)),X2) = hAPP(c_List_Ofoldl(X7,X105,hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),c_Lattices_Osemilattice__sup__class_Osup(X7)),X2)),c_Orderings_Obot__class_Obot(X7)),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__set__fold) ).
fof(fact_finite__UN__I,axiom,
! [X155,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X110] :
( hBOOL(hAPP(hAPP(c_member(X7),X110),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(X155,X110))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN__I) ).
fof(fact_finite__UN,axiom,
! [X155,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(X155,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN) ).
fof(fact_rel__comp__UNION__distrib,axiom,
! [X172,X211,X190,X45,X105,X119,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),X45),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X190,tc_fun(tc_prod(X119,X105),tc_HOL_Obool)),X211),X172)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X190,tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X211),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X119,X105),tc_HOL_Obool),tc_fun(tc_prod(X7,X105),tc_HOL_Obool),X190),hAPP(c_Relation_Orel__comp(X7,X119,X105),X45)),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib) ).
fof(fact_o__assoc,axiom,
! [X200,X1,X190,X2,X7,X105,X119] : hAPP(c_Fun_Ocomp(X119,X105,X7,X2),hAPP(c_Fun_Ocomp(X190,X119,X7,X1),X200)) = hAPP(c_Fun_Ocomp(X190,X105,X7,hAPP(c_Fun_Ocomp(X119,X105,X190,X2),X1)),X200),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__assoc) ).
fof(fact_surj__Compl__image__subset,axiom,
! [X149,X2,X7,X105] :
( hAPP(c_Set_Oimage(X105,X7,X2),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X7,X2),X149))),hAPP(c_Set_Oimage(X105,X7,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X105,tc_HOL_Obool)),X149)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__Compl__image__subset) ).
fof(fact_in__inv__image,axiom,
! [X2,X172,X105,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),hAPP(hAPP(c_Relation_Oinv__image(X105,X7),X172),X2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X105)),hAPP(hAPP(c_Product__Type_OPair(X105,X105),hAPP(X2,X6)),hAPP(X2,X127))),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__inv__image) ).
fof(fact_folding_Oremove,axiom,
! [X6,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(X215,X149) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),hAPP(X2,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oremove) ).
fof(fact_Image__subset,axiom,
! [X193,X155,X149,X172,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X172),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X155))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X105,X172),X193)),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__subset) ).
fof(fact_tl__append,axiom,
! [X293,X292,X7] : hAPP(c_List_Otl(X7),hAPP(hAPP(c_List_Oappend(X7),X292),X293)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X7),X7,hAPP(c_List_Otl(X7),X293),hAPP(c_COMBK(tc_fun(tc_List_Olist(X7),tc_List_Olist(X7)),X7),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Oappend(X7)),X293))),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__append) ).
fof(fact_pos__map__def,axiom,
! [X38,X2,X7,X105] : c_New__Random__Sequence_Opos__map(X105,X7,X2,X38) = c_New__Random__Sequence_Opos__bind(X105,X7,X38,hAPP(c_Fun_Ocomp(X7,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X7))))),X105,c_New__Random__Sequence_Opos__single(X7)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__map__def) ).
fof(fact_inj__image__Compl__subset,axiom,
! [X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),X149)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__Compl__subset) ).
fof(fact_folding_Oinsert__remove,axiom,
! [X6,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),hAPP(X2,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert__remove) ).
fof(fact_folding_Ocommute__left__comp_H_H,axiom,
! [X1,X119,X155,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X215,X155)),hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X215,X149)),X1)) = hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X215,X149)),hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X215,X155)),X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).
fof(fact_map__of__is__SomeI,axiom,
! [X127,X6,X288,X105,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X7),c_Product__Type_Ofst(X7,X105)),X288)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),hAPP(c_List_Oset(tc_prod(X7,X105)),X288)))
=> hAPP(c_Map_Omap__of(X7,X105,X288),X6) = hAPP(c_Option_Ooption_OSome(X105),X127) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__is__SomeI) ).
fof(fact_map__of__eq__Some__iff,axiom,
! [X127,X6,X288,X105,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X7),c_Product__Type_Ofst(X7,X105)),X288)))
=> ( hAPP(c_Map_Omap__of(X7,X105,X288),X6) = hAPP(c_Option_Ooption_OSome(X105),X127)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),hAPP(c_List_Oset(tc_prod(X7,X105)),X288))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__eq__Some__iff) ).
fof(fact_Some__eq__map__of__iff,axiom,
! [X6,X127,X288,X105,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X7),c_Product__Type_Ofst(X7,X105)),X288)))
=> ( hAPP(c_Option_Ooption_OSome(X105),X127) = hAPP(c_Map_Omap__of(X7,X105,X288),X6)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),hAPP(c_List_Oset(tc_prod(X7,X105)),X288))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Some__eq__map__of__iff) ).
fof(fact_finite__SigmaI,axiom,
! [X155,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X110] :
( hBOOL(hAPP(hAPP(c_member(X7),X110),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(X155,X110))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__SigmaI) ).
fof(fact_convex__bound__le,axiom,
! [X139,X63,X98,X71,X86,X87] :
( class_Rings_Olinordered__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X63))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X139))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X63),X139) = c_Groups_Oone__class_Oone(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X63),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X139),X98))),X71)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(fact_convex__bound__lt,axiom,
! [X139,X63,X98,X71,X86,X87] :
( class_Rings_Olinordered__semiring__1__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X63))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X139))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X63),X139) = c_Groups_Oone__class_Oone(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X63),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X139),X98))),X71)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_aset_I6_J,axiom,
! [X149,X46,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X46),c_Groups_Oone__class_Oone(tc_Int_Oint))),X149))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X149))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X207),X206) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X46))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X192)),X46)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I6_J) ).
fof(fact_folding_Ocommute__left__comp_H,axiom,
! [X1,X6,X119,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X2,X6)),hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X215,X149)),X1)) = hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X215,X149)),hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X2,X6)),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).
fof(fact_listrel1I,axiom,
! [X293,X323,X324,X292,X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172))
=> ( X292 = hAPP(hAPP(c_List_Oappend(X7),X324),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X323))
=> ( X293 = hAPP(hAPP(c_List_Oappend(X7),X324),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X323))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel1(X7,X172))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I) ).
fof(fact_sum__case__inject,axiom,
! [X202,X203,X21,X22,X105,X119,X7] :
( c_Sum__Type_Osum_Osum__case(X7,X119,X105,X22,X21) = c_Sum__Type_Osum_Osum__case(X7,X119,X105,X203,X202)
=> ~ ( X22 = X203
=> X21 != X202 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__inject) ).
fof(fact_inf__le__fold__inf,axiom,
! [X23,X24,X149,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),X3)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X24),X23)),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),X23),X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le__fold__inf) ).
fof(fact_min__max_Oinf__le__fold__inf,axiom,
! [X23,X24,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),X3)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X24),X23)),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omin(X7)),X23),X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).
fof(fact_setsum__shift__bounds__nat__ivl,axiom,
! [X44,X94,X95,X2,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X94))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X94))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).
fof(fact_in__rtrancl__UnI,axiom,
! [X209,X191,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X6),c_Transitive__Closure_Ortrancl(X7,X191)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X6),c_Transitive__Closure_Ortrancl(X7,X209))) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X6),c_Transitive__Closure_Ortrancl(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X191),X209)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).
fof(fact_folding_Ocommute__left__comp,axiom,
! [X1,X6,X127,X119,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X2,X127)),hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X2,X6)),X1)) = hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X2,X6)),hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X2,X127)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp) ).
fof(fact_range__ex1__eq,axiom,
! [X24,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X105),X24),hAPP(c_Set_Oimage(X7,X105,X2),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))))
<=> ? [X3] :
( X24 = hAPP(X2,X3)
& ! [X82] :
( X24 = hAPP(X2,X82)
=> X82 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_setsum__Un,axiom,
! [X2,X155,X149,X7,X105] :
( class_Groups_Oab__group__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X155))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un) ).
fof(fact_rev__update,axiom,
! [X98,X300,X87,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(c_List_Orev(X87),hAPP(hAPP(c_List_Olist__update(X87,X300),X96),X98)) = hAPP(hAPP(c_List_Olist__update(X87,hAPP(c_List_Orev(X87),X300)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X96)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__update) ).
fof(fact_equiv__imp__dvd__card,axiom,
! [X94,X172,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),hAPP(c_Finite__Set_Ocard(X7),X3))) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),hAPP(c_Finite__Set_Ocard(X7),X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__imp__dvd__card) ).
fof(fact_Collect__imp__eq,axiom,
! [X194,X38,X7] : hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fimplies),X38)),X194)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7),X38))),hAPP(c_Set_OCollect(X7),X194)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__imp__eq) ).
fof(fact_single__valued__def,axiom,
! [X172,X105,X7] :
( c_Relation_Osingle__valued(X7,X105,X172)
<=> ! [X3,X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X3),X82)),X172))
=> ! [X154] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X3),X154)),X172))
=> X82 = X154 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).
fof(fact_prod__size__simp,axiom,
! [X161,X1,X2,X105,X7] : c_Product__Type_Oprod_Oprod__size(X7,X105,X2,X1,X161) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,hAPP(c_Product__Type_Ofst(X7,X105),X161))),hAPP(X1,hAPP(c_Product__Type_Osnd(X7,X105),X161)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__size__simp) ).
fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
! [X44,X94,X95,X2,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X94))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X94))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__nat__ivl) ).
fof(fact_bset_I8_J,axiom,
! [X155,X46,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X46),c_Groups_Oone__class_Oone(tc_Int_Oint))),X155))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X155))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X207),X206) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X46),X3))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X46),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X192))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I8_J) ).
fof(fact_finite__equiv__class,axiom,
! [X39,X172,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),hAPP(hAPP(c_Product__Type_OSigma(X7,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),X149))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X39),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__equiv__class) ).
fof(fact_quotient__eqI,axiom,
! [X127,X6,X60,X39,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X39),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X60),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X39))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X127),X60))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172))
=> X39 = X60 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eqI) ).
fof(fact_quotient__eq__iff,axiom,
! [X127,X6,X60,X39,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X39),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X60),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X39))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X127),X60))
=> ( X39 = X60
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eq__iff) ).
fof(fact_field__le__mult__one__interval,axiom,
! [X98,X86,X87] :
( class_Fields_Olinordered__field__inverse__zero(X87)
=> ( ! [X154] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X154),c_Groups_Oone__class_Oone(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X154),X86)),X98)) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).
fof(fact_curryE,axiom,
! [X24,X25,X2,X105,X7] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X7,X105,tc_HOL_Obool,X2),X25),X24))
=> hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryE) ).
fof(fact_curryD,axiom,
! [X24,X25,X2,X105,X7] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X7,X105,tc_HOL_Obool,X2),X25),X24))
=> hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryD) ).
fof(fact_vimage__eq__UN,axiom,
! [X155,X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X155),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),c_Set_Ovimage(X7,X105,X2)),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),c_Set_Oinsert(X105)),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__eq__UN) ).
fof(fact_Image__eq__UN,axiom,
! [X155,X172,X7,X105] : hAPP(c_Relation_OImage(X105,X7,X172),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X155),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),c_Relation_OImage(X105,X7,X172)),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool)),c_Set_Oinsert(X105)),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__eq__UN) ).
fof(fact_distrib__inf__le,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X97))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),X97)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__inf__le) ).
fof(fact_min__max_Odistrib__inf__le,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X97))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X98),X97)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Odistrib__inf__le) ).
fof(fact_map__of__inject__set,axiom,
! [X293,X292,X105,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X7),c_Product__Type_Ofst(X7,X105)),X292)))
=> ( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X7),c_Product__Type_Ofst(X7,X105)),X293)))
=> ( c_Map_Omap__of(X7,X105,X292) = c_Map_Omap__of(X7,X105,X293)
<=> hAPP(c_List_Oset(tc_prod(X7,X105)),X292) = hAPP(c_List_Oset(tc_prod(X7,X105)),X293) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__inject__set) ).
fof(fact_SUP2__I,axiom,
! [X119,X105,X23,X24,X155,X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ( hBOOL(hAPP(hAPP(hAPP(X155,X25),X24),X23))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_fun(X119,tc_HOL_Obool))),X149),X155),X24),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__I) ).
fof(fact_splitD_H,axiom,
! [X23,X24,X25,X191,X119,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_fun(X119,tc_HOL_Obool)),X191),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),X23))
=> hBOOL(hAPP(hAPP(hAPP(X191,X25),X24),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD_H) ).
fof(fact_rel__comp__distrib2,axiom,
! [X191,X238,X209,X105,X119,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X119),tc_HOL_Obool)),X209),X238)),X191) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),X209),X191)),hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),X238),X191)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__distrib2) ).
fof(fact_inf__INFI__fold__inf,axiom,
! [X2,X155,X149,X7,X105] :
( class_Complete__Lattice_Ocomplete__lattice(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X105),X155),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X105),X149),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,hAPP(hAPP(c_COMBB(X105,tc_fun(X105,X105),X7),c_Lattices_Osemilattice__inf__class_Oinf(X105)),X2)),X155),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__INFI__fold__inf) ).
fof(fact_sup__SUPR__fold__sup,axiom,
! [X2,X155,X149,X7,X105] :
( class_Complete__Lattice_Ocomplete__lattice(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X105),X155),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X105),X149),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,hAPP(hAPP(c_COMBB(X105,tc_fun(X105,X105),X7),c_Lattices_Osemilattice__sup__class_Osup(X105)),X2)),X155),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__SUPR__fold__sup) ).
fof(fact_fun__upd__twist,axiom,
! [X136,X24,X95,X105,X7,X23,X25] :
( X25 != X23
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X95),X25),X24)),X23),X136) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X95),X23),X136)),X25),X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
fof(fact_setsum__Un__nat,axiom,
! [X2,X155,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X155))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__nat) ).
fof(fact_finite__Collect__not,axiom,
! [X38,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),X38)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),X38))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__not) ).
fof(fact_zmult2__lemma__aux1,axiom,
! [X144,X138,X84,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X138))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X138),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,X144,X10))),X138))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).
fof(fact_nat__diff__add__eq2,axiom,
! [X33,X90,X63,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X114),X63)),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X113),X63)),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X113),X114)),X63)),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_abs__setsum__abs,axiom,
! [X149,X2,X105,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> hAPP(c_Groups_Oabs__class_Oabs(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBB(X7,X7,X105),c_Groups_Oabs__class_Oabs(X7)),X2)),X149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBB(X7,X7,X105),c_Groups_Oabs__class_Oabs(X7)),X2)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__setsum__abs) ).
fof(fact_map__upds__list__update2__drop,axiom,
! [X127,X95,X293,X105,X107,X292,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)),X107))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)))
=> c_Map_Omap__upds(X7,X105,X95,X292,hAPP(hAPP(c_List_Olist__update(X105,X293),X107),X127)) = c_Map_Omap__upds(X7,X105,X95,X292,X293) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__list__update2__drop) ).
fof(fact_inj__image__subset__iff,axiom,
! [X155,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),X149)),hAPP(c_Set_Oimage(X7,X105,X2),X155)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
fof(fact_gt__half__sum,axiom,
! [X84,X71,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Oone__class_Oone(X87)),c_Groups_Oone__class_Oone(X87)))),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gt__half__sum) ).
fof(fact_q__neg__lemma,axiom,
! [X145,X146,X124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X124),X146)),X145)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X145))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X124))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X146),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_zip__same,axiom,
! [X292,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),hAPP(c_List_Oset(tc_prod(X7,X7)),hAPP(hAPP(c_List_Ozip(X7,X7),X292),X292))))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_List_Oset(X7),X292)))
& X25 = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__same) ).
fof(fact_set__zip__leftD,axiom,
! [X293,X292,X127,X6,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),hAPP(c_List_Oset(tc_prod(X7,X105)),hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293))))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip__leftD) ).
fof(fact_set__zip__rightD,axiom,
! [X293,X292,X127,X6,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),hAPP(c_List_Oset(tc_prod(X7,X105)),hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293))))
=> hBOOL(hAPP(hAPP(c_member(X105),X127),hAPP(c_List_Oset(X105),X293))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip__rightD) ).
fof(fact_folding_Ounion__inter,axiom,
! [X155,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,X149)),hAPP(X215,X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion__inter) ).
fof(fact_abs__triangle__ineq3,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84)))),hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).
fof(fact_odd__less__0,axiom,
! [X26] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26)),X26)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).
fof(fact_INFI__fold__inf,axiom,
! [X2,X149,X7,X105] :
( class_Complete__Lattice_Ocomplete__lattice(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X105),X149),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,hAPP(hAPP(c_COMBB(X105,tc_fun(X105,X105),X7),c_Lattices_Osemilattice__inf__class_Oinf(X105)),X2)),c_Orderings_Otop__class_Otop(X105)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__fold__inf) ).
fof(fact_SUPR__fold__sup,axiom,
! [X2,X149,X7,X105] :
( class_Complete__Lattice_Ocomplete__lattice(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X105),X149),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,hAPP(hAPP(c_COMBB(X105,tc_fun(X105,X105),X7),c_Lattices_Osemilattice__sup__class_Osup(X105)),X2)),c_Orderings_Obot__class_Obot(X105)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__fold__sup) ).
fof(fact_single__valuedD,axiom,
! [X26,X127,X6,X172,X105,X7] :
( c_Relation_Osingle__valued(X7,X105,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),X172))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X26)),X172))
=> X127 = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedD) ).
fof(fact_evalc_OLocal,axiom,
! [X58,X25,X60,X77,X23] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),hAPP(hAPP(hAPP(c_Natural_Oupdate,X77),c_Com_Ovname_OLoc(X60)),hAPP(X25,X77))),X58))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X60,X25,X23)),X77),hAPP(hAPP(hAPP(c_Natural_Oupdate,X58),c_Com_Ovname_OLoc(X60)),hAPP(hAPP(c_Natural_Ogetlocs,X77),X60)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OLocal) ).
fof(fact_Collect__disj__eq,axiom,
! [X194,X38,X7] : hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fdisj),X38)),X194)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7),X38)),hAPP(c_Set_OCollect(X7),X194)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__disj__eq) ).
fof(fact_Collect__conj__eq,axiom,
! [X194,X38,X7] : hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),X38)),X194)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7),X38)),hAPP(c_Set_OCollect(X7),X194)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conj__eq) ).
fof(fact_map__of__zip__is__Some,axiom,
! [X6,X293,X105,X292,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
<=> ? [X82] : hAPP(c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293)),X6) = hAPP(c_Option_Ooption_OSome(X105),X82) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__is__Some) ).
fof(fact_rtrancl__converseD,axiom,
! [X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,hAPP(c_Relation_Oconverse(X7,X7),X172))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X6)),c_Transitive__Closure_Ortrancl(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).
fof(fact_listsum__const__mult,axiom,
! [X292,X2,X23,X105,X7] :
( class_Rings_Osemiring__0(X7)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),hAPP(hAPP(c_COMBB(X7,X7,X105),hAPP(c_Groups_Otimes__class_Otimes(X7),X23)),X2)),X292)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__const__mult) ).
fof(fact_Image__mono,axiom,
! [X149,X246,X172,X247,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X247),X172))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X246),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X105,X247),X246)),hAPP(c_Relation_OImage(X7,X105,X172),X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__mono) ).
fof(fact_mlex__leq,axiom,
! [X191,X7,X127,X6,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X2,X6)),hAPP(X2,X127)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X191))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Wellfounded_Omlex__prod(X7,X2,X191))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(fact_swap__product,axiom,
! [X155,X149,X7,X105] : hAPP(c_Set_Oimage(tc_prod(X105,X7),tc_prod(X7,X105),hAPP(c_Product__Type_Oprod_Oprod__case(X105,X7,tc_prod(X7,X105)),hAPP(c_COMBC(X7,X105,tc_prod(X7,X105)),c_Product__Type_OPair(X7,X105)))),hAPP(hAPP(c_Product__Type_OSigma(X105,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X105),X155))) = hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X155),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__product) ).
fof(fact_quotientI,axiom,
! [X172,X149,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientI) ).
fof(fact_evaln_OCall,axiom,
! [X39,X58,X44,X25,X77,X40] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X40),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X77),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X25,X77)),X44,X58)
=> c_Natural_Oevaln(c_Com_Ocom_OCall(X39,X40,X25),X77,X44,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X58),hAPP(c_Natural_Ogetlocs,X77))),X39),hAPP(hAPP(c_Natural_Ogetlocs,X58),c_Com_ORes))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OCall) ).
fof(fact_Image__singleton__iff,axiom,
! [X25,X172,X105,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(c_Relation_OImage(X105,X7,X172),hAPP(hAPP(c_Set_Oinsert(X105),X25),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X25),X24)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).
fof(fact_norm__frac_Opinduct,axiom,
! [X38,X42,X187] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X42)))
=> ( ! [X110,X188] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X110),X188)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X188),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(X38,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X110)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X188))) )
=> hBOOL(hAPP(hAPP(X38,X110),X188)) ) )
=> hBOOL(hAPP(hAPP(X38,X187),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Opinduct) ).
fof(fact_aset_I5_J,axiom,
! [X149,X46,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X46),X149))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X149))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X207),X206) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X46))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X192)),X46)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I5_J) ).
fof(fact_div__mod__equality2,axiom,
! [X10,X71,X84,X87] :
( class_Divides_Osemiring__div(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84))),c_Divides_Odiv__class_Omod(X87,X71,X84))),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality2) ).
fof(fact_map__upds__Cons,axiom,
! [X321,X24,X322,X25,X95,X105,X7] : c_Map_Omap__upds(X7,X105,X95,hAPP(hAPP(c_List_Olist_OCons(X7),X25),X322),hAPP(hAPP(c_List_Olist_OCons(X105),X24),X321)) = c_Map_Omap__upds(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X95),X25),hAPP(c_Option_Ooption_OSome(X105),X24)),X322,X321),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__Cons) ).
fof(fact_lexord__Nil__left,axiom,
! [X172,X127,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_ONil(X7)),X127)),c_List_Olexord(X7,X172)))
<=> ? [X110,X3] : X127 = hAPP(hAPP(c_List_Olist_OCons(X7),X110),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).
fof(fact_image__vimage__subset,axiom,
! [X149,X2,X105,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X7,X2),hAPP(c_Set_Ovimage(X105,X7,X2),X149))),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__subset) ).
fof(fact_map__sorted__distinct__set__unique,axiom,
! [X293,X292,X2,X7,X105] :
( class_Orderings_Olinorder(X105)
=> ( c_Fun_Oinj__on(X7,X105,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X292)),hAPP(c_List_Oset(X7),X293)))
=> ( c_List_Olinorder__class_Osorted(X105,hAPP(hAPP(c_List_Omap(X7,X105),X2),X292))
=> ( hBOOL(hAPP(c_List_Odistinct(X105),hAPP(hAPP(c_List_Omap(X7,X105),X2),X292)))
=> ( c_List_Olinorder__class_Osorted(X105,hAPP(hAPP(c_List_Omap(X7,X105),X2),X293))
=> ( hBOOL(hAPP(c_List_Odistinct(X105),hAPP(hAPP(c_List_Omap(X7,X105),X2),X293)))
=> ( hAPP(c_List_Oset(X7),X292) = hAPP(c_List_Oset(X7),X293)
=> X292 = X293 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__sorted__distinct__set__unique) ).
fof(fact_zmult2__lemma__aux3,axiom,
! [X144,X84,X138,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X138))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X138),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,X144,X10))),X138))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).
fof(fact_finite__quotient,axiom,
! [X172,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),hAPP(hAPP(c_Product__Type_OSigma(X7,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),X149))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__quotient) ).
fof(fact_foldl__append,axiom,
! [X293,X292,X25,X2,X105,X7] : hAPP(c_List_Ofoldl(X7,X105,X2,X25),hAPP(hAPP(c_List_Oappend(X105),X292),X293)) = hAPP(c_List_Ofoldl(X7,X105,X2,hAPP(c_List_Ofoldl(X7,X105,X2,X25),X292)),X293),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__append) ).
fof(fact_rtrancl__converseI,axiom,
! [X172,X6,X127,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X6)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,hAPP(c_Relation_Oconverse(X7,X7),X172)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).
fof(fact_zip__append1,axiom,
! [X299,X301,X300,X7,X87] : hAPP(hAPP(c_List_Ozip(X87,X7),hAPP(hAPP(c_List_Oappend(X87),X300),X301)),X299) = hAPP(hAPP(c_List_Oappend(tc_prod(X87,X7)),hAPP(hAPP(c_List_Ozip(X87,X7),X300),hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X299))),hAPP(hAPP(c_List_Ozip(X87,X7),X301),hAPP(hAPP(c_List_Odrop(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X299))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append1) ).
fof(fact_Diff__subset__conv,axiom,
! [X193,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X193))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X193))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).
fof(fact_evaln_Oequations_I4_J,axiom,
! [X72,X41,X43,X61,X42] :
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X42,X61),X43,X41,X72)
<=> ? [X62] :
( c_Natural_Oevaln(X42,X43,X41,X62)
& c_Natural_Oevaln(X61,X62,X41,X72) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I4_J) ).
fof(fact_map__add__upd,axiom,
! [X127,X6,X1,X2,X105,X7] : c_Map_Omap__add(X7,X105,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X1),X6),hAPP(c_Option_Ooption_OSome(X105),X127))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Omap__add(X7,X105,X2,X1)),X6),hAPP(c_Option_Ooption_OSome(X105),X127)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__upd) ).
fof(fact_bset_I6_J,axiom,
! [X46,X155,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X155))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X207),X206) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X46))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X192)),X46)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I6_J) ).
fof(fact_bset_I5_J,axiom,
! [X46,X155,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X155))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X207),X206) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X46))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X192)),X46)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I5_J) ).
fof(fact_setprod__Un__Int,axiom,
! [X1,X155,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__Int) ).
fof(fact_setprod_Ounion__inter,axiom,
! [X1,X155,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__inter) ).
fof(fact_setsum__Un__Int,axiom,
! [X1,X155,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__Int) ).
fof(fact_inf2I,axiom,
! [X105,X7,X155,X127,X6,X149] :
( hBOOL(hAPP(hAPP(X149,X6),X127))
=> ( hBOOL(hAPP(hAPP(X155,X6),X127))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X149),X155),X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2I) ).
fof(fact_vimage__subsetD,axiom,
! [X149,X155,X2,X7,X105] :
( hAPP(c_Set_Oimage(X105,X7,X2),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X105,X7,X2),X155)),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(c_Set_Oimage(X105,X7,X2),X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetD) ).
fof(fact_bset_I7_J,axiom,
! [X155,X46,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X46),X155))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X155))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X207),X206) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),X3))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X192))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I7_J) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [X145,X146,X124,X138,X144,X84] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X144)),X138) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X124),X146)),X145)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X124),X146)),X145)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X145),X124))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X138))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X124))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X124),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X144),X146)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_converse__INTER,axiom,
! [X172,X209,X119,X7,X105] : hAPP(c_Relation_Oconverse(X105,X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(tc_prod(X105,X7),tc_HOL_Obool)),X209),X172)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X209),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X105,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X105),tc_HOL_Obool),X119),c_Relation_Oconverse(X105,X7)),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__INTER) ).
fof(fact_converse__UNION,axiom,
! [X172,X209,X119,X7,X105] : hAPP(c_Relation_Oconverse(X105,X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(tc_prod(X105,X7),tc_HOL_Obool)),X209),X172)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X209),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X105,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X105),tc_HOL_Obool),X119),c_Relation_Oconverse(X105,X7)),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__UNION) ).
fof(fact_eq__Abs__Integ,axiom,
! [X26] :
~ ! [X3,X82] : X26 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X82)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__Abs__Integ) ).
fof(fact_image__iff,axiom,
! [X149,X2,X105,X26,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X26),hAPP(c_Set_Oimage(X105,X7,X2),X149)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
& X26 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_eq__equiv__class__iff2,axiom,
! [X127,X6,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X127),X149))
=> ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X172) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),hAPP(hAPP(c_Set_Oinsert(X7),X127),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X172)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff2) ).
fof(fact_split__comp,axiom,
! [X6,X1,X2,X190,X7,X119,X105] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,X7),hAPP(c_Fun_Ocomp(X190,tc_fun(X119,X7),X105,X2),X1)),X6) = hAPP(hAPP(X2,hAPP(X1,hAPP(c_Product__Type_Ofst(X105,X119),X6))),hAPP(c_Product__Type_Osnd(X105,X119),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__comp) ).
fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
! [X155,X149] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X149),X155))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X149)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I5_J) ).
fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
! [X155,X149] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X149),X155))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X149)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I4_J) ).
fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
! [X214,X200,X7] :
( class_Orderings_Olinorder(X7)
=> ( ! [X3,X82] : hAPP(X200,hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X3),X82)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),hAPP(X200,X3)),hAPP(X200,X82))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> ( X214 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X200,c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X214)) = c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(c_Set_Oimage(X7,X7,X200),X214)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).
fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
! [X214,X200,X7] :
( class_Orderings_Olinorder(X7)
=> ( ! [X3,X82] : hAPP(X200,hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X3),X82)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),hAPP(X200,X3)),hAPP(X200,X82))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> ( X214 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X200,c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X214)) = c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(c_Set_Oimage(X7,X7,X200),X214)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).
fof(fact_vimage__subsetI,axiom,
! [X149,X155,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),X155),hAPP(c_Set_Oimage(X7,X105,X2),X149)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7,X105,X2),X155)),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetI) ).
fof(fact_converse__iff,axiom,
! [X172,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),hAPP(c_Relation_Oconverse(X105,X7),X172)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X24),X25)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__iff) ).
fof(fact_converseD,axiom,
! [X172,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),hAPP(c_Relation_Oconverse(X105,X7),X172)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X24),X25)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseD) ).
fof(fact_sup2I1,axiom,
! [X155,X105,X7,X127,X6,X149] :
( hBOOL(hAPP(hAPP(X149,X6),X127))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X149),X155),X6),X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I1) ).
fof(fact_sup2I2,axiom,
! [X149,X105,X7,X127,X6,X155] :
( hBOOL(hAPP(hAPP(X155,X6),X127))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X149),X155),X6),X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I2) ).
fof(fact_Int__mono,axiom,
! [X192,X155,X193,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X193))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X192))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X193),X192))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).
fof(fact_Un__mono,axiom,
! [X192,X155,X193,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X193))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X192))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X193),X192))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).
fof(fact_Diff__mono,axiom,
! [X155,X192,X193,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X193))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X192),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X193),X192))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__mono) ).
fof(fact_hom__fold1__commute,axiom,
! [X214,X200,X7] :
( class_Lattices_Oab__semigroup__idem__mult(X7)
=> ( ! [X3,X82] : hAPP(X200,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X3),X82)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(X200,X3)),hAPP(X200,X82))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> ( X214 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X200,hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),X214)) = hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),hAPP(c_Set_Oimage(X7,X7,X200),X214)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hom__fold1__commute) ).
fof(fact_setprod_Oreindex,axiom,
! [X1,X200,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( c_Fun_Oinj__on(X7,X7,X200,X149)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(c_Set_Oimage(X7,X7,X200),X149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(c_Fun_Ocomp(X7,X105,X7,X1),X200)),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oreindex) ).
fof(fact_setsum_Oreindex,axiom,
! [X1,X200,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( c_Fun_Oinj__on(X7,X7,X200,X149)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(c_Set_Oimage(X7,X7,X200),X149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(c_Fun_Ocomp(X7,X105,X7,X1),X200)),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oreindex) ).
fof(fact_acc_OaccI,axiom,
! [X172,X6,X7] :
( ! [X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X6)),X172))
=> hBOOL(hAPP(hAPP(c_member(X7),X82),c_Wellfounded_Oacc(X7,X172))) )
=> hBOOL(hAPP(hAPP(c_member(X7),X6),c_Wellfounded_Oacc(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
fof(fact_acc_Osimps,axiom,
! [X172,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Wellfounded_Oacc(X7,X172)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X25)),X172))
=> hBOOL(hAPP(hAPP(c_member(X7),X3),c_Wellfounded_Oacc(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
fof(fact_rtrancl__listrel1__eq__len,axiom,
! [X172,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),X127)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X7),c_List_Olistrel1(X7,X172))))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X6) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X127) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
fof(fact_list__update_Osimps_I2_J,axiom,
! [X163,X107,X292,X6,X7] : hAPP(hAPP(c_List_Olist__update(X7,hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),X107),X163) = c_Nat_Onat_Onat__case(tc_List_Olist(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X163),X292),hAPP(hAPP(c_COMBB(tc_List_Olist(X7),tc_List_Olist(X7),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X7),X6)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X7,tc_List_Olist(X7)),c_List_Olist__update(X7,X292)),X163)),X107),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update_Osimps_I2_J) ).
fof(fact_split__eta,axiom,
! [X2,X119,X105,X7] : hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,X119),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_prod(X7,X105)),tc_fun(X105,X119),X7),hAPP(c_COMBB(tc_prod(X7,X105),X119,X105),X2)),c_Product__Type_OPair(X7,X105))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__eta) ).
fof(fact_aset_I8_J,axiom,
! [X46,X149,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X149))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X207),X206) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X46),X3))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X46),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X192))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I8_J) ).
fof(fact_aset_I7_J,axiom,
! [X46,X149,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X149))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X207),X206) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),X3))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X192))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I7_J) ).
fof(fact_nth__take__lemma,axiom,
! [X301,X300,X87,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X301)))
=> ( ! [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X147),X96))
=> hAPP(hAPP(c_List_Onth(X87),X300),X147) = hAPP(hAPP(c_List_Onth(X87),X301),X147) )
=> hAPP(hAPP(c_List_Otake(X87),X96),X300) = hAPP(hAPP(c_List_Otake(X87),X96),X301) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__take__lemma) ).
fof(fact_rel__pow__0__E,axiom,
! [X191,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X191)))
=> X6 = X127 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__0__E) ).
fof(fact_exI__realizer,axiom,
! [X7,X105,X6,X127,X38] :
( hBOOL(hAPP(hAPP(X38,X127),X6))
=> hBOOL(hAPP(hAPP(X38,hAPP(c_Product__Type_Osnd(X105,X7),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X6),X127))),hAPP(c_Product__Type_Ofst(X105,X7),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X6),X127)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exI__realizer) ).
fof(fact_comp__inj__on__iff,axiom,
! [X245,X119,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( c_Fun_Oinj__on(X105,X119,X245,hAPP(c_Set_Oimage(X7,X105,X2),X149))
<=> c_Fun_Oinj__on(X7,X119,hAPP(c_Fun_Ocomp(X105,X119,X7,X245),X2),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on__iff) ).
fof(fact_comp__surj,axiom,
! [X1,X119,X2,X7,X105] :
( hAPP(c_Set_Oimage(X105,X7,X2),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))
=> ( hAPP(c_Set_Oimage(X7,X119,X1),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X119,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(X105,X119,hAPP(c_Fun_Ocomp(X7,X119,X105,X1),X2)),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X119,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__surj) ).
fof(fact_zdiv__zmod__equality,axiom,
! [X96,X71,X84] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84))),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).
fof(fact_setprod__reindex,axiom,
! [X200,X155,X2,X105,X7,X119] :
( class_Groups_Ocomm__monoid__mult(X119)
=> ( c_Fun_Oinj__on(X7,X105,X2,X155)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X119),X200),hAPP(c_Set_Oimage(X7,X105,X2),X155)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X119),hAPP(c_Fun_Ocomp(X105,X119,X7,X200),X2)),X155) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex) ).
fof(fact_setsum__reindex,axiom,
! [X200,X155,X2,X105,X7,X119] :
( class_Groups_Ocomm__monoid__add(X119)
=> ( c_Fun_Oinj__on(X7,X105,X2,X155)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X119),X200),hAPP(c_Set_Oimage(X7,X105,X2),X155)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X119),hAPP(c_Fun_Ocomp(X105,X119,X7,X200),X2)),X155) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex) ).
fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).
fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).
fof(fact_lexn__length,axiom,
! [X44,X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),hAPP(c_List_Olexn(X7,X172),X44)))
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = X44
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X293) = X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn__length) ).
fof(fact_converseI,axiom,
! [X172,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),X172))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X24),X25)),hAPP(c_Relation_Oconverse(X7,X105),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseI) ).
fof(fact_rel__comp__distrib,axiom,
! [X238,X209,X191,X105,X119,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),X191),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X119,X105),tc_HOL_Obool)),X209),X238)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),X191),X209)),hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),X191),X238)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__distrib) ).
fof(fact_bot__empty__eq2,axiom,
! [X127,X6,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X6),X127))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).
fof(fact_transpose__transpose,axiom,
! [X292,X7] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X7))),X292)))
=> c_List_Otranspose(X7,c_List_Otranspose(X7,X292)) = c_List_OtakeWhile(tc_List_Olist(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X7)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_List_Olist(X7),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X7))),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__transpose) ).
fof(fact_Inf__fin_Ohom__commute,axiom,
! [X214,X200,X7] :
( class_Lattices_Olattice(X7)
=> ( ! [X3,X82] : hAPP(X200,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X3),X82)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),hAPP(X200,X3)),hAPP(X200,X82))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> ( X214 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X200,c_Big__Operators_Olattice__class_OInf__fin(X7,X214)) = c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(c_Set_Oimage(X7,X7,X200),X214)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ohom__commute) ).
fof(fact_Min_Ohom__commute,axiom,
! [X214,X200,X7] :
( class_Orderings_Olinorder(X7)
=> ( ! [X3,X82] : hAPP(X200,hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X3),X82)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),hAPP(X200,X3)),hAPP(X200,X82))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> ( X214 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X200,c_Big__Operators_Olinorder__class_OMin(X7,X214)) = c_Big__Operators_Olinorder__class_OMin(X7,hAPP(c_Set_Oimage(X7,X7,X200),X214)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ohom__commute) ).
fof(fact_Max_Ohom__commute,axiom,
! [X214,X200,X7] :
( class_Orderings_Olinorder(X7)
=> ( ! [X3,X82] : hAPP(X200,hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X3),X82)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),hAPP(X200,X3)),hAPP(X200,X82))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> ( X214 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X200,c_Big__Operators_Olinorder__class_OMax(X7,X214)) = c_Big__Operators_Olinorder__class_OMax(X7,hAPP(c_Set_Oimage(X7,X7,X200),X214)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ohom__commute) ).
fof(fact_Sup__fin_Ohom__commute,axiom,
! [X214,X200,X7] :
( class_Lattices_Olattice(X7)
=> ( ! [X3,X82] : hAPP(X200,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X3),X82)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),hAPP(X200,X3)),hAPP(X200,X82))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> ( X214 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X200,c_Big__Operators_Olattice__class_OSup__fin(X7,X214)) = c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(c_Set_Oimage(X7,X7,X200),X214)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ohom__commute) ).
fof(fact_periodic__finite__ex,axiom,
! [X38,X136] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X136))
=> ( ! [X3,X118] :
( hBOOL(hAPP(X38,X3))
<=> hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X118),X136)))) )
=> ( ? [X142] : hBOOL(hAPP(X38,X142))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X136)))
& hBOOL(hAPP(X38,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_periodic__finite__ex) ).
fof(fact_listrel__Nil1,axiom,
! [X172,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_ONil(X7)),X292)),c_List_Olistrel(X7,X172)))
=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil1) ).
fof(fact_the__elem__def,axiom,
! [X39,X7] : c_Set_Othe__elem(X7,X39) = c_HOL_OThe(X7,hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7),hAPP(c_fequal,X39)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__def) ).
fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
! [X155,X149] :
( c_Nat__Transfer_Onat__set(X149)
=> ( c_Nat__Transfer_Onat__set(X155)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X149),X155))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X149)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X155))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I5_J) ).
fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
! [X155,X149] :
( c_Nat__Transfer_Onat__set(X149)
=> ( c_Nat__Transfer_Onat__set(X155)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X149),X155))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X149)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X155))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I4_J) ).
fof(fact_union__comp__emptyL,axiom,
! [X155,X193,X149,X7] :
( hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X149),X193) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))
=> ( hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X155),X193) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))
=> hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X149),X155)),X193) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__comp__emptyL) ).
fof(fact_int__def,axiom,
! [X95] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X95),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__def) ).
fof(fact_distrib__sup__le,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),X97))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X97)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__sup__le) ).
fof(fact_min__max_Odistrib__sup__le,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X98),X97))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X97)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Odistrib__sup__le) ).
fof(fact_fold__inf__le__inf,axiom,
! [X24,X25,X149,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),X24),X149)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X25),X24))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__inf__le__inf) ).
fof(fact_min__max_Ofold__inf__le__inf,axiom,
! [X24,X25,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omin(X7)),X24),X149)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X25),X24))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).
fof(fact_set__update__subsetI,axiom,
! [X107,X6,X149,X292,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X292)),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist__update(X7,X292),X107),X6))),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__subsetI) ).
fof(fact_setsum__ub__add__nat,axiom,
! [X161,X2,X44,X95,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X161))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X161)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__ub__add__nat) ).
fof(fact_Times__Int__distrib1,axiom,
! [X193,X155,X149,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X193)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X193))),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X155),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X193))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).
fof(fact_Times__Un__distrib1,axiom,
! [X193,X155,X149,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X193)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X193))),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X155),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X193))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Un__distrib1) ).
fof(fact_Times__Diff__distrib1,axiom,
! [X193,X155,X149,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X193)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X193))),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X155),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X193))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Diff__distrib1) ).
fof(fact_card__inj__on__le,axiom,
! [X155,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),X149)),X155))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X105),X155))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_fold__image__1,axiom,
! [X2,X209,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X209))
=> hAPP(X2,X3) = c_Groups_Oone__class_Oone(X105) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X2),c_Groups_Oone__class_Oone(X105)),X209) = c_Groups_Oone__class_Oone(X105) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__1) ).
fof(fact_surjective__sum,axiom,
! [X2,X105,X119,X7] : c_Sum__Type_Osum_Osum__case(X7,X119,X105,hAPP(hAPP(c_COMBB(tc_sum(X7,X105),X119,X7),X2),c_Sum__Type_OInl(X7,X105)),hAPP(hAPP(c_COMBB(tc_sum(X7,X105),X119,X105),X2),c_Sum__Type_OInr(X105,X7))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surjective__sum) ).
fof(fact_sum__case__KK,axiom,
! [X6,X25,X119,X7,X105] : hAPP(c_Sum__Type_Osum_Osum__case(X105,X7,X119,hAPP(c_COMBK(X7,X105),X25),hAPP(c_COMBK(X7,X119),X25)),X6) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__KK) ).
fof(fact_map__of__filter__in,axiom,
! [X38,X26,X94,X292,X7,X105] :
( hAPP(c_Map_Omap__of(X105,X7,X292),X94) = hAPP(c_Option_Ooption_OSome(X7),X26)
=> ( hBOOL(hAPP(hAPP(X38,X94),X26))
=> hAPP(c_Map_Omap__of(X105,X7,hAPP(c_List_Ofilter(tc_prod(X105,X7),hAPP(c_Product__Type_Oprod_Oprod__case(X105,X7,tc_HOL_Obool),X38)),X292)),X94) = hAPP(c_Option_Ooption_OSome(X7),X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__filter__in) ).
fof(fact_listrel__Nil2,axiom,
! [X172,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),c_List_Olist_ONil(X7))),c_List_Olistrel(X7,X172)))
=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil2) ).
fof(fact_INF__commute,axiom,
! [X2,X155,X119,X149,X105,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,X7),X149),hAPP(hAPP(c_COMBB(tc_fun(X119,X7),X7,X105),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,X7),X155)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,X7),X155),hAPP(hAPP(c_COMBB(tc_fun(X105,X7),X7,X119),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,X7),X149)),hAPP(c_COMBC(X105,X119,X7),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__commute) ).
fof(fact_SUP__commute,axiom,
! [X2,X155,X119,X149,X105,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,X7),X149),hAPP(hAPP(c_COMBB(tc_fun(X119,X7),X7,X105),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,X7),X155)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,X7),X155),hAPP(hAPP(c_COMBB(tc_fun(X105,X7),X7,X119),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,X7),X149)),hAPP(c_COMBC(X105,X119,X7),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__commute) ).
fof(fact_eq__equiv__class__iff,axiom,
! [X127,X6,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X127),X149))
=> ( hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X127),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff) ).
fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
! [X2,X149,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,tc_Int_Oint),X2),X149) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X7),c_Int_Onat),X2)),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).
fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
! [X2,X149,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Int_Oint),X2),X149) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X7),c_Int_Onat),X2)),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).
fof(fact_listrel1__eq__len,axiom,
! [X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel1(X7,X172)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X293) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).
fof(fact_listrel__eq__len,axiom,
! [X172,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X293)),c_List_Olistrel(X7,X172)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X293) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__eq__len) ).
fof(fact_Sigma__Union,axiom,
! [X155,X39,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X39)),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X39),hAPP(hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(X105,tc_HOL_Obool)),tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),c_Product__Type_OSigma(X7,X105)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Union) ).
fof(fact_bset_I4_J,axiom,
! [X155,X46,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X46),X155))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X155))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X207),X206) ) )
=> ( X3 != X46
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X192) != X46 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I4_J) ).
fof(fact_aset_I4_J,axiom,
! [X149,X46,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X46),X149))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X149))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X207),X206) ) )
=> ( X3 != X46
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X192) != X46 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I4_J) ).
fof(fact_fold__def,axiom,
! [X149,X26,X2,X7,X105] : hAPP(hAPP(c_Finite__Set_Ofold(X105,X7,X2),X26),X149) = c_HOL_OThe(X7,c_Finite__Set_Ofold__graph(X105,X7,X2,X26,X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__def) ).
fof(fact_split__paired__All,axiom,
! [X105,X7,X38] :
( ! [X142] : hBOOL(hAPP(X38,X142))
<=> ! [X110,X188] : hBOOL(hAPP(X38,hAPP(hAPP(c_Product__Type_OPair(X7,X105),X110),X188))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
fof(fact_curryI,axiom,
! [X24,X25,X105,X7,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)))
=> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X7,X105,tc_HOL_Obool,X2),X25),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryI) ).
fof(fact_diff__card__le__card__Diff,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X7),X155))),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__card__le__card__Diff) ).
fof(fact_inj__on__Inter,axiom,
! [X2,X105,X7,X209] :
( X209 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))
=> ( ! [X239] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X239),X209))
=> c_Fun_Oinj__on(X7,X105,X2,X239) )
=> c_Fun_Oinj__on(X7,X105,X2,c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X209)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Inter) ).
fof(fact_card__UNIV__bool,axiom,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__bool) ).
fof(fact_Nitpick_Orefl_H__def,axiom,
! [X172,X7] :
( c_Nitpick_Orefl_H(X7,X172)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_decr__mult__lemma,axiom,
! [X94,X38,X136] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X136))
=> ( ! [X3] :
( hBOOL(hAPP(X38,X3))
=> hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X136))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
=> ! [X3] :
( hBOOL(hAPP(X38,X3))
=> hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X136)))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).
fof(fact_incr__mult__lemma,axiom,
! [X94,X38,X136] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X136))
=> ( ! [X3] :
( hBOOL(hAPP(X38,X3))
=> hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X136))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
=> ! [X3] :
( hBOOL(hAPP(X38,X3))
=> hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X136)))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).
fof(fact_nat__1__add__1,axiom,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
fof(fact_folding__idem_Oidem__left__comp,axiom,
! [X1,X6,X119,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding__idem(X7,X105,X2,X215)
=> hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X2,X6)),hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X2,X6)),X1)) = hAPP(c_Fun_Ocomp(X105,X105,X119,hAPP(X2,X6)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).
fof(fact_mem__splitI,axiom,
! [X119,X105,X24,X25,X23,X26,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X26),hAPP(hAPP(X23,X25),X24)))
=> hBOOL(hAPP(hAPP(c_member(X7),X26),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,tc_fun(X7,tc_HOL_Obool)),X23),hAPP(hAPP(c_Product__Type_OPair(X105,X119),X25),X24)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI) ).
fof(fact_listrel__Cons,axiom,
! [X292,X6,X172,X7] : hAPP(c_Relation_OImage(tc_List_Olist(X7),tc_List_Olist(X7),c_List_Olistrel(X7,X172)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X7),tc_HOL_Obool)))) = c_List_Oset__Cons(X7,hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X7),tc_List_Olist(X7),c_List_Olistrel(X7,X172)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X7)),X292),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X7),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons) ).
fof(fact_UN__le__add__shift,axiom,
! [X94,X210,X44,X7] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X44)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool),tc_Nat_Onat),X210),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X94))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X94))),X210),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__le__add__shift) ).
fof(fact_numeral__2__eq__2,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
fof(fact_semiring__norm_I115_J,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(fact_fun__upds__append__drop,axiom,
! [X302,X95,X293,X105,X292,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)
=> c_Map_Omap__upds(X7,X105,X95,hAPP(hAPP(c_List_Oappend(X7),X292),X302),X293) = c_Map_Omap__upds(X7,X105,X95,X292,X293) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upds__append__drop) ).
fof(fact_fun__upds__append2__drop,axiom,
! [X302,X95,X293,X105,X292,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)
=> c_Map_Omap__upds(X7,X105,X95,X292,hAPP(hAPP(c_List_Oappend(X105),X293),X302)) = c_Map_Omap__upds(X7,X105,X95,X292,X293) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upds__append2__drop) ).
fof(fact_option__map__eq__Some,axiom,
! [X127,X217,X2,X7,X105] :
( hAPP(hAPP(c_Option_Omap(X105,X7),X2),X217) = hAPP(c_Option_Ooption_OSome(X7),X127)
<=> ? [X154] :
( X217 = hAPP(c_Option_Ooption_OSome(X105),X154)
& hAPP(X2,X154) = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__eq__Some) ).
fof(fact_override__on__apply__in,axiom,
! [X1,X2,X105,X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(c_Fun_Ooverride__on(X7,X105,X2,X1,X149),X25) = hAPP(X1,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__apply__in) ).
fof(fact_restrict__map__insert,axiom,
! [X149,X25,X2,X105,X7] : c_Map_Orestrict__map(X7,X105,X2,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Orestrict__map(X7,X105,X2,X149)),X25),hAPP(X2,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__insert) ).
fof(fact_lexord__append__rightI,axiom,
! [X172,X6,X7,X127] :
( ? [X188,X154] : X127 = hAPP(hAPP(c_List_Olist_OCons(X7),X188),X154)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),hAPP(hAPP(c_List_Oappend(X7),X6),X127))),c_List_Olexord(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).
fof(fact_list__eq__iff__zip__eq,axiom,
! [X7,X293,X292] :
( X292 = X293
<=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X293)
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X3),hAPP(c_List_Oset(tc_prod(X7,X7)),hAPP(hAPP(c_List_Ozip(X7,X7),X292),X293))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),c_fequal),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__eq__iff__zip__eq) ).
fof(fact_nat__gcd_Opinduct,axiom,
! [X38,X42,X187] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X187),X42)))
=> ( ! [X3,X82] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X82)))
=> ( ( X82 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(X38,X82),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X82))) )
=> hBOOL(hAPP(hAPP(X38,X3),X82)) ) )
=> hBOOL(hAPP(hAPP(X38,X187),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Opinduct) ).
fof(fact_inj__on__strict__subset,axiom,
! [X149,X155,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X155)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),X149)),hAPP(c_Set_Oimage(X7,X105,X2),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
fof(fact_evalc_Oequations_I4_J,axiom,
! [X61,X43,X47,X42] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X42,X47)),X43),X61))
<=> ? [X62] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X42),X43),X62))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X47),X62),X61)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I4_J) ).
fof(fact_inj__on__image__Int,axiom,
! [X155,X149,X193,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X193)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X193))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X193))
=> hAPP(c_Set_Oimage(X7,X105,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),X149)),hAPP(c_Set_Oimage(X7,X105,X2),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__Int) ).
fof(fact_inj__on__image__set__diff,axiom,
! [X155,X149,X193,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X193)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X193))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X193))
=> hAPP(c_Set_Oimage(X7,X105,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),X149)),hAPP(c_Set_Oimage(X7,X105,X2),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__set__diff) ).
fof(fact_filter__in__sublist,axiom,
! [X45,X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> hAPP(c_List_Ofilter(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),hAPP(c_List_Oset(X7),c_List_Osublist(X7,X292,X45)))),X292) = c_List_Osublist(X7,X292,X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__in__sublist) ).
fof(fact_endo__inj__surj,axiom,
! [X2,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X7,X2),X149)),X149))
=> ( c_Fun_Oinj__on(X7,X7,X2,X149)
=> hAPP(c_Set_Oimage(X7,X7,X2),X149) = X149 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
fof(fact_insort__insert__key__triv,axiom,
! [X292,X105,X6,X2,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X6)),hAPP(c_Set_Oimage(X105,X7,X2),hAPP(c_List_Oset(X105),X292))))
=> c_List_Olinorder__class_Oinsort__insert__key(X105,X7,X2,X6,X292) = X292 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__key__triv) ).
fof(fact_set__insort__insert,axiom,
! [X292,X6,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(c_List_Oset(X7),c_List_Olinorder__class_Oinsort__insert__key(X7,X7,c_COMBI(X7),X6,X292)) = hAPP(hAPP(c_Set_Oinsert(X7),X6),hAPP(c_List_Oset(X7),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__insort__insert) ).
fof(fact_listrel1__subset__listrel,axiom,
! [X247,X172,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X247))
=> ( c_Relation_Orefl__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),X247)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool)),c_List_Olistrel1(X7,X172)),c_List_Olistrel(X7,X247))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__subset__listrel) ).
fof(fact_folding__image_Oeq__fold,axiom,
! [X1,X149,X215,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image(X7,X105,X2,X26,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> hAPP(hAPP(X215,X1),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X105,X2),X1),X26),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oeq__fold) ).
fof(fact_fun__left__comm_Ofold__rec,axiom,
! [X26,X6,X149,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),X149) = hAPP(hAPP(X2,X6),hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).
fof(fact_hoare__valids__def,axiom,
! [X223,X216,X7] :
( c_Hoare__Mirabelle_Ohoare__valids(X7,X216,X223)
<=> ! [X70] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X7)),X3),X216))
=> c_Hoare__Mirabelle_Otriple__valid(X7,X70,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X7)),X3),X223))
=> c_Hoare__Mirabelle_Otriple__valid(X7,X70,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__valids__def) ).
fof(fact_sum_Osimps_I5_J,axiom,
! [X25,X21,X22,X119,X7,X105] : hAPP(c_Sum__Type_Osum_Osum__case(X105,X7,X119,X22,X21),hAPP(c_Sum__Type_OInl(X105,X119),X25)) = hAPP(X22,X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I5_J) ).
fof(fact_sum_Osimps_I6_J,axiom,
! [X24,X21,X22,X119,X7,X105] : hAPP(c_Sum__Type_Osum_Osum__case(X105,X7,X119,X22,X21),hAPP(c_Sum__Type_OInr(X119,X105),X24)) = hAPP(X21,X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I6_J) ).
fof(fact_vimage__compose,axiom,
! [X6,X2,X1,X119,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,hAPP(c_Fun_Ocomp(X119,X105,X7,X1),X2)),X6) = hAPP(c_Set_Ovimage(X7,X119,X2),hAPP(c_Set_Ovimage(X119,X105,X1),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__compose) ).
fof(fact_image__compose,axiom,
! [X172,X1,X2,X119,X7,X105] : hAPP(c_Set_Oimage(X105,X7,hAPP(c_Fun_Ocomp(X119,X7,X105,X2),X1)),X172) = hAPP(c_Set_Oimage(X119,X7,X2),hAPP(c_Set_Oimage(X105,X119,X1),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__compose) ).
fof(fact_rtrancl__power,axiom,
! [X191,X161,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),c_Transitive__Closure_Ortrancl(X7,X191)))
<=> ? [X70] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X70),X191))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__power) ).
fof(fact_scomp__unfold,axiom,
! [X6,X1,X2,X7,X190,X119,X105] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X105,X119,X190,X7),X2),X1),X6) = hAPP(hAPP(X1,hAPP(c_Product__Type_Ofst(X119,X190),hAPP(X2,X6))),hAPP(c_Product__Type_Osnd(X119,X190),hAPP(X2,X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__unfold) ).
fof(fact_equiv__class__eq__iff,axiom,
! [X127,X6,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172))
<=> ( hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X127),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
& hBOOL(hAPP(hAPP(c_member(X7),X127),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq__iff) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [X127,X6,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X127),X127))))
<=> ( X6 != c_Groups_Ozero__class_Ozero(X7)
| X127 != c_Groups_Ozero__class_Ozero(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_rtrancl__is__UN__rel__pow,axiom,
! [X191,X7] : c_Transitive__Closure_Ortrancl(X7,X191) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool)),X191)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).
fof(fact_inj__on__imageI,axiom,
! [X149,X2,X1,X119,X105,X7] :
( c_Fun_Oinj__on(X7,X105,hAPP(c_Fun_Ocomp(X119,X105,X7,X1),X2),X149)
=> c_Fun_Oinj__on(X119,X105,X1,hAPP(c_Set_Oimage(X7,X119,X2),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI) ).
fof(fact_setsum__eq__Suc0__iff,axiom,
! [X2,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X149) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& hAPP(X2,X3) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& ! [X206] :
( hBOOL(hAPP(hAPP(c_member(X7),X206),X149))
=> ( X3 != X206
=> hAPP(X2,X206) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__Suc0__iff) ).
fof(fact_sorted__insort__insert,axiom,
! [X6,X292,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,X292)
=> c_List_Olinorder__class_Osorted(X7,c_List_Olinorder__class_Oinsort__insert__key(X7,X7,c_COMBI(X7),X6,X292)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__insert) ).
fof(fact_abs__mult__less,axiom,
! [X106,X84,X10,X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X84)),X106))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X106))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__less) ).
fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
! [X6,X26,X149,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(X2,X6),hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).
fof(fact_takeWhile__map,axiom,
! [X292,X2,X105,X38,X7] : c_List_OtakeWhile(X7,X38,hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)) = hAPP(hAPP(c_List_Omap(X105,X7),X2),c_List_OtakeWhile(X105,hAPP(c_Fun_Ocomp(X7,tc_HOL_Obool,X105,X38),X2),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__map) ).
fof(fact_setsum__eq__1__iff,axiom,
! [X2,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X149) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& hAPP(X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& ! [X206] :
( hBOOL(hAPP(hAPP(c_member(X7),X206),X149))
=> ( X3 != X206
=> hAPP(X2,X206) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).
fof(fact_refl__on__comp__subset,axiom,
! [X172,X149,X7] :
( c_Relation_Orefl__on(X7,X149,X172)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),hAPP(c_Relation_Oconverse(X7,X7),X172)),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__comp__subset) ).
fof(fact_comp__inj__on,axiom,
! [X1,X119,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( c_Fun_Oinj__on(X105,X119,X1,hAPP(c_Set_Oimage(X7,X105,X2),X149))
=> c_Fun_Oinj__on(X7,X119,hAPP(c_Fun_Ocomp(X105,X119,X7,X1),X2),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on) ).
fof(fact_elem__le__sum,axiom,
! [X308,X44] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X44),hAPP(c_List_Oset(tc_Nat_Onat),X308)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X308))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__le__sum) ).
fof(fact_rev__ImageI,axiom,
! [X172,X24,X105,X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),X172))
=> hBOOL(hAPP(hAPP(c_member(X105),X24),hAPP(c_Relation_OImage(X7,X105,X172),X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__ImageI) ).
fof(fact_Option_Omap_Ocompositionality,axiom,
! [X296,X1,X119,X2,X7,X105] : hAPP(hAPP(c_Option_Omap(X105,X7),X2),hAPP(hAPP(c_Option_Omap(X119,X105),X1),X296)) = hAPP(hAPP(c_Option_Omap(X119,X7),hAPP(c_Fun_Ocomp(X105,X7,X119,X2),X1)),X296),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap_Ocompositionality) ).
fof(fact_option__map__comp,axiom,
! [X295,X1,X119,X2,X7,X105] : hAPP(hAPP(c_Option_Omap(X105,X7),X2),hAPP(hAPP(c_Option_Omap(X119,X105),X1),X295)) = hAPP(hAPP(c_Option_Omap(X119,X7),hAPP(c_Fun_Ocomp(X105,X7,X119,X2),X1)),X295),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__comp) ).
fof(fact_map__map,axiom,
! [X292,X1,X119,X2,X7,X105] : hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(hAPP(c_List_Omap(X119,X105),X1),X292)) = hAPP(hAPP(c_List_Omap(X119,X7),hAPP(c_Fun_Ocomp(X105,X7,X119,X2),X1)),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__map) ).
fof(fact_List_Omap_Ocompositionality,axiom,
! [X294,X1,X119,X2,X7,X105] : hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(hAPP(c_List_Omap(X119,X105),X1),X294)) = hAPP(hAPP(c_List_Omap(X119,X7),hAPP(c_Fun_Ocomp(X105,X7,X119,X2),X1)),X294),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Ocompositionality) ).
fof(fact_take__Cons,axiom,
! [X292,X6,X44,X7] : hAPP(hAPP(c_List_Otake(X7),X44),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)) = c_Nat_Onat_Onat__case(tc_List_Olist(X7),c_List_Olist_ONil(X7),hAPP(hAPP(c_COMBB(tc_List_Olist(X7),tc_List_Olist(X7),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X7),X6)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Otake(X7)),X292)),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons) ).
fof(fact_Un__Image,axiom,
! [X149,X209,X191,X7,X105] : hAPP(c_Relation_OImage(X105,X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X105,X7),tc_HOL_Obool)),X191),X209)),X149) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X105,X7,X191),X149)),hAPP(c_Relation_OImage(X105,X7,X209),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Image) ).
fof(fact_iterate_Osimps,axiom,
! [X6,X2,X7,X105,X94] :
( ( X94 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Random_Oiterate(X105,X7,X94,X2),X6) = hAPP(c_Product__Type_OPair(X105,X7),X6) )
& ( X94 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Random_Oiterate(X105,X7,X94,X2),X6) = hAPP(hAPP(c_Product__Type_Oscomp(X7,X105,X7,tc_prod(X105,X7)),hAPP(X2,X6)),c_Random_Oiterate(X105,X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X94),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iterate_Osimps) ).
fof(fact_equiv__class__eq,axiom,
! [X24,X25,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172))
=> hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq) ).
fof(fact_mem__Sigma__iff,axiom,
! [X155,X149,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155)))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
& hBOOL(hAPP(hAPP(c_member(X105),X24),hAPP(X155,X25))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).
fof(fact_SigmaD2,axiom,
! [X155,X149,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155)))
=> hBOOL(hAPP(hAPP(c_member(X105),X24),hAPP(X155,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD2) ).
fof(fact_listrel1__mono,axiom,
! [X45,X172,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X45))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool)),c_List_Olistrel1(X7,X172)),c_List_Olistrel1(X7,X45))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__mono) ).
fof(fact_listrel__mono,axiom,
! [X45,X172,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X45))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool)),c_List_Olistrel(X7,X172)),c_List_Olistrel(X7,X45))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__mono) ).
fof(fact_scomp__def,axiom,
! [X6,X1,X2,X7,X190,X119,X105] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X105,X119,X190,X7),X2),X1),X6) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X119,X190,X7),X1),hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__def) ).
fof(fact_scomp__apply,axiom,
! [X6,X1,X2,X7,X190,X119,X105] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X105,X119,X190,X7),X2),X1),X6) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X119,X190,X7),X1),hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__apply) ).
fof(fact_Un__least,axiom,
! [X155,X193,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X193))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X193))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X193)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).
fof(fact_folding__one_Ounion__inter,axiom,
! [X155,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(X2,hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(X2,hAPP(X215,X149)),hAPP(X215,X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__inter) ).
fof(fact_f__the__inv__into__f,axiom,
! [X127,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( hBOOL(hAPP(hAPP(c_member(X105),X127),hAPP(c_Set_Oimage(X7,X105,X2),X149)))
=> hAPP(X2,hAPP(c_Fun_Othe__inv__into(X7,X105,X149,X2),X127)) = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
fof(fact_INT__extend__simps_I8_J,axiom,
! [X155,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool))),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X105,tc_HOL_Obool),X149)),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I8_J) ).
fof(fact_UN__extend__simps_I8_J,axiom,
! [X155,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool))),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X105,tc_HOL_Obool),X149)),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I8_J) ).
fof(fact_INT__simps_I8_J,axiom,
! [X155,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X105,tc_HOL_Obool),X149)),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool))),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I8_J) ).
fof(fact_UN__simps_I8_J,axiom,
! [X155,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X105,tc_HOL_Obool),X149)),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool))),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I8_J) ).
fof(fact_inj__on__def,axiom,
! [X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> ! [X206] :
( hBOOL(hAPP(hAPP(c_member(X7),X206),X149))
=> ( hAPP(X2,X3) = hAPP(X2,X206)
=> X3 = X206 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_rtrancl__subset,axiom,
! [X209,X191,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X191),X209))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X209),c_Transitive__Closure_Ortrancl(X7,X191)))
=> c_Transitive__Closure_Ortrancl(X7,X209) = c_Transitive__Closure_Ortrancl(X7,X191) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_eq__equiv__class,axiom,
! [X149,X24,X25,X172,X7] :
( hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> ( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X24),X149))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class) ).
fof(fact_map__of__Cons__code_I2_J,axiom,
! [X304,X139,X105,X7,X96,X115] :
( ( X115 = X96
=> hAPP(c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X115),X139)),X304)),X96) = hAPP(c_Option_Ooption_OSome(X105),X139) )
& ( X115 != X96
=> hAPP(c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X115),X139)),X304)),X96) = hAPP(c_Map_Omap__of(X7,X105,X304),X96) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__Cons__code_I2_J) ).
fof(fact_SigmaD1,axiom,
! [X155,X149,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155)))
=> hBOOL(hAPP(hAPP(c_member(X7),X25),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD1) ).
fof(fact_setprod__zero__iff,axiom,
! [X2,X149,X7,X105] :
( ( class_Rings_Ocomm__semiring__1(X105)
& class_Rings_Ono__zero__divisors(X105) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149) = c_Groups_Ozero__class_Ozero(X105)
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X105) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__zero__iff) ).
fof(fact_card__image__le,axiom,
! [X2,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X105),hAPP(c_Set_Oimage(X7,X105,X2),X149))),hAPP(c_Finite__Set_Ocard(X7),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
fof(fact_INTER__UNIV__conv_I2_J,axiom,
! [X155,X149,X7,X105] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
=> hAPP(X155,X3) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).
fof(fact_UNION__empty__conv_I2_J,axiom,
! [X155,X149,X7,X105] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
=> hAPP(X155,X3) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I2_J) ).
fof(fact_UNION__empty__conv_I1_J,axiom,
! [X155,X149,X105,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
=> hAPP(X155,X3) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I1_J) ).
fof(fact_INTER__UNIV__conv_I1_J,axiom,
! [X155,X149,X105,X7] :
( c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X105),X3),X149))
=> hAPP(X155,X3) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).
fof(fact_setsum__SucD,axiom,
! [X44,X149,X2,X7] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X149) = hAPP(c_Nat_OSuc,X44)
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__SucD) ).
fof(fact_Inf__fin_Ounion__inter,axiom,
! [X155,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)),c_Big__Operators_Olattice__class_OInf__fin(X7,X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__inter) ).
fof(fact_Sup__fin_Ounion__inter,axiom,
! [X155,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)),c_Big__Operators_Olattice__class_OSup__fin(X7,X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__inter) ).
fof(fact_Max_Ounion__inter,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),c_Big__Operators_Olinorder__class_OMax(X7,X149)),c_Big__Operators_Olinorder__class_OMax(X7,X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ounion__inter) ).
fof(fact_Min_Ounion__inter,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),c_Big__Operators_Olinorder__class_OMin(X7,X149)),c_Big__Operators_Olinorder__class_OMin(X7,X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ounion__inter) ).
fof(fact_type__definition_OAbs__inject,axiom,
! [X127,X6,X149,X212,X213,X105,X7] :
( c_Typedef_Otype__definition(X7,X105,X213,X212,X149)
=> ( hBOOL(hAPP(hAPP(c_member(X105),X6),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X105),X127),X149))
=> ( hAPP(X212,X6) = hAPP(X212,X127)
<=> X6 = X127 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).
fof(fact_Field__insert,axiom,
! [X172,X24,X25,X7] : hAPP(c_Relation_OField(X7),hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),hAPP(c_Relation_OField(X7),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__insert) ).
fof(fact_start__le__sum,axiom,
! [X308,X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X308))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_start__le__sum) ).
fof(fact_pair__box_Osize_I1_J,axiom,
! [X24,X25,X109,X85,X105,X7] : c_Nitpick_Opair__box_Opair__box__size(X7,X105,X85,X109,c_Nitpick_Opair__box_OPairBox(X7,X105,X25,X24)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X85,X25)),hAPP(X109,X24))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osize_I1_J) ).
fof(fact_card__partition,axiom,
! [X94,X193,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X7,tc_HOL_Obool)),X193))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X193)))
=> ( ! [X269] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X269),X193))
=> hAPP(c_Finite__Set_Ocard(X7),X269) = X94 )
=> ( ! [X270] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X270),X193))
=> ! [X271] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X271),X193))
=> ( X270 != X271
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X270),X271) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),hAPP(c_Finite__Set_Ocard(tc_fun(X7,tc_HOL_Obool)),X193)) = hAPP(c_Finite__Set_Ocard(X7),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X193)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__partition) ).
fof(fact_sorted__same,axiom,
! [X292,X1,X7] :
( class_Orderings_Olinorder(X7)
=> c_List_Olinorder__class_Osorted(X7,hAPP(c_List_Ofilter(X7,hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),hAPP(X1,X292))),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__same) ).
fof(fact_inj__comp,axiom,
! [X1,X119,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(X119,X7,X1,c_Orderings_Otop__class_Otop(tc_fun(X119,tc_HOL_Obool)))
=> c_Fun_Oinj__on(X119,X105,hAPP(c_Fun_Ocomp(X7,X105,X119,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X119,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__comp) ).
fof(fact_set__update__subset__insert,axiom,
! [X6,X107,X292,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist__update(X7,X292),X107),X6))),hAPP(hAPP(c_Set_Oinsert(X7),X6),hAPP(c_List_Oset(X7),X292)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__subset__insert) ).
fof(fact_min__max_OInf__fin_Oremove,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oremove) ).
fof(fact_min__max_OSup__fin_Oremove,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).
fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
! [X149,X2,X7] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,tc_Nat_Onat),X2),X149) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X7),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).
fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
! [X149,X2,X7] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X149) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X7),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I1_J) ).
fof(fact_vimage__singleton__eq,axiom,
! [X24,X2,X105,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(hAPP(c_Set_Oinsert(X105),X24),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))))))
<=> hAPP(X2,X25) = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__singleton__eq) ).
fof(fact_inj__on__imageI2,axiom,
! [X149,X2,X245,X119,X105,X7] :
( c_Fun_Oinj__on(X7,X105,hAPP(c_Fun_Ocomp(X119,X105,X7,X245),X2),X149)
=> c_Fun_Oinj__on(X7,X119,X2,X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI2) ).
fof(fact_finite__Diff__insert,axiom,
! [X155,X25,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff__insert) ).
fof(fact_insert__def,axiom,
! [X155,X25,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X25),X155) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__def) ).
fof(fact_eq__add__iff1,axiom,
! [X136,X24,X23,X156,X25,X7] :
( class_Rings_Oring(X7)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X156)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X156)),X136)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X25),X24)),X156)),X23) = X136 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [X136,X24,X23,X156,X25,X7] :
( class_Rings_Oring(X7)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X156)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X156)),X136)
<=> X23 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X24),X25)),X156)),X136) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_Image__INT__eq,axiom,
! [X155,X119,X149,X172,X105,X7] :
( c_Relation_Osingle__valued(X7,X105,hAPP(c_Relation_Oconverse(X105,X7),X172))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X119,tc_HOL_Obool))
=> hAPP(c_Relation_OImage(X105,X7,X172),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X119),c_Relation_OImage(X105,X7,X172)),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__INT__eq) ).
fof(fact_partition__filter2,axiom,
! [X292,X38,X7] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Opartition(X7,X38,X292)) = hAPP(c_List_Ofilter(X7,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X7,c_fNot),X38)),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter2) ).
fof(fact_vimage__mono,axiom,
! [X2,X105,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X105,X7,X2),X149)),hAPP(c_Set_Ovimage(X105,X7,X2),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__mono) ).
fof(fact_image__mono,axiom,
! [X2,X105,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),X149)),hAPP(c_Set_Oimage(X7,X105,X2),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_UN__equiv__class,axiom,
! [X25,X2,X105,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( c_Equiv__Relations_Ocongruent(X7,tc_fun(X105,tc_HOL_Obool),X172,X2)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X2) = hAPP(X2,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class) ).
fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).
fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).
fof(fact_comp__cong,axiom,
! [X189,X190,X119,X7,X105,X243,X244,X245,X6,X1,X2] :
( hAPP(X2,hAPP(X1,X6)) = hAPP(X245,hAPP(X244,X243))
=> hAPP(hAPP(c_Fun_Ocomp(X105,X7,X119,X2),X1),X6) = hAPP(hAPP(c_Fun_Ocomp(X190,X7,X189,X245),X244),X243) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__cong) ).
fof(fact_folding__one_Oremove,axiom,
! [X6,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X215,X149) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X215,X149) = hAPP(hAPP(X2,X6),hAPP(X215,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oremove) ).
fof(fact_card_Ounion__inter,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X7),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter) ).
fof(fact_card__Un__Int,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X7),X155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__Int) ).
fof(fact_wf__same__fst,axiom,
! [X7,X191,X105,X38] :
( ! [X3] :
( hBOOL(hAPP(X38,X3))
=> c_Wellfounded_Owf(X105,hAPP(X191,X3)) )
=> c_Wellfounded_Owf(tc_prod(X7,X105),c_Recdef_Osame__fst(X7,X105,X38,X191)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__same__fst) ).
fof(fact_in__rel__def,axiom,
! [X127,X6,X191,X105,X7] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X7,X105,X191),X6),X127))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),X191)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_ran__distinct,axiom,
! [X298,X105,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X7),c_Product__Type_Ofst(X7,X105)),X298)))
=> c_Map_Oran(X7,X105,c_Map_Omap__of(X7,X105,X298)) = hAPP(c_Set_Oimage(tc_prod(X7,X105),X105,c_Product__Type_Osnd(X7,X105)),hAPP(c_List_Oset(tc_prod(X7,X105)),X298)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__distinct) ).
fof(fact_restrict__upd__same,axiom,
! [X127,X6,X95,X105,X7] : c_Map_Orestrict__map(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X95),X6),hAPP(c_Option_Ooption_OSome(X105),X127)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = c_Map_Orestrict__map(X7,X105,X95,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__upd__same) ).
fof(fact_Image__closed__trancl,axiom,
! [X39,X172,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X172),X39)),X39))
=> hAPP(c_Relation_OImage(X7,X7,c_Transitive__Closure_Ortrancl(X7,X172)),X39) = X39 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).
fof(fact_acc__downwards__aux,axiom,
! [X172,X25,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X25)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Wellfounded_Oacc(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(X7),X24),c_Wellfounded_Oacc(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_acc__downwards,axiom,
! [X24,X172,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Wellfounded_Oacc(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X25)),c_Transitive__Closure_Ortrancl(X7,X172)))
=> hBOOL(hAPP(hAPP(c_member(X7),X24),c_Wellfounded_Oacc(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).
fof(fact_INT__simps_I2_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149)),X155)) = c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)) )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I2_J) ).
fof(fact_INT__simps_I4_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),X149)),X155)) = c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)) )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),X149)),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I4_J) ).
fof(fact_UN__simps_I3_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149)),X155)) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I3_J) ).
fof(fact_INT__extend__simps_I2_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) = X149 )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149)),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I2_J) ).
fof(fact_UN__extend__simps_I3_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) = X149 )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149)),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I3_J) ).
fof(fact_INT__extend__simps_I4_J,axiom,
! [X155,X149,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) = X149 )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),X149)),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I4_J) ).
fof(fact_folding__one_Oinsert__remove,axiom,
! [X6,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(X2,X6),hAPP(X215,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert__remove) ).
fof(fact_Inf__fin_Oremove,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,X149) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,X149) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X6),c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oremove) ).
fof(fact_Min_Oremove,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X7,X149) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X7,X149) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oremove) ).
fof(fact_Max_Oremove,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X7,X149) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X7,X149) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oremove) ).
fof(fact_Sup__fin_Oremove,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,X149) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,X149) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6),c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oremove) ).
fof(fact_type__definition_ORep,axiom,
! [X6,X149,X212,X213,X105,X7] :
( c_Typedef_Otype__definition(X7,X105,X213,X212,X149)
=> hBOOL(hAPP(hAPP(c_member(X105),hAPP(X213,X6)),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep) ).
fof(fact_type__definition_OAbs__inverse,axiom,
! [X127,X149,X212,X213,X105,X7] :
( c_Typedef_Otype__definition(X7,X105,X213,X212,X149)
=> ( hBOOL(hAPP(hAPP(c_member(X105),X127),X149))
=> hAPP(X213,hAPP(X212,X127)) = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).
fof(fact_sorted__insort__key,axiom,
! [X292,X6,X2,X105,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),X292)))
<=> c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__key) ).
fof(fact_mod__induct__0,axiom,
! [X107,X38,X161] :
( ! [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X147),X161))
=> ( hBOOL(hAPP(X38,X147))
=> hBOOL(hAPP(X38,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X147),X161))) ) )
=> ( hBOOL(hAPP(X38,X107))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),X161))
=> hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__induct__0) ).
fof(fact_zdiv__zmult1__eq,axiom,
! [X10,X84,X71] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X84)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X10))),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).
fof(fact_div__mult1__eq,axiom,
! [X10,X84,X71] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X71),X84)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X71),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X84),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X71),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X84,X10))),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult1__eq) ).
fof(fact_nat__eq__add__iff1,axiom,
! [X44,X95,X160,X107,X158] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X158),X107))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X160)),X95) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X158),X160)),X44)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X107),X158)),X160)),X95) = X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__eq__add__iff2,axiom,
! [X44,X95,X160,X158,X107] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X158))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X160)),X95) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X158),X160)),X44)
<=> X95 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X158),X107)),X160)),X44) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_Un__Int__assoc__eq,axiom,
! [X193,X155,X149,X7] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X193) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X193))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X193),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).
fof(fact_INT__simps_I7_J,axiom,
! [X155,X149,X193,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I7_J) ).
fof(fact_UN__simps_I5_J,axiom,
! [X155,X149,X193,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I5_J) ).
fof(fact_UN__simps_I7_J,axiom,
! [X155,X149,X193,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149)),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I7_J) ).
fof(fact_Int__UN__distrib,axiom,
! [X149,X211,X105,X155,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X211),X149)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X211),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155)),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib) ).
fof(fact_UN__extend__simps_I5_J,axiom,
! [X155,X193,X105,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I5_J) ).
fof(fact_INT__extend__simps_I7_J,axiom,
! [X155,X193,X105,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I7_J) ).
fof(fact_Un__INT__distrib,axiom,
! [X149,X211,X105,X155,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X211),X149)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X211),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155)),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib) ).
fof(fact_UN__extend__simps_I7_J,axiom,
! [X155,X193,X105,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I7_J) ).
fof(fact_union__comp__emptyR,axiom,
! [X193,X155,X149,X7] :
( hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))
=> ( hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X149),X193) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))
=> hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X149),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X155),X193)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__comp__emptyR) ).
fof(fact_type__definition_ORep__range,axiom,
! [X149,X212,X213,X105,X7] :
( c_Typedef_Otype__definition(X7,X105,X213,X212,X149)
=> hAPP(c_Set_Oimage(X7,X105,X213),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__range) ).
fof(fact_singleton__quotient,axiom,
! [X172,X6,X7] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X172) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__quotient) ).
fof(fact_congruentD,axiom,
! [X26,X127,X2,X172,X105,X7] :
( c_Equiv__Relations_Ocongruent(X7,X105,X172,X2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X26)),X172))
=> hAPP(X2,X127) = hAPP(X2,X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruentD) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [X45,X172,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),c_Transitive__Closure_Ortrancl(X7,X45)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X7,X172)),c_Transitive__Closure_Ortrancl(X7,X45))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_rel__pow__imp__rtrancl,axiom,
! [X191,X44,X161,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),c_Transitive__Closure_Ortrancl(X7,X191))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__imp__rtrancl) ).
fof(fact_acc__downward,axiom,
! [X25,X172,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),c_Wellfounded_Oacc(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),X172))
=> hBOOL(hAPP(hAPP(c_member(X7),X25),c_Wellfounded_Oacc(X7,X172))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downward) ).
fof(fact_Inf__fin_Oinsert__remove,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X6),c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).
fof(fact_Min_Oinsert__remove,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oinsert__remove) ).
fof(fact_Max_Oinsert__remove,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oinsert__remove) ).
fof(fact_Sup__fin_Oinsert__remove,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = X6 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6),c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).
fof(fact_type__definition_OAbs__image,axiom,
! [X149,X212,X213,X105,X7] :
( c_Typedef_Otype__definition(X7,X105,X213,X212,X149)
=> hAPP(c_Set_Oimage(X105,X7,X212),X149) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__image) ).
fof(fact_inj__on__mapI,axiom,
! [X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X7),tc_fun(X7,tc_HOL_Obool),c_List_Oset(X7)),X149)))
=> c_Fun_Oinj__on(tc_List_Olist(X7),tc_List_Olist(X105),hAPP(c_List_Omap(X7,X105),X2),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__mapI) ).
fof(fact_update__zip,axiom,
! [X312,X114,X301,X300,X7,X87] : hAPP(hAPP(c_List_Olist__update(tc_prod(X87,X7),hAPP(hAPP(c_List_Ozip(X87,X7),X300),X301)),X114),X312) = hAPP(hAPP(c_List_Ozip(X87,X7),hAPP(hAPP(c_List_Olist__update(X87,X300),X114),hAPP(c_Product__Type_Ofst(X87,X7),X312))),hAPP(hAPP(c_List_Olist__update(X7,X301),X114),hAPP(c_Product__Type_Osnd(X87,X7),X312))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_update__zip) ).
fof(fact_finite__Collect__le__nat,axiom,
! [X94] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X94)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__le__nat) ).
fof(fact_finite__Collect__less__nat,axiom,
! [X94] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X94)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__less__nat) ).
fof(fact_O__assoc,axiom,
! [X238,X209,X191,X190,X105,X119,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),hAPP(hAPP(c_Relation_Orel__comp(X7,X190,X119),X191),X209)),X238) = hAPP(hAPP(c_Relation_Orel__comp(X7,X190,X105),X191),hAPP(hAPP(c_Relation_Orel__comp(X190,X119,X105),X209),X238)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_O__assoc) ).
fof(fact_setprod_Oremove,axiom,
! [X1,X6,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(X1,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oremove) ).
fof(fact_setsum_Oremove,axiom,
! [X1,X6,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(X1,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oremove) ).
fof(fact_setsum__diff1_H,axiom,
! [X2,X25,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(X2,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1_H) ).
fof(fact_Pow__INT__eq,axiom,
! [X155,X149,X105,X7] : hAPP(c_Set_OPow(X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),X105),c_Set_OPow(X7)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__INT__eq) ).
fof(fact_q__pos__lemma,axiom,
! [X145,X146,X124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X124),X146)),X145)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X145),X124))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X124))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X146)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_UN__le__eq__Un0,axiom,
! [X210,X44,X7] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X44)),X210) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X44)),X210)),hAPP(X210,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__le__eq__Un0) ).
fof(fact_card__Diff__subset__Int,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__subset__Int) ).
fof(fact_pair__leq__def,axiom,
c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leq__def) ).
fof(fact_INT__Un,axiom,
! [X210,X155,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),X155)),X210) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X210)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X155),X210)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Un) ).
fof(fact_UN__Un,axiom,
! [X210,X155,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),X155)),X210) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),X210)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X155),X210)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un) ).
fof(fact_dom__eq__singleton__conv,axiom,
! [X6,X2,X105,X7] :
( c_Map_Odom(X7,X105,X2) = hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))
<=> ? [X242] : X2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),hAPP(c_COMBK(tc_Option_Ooption(X105),X7),c_Option_Ooption_ONone(X105))),X6),hAPP(c_Option_Ooption_OSome(X105),X242)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__eq__singleton__conv) ).
fof(fact_Compl__subset__Compl__iff,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X155)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__subset__Compl__iff) ).
fof(fact_INT__lower,axiom,
! [X155,X105,X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155)),hAPP(X155,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__lower) ).
fof(fact_rtrancl__mono,axiom,
! [X45,X172,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X45))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X7,X172)),c_Transitive__Closure_Ortrancl(X7,X45))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_vimage__INT,axiom,
! [X155,X149,X119,X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X119),c_Set_Ovimage(X7,X105,X2)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__INT) ).
fof(fact_vimage__UN,axiom,
! [X155,X149,X119,X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X119),c_Set_Ovimage(X7,X105,X2)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UN) ).
fof(fact_Image__UN,axiom,
! [X155,X149,X119,X172,X7,X105] : hAPP(c_Relation_OImage(X105,X7,X172),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X119),c_Relation_OImage(X105,X7,X172)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__UN) ).
fof(fact_image__UN,axiom,
! [X155,X149,X119,X2,X7,X105] : hAPP(c_Set_Oimage(X105,X7,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X119),c_Set_Oimage(X105,X7,X2)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__UN) ).
fof(fact_diff__frac__eq,axiom,
! [X128,X86,X97,X98,X87] :
( class_Fields_Ofield(X87)
=> ( X98 != c_Groups_Ozero__class_Ozero(X87)
=> ( X97 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X128),X97)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X97)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X128),X98))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X98),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__frac__eq) ).
fof(fact_add__frac__eq,axiom,
! [X128,X86,X97,X98,X87] :
( class_Fields_Ofield(X87)
=> ( X98 != c_Groups_Ozero__class_Ozero(X87)
=> ( X97 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X128),X97)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X97)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X128),X98))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X98),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__eq) ).
fof(fact_Compl__eq,axiom,
! [X149,X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq) ).
fof(fact_Suc__mult__le__cancel1,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(fact_Suc__mult__less__cancel1,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_split__pos__lemma,axiom,
! [X44,X38,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
=> ( hBOOL(hAPP(hAPP(X38,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X44),X94)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X44,X94)))
<=> ! [X147,X117] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X117))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X117),X94))
& X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X147)),X117) )
=> hBOOL(hAPP(hAPP(X38,X147),X117)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__pos__lemma) ).
fof(fact_UN__o,axiom,
! [X2,X1,X119,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Fun_Ocomp(X119,tc_fun(X7,tc_HOL_Obool),X105,X1),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X119,X2),X149)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__o) ).
fof(fact_setprod_Oinsert__remove,axiom,
! [X6,X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(X1,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinsert__remove) ).
fof(fact_setsum_Oinsert__remove,axiom,
! [X6,X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(X1,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinsert__remove) ).
fof(fact_fun__upd__upd,axiom,
! [X26,X127,X6,X2,X105,X7] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X127)),X6),X26) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
fof(fact_split__neg__lemma,axiom,
! [X44,X38,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(X38,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X44),X94)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X44,X94)))
<=> ! [X147,X117] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X117))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X117),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X147)),X117) )
=> hBOOL(hAPP(hAPP(X38,X147),X117)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__neg__lemma) ).
fof(fact_zip__same__conv__map,axiom,
! [X292,X7] : hAPP(hAPP(c_List_Ozip(X7,X7),X292),X292) = hAPP(hAPP(c_List_Omap(X7,tc_prod(X7,X7)),hAPP(hAPP(c_COMBS(X7,X7,tc_prod(X7,X7)),c_Product__Type_OPair(X7,X7)),c_COMBI(X7))),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__same__conv__map) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
! [X155,X149] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X149),X155) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X149)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
! [X155,X149] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X149),X155) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X149)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) ).
fof(fact_Plus__def,axiom,
! [X155,X149,X105,X7] : c_Sum__Type_OPlus(X7,X105,X149,X155) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(X7,X105),tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,tc_sum(X7,X105),c_Sum__Type_OInl(X7,X105)),X149)),hAPP(c_Set_Oimage(X105,tc_sum(X7,X105),c_Sum__Type_OInr(X105,X7)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Plus__def) ).
fof(fact_power__Suc__less,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Oone__class_Oone(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33))),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(fact_type__definition_ORep__inject,axiom,
! [X127,X6,X149,X212,X213,X105,X7] :
( c_Typedef_Otype__definition(X7,X105,X213,X212,X149)
=> ( hAPP(X213,X6) = hAPP(X213,X127)
<=> X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
fof(fact_finite__cartesian__productD2,axiom,
! [X155,X149,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X155))))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD2) ).
fof(fact_finite__cartesian__productD1,axiom,
! [X155,X149,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X155))))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD1) ).
fof(fact_type__definition_ORep__inverse,axiom,
! [X6,X149,X212,X213,X105,X7] :
( c_Typedef_Otype__definition(X7,X105,X213,X212,X149)
=> hAPP(X212,hAPP(X213,X6)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
fof(fact_abs__triangle__ineq2,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84))),hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).
fof(fact_abs__triangle__ineq2__sym,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84))),hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X84),X71)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).
fof(fact_vimage__insert,axiom,
! [X155,X25,X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(hAPP(c_Set_Oinsert(X105),X25),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(hAPP(c_Set_Oinsert(X105),X25),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X7,X105,X2),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__insert) ).
fof(fact_DomainI,axiom,
! [X172,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),X172))
=> hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Relation_ODomain(X7,X105),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainI) ).
fof(fact_RangeI,axiom,
! [X172,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),X172))
=> hBOOL(hAPP(hAPP(c_member(X105),X24),hAPP(c_Relation_ORange(X7,X105),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeI) ).
fof(fact_set__drop__subset__set__drop,axiom,
! [X292,X7,X95,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X95))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Odrop(X7),X95),X292))),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Odrop(X7),X44),X292)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__drop__subset__set__drop) ).
fof(fact_set__take__subset__set__take,axiom,
! [X292,X7,X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Otake(X7),X95),X292))),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Otake(X7),X44),X292)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__take__subset__set__take) ).
fof(fact_sorted__list__of__set__insert,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_List_Olinorder__class_Osorted__list__of__set(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7)),X6),c_List_Olinorder__class_Osorted__list__of__set(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__insert) ).
fof(fact_power__le__imp__le__base,axiom,
! [X84,X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Nat_OSuc,X33))),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X84),hAPP(c_Nat_OSuc,X33))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_sup__le__fold__sup,axiom,
! [X24,X25,X149,X7] :
( class_Lattices_Osemilattice__sup(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X25),X24)),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7)),X24),X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__le__fold__sup) ).
fof(fact_min__max_Osup__le__fold__sup,axiom,
! [X24,X25,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X25),X24)),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omax(X7)),X24),X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).
fof(fact_Domain__mono,axiom,
! [X45,X172,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X172),X45))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X7,X105),X172)),hAPP(c_Relation_ODomain(X7,X105),X45))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__mono) ).
fof(fact_less__half__sum,axiom,
! [X84,X71,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Oone__class_Oone(X87)),c_Groups_Oone__class_Oone(X87))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__half__sum) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
! [X155,X149] :
( c_Nat__Transfer_Onat__set(X149)
=> ( c_Nat__Transfer_Onat__set(X155)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X149),X155) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X149)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
! [X155,X149] :
( c_Nat__Transfer_Onat__set(X149)
=> ( c_Nat__Transfer_Onat__set(X155)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X149),X155) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X149)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) ).
fof(fact_combine__common__factor,axiom,
! [X10,X84,X137,X71,X87] :
( class_Rings_Osemiring(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X137)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X137)),X10)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),X137)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(fact_Id__on__subset__Times,axiom,
! [X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Relation_OId__on(X7,X149)),hAPP(hAPP(c_Product__Type_OSigma(X7,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),X149)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__subset__Times) ).
fof(fact_WT__bodies__def,axiom,
( c_Com_OWT__bodies
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X3),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT__bodies__def) ).
fof(fact_Range__Collect__split,axiom,
! [X38,X7,X105] : hAPP(c_Relation_ORange(X105,X7),hAPP(c_Set_OCollect(tc_prod(X105,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X105,X7,tc_HOL_Obool),X38))) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X105)),hAPP(c_COMBC(X105,X7,tc_HOL_Obool),X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Collect__split) ).
fof(fact_equiv__type,axiom,
! [X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),hAPP(hAPP(c_Product__Type_OSigma(X7,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),X149)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__type) ).
fof(fact_map__comp__map,axiom,
! [X1,X2,X7,X105,X119] : hAPP(c_Fun_Ocomp(tc_List_Olist(X119),tc_List_Olist(X105),tc_List_Olist(X7),hAPP(c_List_Omap(X119,X105),X2)),hAPP(c_List_Omap(X7,X119),X1)) = hAPP(c_List_Omap(X7,X105),hAPP(c_Fun_Ocomp(X119,X105,X7,X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__map) ).
fof(fact_List_Omap_Ocomp,axiom,
! [X1,X2,X7,X105,X119] : hAPP(c_Fun_Ocomp(tc_List_Olist(X119),tc_List_Olist(X105),tc_List_Olist(X7),hAPP(c_List_Omap(X119,X105),X2)),hAPP(c_List_Omap(X7,X119),X1)) = hAPP(c_List_Omap(X7,X105),hAPP(c_Fun_Ocomp(X119,X105,X7,X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Ocomp) ).
fof(fact_Option_Omap_Ocomp,axiom,
! [X1,X2,X7,X105,X119] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X119),tc_Option_Ooption(X105),tc_Option_Ooption(X7),hAPP(c_Option_Omap(X119,X105),X2)),hAPP(c_Option_Omap(X7,X119),X1)) = hAPP(c_Option_Omap(X7,X105),hAPP(c_Fun_Ocomp(X119,X105,X7,X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap_Ocomp) ).
fof(fact_refl__onD1,axiom,
! [X127,X6,X172,X149,X7] :
( c_Relation_Orefl__on(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD1) ).
fof(fact_refl__onD2,axiom,
! [X127,X6,X172,X149,X7] :
( c_Relation_Orefl__on(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),X172))
=> hBOOL(hAPP(hAPP(c_member(X7),X127),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD2) ).
fof(fact_listrel_ONil,axiom,
! [X172,X7] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_ONil(X7)),c_List_Olist_ONil(X7))),c_List_Olistrel(X7,X172))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel_ONil) ).
fof(fact_Int__Union2,axiom,
! [X149,X155,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X155)),X149) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X155),hAPP(hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool))),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union2) ).
fof(fact_Id__on__iff,axiom,
! [X149,X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Relation_OId__on(X7,X149)))
<=> ( X6 = X127
& hBOOL(hAPP(hAPP(c_member(X7),X6),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__iff) ).
fof(fact_finite__Plus__iff,axiom,
! [X155,X149,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X7,X105)),c_Sum__Type_OPlus(X7,X105,X149,X155)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__PlusD_I1_J,axiom,
! [X155,X149,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X7,X105)),c_Sum__Type_OPlus(X7,X105,X149,X155)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
fof(fact_finite__PlusD_I2_J,axiom,
! [X155,X149,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X7,X105)),c_Sum__Type_OPlus(X7,X105,X149,X155)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
fof(fact_SigmaI,axiom,
! [X155,X24,X105,X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X105),X24),hAPP(X155,X25)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaI) ).
fof(fact_foldl__assoc,axiom,
! [X302,X127,X6,X7] :
( class_Groups_Osemigroup__add(X7)
=> hAPP(c_List_Ofoldl(X7,X7,c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X6),X127)),X302) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X6),hAPP(c_List_Ofoldl(X7,X7,c_Groups_Oplus__class_Oplus(X7),X127),X302)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__assoc) ).
fof(fact_rel__pow__0__I,axiom,
! [X191,X6,X7] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X6)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X191))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__0__I) ).
fof(fact_quotient__disj,axiom,
! [X60,X39,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X39),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X60),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> ( X39 = X60
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X39),X60) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__disj) ).
fof(fact_pick__same,axiom,
! [X292,X7,X157] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X157),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> hAPP(c_Random_Opick(X7,hAPP(hAPP(c_List_Omap(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,X7)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X7),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X292)),hAPP(c_Code__Numeral_Oof__nat,X157)) = hAPP(hAPP(c_List_Onth(X7),X292),X157) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick__same) ).
fof(fact_subset__card__intvl__is__intvl,axiom,
! [X94,X149] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X149),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X149)))))
=> X149 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
fof(fact_ord_OgreaterThanLessThan__iff,axiom,
! [X160,X157,X219,X107,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X107),c_SetInterval_Oord_OgreaterThanLessThan(X7,X219,X157,X160)))
<=> ( hBOOL(hAPP(hAPP(X219,X157),X107))
& hBOOL(hAPP(hAPP(X219,X107),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
fof(fact_ord_OatLeastAtMost__iff,axiom,
! [X160,X157,X218,X107,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X107),c_SetInterval_Oord_OatLeastAtMost(X7,X218,X157,X160)))
<=> ( hBOOL(hAPP(hAPP(X218,X157),X107))
& hBOOL(hAPP(hAPP(X218,X107),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
fof(fact_set__Cons__sing__Nil,axiom,
! [X149,X7] : c_List_Oset__Cons(X7,X149,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X7)),c_List_Olist_ONil(X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X7),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X7,tc_List_Olist(X7),hAPP(hAPP(c_COMBC(X7,tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_OCons(X7)),c_List_Olist_ONil(X7))),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__Cons__sing__Nil) ).
fof(fact_INT__insert__distrib,axiom,
! [X155,X25,X105,X149,X160,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X160),X149))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Set_Oinsert(X105),X25)),X155)) = hAPP(hAPP(c_Set_Oinsert(X105),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert__distrib) ).
fof(fact_UN__insert__distrib,axiom,
! [X155,X25,X105,X149,X160,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X160),X149))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Set_Oinsert(X105),X25)),X155)) = hAPP(hAPP(c_Set_Oinsert(X105),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert__distrib) ).
fof(fact_finite__conv__nat__seg__image,axiom,
! [X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
<=> ? [X70,X240] : X149 = hAPP(c_Set_Oimage(tc_Nat_Onat,X7,X240),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X70))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__conv__nat__seg__image) ).
fof(fact_nat__seg__image__imp__finite,axiom,
! [X44,X2,X7,X149] :
( X149 = hAPP(c_Set_Oimage(tc_Nat_Onat,X7,X2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X44)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__seg__image__imp__finite) ).
fof(fact_take__hd__drop,axiom,
! [X300,X87,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Otake(X87),X33),X300)),hAPP(hAPP(c_List_Olist_OCons(X87),hAPP(c_List_Ohd(X87),hAPP(hAPP(c_List_Odrop(X87),X33),X300))),c_List_Olist_ONil(X87))) = hAPP(hAPP(c_List_Otake(X87),hAPP(c_Nat_OSuc,X33)),X300) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__hd__drop) ).
fof(fact_Diff__insert2,axiom,
! [X155,X25,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert2) ).
fof(fact_listrel__rtrancl__refl,axiom,
! [X172,X292,X7] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),X292)),c_List_Olistrel(X7,c_Transitive__Closure_Ortrancl(X7,X172)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).
fof(fact_InlI,axiom,
! [X155,X105,X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_member(tc_sum(X7,X105)),hAPP(c_Sum__Type_OInl(X7,X105),X25)),c_Sum__Type_OPlus(X7,X105,X149,X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InlI) ).
fof(fact_InrI,axiom,
! [X149,X105,X155,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),X155))
=> hBOOL(hAPP(hAPP(c_member(tc_sum(X105,X7)),hAPP(c_Sum__Type_OInr(X7,X105),X24)),c_Sum__Type_OPlus(X105,X7,X149,X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InrI) ).
fof(fact_Inter__subset,axiom,
! [X155,X149,X7] :
( ! [X273] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X273),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X273),X155)) )
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X149)),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__subset) ).
fof(fact_zmod__zmult2__eq,axiom,
! [X84,X71,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X10)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84),X10))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).
fof(fact_Int__greatest,axiom,
! [X155,X149,X193,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X193),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X193),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).
fof(fact_max__Suc2,axiom,
! [X44,X95] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X44)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X44),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),X44)),X95),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc2) ).
fof(fact_rel__pow__add,axiom,
! [X191,X44,X95,X7] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X44)),X191) = hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X95),X191)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__add) ).
fof(fact_Union__mono,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X149)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__mono) ).
fof(fact_Inter__anti__mono,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X155),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X149)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__anti__mono) ).
fof(fact_abs__triangle__ineq4,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).
fof(fact_abs__triangle__ineq,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).
fof(fact_min__Suc2,axiom,
! [X44,X95] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X44)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),X44)),X95),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc2) ).
fof(fact_card_Oremove,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),X149) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oremove) ).
fof(fact_zip__update,axiom,
! [X98,X301,X86,X114,X300,X7,X87] : hAPP(hAPP(c_List_Ozip(X87,X7),hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X86)),hAPP(hAPP(c_List_Olist__update(X7,X301),X114),X98)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X87,X7),hAPP(hAPP(c_List_Ozip(X87,X7),X300),X301)),X114),hAPP(hAPP(c_Product__Type_OPair(X87,X7),X86),X98)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__update) ).
fof(fact_image__Int,axiom,
! [X155,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(X7,X105,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),X149)),hAPP(c_Set_Oimage(X7,X105,X2),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int) ).
fof(fact_image__set__diff,axiom,
! [X155,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(X7,X105,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X105,X2),X149)),hAPP(c_Set_Oimage(X7,X105,X2),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__set__diff) ).
fof(fact_the__inv__into__onto,axiom,
! [X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> hAPP(c_Set_Oimage(X105,X7,c_Fun_Othe__inv__into(X7,X105,X149,X2)),hAPP(c_Set_Oimage(X7,X105,X2),X149)) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
fof(fact_pair__box_Orecs,axiom,
! [X24,X25,X22,X7,X119,X105] : c_Nitpick_Opair__box_Opair__box__rec(X105,X119,X7,X22,c_Nitpick_Opair__box_OPairBox(X105,X119,X25,X24)) = hAPP(hAPP(X22,X25),X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
fof(fact_pair__box_Osimps_I2_J,axiom,
! [X24,X25,X22,X7,X119,X105] : c_Nitpick_Opair__box_Opair__box__case(X105,X119,X7,X22,c_Nitpick_Opair__box_OPairBox(X105,X119,X25,X24)) = hAPP(hAPP(X22,X25),X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
fof(fact_setprod__dvd__setprod__subset,axiom,
! [X2,X149,X155,X7,X105] :
( ( class_Groups_Ocomm__monoid__mult(X105)
& class_Rings_Odvd(X105) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X155))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__dvd__setprod__subset) ).
fof(fact_zmult__zless__mono2__lemma,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X96))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X96)),X114)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X96)),X113))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).
fof(fact_Diff__Int2,axiom,
! [X155,X193,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X193)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X193)),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int2) ).
fof(fact_Int__Un__distrib2,axiom,
! [X149,X193,X155,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X193)),X149) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X149)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X193),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).
fof(fact_Diff__Int__distrib2,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X193) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X193)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib2) ).
fof(fact_Un__Int__distrib2,axiom,
! [X149,X193,X155,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193)),X149) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X149)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X193),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).
fof(fact_Un__Diff,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X193) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X193)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X155),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff) ).
fof(fact_bset_I3_J,axiom,
! [X155,X46,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X46),c_Groups_Oone__class_Oone(tc_Int_Oint))),X155))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),X155))
=> X46 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X206),X3) ) )
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X46),X192) = X46 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I3_J) ).
fof(fact_aset_I3_J,axiom,
! [X149,X46,X192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X192))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X46),c_Groups_Oone__class_Oone(tc_Int_Oint))),X149))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),X149))
=> X46 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X206),X3) ) )
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X46),X192) = X46 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I3_J) ).
fof(fact_take__add,axiom,
! [X300,X87,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X113)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Otake(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X113)),X300) = hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Otake(X87),X114),X300)),hAPP(hAPP(c_List_Otake(X87),X113),hAPP(hAPP(c_List_Odrop(X87),X114),X300))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__add) ).
fof(fact_card_Ounion__inter__neutral,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X7),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter__neutral) ).
fof(fact_inj__on__map__add__dom,axiom,
! [X286,X95,X105,X7] :
( c_Fun_Oinj__on(X7,tc_Option_Ooption(X105),c_Map_Omap__add(X7,X105,X95,X286),c_Map_Odom(X7,X105,X286))
<=> c_Fun_Oinj__on(X7,tc_Option_Ooption(X105),X286,c_Map_Odom(X7,X105,X286)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__map__add__dom) ).
fof(fact_card__Suc__Diff1,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X7),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__Diff1) ).
fof(fact_folding_Ocommute__comp_H_H,axiom,
! [X155,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,X155)),hAPP(X215,X149)) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,X149)),hAPP(X215,X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).
fof(fact_Compl__INT,axiom,
! [X155,X149,X105,X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool))),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__INT) ).
fof(fact_Compl__UN,axiom,
! [X155,X149,X105,X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool))),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UN) ).
fof(fact_fold1Set__sing,axiom,
! [X24,X25,X2,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,X2,hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X24))
<=> X25 = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__sing) ).
fof(fact_folding_Ounion,axiom,
! [X155,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,X149)),hAPP(X215,X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion) ).
fof(fact_split__div_H,axiom,
! [X44,X95,X38] :
( hBOOL(hAPP(X38,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X95),X44)))
<=> ( ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X148] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X148)),X95))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X148))))
& hBOOL(hAPP(X38,X148)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div_H) ).
fof(fact_card_Oinsert__remove,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert__remove) ).
fof(fact_o__eq__dest,axiom,
! [X163,X136,X23,X190,X24,X25,X7,X105,X119] :
( hAPP(c_Fun_Ocomp(X119,X105,X7,X25),X24) = hAPP(c_Fun_Ocomp(X190,X105,X7,X23),X136)
=> hAPP(X25,hAPP(X24,X163)) = hAPP(X23,hAPP(X136,X163)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest) ).
fof(fact_o__eq__elim,axiom,
! [X136,X23,X190,X24,X25,X7,X105,X119] :
( hAPP(c_Fun_Ocomp(X119,X105,X7,X25),X24) = hAPP(c_Fun_Ocomp(X190,X105,X7,X23),X136)
=> ! [X242] : hAPP(X25,hAPP(X24,X242)) = hAPP(X23,hAPP(X136,X242)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__elim) ).
fof(fact_insort__left__comm,axiom,
! [X292,X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7)),X6),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7)),X127),X292)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7)),X127),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7)),X6),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__left__comm) ).
fof(fact_o__eq__id__dest,axiom,
! [X163,X23,X24,X25,X7,X105,X119] :
( hAPP(c_Fun_Ocomp(X119,X105,X7,X25),X24) = hAPP(c_Fun_Ocomp(X105,X105,X7,c_Fun_Oid(X105)),X23)
=> hAPP(X25,hAPP(X24,X163)) = hAPP(X23,X163) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__id__dest) ).
fof(fact_equiv__class__self,axiom,
! [X25,X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__self) ).
fof(fact_inj__image__mem__iff,axiom,
! [X149,X25,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X105),hAPP(X2,X25)),hAPP(c_Set_Oimage(X7,X105,X2),X149)))
<=> hBOOL(hAPP(hAPP(c_member(X7),X25),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_INF__subset,axiom,
! [X2,X155,X149,X7,X105] :
( class_Complete__Lattice_Ocomplete__lattice(X105)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X105),X155),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X105),X149),X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__subset) ).
fof(fact_SUP__subset,axiom,
! [X2,X155,X149,X7,X105] :
( class_Complete__Lattice_Ocomplete__lattice(X105)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X105),X149),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X105),X155),X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__subset) ).
fof(fact_finite__range__map__of,axiom,
! [X288,X105,X7] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X7)),hAPP(c_Set_Oimage(X105,tc_Option_Ooption(X7),c_Map_Omap__of(X105,X7,X288)),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__map__of) ).
fof(fact_UN__simps_I1_J,axiom,
! [X155,X25,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Set_Oinsert(X105),X25)),X155)) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Set_Oinsert(X105),X25)),X155)) = hAPP(hAPP(c_Set_Oinsert(X105),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I1_J) ).
fof(fact_UN__extend__simps_I1_J,axiom,
! [X155,X25,X105,X7,X193] :
( ( X193 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Set_Oinsert(X105),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) = hAPP(hAPP(c_Set_Oinsert(X105),X25),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) )
& ( X193 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Set_Oinsert(X105),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Set_Oinsert(X105),X25)),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I1_J) ).
fof(fact_setsum__right__distrib,axiom,
! [X149,X2,X105,X172,X7] :
( class_Rings_Osemiring__0(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X172),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X2),X149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBB(X7,X7,X105),hAPP(c_Groups_Otimes__class_Otimes(X7),X172)),X2)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__right__distrib) ).
fof(fact_mlex__less,axiom,
! [X191,X7,X127,X6,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X6)),hAPP(X2,X127)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Wellfounded_Omlex__prod(X7,X2,X191))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
fof(fact_range__composition,axiom,
! [X1,X2,X119,X7,X105] : hAPP(c_Set_Oimage(X105,X7,hAPP(hAPP(c_COMBB(X119,X7,X105),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X119,X7,X2),hAPP(c_Set_Oimage(X105,X119,X1),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).
fof(fact_sorted__equals__nth__mono,axiom,
! [X292,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,X292)
<=> ! [X117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X117),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> ! [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X147),X117))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_List_Onth(X7),X292),X147)),hAPP(hAPP(c_List_Onth(X7),X292),X117))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__equals__nth__mono) ).
fof(fact_INT__D,axiom,
! [X25,X155,X149,X105,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> ( hBOOL(hAPP(hAPP(c_member(X105),X25),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(X155,X25))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__D) ).
fof(fact_foldl__absorb0,axiom,
! [X302,X6,X7] :
( class_Groups_Omonoid__add(X7)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X6),hAPP(c_List_Ofoldl(X7,X7,c_Groups_Oplus__class_Oplus(X7),c_Groups_Ozero__class_Ozero(X7)),X302)) = hAPP(c_List_Ofoldl(X7,X7,c_Groups_Oplus__class_Oplus(X7),X6),X302) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__absorb0) ).
fof(fact_list__update__swap,axiom,
! [X313,X86,X300,X87,X314,X114] :
( X114 != X314
=> hAPP(hAPP(c_List_Olist__update(X87,hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X86)),X314),X313) = hAPP(hAPP(c_List_Olist__update(X87,hAPP(hAPP(c_List_Olist__update(X87,X300),X314),X313)),X114),X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__swap) ).
fof(fact_rel__pow__commute,axiom,
! [X44,X191,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X191),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)) = hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)),X191),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__commute) ).
fof(fact_card__insert,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert) ).
fof(fact_divide__left__mono,axiom,
! [X10,X71,X84,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X10),X71)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X10),X84))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono) ).
fof(fact_divide__strict__left__mono,axiom,
! [X10,X71,X84,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X10),X71)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X10),X84))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).
fof(fact_mono__Field,axiom,
! [X45,X172,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X45))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OField(X7),X172)),hAPP(c_Relation_OField(X7),X45))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__Field) ).
fof(fact_folding_Ocommute__comp_H,axiom,
! [X6,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X2,X6)),hAPP(X215,X149)) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,X149)),hAPP(X2,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H) ).
fof(fact_INT__simps_I5_J,axiom,
! [X155,X25,X193,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Set_Oinsert(X7),X25)),X155)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I5_J) ).
fof(fact_INT__extend__simps_I5_J,axiom,
! [X155,X193,X105,X25,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X105),hAPP(c_Set_Oinsert(X7),X25)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I5_J) ).
fof(fact_left__add__mult__distrib,axiom,
! [X96,X113,X63,X114] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X114),X63)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X113),X63)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X113)),X63)),X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_option__map__o__empty,axiom,
! [X6,X2,X119,X7,X105] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(X105),tc_Option_Ooption(X7),X119,hAPP(c_Option_Omap(X105,X7),X2)),hAPP(c_COMBK(tc_Option_Ooption(X105),X119),c_Option_Ooption_ONone(X105))),X6) = c_Option_Ooption_ONone(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__o__empty) ).
fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
! [X2,X6,X7,X105,X107] :
( ( X107 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Oneg__decr__bind(X105,X7,X6,X2),X107) = c_Lazy__Sequence_Ohit__bound(X7) )
& ( X107 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Oneg__decr__bind(X105,X7,X6,X2),X107) = c_Lazy__Sequence_Ohb__bind(X105,X7,hAPP(X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X107),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X7))),X2),X107)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).
fof(fact_inj__fun,axiom,
! [X119,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> c_Fun_Oinj__on(X7,tc_fun(X119,X105),hAPP(hAPP(c_COMBB(X105,tc_fun(X119,X105),X7),c_COMBK(X105,X119)),X2),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).
fof(fact_Int__eq__Inter,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),X155),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__eq__Inter) ).
fof(fact_Un__eq__Union,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),X155),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__eq__Union) ).
fof(fact_divide__left__mono__neg,axiom,
! [X10,X84,X71,X87] :
( class_Fields_Olinordered__field__inverse__zero(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X10),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X10),X71)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X10),X84))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).
fof(fact_divide__strict__left__mono__neg,axiom,
! [X10,X84,X71,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X10),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X10),X71)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X10),X84))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).
fof(fact_nth__zip,axiom,
! [X301,X7,X300,X87,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X301)))
=> hAPP(hAPP(c_List_Onth(tc_prod(X87,X7)),hAPP(hAPP(c_List_Ozip(X87,X7),X300),X301)),X114) = hAPP(hAPP(c_Product__Type_OPair(X87,X7),hAPP(hAPP(c_List_Onth(X87),X300),X114)),hAPP(hAPP(c_List_Onth(X7),X301),X114)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__zip) ).
fof(fact_mod__mult2__eq,axiom,
! [X10,X84,X71] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X71,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X10)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X71),X84),X10))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X71,X84)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).
fof(fact_list__update__length,axiom,
! [X98,X301,X86,X300,X87] : hAPP(hAPP(c_List_Olist__update(X87,hAPP(hAPP(c_List_Oappend(X87),X300),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X301))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X98) = hAPP(hAPP(c_List_Oappend(X87),X300),hAPP(hAPP(c_List_Olist_OCons(X87),X98),X301)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__length) ).
fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
! [X172,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool)),c_List_Olistrel1(X7,c_Transitive__Closure_Ortrancl(X7,X172))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X7),c_List_Olistrel1(X7,X172)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
fof(fact_rtrancl__Un__rtrancl,axiom,
! [X209,X191,X7] : c_Transitive__Closure_Ortrancl(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X7,X191)),c_Transitive__Closure_Ortrancl(X7,X209))) = c_Transitive__Closure_Ortrancl(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X191),X209)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
fof(fact_div__dvd__div,axiom,
! [X23,X24,X25,X7] :
( class_Divides_Osemiring__div(X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X25),X24))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X25),X23))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7),X24),X25)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7),X23),X25)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X24),X23)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__dvd__div) ).
fof(fact_unity__coeff__ex,axiom,
! [X157,X38,X7] :
( ( class_Rings_Odvd(X7)
& class_Rings_Osemiring__0(X7) )
=> ( ? [X3] : hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X157),X3)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X3),c_Groups_Ozero__class_Ozero(X7))))
& hBOOL(hAPP(X38,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_zip__map__fst__snd,axiom,
! [X302,X105,X7] : hAPP(hAPP(c_List_Ozip(X7,X105),hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X7),c_Product__Type_Ofst(X7,X105)),X302)),hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X105),c_Product__Type_Osnd(X7,X105)),X302)) = X302,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map__fst__snd) ).
fof(fact_setprod__reindex__cong,axiom,
! [X200,X1,X155,X149,X2,X105,X7,X119] :
( class_Groups_Ocomm__monoid__mult(X119)
=> ( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( X155 = hAPP(c_Set_Oimage(X7,X105,X2),X149)
=> ( X1 = hAPP(c_Fun_Ocomp(X105,X119,X7,X200),X2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X119),X200),X155) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X119),X1),X149) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex__cong) ).
fof(fact_sum__squares__ge__zero,axiom,
! [X98,X86,X87] :
( class_Rings_Olinordered__ring(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X98),X98)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_pred__nat__trancl__eq__le,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X95),X44)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).
fof(fact_folding_Ocommute__comp,axiom,
! [X6,X127,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X2,X127)),hAPP(X2,X6)) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X2,X6)),hAPP(X2,X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp) ).
fof(fact_Sigma__Int__distrib1,axiom,
! [X193,X252,X211,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X211),X252)),X193) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),X193)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X252),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).
fof(fact_Sigma__Un__distrib1,axiom,
! [X193,X252,X211,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X211),X252)),X193) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),X193)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X252),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib1) ).
fof(fact_Sigma__Diff__distrib1,axiom,
! [X193,X252,X211,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X211),X252)),X193) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X211),X193)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X252),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib1) ).
fof(fact_in__set__butlast__appendI,axiom,
! [X293,X292,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),c_List_Obutlast(X7,X292))))
| hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),c_List_Obutlast(X7,X293)))) )
=> hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),c_List_Obutlast(X7,hAPP(hAPP(c_List_Oappend(X7),X292),X293))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__butlast__appendI) ).
fof(fact_acc__subset,axiom,
! [X181,X182,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X182),X181))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),c_Wellfounded_Oacc(X7,X181)),c_Wellfounded_Oacc(X7,X182))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__subset) ).
fof(fact_insort__key__left__comm,axiom,
! [X292,X105,X127,X6,X2,X7] :
( class_Orderings_Olinorder(X7)
=> ( hAPP(X2,X6) != hAPP(X2,X127)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X127),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),X292)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X127),X292)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key__left__comm) ).
fof(fact_map__of__is__SomeD,axiom,
! [X127,X6,X288,X7,X105] :
( hAPP(c_Map_Omap__of(X105,X7,X288),X6) = hAPP(c_Option_Ooption_OSome(X7),X127)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X6),X127)),hAPP(c_List_Oset(tc_prod(X105,X7)),X288))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__is__SomeD) ).
fof(fact_map__of__SomeD,axiom,
! [X127,X94,X292,X7,X105] :
( hAPP(c_Map_Omap__of(X105,X7,X292),X94) = hAPP(c_Option_Ooption_OSome(X7),X127)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X94),X127)),hAPP(c_List_Oset(tc_prod(X105,X7)),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__SomeD) ).
fof(fact_divmod__int__rel__div__mod,axiom,
! [X71,X84] :
( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__mod) ).
fof(fact_INT__extend__simps_I10_J,axiom,
! [X2,X155,X119,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(X119,tc_fun(X7,tc_HOL_Obool),X105),X155),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X119,X2),X149)),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I10_J) ).
fof(fact_UN__extend__simps_I10_J,axiom,
! [X2,X155,X119,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(X119,tc_fun(X7,tc_HOL_Obool),X105),X155),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X119,X2),X149)),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I10_J) ).
fof(fact_INT__simps_I10_J,axiom,
! [X155,X149,X2,X119,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X119,X105,X2),X149)),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X119,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(X105,tc_fun(X7,tc_HOL_Obool),X119),X155),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I10_J) ).
fof(fact_UN__simps_I10_J,axiom,
! [X155,X149,X2,X119,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X119,X105,X2),X149)),X155) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X119,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBB(X105,tc_fun(X7,tc_HOL_Obool),X119),X155),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I10_J) ).
fof(fact_divmod__nat__rel,axiom,
! [X33,X90] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X90,X33),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel) ).
fof(fact_Compl__anti__mono,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X155)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__anti__mono) ).
fof(fact_finite__surj__inj,axiom,
! [X2,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Set_Oimage(X7,X7,X2),X149)))
=> c_Fun_Oinj__on(X7,X7,X2,X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
fof(fact_Compl__Times__UNIV1,axiom,
! [X149,X105,X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X149))) = hAPP(hAPP(c_Product__Type_OSigma(X7,X105),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X105,tc_HOL_Obool)),X149))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV1) ).
fof(fact_Compl__Times__UNIV2,axiom,
! [X149,X105,X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV2) ).
fof(fact_Cons__acc__listrel1I,axiom,
! [X292,X172,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Wellfounded_Oacc(X7,X172)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X292),c_Wellfounded_Oacc(tc_List_Olist(X7),c_List_Olistrel1(X7,X172))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),c_Wellfounded_Oacc(tc_List_Olist(X7),c_List_Olistrel1(X7,X172)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).
fof(fact_neg__divide__le__eq,axiom,
! [X25,X24,X23,X7] :
( class_Fields_Olinordered__field(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),X25))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).
fof(fact_neg__divide__less__eq,axiom,
! [X25,X24,X23,X7] :
( class_Fields_Olinordered__field(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),X25))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
! [X2,X6,X7,X105,X107] :
( ( X107 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Opos__decr__bind(X105,X7,X6,X2),X107) = c_Lazy__Sequence_Oempty(X7) )
& ( X107 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Opos__decr__bind(X105,X7,X6,X2),X107) = c_Lazy__Sequence_Obind(X105,X7,hAPP(X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X107),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X7)),X2),X107)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).
fof(fact_accp__subset,axiom,
! [X181,X182,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),X182),X181))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),c_Wellfounded_Oaccp(X7,X181)),c_Wellfounded_Oaccp(X7,X182))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__subset) ).
fof(fact_folding__idem_Osubset__comp__idem,axiom,
! [X155,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding__idem(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,X149)),hAPP(X215,X155)) = hAPP(X215,X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).
fof(fact_insort__insert__triv,axiom,
! [X292,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> c_List_Olinorder__class_Oinsort__insert__key(X7,X7,c_COMBI(X7),X6,X292) = X292 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__triv) ).
fof(fact_split__div__lemma,axiom,
! [X95,X153,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X153)),X95))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X153)))) )
<=> X153 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X95),X44) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div__lemma) ).
fof(fact_setsum__diff,axiom,
! [X2,X155,X149,X7,X105] :
( class_Groups_Oab__group__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff) ).
fof(fact_id__take__nth__drop,axiom,
! [X300,X87,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> X300 = hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Otake(X87),X114),X300)),hAPP(hAPP(c_List_Olist_OCons(X87),hAPP(hAPP(c_List_Onth(X87),X300),X114)),hAPP(hAPP(c_List_Odrop(X87),hAPP(c_Nat_OSuc,X114)),X300))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__take__nth__drop) ).
fof(fact_less__than__iff,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X127)),c_Wellfounded_Oless__than))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__than__iff) ).
fof(fact_image__image,axiom,
! [X149,X1,X119,X2,X7,X105] : hAPP(c_Set_Oimage(X105,X7,X2),hAPP(c_Set_Oimage(X119,X105,X1),X149)) = hAPP(c_Set_Oimage(X119,X7,hAPP(hAPP(c_COMBB(X105,X7,X119),X2),X1)),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_map__inj__on,axiom,
! [X293,X292,X2,X7,X105] :
( hAPP(hAPP(c_List_Omap(X105,X7),X2),X292) = hAPP(hAPP(c_List_Omap(X105,X7),X2),X293)
=> ( c_Fun_Oinj__on(X105,X7,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),hAPP(c_List_Oset(X105),X292)),hAPP(c_List_Oset(X105),X293)))
=> X292 = X293 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__inj__on) ).
fof(fact_inj__on__map__eq__map,axiom,
! [X293,X292,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X292)),hAPP(c_List_Oset(X7),X293)))
=> ( hAPP(hAPP(c_List_Omap(X7,X105),X2),X292) = hAPP(hAPP(c_List_Omap(X7,X105),X2),X293)
<=> X292 = X293 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__map__eq__map) ).
fof(fact_zdiff__int__split,axiom,
! [X127,X6,X38] :
( hBOOL(hAPP(X38,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X127))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X127),X6))
=> hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X127)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X127))
=> hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__int__split) ).
fof(fact_power__le__dvd,axiom,
! [X90,X84,X33,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X90)),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__dvd) ).
fof(fact_map__add__assoc,axiom,
! [X283,X284,X285,X105,X7] : c_Map_Omap__add(X7,X105,X285,c_Map_Omap__add(X7,X105,X284,X283)) = c_Map_Omap__add(X7,X105,c_Map_Omap__add(X7,X105,X285,X284),X283),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__assoc) ).
fof(fact_Image__Int__eq,axiom,
! [X155,X149,X191,X105,X7] :
( c_Relation_Osingle__valued(X7,X105,hAPP(c_Relation_Oconverse(X105,X7),X191))
=> hAPP(c_Relation_OImage(X105,X7,X191),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X105,X7,X191),X149)),hAPP(c_Relation_OImage(X105,X7,X191),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__eq) ).
fof(fact_frac__le,axiom,
! [X97,X128,X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X128))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X128),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X97)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X98),X128))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__le) ).
fof(fact_mult__mono_H,axiom,
! [X106,X10,X84,X71,X87] :
( class_Rings_Oordered__semiring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X10),X106))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X106))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__mono,axiom,
! [X106,X10,X84,X71,X87] :
( class_Rings_Oordered__semiring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X10),X106))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X106))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(fact_frac__less,axiom,
! [X97,X128,X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X128))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X128),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X97)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X98),X128))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less) ).
fof(fact_frac__less2,axiom,
! [X97,X128,X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X128))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X128),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X97)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X98),X128))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less2) ).
fof(fact_mult__less__le__imp__less,axiom,
! [X106,X10,X84,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X10),X106))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X106))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__le__less__imp__less,axiom,
! [X106,X10,X84,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X10),X106))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X106))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__strict__mono_H,axiom,
! [X106,X10,X84,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X10),X106))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X106))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__strict__mono,axiom,
! [X106,X10,X84,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X10),X106))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X106))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_setsum__diff1__ring,axiom,
! [X2,X25,X149,X7,X105] :
( class_Rings_Oring(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149)),hAPP(X2,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1__ring) ).
fof(fact_geometric__sum,axiom,
! [X44,X6,X7] :
( class_Fields_Ofield(X7)
=> ( X6 != c_Groups_Oone__class_Oone(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(c_Power_Opower__class_Opower(X7),X6)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X6),X44)),c_Groups_Oone__class_Oone(X7))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X6),c_Groups_Oone__class_Oone(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_geometric__sum) ).
fof(fact_listsum__abs,axiom,
! [X292,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Groups_Oabs__class_Oabs(X7),hAPP(c_List_Omonoid__add__class_Olistsum(X7),X292))),hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X7,X7),c_Groups_Oabs__class_Oabs(X7)),X292)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__abs) ).
fof(fact_evaln_OLocal,axiom,
! [X58,X44,X25,X60,X77,X23] :
( c_Natural_Oevaln(X23,hAPP(hAPP(hAPP(c_Natural_Oupdate,X77),c_Com_Ovname_OLoc(X60)),hAPP(X25,X77)),X44,X58)
=> c_Natural_Oevaln(c_Com_Ocom_OLocal(X60,X25,X23),X77,X44,hAPP(hAPP(hAPP(c_Natural_Oupdate,X58),c_Com_Ovname_OLoc(X60)),hAPP(hAPP(c_Natural_Ogetlocs,X77),X60))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OLocal) ).
fof(fact_image__add__atLeastLessThan,axiom,
! [X158,X107,X94] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X94)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X107),X158)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X158),X94)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
fof(fact_setsum__diff__nat__ivl,axiom,
! [X2,X161,X44,X95,X7] :
( class_Groups_Oab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X161))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X161))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X44))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X44),X161)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff__nat__ivl) ).
fof(fact_setsum__add__nat__ivl,axiom,
! [X2,X161,X44,X95,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X161))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X44))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X44),X161))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X161)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).
fof(fact_mult__right__le__imp__le,axiom,
! [X84,X10,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__left__le__imp__le,axiom,
! [X84,X71,X10,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [X24,X25,X23,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X24)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__right__less__imp__less,axiom,
! [X84,X10,X71,X87] :
( class_Rings_Olinordered__semiring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [X84,X10,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_power__less__imp__less__base,axiom,
! [X84,X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X84),X33)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_mult__left__less__imp__less,axiom,
! [X84,X71,X10,X87] :
( class_Rings_Olinordered__semiring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [X84,X71,X10,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [X24,X25,X23,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X24)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_setsum__diff__nat,axiom,
! [X2,X149,X155,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff__nat) ).
fof(fact_fold1__strict__below__iff,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Finite__Set_Ofold1(X7,c_Orderings_Oord__class_Omin(X7)),X149)),X6))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X3),X6)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__strict__below__iff) ).
fof(fact_fold1__below__iff,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Finite__Set_Ofold1(X7,c_Orderings_Oord__class_Omin(X7)),X149)),X6))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X3),X6)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__below__iff) ).
fof(fact_INF1__D,axiom,
! [X25,X24,X155,X149,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155),X24))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(X155,X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__D) ).
fof(fact_power__increasing__iff,axiom,
! [X127,X6,X24,X7] :
( class_Rings_Olinordered__semidom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Oone__class_Oone(X7)),X24))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X24),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X24),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),X127)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__le__imp__le__exp,axiom,
! [X33,X90,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X90)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__less__imp__less__exp,axiom,
! [X33,X90,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X90)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__strict__increasing__iff,axiom,
! [X127,X6,X24,X7] :
( class_Rings_Olinordered__semidom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Oone__class_Oone(X7)),X24))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X24),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X24),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X127)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_select,axiom,
! [X45,X7,X292] :
( X292 != c_List_Olist_ONil(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Product__Type_Ofst(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X7,X292),X45))),hAPP(c_List_Oset(X7),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select) ).
fof(fact_card__cartesian__product__singleton,axiom,
! [X149,X6,X105,X7] : hAPP(c_Finite__Set_Ocard(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X149))) = hAPP(c_Finite__Set_Ocard(X105),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product__singleton) ).
fof(fact_evalc_Oequations_I9_J,axiom,
! [X41,X43,X42] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X42)),X43),X41))
<=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X42))),X43),X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I9_J) ).
fof(fact_evalc_OBody,axiom,
! [X51,X52,X78] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X78))),X52),X51))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X78)),X52),X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OBody) ).
fof(fact_splitD,axiom,
! [X24,X25,X2,X105,X7] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)))
=> hBOOL(hAPP(hAPP(X2,X25),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD) ).
fof(fact_swap__inj__on,axiom,
! [X149,X105,X7] : c_Fun_Oinj__on(tc_prod(X7,X105),tc_prod(X105,X7),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_prod(X105,X7)),hAPP(c_COMBC(X105,X7,tc_prod(X105,X7)),c_Product__Type_OPair(X105,X7))),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__inj__on) ).
fof(fact_setprod__pos__nat,axiom,
! [X2,X209,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X209))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,X3))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,tc_Nat_Onat),X2),X209))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__pos__nat) ).
fof(fact_setprod__pos__nat__iff,axiom,
! [X2,X209,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,tc_Nat_Onat),X2),X209)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X209))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__pos__nat__iff) ).
fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
! [X44,X95,X2,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X95),hAPP(c_Nat_OSuc,X44))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Nat_Onat),X2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__Suc__ivl) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [X24,X25,X23,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X24)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [X24,X25,X23,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X24)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_empty__upd__none,axiom,
! [X235,X6,X7,X105] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,tc_Option_Ooption(X7)),hAPP(c_COMBK(tc_Option_Ooption(X7),X105),c_Option_Ooption_ONone(X7))),X6),c_Option_Ooption_ONone(X7)),X235) = c_Option_Ooption_ONone(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__upd__none) ).
fof(fact_Int__lower1,axiom,
! [X155,X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).
fof(fact_Int__lower2,axiom,
! [X155,X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
fof(fact_Diff__subset,axiom,
! [X155,X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset) ).
fof(fact_listsum__map__remove1,axiom,
! [X2,X292,X6,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hAPP(c_List_Omonoid__add__class_Olistsum(X105),hAPP(hAPP(c_List_Omap(X7,X105),X2),X292)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(X2,X6)),hAPP(c_List_Omonoid__add__class_Olistsum(X105),hAPP(hAPP(c_List_Omap(X7,X105),X2),c_List_Oremove1(X7,X6,X292)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__map__remove1) ).
fof(fact_Int__Un__distrib,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X193)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).
fof(fact_Diff__Int__distrib,axiom,
! [X155,X149,X193,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X193),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X193),X149)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X193),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib) ).
fof(fact_Un__Int__distrib,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).
fof(fact_Diff__Int,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int) ).
fof(fact_Diff__Un,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X193)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Un) ).
fof(fact_prod_Orecs,axiom,
! [X24,X25,X22,X7,X119,X105] : c_Product__Type_Oprod_Oprod__rec(X105,X119,X7,X22,hAPP(hAPP(c_Product__Type_OPair(X105,X119),X25),X24)) = hAPP(hAPP(X22,X25),X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
fof(fact_New__DSequence_Oneg__bind__def,axiom,
! [X107,X2,X6,X7,X105] : hAPP(c_New__DSequence_Oneg__bind(X105,X7,X6,X2),X107) = c_Lazy__Sequence_Ohb__bind(X105,X7,hAPP(X6,X107),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X7))),X2),X107)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).
fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
! [X44,X95,X2,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X95)),hAPP(c_Nat_OSuc,X44))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Nat_Onat),X2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).
fof(fact_image__add__atLeastAtMost,axiom,
! [X158,X107,X94] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X94)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X107,X158)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X158),X94)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastAtMost) ).
fof(fact_Int__Collect,axiom,
! [X38,X149,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Set_OCollect(X7),X38))))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
& hBOOL(hAPP(X38,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect) ).
fof(fact_atLeastLessThan__subset__iff,axiom,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X25),X24)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X23),X136)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),X25))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X23),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),X136)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
fof(fact_sum_Osize_I1_J,axiom,
! [X25,X109,X85,X105,X7] : c_Sum__Type_Osum_Osum__size(X7,X105,X85,X109,hAPP(c_Sum__Type_OInl(X7,X105),X25)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X85,X25)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osize_I1_J) ).
fof(fact_sum_Osize_I2_J,axiom,
! [X24,X109,X85,X105,X7] : c_Sum__Type_Osum_Osum__size(X7,X105,X85,X109,hAPP(c_Sum__Type_OInr(X105,X7),X24)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X109,X24)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osize_I2_J) ).
fof(fact_folding__idem_Ounion__idem,axiom,
! [X155,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding__idem(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,X149)),hAPP(X215,X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Ounion__idem) ).
fof(fact_wf__Un,axiom,
! [X45,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ( c_Wellfounded_Owf(X7,X45)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X7,X7),X172)),hAPP(c_Relation_ORange(X7,X7),X45)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Wellfounded_Owf(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X45)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Un) ).
fof(fact_le__diff__iff,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X94)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(fact_less__diff__iff,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X94)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [X24,X25,X23,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X24)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),X25)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [X24,X23,X25,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X23)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),X25)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_insert__subset,axiom,
! [X155,X149,X6,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),X155))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
! [X2,X149,X7] :
( ( class_Groups_Ocomm__monoid__add(X7)
& class_Groups_Ocomm__monoid__mult(X7) )
=> ( c_Nat__Transfer_Onat__set(X149)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X7),X2),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X7),hAPP(hAPP(c_COMBB(tc_Int_Oint,X7,tc_Nat_Onat),X2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).
fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
! [X2,X149,X7] :
( ( class_Groups_Ocomm__monoid__add(X7)
& class_Groups_Ocomm__monoid__mult(X7) )
=> ( c_Nat__Transfer_Onat__set(X149)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X7),X2),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(hAPP(c_COMBB(tc_Int_Oint,X7,tc_Nat_Onat),X2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I1_J) ).
fof(fact_map__of_Osimps_I2_J,axiom,
! [X289,X161,X105,X7] : c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X7,X105)),X161),X289)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Omap__of(X7,X105,X289)),hAPP(c_Product__Type_Ofst(X7,X105),X161)),hAPP(c_Option_Ooption_OSome(X105),hAPP(c_Product__Type_Osnd(X7,X105),X161))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of_Osimps_I2_J) ).
fof(fact_setprod__Un__disjoint,axiom,
! [X1,X155,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__disjoint) ).
fof(fact_setprod_Ounion__disjoint,axiom,
! [X1,X155,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__disjoint) ).
fof(fact_setsum__Un__disjoint,axiom,
! [X1,X155,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X155)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__disjoint) ).
fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
! [X149,X2,X7] :
( ( class_Groups_Ocomm__monoid__add(X7)
& class_Groups_Ocomm__monoid__mult(X7) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X7),X2),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).
fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
! [X149,X2,X7] :
( ( class_Groups_Ocomm__monoid__add(X7)
& class_Groups_Ocomm__monoid__mult(X7) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I1_J) ).
fof(fact_listrel__subset__rtrancl__listrel1,axiom,
! [X172,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool)),c_List_Olistrel(X7,X172)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X7),c_List_Olistrel1(X7,X172)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).
fof(fact_image__add__int__atLeastLessThan,axiom,
! [X160,X157] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),X157)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X160),X157))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X157),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__int__atLeastLessThan) ).
fof(fact_drop__append,axiom,
! [X301,X300,X33,X87] : hAPP(hAPP(c_List_Odrop(X87),X33),hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Odrop(X87),X33),X300)),hAPP(hAPP(c_List_Odrop(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300))),X301)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__append) ).
fof(fact_take__append,axiom,
! [X301,X300,X33,X87] : hAPP(hAPP(c_List_Otake(X87),X33),hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Otake(X87),X33),X300)),hAPP(hAPP(c_List_Otake(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300))),X301)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__append) ).
fof(fact_set__sublist__subset,axiom,
! [X211,X292,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),c_List_Osublist(X7,X292,X211))),hAPP(c_List_Oset(X7),X292))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sublist__subset) ).
fof(fact_set__remove1__subset,axiom,
! [X292,X6,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),c_List_Oremove1(X7,X6,X292))),hAPP(c_List_Oset(X7),X292))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remove1__subset) ).
fof(fact_inj__on__the__inv__into,axiom,
! [X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> c_Fun_Oinj__on(X105,X7,c_Fun_Othe__inv__into(X7,X105,X149,X2),hAPP(c_Set_Oimage(X7,X105,X2),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
fof(fact_Domain__Collect__split,axiom,
! [X38,X105,X7] : hAPP(c_Relation_ODomain(X7,X105),hAPP(c_Set_OCollect(tc_prod(X7,X105)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),X38))) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X105)),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Collect__split) ).
fof(fact_fun__left__comm__idem_Ofold__set,axiom,
! [X292,X127,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm__idem(X7,X105,X2)
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X127),hAPP(c_List_Oset(X7),X292)) = hAPP(c_List_Ofoldl(X105,X7,hAPP(c_COMBC(X7,X105,X105),X2),X127),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).
fof(fact_setsum__negf,axiom,
! [X149,X2,X105,X7] :
( class_Groups_Oab__group__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBB(X7,X7,X105),c_Groups_Ouminus__class_Ouminus(X7)),X2)),X149) = hAPP(c_Groups_Ouminus__class_Ouminus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X2),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__negf) ).
fof(fact_abs__setprod,axiom,
! [X149,X2,X105,X7] :
( class_Fields_Olinordered__field(X7)
=> hAPP(c_Groups_Oabs__class_Oabs(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X7),X2),X149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X7),hAPP(hAPP(c_COMBB(X7,X7,X105),c_Groups_Oabs__class_Oabs(X7)),X2)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__setprod) ).
fof(fact_all__set__conv__all__nth,axiom,
! [X38,X292,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X292)))
=> hBOOL(hAPP(X38,X3)) )
<=> ! [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X147),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> hBOOL(hAPP(X38,hAPP(hAPP(c_List_Onth(X7),X292),X147))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__set__conv__all__nth) ).
fof(fact_insert__mono,axiom,
! [X25,X192,X193,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X193),X192))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X193)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X192))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
fof(fact_sorted__append,axiom,
! [X293,X292,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Oappend(X7),X292),X293))
<=> ( c_List_Olinorder__class_Osorted(X7,X292)
& c_List_Olinorder__class_Osorted(X7,X293)
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X292)))
=> ! [X206] :
( hBOOL(hAPP(hAPP(c_member(X7),X206),hAPP(c_List_Oset(X7),X293)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X3),X206)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__append) ).
fof(fact_power__less__power__Suc,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_double__diff,axiom,
! [X193,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X193))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X193),X149)) = X149 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__diff) ).
fof(fact_Pow__mono,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X7),X149)),hAPP(c_Set_OPow(X7),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__mono) ).
fof(fact_K__record__comp,axiom,
! [X6,X2,X23,X119,X7,X105] : hAPP(hAPP(c_Fun_Ocomp(X105,X7,X119,hAPP(c_COMBK(X7,X105),X23)),X2),X6) = X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_K__record__comp) ).
fof(fact_set__drop__subset,axiom,
! [X292,X44,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Odrop(X7),X44),X292))),hAPP(c_List_Oset(X7),X292))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__drop__subset) ).
fof(fact_set__take__subset,axiom,
! [X292,X44,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Otake(X7),X44),X292))),hAPP(c_List_Oset(X7),X292))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__take__subset) ).
fof(fact_pos__le__divide__eq,axiom,
! [X24,X25,X23,X7] :
( class_Fields_Olinordered__field(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).
fof(fact_pos__divide__le__eq,axiom,
! [X25,X24,X23,X7] :
( class_Fields_Olinordered__field(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),X25))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).
fof(fact_mult__imp__le__div__pos,axiom,
! [X86,X97,X98,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),X98)),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X97),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).
fof(fact_pos__less__divide__eq,axiom,
! [X24,X25,X23,X7] :
( class_Fields_Olinordered__field(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
fof(fact_pos__divide__less__eq,axiom,
! [X25,X24,X23,X7] :
( class_Fields_Olinordered__field(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),X25))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
fof(fact_mult__imp__less__div__pos,axiom,
! [X86,X97,X98,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),X98)),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X97),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).
fof(fact_of__int__setprod,axiom,
! [X149,X2,X105,X7] :
( ( class_Groups_Ocomm__monoid__mult(X7)
& class_Rings_Oring__1(X7) )
=> hAPP(c_Int_Oring__1__class_Oof__int(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,tc_Int_Oint),X2),X149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X7),hAPP(hAPP(c_COMBB(tc_Int_Oint,X7,X105),c_Int_Oring__1__class_Oof__int(X7)),X2)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__setprod) ).
fof(fact_of__nat__setprod,axiom,
! [X149,X2,X105,X7] :
( ( class_Groups_Ocomm__monoid__mult(X7)
& class_Rings_Osemiring__1(X7) )
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,tc_Nat_Onat),X2),X149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,X105),c_Nat_Osemiring__1__class_Oof__nat(X7)),X2)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__setprod) ).
fof(fact_converse__Int,axiom,
! [X45,X172,X7,X105] : hAPP(c_Relation_Oconverse(X105,X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X105,X7),tc_HOL_Obool)),X172),X45)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X105,X7),X172)),hAPP(c_Relation_Oconverse(X105,X7),X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Int) ).
fof(fact_converse__Un,axiom,
! [X45,X172,X7,X105] : hAPP(c_Relation_Oconverse(X105,X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X105,X7),tc_HOL_Obool)),X172),X45)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X105,X7),X172)),hAPP(c_Relation_Oconverse(X105,X7),X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Un) ).
fof(fact_funpow__add,axiom,
! [X2,X44,X95,X7] : hAPP(hAPP(c_Nat_Ocompow(X7,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X44)),X2) = hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(hAPP(c_Nat_Ocompow(X7,X7),X95),X2)),hAPP(hAPP(c_Nat_Ocompow(X7,X7),X44),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__add) ).
fof(fact_of__int__setsum,axiom,
! [X149,X2,X105,X7] :
( class_Rings_Oring__1(X7)
=> hAPP(c_Int_Oring__1__class_Oof__int(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,tc_Int_Oint),X2),X149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBB(tc_Int_Oint,X7,X105),c_Int_Oring__1__class_Oof__int(X7)),X2)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__setsum) ).
fof(fact_of__nat__setsum,axiom,
! [X149,X2,X105,X7] :
( class_Rings_Osemiring__1(X7)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,tc_Nat_Onat),X2),X149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,X105),c_Nat_Osemiring__1__class_Oof__nat(X7)),X2)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__setsum) ).
fof(fact_inj__singleton,axiom,
! [X7] : c_Fun_Oinj__on(X7,tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__singleton) ).
fof(fact_New__DSequence_Opos__bind__def,axiom,
! [X107,X2,X6,X7,X105] : hAPP(c_New__DSequence_Opos__bind(X105,X7,X6,X2),X107) = c_Lazy__Sequence_Obind(X105,X7,hAPP(X6,X107),hAPP(hAPP(c_COMBC(X105,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X7)),X2),X107)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).
fof(fact_finite__cartesian__product,axiom,
! [X155,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X155)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__product) ).
fof(fact_card__psubset,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X7),X155)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
fof(fact_finite__surj,axiom,
! [X2,X155,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),X155),hAPP(c_Set_Oimage(X7,X105,X2),X149)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
fof(fact_inj__on__Int,axiom,
! [X155,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( c_Fun_Oinj__on(X7,X105,X2,X155)
=> c_Fun_Oinj__on(X7,X105,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Int) ).
fof(fact_nth__drop,axiom,
! [X300,X87,X114,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X114)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Odrop(X87),X33),X300)),X114) = hAPP(hAPP(c_List_Onth(X87),X300),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X114)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__drop) ).
fof(fact_sorted__rev__nth__mono,axiom,
! [X113,X114,X300,X87] :
( class_Orderings_Olinorder(X87)
=> ( c_List_Olinorder__class_Osorted(X87,hAPP(c_List_Orev(X87),X300))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_List_Onth(X87),X300),X113)),hAPP(hAPP(c_List_Onth(X87),X300),X114))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__rev__nth__mono) ).
fof(fact_zip__append,axiom,
! [X315,X301,X316,X7,X300,X87] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X316)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X301) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X315)
=> hAPP(hAPP(c_List_Ozip(X87,X7),hAPP(hAPP(c_List_Oappend(X87),X300),X301)),hAPP(hAPP(c_List_Oappend(X7),X316),X315)) = hAPP(hAPP(c_List_Oappend(tc_prod(X87,X7)),hAPP(hAPP(c_List_Ozip(X87,X7),X300),X316)),hAPP(hAPP(c_List_Ozip(X87,X7),X301),X315)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append) ).
fof(fact_list__size__map,axiom,
! [X292,X1,X105,X2,X7] : c_List_Olist_Olist__size(X7,X2,hAPP(hAPP(c_List_Omap(X105,X7),X1),X292)) = c_List_Olist_Olist__size(X105,hAPP(c_Fun_Ocomp(X7,tc_Nat_Onat,X105,X2),X1),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__map) ).
fof(fact_refl__onD,axiom,
! [X25,X172,X149,X7] :
( c_Relation_Orefl__on(X7,X149,X172)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X25)),X172)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD) ).
fof(fact_UN__upper,axiom,
! [X155,X105,X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X105,tc_HOL_Obool)),hAPP(X155,X25)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__upper) ).
fof(fact_take__Cons__number__of,axiom,
! [X300,X86,X87,X139] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = c_List_Olist_ONil(X87) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_List_Olist_OCons(X87),X86),hAPP(hAPP(c_List_Otake(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X300)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons__number__of) ).
fof(fact_evalc_Oequations_I7_J,axiom,
! [X43,X41,X42] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X42,X41)),X43),X43))
<=> ( hBOOL(hAPP(X42,X43))
=> ? [X62] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X41),X43),X62))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X42,X41)),X62),X43)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I7_J) ).
fof(fact_predicate2D,axiom,
! [X127,X6,X194,X38,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X38),X194))
=> ( hBOOL(hAPP(hAPP(X38,X6),X127))
=> hBOOL(hAPP(hAPP(X194,X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X194,X105,X7,X127,X6,X38] :
( hBOOL(hAPP(hAPP(X38,X6),X127))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X38),X194))
=> hBOOL(hAPP(hAPP(X194,X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_fold1__antimono,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Finite__Set_Ofold1(X7,c_Orderings_Oord__class_Omin(X7)),X155)),hAPP(c_Finite__Set_Ofold1(X7,c_Orderings_Oord__class_Omin(X7)),X149))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__antimono) ).
fof(fact_Un__iff,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
| hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__iff) ).
fof(fact_field__le__epsilon,axiom,
! [X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( ! [X173] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X173))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X98),X173))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__le__epsilon) ).
fof(fact_restrict__restrict,axiom,
! [X155,X149,X95,X105,X7] : c_Map_Orestrict__map(X7,X105,c_Map_Orestrict__map(X7,X105,X95,X149),X155) = c_Map_Orestrict__map(X7,X105,X95,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__restrict) ).
fof(fact_foldl__Cons,axiom,
! [X292,X6,X25,X2,X105,X7] : hAPP(c_List_Ofoldl(X7,X105,X2,X25),hAPP(hAPP(c_List_Olist_OCons(X105),X6),X292)) = hAPP(c_List_Ofoldl(X7,X105,X2,hAPP(hAPP(X2,X25),X6)),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__Cons) ).
fof(fact_length__transpose__sorted,axiom,
! [X292,X7] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X7))),X292)))
=> ( ( X292 = c_List_Olist_ONil(tc_List_Olist(X7))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),c_List_Otranspose(X7,X292)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X292 != c_List_Olist_ONil(tc_List_Olist(X7))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7))),c_List_Otranspose(X7,X292)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X7)),X292),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__transpose__sorted) ).
fof(fact_power__strict__mono,axiom,
! [X33,X84,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X84),X33))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(fact_power__decreasing,axiom,
! [X71,X164,X33,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X164))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),c_Groups_Oone__class_Oone(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X164)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(fact_power__strict__decreasing,axiom,
! [X71,X164,X33,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X164))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Oone__class_Oone(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X164)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_vimage__Int,axiom,
! [X155,X149,X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7,X105,X2),X149)),hAPP(c_Set_Ovimage(X7,X105,X2),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Int) ).
fof(fact_vimage__Un,axiom,
! [X155,X149,X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7,X105,X2),X149)),hAPP(c_Set_Ovimage(X7,X105,X2),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Un) ).
fof(fact_vimage__Diff,axiom,
! [X155,X149,X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7,X105,X2),X149)),hAPP(c_Set_Ovimage(X7,X105,X2),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Diff) ).
fof(fact_Image__Un,axiom,
! [X155,X149,X191,X7,X105] : hAPP(c_Relation_OImage(X105,X7,X191),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X105,X7,X191),X149)),hAPP(c_Relation_OImage(X105,X7,X191),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Un) ).
fof(fact_image__Un,axiom,
! [X155,X149,X2,X7,X105] : hAPP(c_Set_Oimage(X105,X7,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X105,X7,X2),X149)),hAPP(c_Set_Oimage(X105,X7,X2),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Un) ).
fof(fact_append__in__lists__conv,axiom,
! [X149,X293,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),hAPP(hAPP(c_List_Oappend(X7),X292),X293)),c_List_Olists(X7,X149)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X292),c_List_Olists(X7,X149)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X293),c_List_Olists(X7,X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).
fof(fact_Powp__mono,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X7,X149)),c_Predicate_OPowp(X7,X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__mono) ).
fof(fact_map__add__comm,axiom,
! [X284,X285,X105,X7] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Map_Odom(X7,X105,X285)),c_Map_Odom(X7,X105,X284)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Map_Omap__add(X7,X105,X285,X284) = c_Map_Omap__add(X7,X105,X284,X285) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__comm) ).
fof(fact_finite__Plus,axiom,
! [X155,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X7,X105)),c_Sum__Type_OPlus(X7,X105,X149,X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).
fof(fact_Id__on__eqI,axiom,
! [X149,X7,X24,X25] :
( X25 = X24
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X24)),c_Relation_OId__on(X7,X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
fof(fact_Rep__Integ__induct,axiom,
! [X38,X127] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X127),c_Int_OInteg))
=> ( ! [X3] : hBOOL(hAPP(X38,hAPP(c_Int_ORep__Integ,X3)))
=> hBOOL(hAPP(X38,X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__induct) ).
fof(fact_list__update__append1,axiom,
! [X86,X301,X300,X87,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Olist__update(X87,hAPP(hAPP(c_List_Oappend(X87),X300),X301)),X114),X86) = hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X86)),X301) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__append1) ).
fof(fact_nat__mult__dvd__cancel1,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X44)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X95),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(fact_dvd__mult__cancel,axiom,
! [X33,X90,X96] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X33)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X96))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X90),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
fof(fact_mult__le__cancel2,axiom,
! [X44,X94,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X94)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_power__dvd__imp__le,axiom,
! [X33,X90,X114] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X114),X90)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X114),X33)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X114))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_mult__le__cancel1,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X44)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_nat__power__less__imp__less,axiom,
! [X33,X90,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X114))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X114),X90)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X114),X33)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_wfE__pf,axiom,
! [X149,X191,X7] :
( c_Wellfounded_Owf(X7,X191)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Relation_OImage(X7,X7,X191),X149)))
=> X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfE__pf) ).
fof(fact_int__setprod,axiom,
! [X149,X2,X7] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,tc_Nat_Onat),X2),X149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X7),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__setprod) ).
fof(fact_int__setsum,axiom,
! [X149,X2,X7] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X7),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__setsum) ).
fof(fact_override__on__emptyset,axiom,
! [X1,X2,X105,X7] : c_Fun_Ooverride__on(X7,X105,X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__emptyset) ).
fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
! [X127,X6,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X2,X6)),hAPP(X2,X127)) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X2,X127)),hAPP(X2,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).
fof(fact_hoare__derivs_Oequations_I7_J,axiom,
! [X43,X42,X7] : c_Hoare__Mirabelle_Ohoare__derivs(X7,X42,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X43),c_Com_Ocom_OSKIP),X43)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I7_J) ).
fof(fact_hoare__derivs_OSkip,axiom,
! [X38,X216,X7] : c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X38),c_Com_Ocom_OSKIP),X38)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OSkip) ).
fof(fact_option_Orecs_I2_J,axiom,
! [X25,X21,X22,X105,X7] : c_Option_Ooption_Ooption__rec(X7,X105,X22,X21,hAPP(c_Option_Ooption_OSome(X105),X25)) = hAPP(X21,X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Orecs_I2_J) ).
fof(fact_set__update__memI,axiom,
! [X6,X292,X7,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist__update(X7,X292),X44),X6)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__memI) ).
fof(fact_UN__I,axiom,
! [X155,X24,X105,X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X105),X24),hAPP(X155,X25)))
=> hBOOL(hAPP(hAPP(c_member(X105),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__I) ).
fof(fact_unique__quotient,axiom,
! [X145,X146,X138,X144,X84,X71] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),X138)))
=> ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X146),X145)))
=> ( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> X144 = X146 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient) ).
fof(fact_unique__remainder,axiom,
! [X145,X146,X138,X144,X84,X71] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),X138)))
=> ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X146),X145)))
=> ( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> X138 = X145 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__remainder) ).
fof(fact_finite__imageD,axiom,
! [X149,X2,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_Oimage(X105,X7,X2),X149)))
=> ( c_Fun_Oinj__on(X105,X7,X2,X149)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [X24,X25,X23,X7] :
( class_Rings_Oidom(X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X24)))
<=> ( X23 = c_Groups_Ozero__class_Ozero(X7)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X25),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [X24,X23,X25,X7] :
( class_Rings_Oidom(X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X23)))
<=> ( X23 = c_Groups_Ozero__class_Ozero(X7)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X25),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(fact_single__valued__subset,axiom,
! [X45,X172,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X172),X45))
=> ( c_Relation_Osingle__valued(X7,X105,X45)
=> c_Relation_Osingle__valued(X7,X105,X172) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__subset) ).
fof(fact_add__le__cancel__right,axiom,
! [X24,X23,X25,X7] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X24),X23)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__right,axiom,
! [X84,X10,X71,X87] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__left,axiom,
! [X24,X25,X23,X7] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X23),X25)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X23),X24)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__le__imp__le__left,axiom,
! [X84,X71,X10,X87] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X71)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X84)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__less__imp__less__right,axiom,
! [X84,X10,X71,X87] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__right,axiom,
! [X24,X23,X25,X7] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X24),X23)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__left,axiom,
! [X84,X71,X10,X87] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X71)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X84)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__cancel__left,axiom,
! [X24,X25,X23,X7] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X23),X25)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X23),X24)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_evaln_Oequations_I7_J,axiom,
! [X47,X43,X41,X42] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X42,X41),X43,X47,X43)
<=> ( hBOOL(hAPP(X42,X43))
=> ? [X62] :
( c_Natural_Oevaln(X41,X43,X47,X62)
& c_Natural_Oevaln(c_Com_Ocom_OWhile(X42,X41),X62,X47,X43) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I7_J) ).
fof(fact_sorted__nth__mono,axiom,
! [X113,X114,X300,X87] :
( class_Orderings_Olinorder(X87)
=> ( c_List_Olinorder__class_Osorted(X87,X300)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_List_Onth(X87),X300),X114)),hAPP(hAPP(c_List_Onth(X87),X300),X113))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__nth__mono) ).
fof(fact_relpow_Osimps_I2_J,axiom,
! [X191,X44,X7] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),hAPP(c_Nat_OSuc,X44)),X191) = hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)),X191),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_relpow_Osimps_I2_J) ).
fof(fact_diff__divide__eq__iff,axiom,
! [X98,X86,X97,X87] :
( class_Fields_Ofield(X87)
=> ( X97 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X86),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X98),X97)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),X86)),X98)),X97) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).
fof(fact_add__divide__eq__iff,axiom,
! [X98,X86,X97,X87] :
( class_Fields_Ofield(X87)
=> ( X97 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X86),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X98),X97)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),X86)),X98)),X97) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
fof(fact_filter__insort,axiom,
! [X6,X38,X292,X2,X105,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),X292))
=> ( hBOOL(hAPP(X38,X6))
=> hAPP(c_List_Ofilter(X105,X38),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),X292)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),hAPP(c_List_Ofilter(X105,X38),X292)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__insort) ).
fof(fact_subset__singletonD,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))
=> ( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
| X149 = hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).
fof(fact_DiffE,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffE) ).
fof(fact_folding__idem_Oin__comp__idem,axiom,
! [X6,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding__idem(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,X149)),hAPP(X2,X6)) = hAPP(X215,X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).
fof(fact_take__Suc__conv__app__nth,axiom,
! [X300,X87,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Otake(X87),hAPP(c_Nat_OSuc,X114)),X300) = hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Otake(X87),X114),X300)),hAPP(hAPP(c_List_Olist_OCons(X87),hAPP(hAPP(c_List_Onth(X87),X300),X114)),c_List_Olist_ONil(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc__conv__app__nth) ).
fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X155)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).
fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X155)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).
fof(fact_comp__funpow,axiom,
! [X2,X44,X105,X7] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X7,X105),tc_fun(X7,X105)),X44),c_Fun_Ocomp(X105,X105,X7,X2)) = c_Fun_Ocomp(X105,X105,X7,hAPP(hAPP(c_Nat_Ocompow(X105,X105),X44),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__funpow) ).
fof(fact_curry__conv,axiom,
! [X24,X25,X2,X7,X119,X105] : hAPP(hAPP(c_Product__Type_Ocurry(X105,X119,X7,X2),X25),X24) = hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X105,X119),X25),X24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__conv) ).
fof(fact_curry__def,axiom,
! [X127,X6,X23,X7,X119,X105] : hAPP(hAPP(c_Product__Type_Ocurry(X105,X119,X7,X23),X6),X127) = hAPP(X23,hAPP(hAPP(c_Product__Type_OPair(X105,X119),X6),X127)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__def) ).
fof(fact_inj__on__Un__image__eq__iff,axiom,
! [X155,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hAPP(c_Set_Oimage(X7,X105,X2),X149) = hAPP(c_Set_Oimage(X7,X105,X2),X155)
<=> X149 = X155 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).
fof(fact_mult__imp__div__pos__le,axiom,
! [X97,X86,X98,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),X98)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).
fof(fact_mult__imp__div__pos__less,axiom,
! [X97,X86,X98,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),X98)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).
fof(fact_refl__on__Int,axiom,
! [X45,X155,X172,X149,X7] :
( c_Relation_Orefl__on(X7,X149,X172)
=> ( c_Relation_Orefl__on(X7,X155,X45)
=> c_Relation_Orefl__on(X7,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X45)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Int) ).
fof(fact_refl__on__Un,axiom,
! [X45,X155,X172,X149,X7] :
( c_Relation_Orefl__on(X7,X149,X172)
=> ( c_Relation_Orefl__on(X7,X155,X45)
=> c_Relation_Orefl__on(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X45)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Un) ).
fof(fact_map__upds__Nil1,axiom,
! [X321,X95,X105,X7] : c_Map_Omap__upds(X7,X105,X95,c_List_Olist_ONil(X7),X321) = X95,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__Nil1) ).
fof(fact_map__upds__Nil2,axiom,
! [X322,X95,X105,X7] : c_Map_Omap__upds(X7,X105,X95,X322,c_List_Olist_ONil(X105)) = X95,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__Nil2) ).
fof(fact_option_Orecs_I1_J,axiom,
! [X21,X22,X105,X7] : c_Option_Ooption_Ooption__rec(X7,X105,X22,X21,c_Option_Ooption_ONone(X105)) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Orecs_I1_J) ).
fof(fact_Domain__insert,axiom,
! [X172,X24,X25,X105,X7] : hAPP(c_Relation_ODomain(X7,X105),hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),X172)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(c_Relation_ODomain(X7,X105),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__insert) ).
fof(fact_Range__insert,axiom,
! [X172,X24,X25,X7,X105] : hAPP(c_Relation_ORange(X105,X7),hAPP(hAPP(c_Set_Oinsert(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X25),X24)),X172)) = hAPP(hAPP(c_Set_Oinsert(X7),X24),hAPP(c_Relation_ORange(X105,X7),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__insert) ).
fof(fact_subset__trans,axiom,
! [X193,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X193))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X193)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X193,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X193))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X193)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_subset__psubset__trans,axiom,
! [X193,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X155),X193))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X193)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__trans,axiom,
! [X193,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X155),X193))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X193)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
! [X149,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X6),X149))
<=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I2_J) ).
fof(fact_Pair__scomp,axiom,
! [X2,X6,X105,X119,X7] : hAPP(hAPP(c_Product__Type_Oscomp(X7,X119,X7,X105),hAPP(c_Product__Type_OPair(X119,X7),X6)),X2) = hAPP(X2,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__scomp) ).
fof(fact_mod__div__equality,axiom,
! [X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84)),X84)),c_Divides_Odiv__class_Omod(X87,X71,X84)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__equality) ).
fof(fact_mod__div__decomp,axiom,
! [X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> X71 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84)),X84)),c_Divides_Odiv__class_Omod(X87,X71,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__decomp) ).
fof(fact_evalc__elim__cases_I6_J,axiom,
! [X51,X9,X79] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X79)),X9),X51))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X79))),X9),X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I6_J) ).
fof(fact_UN__singleton,axiom,
! [X149,X7] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__singleton) ).
fof(fact_upd__conv__take__nth__drop,axiom,
! [X71,X300,X87,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X71) = hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Otake(X87),X114),X300)),hAPP(hAPP(c_List_Olist_OCons(X87),X71),hAPP(hAPP(c_List_Odrop(X87),hAPP(c_Nat_OSuc,X114)),X300))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upd__conv__take__nth__drop) ).
fof(fact_Pow__insert,axiom,
! [X149,X25,X7] : hAPP(c_Set_OPow(X7),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X7),X149)),hAPP(c_Set_Oimage(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_Oinsert(X7),X25)),hAPP(c_Set_OPow(X7),X149))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__insert) ).
fof(fact_evalc_OIfTrue,axiom,
! [X57,X58,X59,X45,X24] :
( hBOOL(hAPP(X24,X45))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X59),X45),X58))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X24,X59,X57)),X45),X58)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OIfTrue) ).
fof(fact_finite__vimageD,axiom,
! [X215,X200,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_Ovimage(X7,X105,X200),X215)))
=> ( hAPP(c_Set_Oimage(X7,X105,X200),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X215)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageD) ).
fof(fact_Cons__in__lists__iff,axiom,
! [X149,X292,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),c_List_Olists(X7,X149)))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X292),c_List_Olists(X7,X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).
fof(fact_range,axiom,
! [X9,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X96))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(X96),X9))),X96)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range) ).
fof(fact_Int__iff,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
& hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__iff) ).
fof(fact_IntD1,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD1) ).
fof(fact_DiffD1,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD1) ).
fof(fact_IntD2,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD2) ).
fof(fact_Diff__insert,axiom,
! [X155,X25,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert) ).
fof(fact_fold1__Un,axiom,
! [X155,X149,X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),X149)),hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),X155)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__Un) ).
fof(fact_dvd_OmonoI,axiom,
! [X2,X7] :
( class_Orderings_Oorder(X7)
=> ( ! [X3,X82] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X82))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X2,X3)),hAPP(X2,X82))) )
=> c_Orderings_Oorder_Omono(tc_Nat_Onat,X7,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OmonoI) ).
fof(fact_folding__idem_Oinsert__idem,axiom,
! [X6,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding__idem(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,X149)),hAPP(X2,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oinsert__idem) ).
fof(fact_scomp__Pair,axiom,
! [X6,X119,X105,X7] : hAPP(hAPP(c_Product__Type_Oscomp(X7,X105,X119,tc_prod(X105,X119)),X6),c_Product__Type_OPair(X105,X119)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__Pair) ).
fof(fact_Pow__def,axiom,
! [X149,X7] : hAPP(c_Set_OPow(X7),X149) = hAPP(c_Set_OCollect(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool))),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__def) ).
fof(fact_rev__foldl__cons,axiom,
! [X292,X7] : hAPP(c_List_Orev(X7),X292) = hAPP(c_List_Ofoldl(tc_List_Olist(X7),X7,hAPP(c_COMBC(X7,tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_OCons(X7)),c_List_Olist_ONil(X7)),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__foldl__cons) ).
fof(fact_gauss__sum,axiom,
! [X44,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),c_Groups_Oone__class_Oone(X7)),c_Groups_Oone__class_Oone(X7))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),c_Nat_Osemiring__1__class_Oof__nat(X7)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X44))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X44)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X44)),c_Groups_Oone__class_Oone(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gauss__sum) ).
fof(fact_acyclic__subset,axiom,
! [X172,X45,X7] :
( c_Wellfounded_Oacyclic(X7,X45)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X45))
=> c_Wellfounded_Oacyclic(X7,X172) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__subset) ).
fof(fact_wf__subset,axiom,
! [X161,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X161),X172))
=> c_Wellfounded_Owf(X7,X161) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__subset) ).
fof(fact_in__set__remove1,axiom,
! [X292,X7,X24,X25] :
( X25 != X24
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_List_Oset(X7),c_List_Oremove1(X7,X24,X292))))
<=> hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_List_Oset(X7),X292))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__remove1) ).
fof(fact_Int__assoc,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X193) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).
fof(fact_Un__assoc,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X193) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).
fof(fact_Int__Diff,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X193) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X155),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Diff) ).
fof(fact_le__add__diff,axiom,
! [X90,X33,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X90)),X96))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(fact_in__set__sublistD,axiom,
! [X211,X292,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),c_List_Osublist(X7,X292,X211))))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__sublistD) ).
fof(fact_evaln_OWhileTrue,axiom,
! [X80,X58,X44,X23,X77,X24] :
( hBOOL(hAPP(X24,X77))
=> ( c_Natural_Oevaln(X23,X77,X44,X58)
=> ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X58,X44,X80)
=> c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X77,X44,X80) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileTrue) ).
fof(fact_filter__is__subset,axiom,
! [X292,X38,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),hAPP(c_List_Ofilter(X7,X38),X292))),hAPP(c_List_Oset(X7),X292))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__is__subset) ).
fof(fact_crossproduct__noteq,axiom,
! [X136,X23,X24,X25,X7] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
=> ( ( X25 != X24
& X23 != X136 )
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X136)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_crossproduct__eq,axiom,
! [X26,X6,X127,X125,X7] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X125),X127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X125),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X127))
<=> ( X125 = X6
| X127 = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_reflp__def,axiom,
! [X172,X7] :
( c_Predicate_Oreflp(X7,X172)
<=> c_Relation_Orefl__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X7,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflp__def) ).
fof(fact_le__diff__conv2,axiom,
! [X107,X158,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X158))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X158),X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),X94)),X158)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_vimageD,axiom,
! [X149,X2,X105,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Set_Ovimage(X7,X105,X2),X149)))
=> hBOOL(hAPP(hAPP(c_member(X105),hAPP(X2,X25)),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageD) ).
fof(fact_vimage__eq,axiom,
! [X155,X2,X105,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Set_Ovimage(X7,X105,X2),X155)))
<=> hBOOL(hAPP(hAPP(c_member(X105),hAPP(X2,X25)),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__eq) ).
fof(fact_drop__Cons,axiom,
! [X292,X6,X44,X7] : hAPP(hAPP(c_List_Odrop(X7),X44),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)) = c_Nat_Onat_Onat__case(tc_List_Olist(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Odrop(X7)),X292),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons) ).
fof(fact_mult__right__le__one__le,axiom,
! [X98,X86,X87] :
( class_Rings_Olinordered__idom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),c_Groups_Oone__class_Oone(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X98)),X86)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_mult__left__le__one__le,axiom,
! [X98,X86,X87] :
( class_Rings_Olinordered__idom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),c_Groups_Oone__class_Oone(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X98),X86)),X86)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_Union__disjoint,axiom,
! [X149,X193,X7] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X193)),X149) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X3),X193))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3),X149) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__disjoint) ).
fof(fact_zdiv__mono2,axiom,
! [X84,X124,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X124))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X124),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X124))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
fof(fact_Domain__Un__eq,axiom,
! [X155,X149,X105,X7] : hAPP(c_Relation_ODomain(X7,X105),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X7,X105),X149)),hAPP(c_Relation_ODomain(X7,X105),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).
fof(fact_Range__Un__eq,axiom,
! [X155,X149,X7,X105] : hAPP(c_Relation_ORange(X105,X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X105,X7),tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_ORange(X105,X7),X149)),hAPP(c_Relation_ORange(X105,X7),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Un__eq) ).
fof(fact_map__update,axiom,
! [X127,X94,X292,X2,X7,X105] : hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(hAPP(c_List_Olist__update(X105,X292),X94),X127)) = hAPP(hAPP(c_List_Olist__update(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)),X94),hAPP(X2,X127)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__update) ).
fof(fact_map__add__def,axiom,
! [X6,X284,X285,X7,X105] : hAPP(c_Map_Omap__add(X105,X7,X285,X284),X6) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X7),X7,hAPP(X285,X6),c_Option_Ooption_OSome(X7)),hAPP(X284,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__def) ).
fof(fact_set__ConsD,axiom,
! [X292,X6,X127,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X127),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292))))
=> ( X127 = X6
| hBOOL(hAPP(hAPP(c_member(X7),X127),hAPP(c_List_Oset(X7),X292))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__ConsD) ).
fof(fact_code__numeral__decr,axiom,
! [X96] :
( X96 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X96)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X96))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__decr) ).
fof(fact_in__set__dropD,axiom,
! [X292,X44,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Odrop(X7),X44),X292))))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__dropD) ).
fof(fact_in__set__takeD,axiom,
! [X292,X44,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Otake(X7),X44),X292))))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__takeD) ).
fof(fact_dom__fun__upd,axiom,
! [X6,X2,X105,X7,X127] :
( ( X127 = c_Option_Ooption_ONone(X7)
=> c_Map_Odom(X105,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,tc_Option_Ooption(X7)),X2),X6),X127)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),c_Map_Odom(X105,X7,X2)),hAPP(hAPP(c_Set_Oinsert(X105),X6),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)))) )
& ( X127 != c_Option_Ooption_ONone(X7)
=> c_Map_Odom(X105,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,tc_Option_Ooption(X7)),X2),X6),X127)) = hAPP(hAPP(c_Set_Oinsert(X105),X6),c_Map_Odom(X105,X7,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__fun__upd) ).
fof(fact_power__Suc__less__one,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Oone__class_Oone(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Nat_OSuc,X33))),c_Groups_Oone__class_Oone(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_zdiv__mono2__neg,axiom,
! [X84,X124,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X124))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X124),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X124)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
fof(fact_Id__onE,axiom,
! [X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X23),c_Relation_OId__on(X7,X149)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> X23 != hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__onE) ).
fof(fact_the__inv__f__f,axiom,
! [X6,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> hAPP(c_Fun_Othe__inv__into(X7,X105,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),X2),hAPP(X2,X6)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__f__f) ).
fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
! [X26,X6,X149,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(X2,X6),hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),hAPP(hAPP(X2,X6),X26)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).
fof(fact_wfP__subset,axiom,
! [X161,X172,X7] :
( c_Wellfounded_OwfP(X7,X172)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),X161),X172))
=> c_Wellfounded_OwfP(X7,X161) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__subset) ).
fof(fact_pred__equals__eq,axiom,
! [X209,X191,X7] :
( hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X191) = hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X209)
<=> X191 = X209 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_mult__less__cancel1,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X44)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [X44,X94,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X94)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_divide__right__mono,axiom,
! [X10,X84,X71,X87] :
( class_Fields_Olinordered__field__inverse__zero(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X84),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono) ).
fof(fact_power__mono,axiom,
! [X33,X84,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X84),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).
fof(fact_mult__right__mono,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Oordered__semiring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(fact_comm__mult__left__mono,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Oordered__comm__semiring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Oordered__semiring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(fact_divide__strict__right__mono,axiom,
! [X10,X84,X71,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X84),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Olinordered__comm__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_zip__Cons__Cons,axiom,
! [X301,X98,X300,X86,X7,X87] : hAPP(hAPP(c_List_Ozip(X87,X7),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)),hAPP(hAPP(c_List_Olist_OCons(X7),X98),X301)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X87,X7)),hAPP(hAPP(c_Product__Type_OPair(X87,X7),X86),X98)),hAPP(hAPP(c_List_Ozip(X87,X7),X300),X301)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons__Cons) ).
fof(fact_divide__le__0__iff,axiom,
! [X24,X25,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X25),X24)),c_Groups_Ozero__class_Ozero(X7)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),c_Groups_Ozero__class_Ozero(X7))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),c_Groups_Ozero__class_Ozero(X7)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X24)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).
fof(fact_mult__le__0__iff,axiom,
! [X24,X25,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X24)),c_Groups_Ozero__class_Ozero(X7)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),c_Groups_Ozero__class_Ozero(X7))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),c_Groups_Ozero__class_Ozero(X7)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X24)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_divide__less__0__iff,axiom,
! [X24,X25,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X25),X24)),c_Groups_Ozero__class_Ozero(X7)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),c_Groups_Ozero__class_Ozero(X7))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X24)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).
fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
! [X149,X6] :
( c_Nat__Transfer_Ois__nat(X6)
=> ( c_Nat__Transfer_Onat__set(X149)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X6),X149))
<=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X6)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).
fof(fact_Max__eqI,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X82] :
( hBOOL(hAPP(hAPP(c_member(X7),X82),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X82),X6)) )
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olinorder__class_OMax(X7,X149) = X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__eqI) ).
fof(fact_zdvd__mult__cancel,axiom,
! [X33,X90,X96] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X96),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X96),X33)))
=> ( X96 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X90),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
fof(fact_zdvd__mono,axiom,
! [X46,X95,X94] :
( X94 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X95),X46))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X46))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mono) ).
fof(fact_nat__mult__dvd__cancel__disj,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X44)))
<=> ( X94 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X95),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(fact_mod__pos__neg__1__number__of,axiom,
! [X128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__1__number__of) ).
fof(fact_subset__inj__on,axiom,
! [X149,X155,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X155)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> c_Fun_Oinj__on(X7,X105,X2,X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
fof(fact_length__filter__le,axiom,
! [X292,X38,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(c_List_Ofilter(X7,X38),X292))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__le) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [X172,X25,X7] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X25)),c_Transitive__Closure_Ortrancl(X7,X172))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_zdvd__reduce,axiom,
! [X95,X44,X94] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X95))))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X94),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
fof(fact_the__inv__into__f__f,axiom,
! [X6,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Fun_Othe__inv__into(X7,X105,X149,X2),hAPP(X2,X6)) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
fof(fact_div__pos__neg__1__number__of,axiom,
! [X128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__neg__1__number__of) ).
fof(fact_the__inv__into__f__eq,axiom,
! [X127,X6,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( hAPP(X2,X6) = X127
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Fun_Othe__inv__into(X7,X105,X149,X2),X127) = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
fof(fact_finite__INT,axiom,
! [X149,X105,X211,X7] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X211))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(X149,X3))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X211),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__INT) ).
fof(fact_power__increasing,axiom,
! [X71,X164,X33,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X164))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Oone__class_Oone(X87)),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X164))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(fact_power__strict__increasing,axiom,
! [X71,X164,X33,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X164))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X164))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_divide__right__mono__neg,axiom,
! [X10,X84,X71,X87] :
( class_Fields_Olinordered__field__inverse__zero(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X10),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X84),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [X10,X71,X84,X87] :
( class_Rings_Oordered__ring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X10),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_mult__left__mono__neg,axiom,
! [X10,X71,X84,X87] :
( class_Rings_Oordered__ring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X10),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_divide__strict__right__mono__neg,axiom,
! [X10,X71,X84,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X10),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X84),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [X10,X71,X84,X87] :
( class_Rings_Olinordered__ring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X10),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [X10,X71,X84,X87] :
( class_Rings_Olinordered__ring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X10),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_card__Diff__singleton,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton) ).
fof(fact_finite__Diff2,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff2) ).
fof(fact_listsum__update__nat,axiom,
! [X33,X311,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X311)))
=> hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X311),X96),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X311)),X33)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X311),X96)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__update__nat) ).
fof(fact_o__apply,axiom,
! [X6,X1,X2,X119,X7,X105] : hAPP(hAPP(c_Fun_Ocomp(X105,X7,X119,X2),X1),X6) = hAPP(X2,hAPP(X1,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
fof(fact_o__def,axiom,
! [X6,X1,X2,X119,X7,X105] : hAPP(hAPP(c_Fun_Ocomp(X105,X7,X119,X2),X1),X6) = hAPP(X2,hAPP(X1,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__def) ).
fof(fact_mult__dvd__mono,axiom,
! [X106,X10,X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X10),X106))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X106))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
fof(fact_inf__mono,axiom,
! [X106,X84,X10,X71,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X106))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X10),X106))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__mono) ).
fof(fact_sup__mono,axiom,
! [X106,X84,X10,X71,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X106))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X10),X106))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__mono) ).
fof(fact_min__max_Osup__mono,axiom,
! [X106,X84,X10,X71,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X106))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X10),X106))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__mono) ).
fof(fact_min__max_Oinf__mono,axiom,
! [X106,X84,X10,X71,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X106))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X10),X106))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__mono) ).
fof(fact_add__mono,axiom,
! [X106,X10,X84,X71,X87] :
( class_Groups_Oordered__ab__semigroup__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X10),X106))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X106))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X106,X10,X84,X71,X87] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X10),X106))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X106))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__le__less__mono,axiom,
! [X106,X10,X84,X71,X87] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X10),X106))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X106))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__strict__mono,axiom,
! [X106,X10,X84,X71,X87] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X10),X106))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X106))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_right__diff__distrib__number__of,axiom,
! [X10,X84,X139,X7] :
( ( class_Int_Onumber(X7)
& class_Rings_Oring(X7) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X84),X10)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).
fof(fact_right__distrib__number__of,axiom,
! [X10,X84,X139,X7] :
( ( class_Int_Onumber(X7)
& class_Rings_Osemiring(X7) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X84),X10)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).
fof(fact_div__mult__div__if__dvd,axiom,
! [X128,X97,X86,X98,X87] :
( class_Divides_Osemiring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X98),X86))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X97),X128))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X86),X98)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X128),X97)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X98),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__div__if__dvd) ).
fof(fact_fold__inf__insert,axiom,
! [X25,X24,X149,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),X24),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X25),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),X24),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__inf__insert) ).
fof(fact_fold__sup__insert,axiom,
! [X25,X24,X149,X7] :
( class_Lattices_Osemilattice__sup(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7)),X24),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X25),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7)),X24),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__sup__insert) ).
fof(fact_min__max_Ofold__sup__insert,axiom,
! [X25,X24,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omax(X7)),X24),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X25),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omax(X7)),X24),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__insert) ).
fof(fact_min__max_Ofold__inf__insert,axiom,
! [X25,X24,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omin(X7)),X24),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X25),hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omin(X7)),X24),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__insert) ).
fof(fact_finite__vimageI,axiom,
! [X200,X105,X215,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X215))
=> ( c_Fun_Oinj__on(X105,X7,X200,c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(c_Set_Ovimage(X105,X7,X200),X215))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageI) ).
fof(fact_INF__leI,axiom,
! [X210,X149,X107,X7,X105] :
( class_Complete__Lattice_Ocomplete__lattice(X105)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X107),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X105),X149),X210)),hAPP(X210,X107))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__leI) ).
fof(fact_add__number__of__diff2,axiom,
! [X128,X10,X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X10),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)))),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__diff2) ).
fof(fact_less__eq__nat_Osimps_I2_J,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X95)),X44))
<=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
fof(fact_SUP1__I,axiom,
! [X105,X24,X155,X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ( hBOOL(hAPP(hAPP(X155,X25),X24))
=> hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__I) ).
fof(fact_Sup__le__iff,axiom,
! [X24,X149,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Complete__Lattice_OSup__class_OSup(X7,X149)),X24))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X3),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__le__iff) ).
fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
! [X6,X26,X149,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm__idem(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(X2,X6),hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).
fof(fact_sum__eq__0__conv,axiom,
! [X308,X95] :
( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X308) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_List_Oset(tc_Nat_Onat),X308)))
=> X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__eq__0__conv) ).
fof(fact_evaln_OSemi,axiom,
! [X50,X49,X51,X33,X52,X53] :
( c_Natural_Oevaln(X53,X52,X33,X51)
=> ( c_Natural_Oevaln(X49,X51,X33,X50)
=> c_Natural_Oevaln(c_Com_Ocom_OSemi(X53,X49),X52,X33,X50) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSemi) ).
fof(fact_one__le__mult__iff,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X44)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X95))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
fof(fact_one__less__mult,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X90))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
fof(fact_mod__mult__self4,axiom,
! [X90,X33,X96] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X33)),X90)),X33) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X90),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self4) ).
fof(fact_Union__Un__distrib,axiom,
! [X155,X149,X7] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X149)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Un__distrib) ).
fof(fact_Inter__Un__distrib,axiom,
! [X155,X149,X7] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X149)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__distrib) ).
fof(fact_split__mod,axiom,
! [X94,X44,X38] :
( hBOOL(hAPP(X38,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X44,X94)))
<=> ( ( X94 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(X38,X44)) )
& ( X94 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [X147,X117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X117),X94))
=> ( X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X147)),X117)
=> hBOOL(hAPP(X38,X117)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mod) ).
fof(fact_in__lists__conv__set,axiom,
! [X149,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X292),c_List_Olists(X7,X149)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X292)))
=> hBOOL(hAPP(hAPP(c_member(X7),X3),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lists__conv__set) ).
fof(fact_list_Osize_I2_J,axiom,
! [X294,X25,X85,X7] : c_List_Olist_Olist__size(X7,X85,hAPP(hAPP(c_List_Olist_OCons(X7),X25),X294)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X85,X25)),c_List_Olist_Olist__size(X7,X85,X294))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I2_J) ).
fof(fact_dvd__power__le,axiom,
! [X90,X33,X98,X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),X90))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power__le) ).
fof(fact_restrict__complement__singleton__eq,axiom,
! [X6,X2,X105,X7] : c_Map_Orestrict__map(X7,X105,X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X2),X6),c_Option_Ooption_ONone(X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__complement__singleton__eq) ).
fof(fact_select__weight__cons__zero,axiom,
! [X292,X6,X7] : c_Random_Oselect__weight(X7,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X7)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X7),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X6)),X292)) = c_Random_Oselect__weight(X7,X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__cons__zero) ).
fof(fact_transpose_Opsimps_I2_J,axiom,
! [X331,X7] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X7)),c_List_Otranspose__rel(X7)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X7)),c_List_Olist_ONil(X7)),X331)))
=> c_List_Otranspose(X7,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X7)),c_List_Olist_ONil(X7)),X331)) = c_List_Otranspose(X7,X331) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I2_J) ).
fof(fact_disjoint__eq__subset__Compl,axiom,
! [X155,X149,X7] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__eq__subset__Compl) ).
fof(fact_card__seteq,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X155)),hAPP(c_Finite__Set_Ocard(X7),X149)))
=> X149 = X155 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
fof(fact_Inter__lower,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X149)),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__lower) ).
fof(fact_converse__rel__comp,axiom,
! [X45,X172,X119,X7,X105] : hAPP(c_Relation_Oconverse(X105,X7),hAPP(hAPP(c_Relation_Orel__comp(X105,X119,X7),X172),X45)) = hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),hAPP(c_Relation_Oconverse(X119,X7),X45)),hAPP(c_Relation_Oconverse(X105,X119),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rel__comp) ).
fof(fact_min__le__iff__disj,axiom,
! [X26,X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),X127)),X26))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X26))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X26)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__le__iff__disj) ).
fof(fact_min__less__iff__disj,axiom,
! [X26,X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),X127)),X26))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X26))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X127),X26)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__disj) ).
fof(fact_split__div,axiom,
! [X94,X44,X38] :
( hBOOL(hAPP(X38,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X44),X94)))
<=> ( ( X94 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( X94 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [X147,X117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X117),X94))
=> ( X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X147)),X117)
=> hBOOL(hAPP(X38,X147)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div) ).
fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X155)),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)) = c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).
fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X155)),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)) = c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).
fof(fact_map__add__dom__app__simps_I1_J,axiom,
! [X280,X281,X105,X95,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X95),c_Map_Odom(X7,X105,X281)))
=> hAPP(c_Map_Omap__add(X7,X105,X280,X281),X95) = hAPP(X281,X95) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I1_J) ).
fof(fact_evalc_OWhileTrue,axiom,
! [X80,X58,X23,X77,X24] :
( hBOOL(hAPP(X24,X77))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X77),X58))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X58),X80))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X77),X80)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileTrue) ).
fof(fact_subset__Pow__Union,axiom,
! [X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X149),hAPP(c_Set_OPow(X7),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X149)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Pow__Union) ).
fof(fact_map__of__zip__inject,axiom,
! [X302,X292,X105,X293,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X293) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X292)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X302) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X292)
=> ( hBOOL(hAPP(c_List_Odistinct(X105),X292))
=> ( c_Map_Omap__of(X105,X7,hAPP(hAPP(c_List_Ozip(X105,X7),X292),X293)) = c_Map_Omap__of(X105,X7,hAPP(hAPP(c_List_Ozip(X105,X7),X292),X302))
=> X293 = X302 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__inject) ).
fof(fact_IntI,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X23),X155))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntI) ).
fof(fact_dom__map__add,axiom,
! [X44,X95,X105,X7] : c_Map_Odom(X7,X105,c_Map_Omap__add(X7,X105,X95,X44)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_Map_Odom(X7,X105,X44)),c_Map_Odom(X7,X105,X95)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__map__add) ).
fof(fact_conjI__realizer,axiom,
! [X105,X7,X153,X194,X161,X38] :
( hBOOL(hAPP(X38,X161))
=> ( hBOOL(hAPP(X194,X153))
=> ( hBOOL(hAPP(X38,hAPP(c_Product__Type_Ofst(X7,X105),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X161),X153))))
& hBOOL(hAPP(X194,hAPP(c_Product__Type_Osnd(X7,X105),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X161),X153)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conjI__realizer) ).
fof(fact_INFI__apply,axiom,
! [X6,X2,X149,X119,X105,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X119,X7)),X149),X2),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,X7),X149),hAPP(hAPP(c_COMBC(X105,X119,X7),X2),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__apply) ).
fof(fact_SUPR__apply,axiom,
! [X6,X2,X149,X119,X105,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X119,X7)),X149),X2),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,X7),X149),hAPP(hAPP(c_COMBC(X105,X119,X7),X2),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__apply) ).
fof(fact_finite__Un,axiom,
! [X216,X215,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X215),X216)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X215))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X216)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Un) ).
fof(fact_Un__Diff__Int,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__Int) ).
fof(fact_lists__mono,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),c_List_Olists(X7,X149)),c_List_Olists(X7,X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__mono) ).
fof(fact_neg__le__divide__eq,axiom,
! [X24,X25,X23,X7] :
( class_Fields_Olinordered__field(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).
fof(fact_neg__less__divide__eq,axiom,
! [X24,X25,X23,X7] :
( class_Fields_Olinordered__field(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
fof(fact_wfP__def,axiom,
! [X172,X7] :
( c_Wellfounded_OwfP(X7,X172)
<=> c_Wellfounded_Owf(X7,hAPP(c_Set_OCollect(tc_prod(X7,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__def) ).
fof(fact_pos__imp__zdiv__neg__iff,axiom,
! [X25,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X24)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
fof(fact_Times__eq__cancel2,axiom,
! [X155,X149,X105,X193,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X193))
=> ( hAPP(hAPP(c_Product__Type_OSigma(X105,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X105),X193)) = hAPP(hAPP(c_Product__Type_OSigma(X105,X7),X155),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X105),X193))
<=> X149 = X155 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).
fof(fact_mod__pos__neg__trivial,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).
fof(fact_wfI__pf,axiom,
! [X191,X7] :
( ! [X239] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X239),hAPP(c_Relation_OImage(X7,X7,X191),X239)))
=> X239 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) )
=> c_Wellfounded_Owf(X7,X191) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfI__pf) ).
fof(fact_splitI,axiom,
! [X105,X7,X24,X25,X2] :
( hBOOL(hAPP(hAPP(X2,X25),X24))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitI) ).
fof(fact_prod__caseI,axiom,
! [X105,X7,X24,X25,X22] :
( hBOOL(hAPP(hAPP(X22,X25),X24))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_HOL_Obool),X22),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__caseI) ).
fof(fact_neg__imp__zdiv__neg__iff,axiom,
! [X25,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X24)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
fof(fact_le__diff__conv,axiom,
! [X107,X94,X158] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X158),X94)),X107))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X158),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(fact_less__diff__conv,axiom,
! [X94,X158,X107] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X158),X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),X94)),X158)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(fact_card__Diff__subset,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X7),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__subset) ).
fof(fact_folding__idem_Oidem__comp,axiom,
! [X6,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding__idem(X7,X105,X2,X215)
=> hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X2,X6)),hAPP(X2,X6)) = hAPP(X2,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__comp) ).
fof(fact_Field__Un,axiom,
! [X45,X172,X7] : hAPP(c_Relation_OField(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X45)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OField(X7),X172)),hAPP(c_Relation_OField(X7),X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Un) ).
fof(fact_zip__eq__conv,axiom,
! [X302,X293,X105,X292,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)
=> ( hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293) = X302
<=> ( hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X7),c_Product__Type_Ofst(X7,X105)),X302) = X292
& hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X105),c_Product__Type_Osnd(X7,X105)),X302) = X293 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__eq__conv) ).
fof(fact_map__upd__Some__unfold,axiom,
! [X127,X6,X24,X25,X95,X7,X105] :
( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,tc_Option_Ooption(X7)),X95),X25),hAPP(c_Option_Ooption_OSome(X7),X24)),X6) = hAPP(c_Option_Ooption_OSome(X7),X127)
<=> ( ( X6 = X25
& X24 = X127 )
| ( X6 != X25
& hAPP(X95,X6) = hAPP(c_Option_Ooption_OSome(X7),X127) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__Some__unfold) ).
fof(fact_inf1D1,axiom,
! [X6,X155,X149,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155),X6))
=> hBOOL(hAPP(X149,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
fof(fact_inf1D2,axiom,
! [X6,X155,X149,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155),X6))
=> hBOOL(hAPP(X155,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).
fof(fact_listrelp_Oequations_I2_J,axiom,
! [X47,X43,X41,X42,X172,X7] :
( c_List_Olistrelp(X7,X172,hAPP(hAPP(c_List_Olist_OCons(X7),X42),X41),hAPP(hAPP(c_List_Olist_OCons(X7),X43),X47))
<=> ( hBOOL(hAPP(hAPP(X172,X42),X43))
& c_List_Olistrelp(X7,X172,X41,X47) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
fof(fact_listrelp_OCons,axiom,
! [X293,X292,X7,X127,X6,X172] :
( hBOOL(hAPP(hAPP(X172,X6),X127))
=> ( c_List_Olistrelp(X7,X172,X292,X293)
=> c_List_Olistrelp(X7,X172,hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X293)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_OCons) ).
fof(fact_Rep__Integ__cases,axiom,
! [X127] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X127),c_Int_OInteg))
=> ~ ! [X3] : X127 != hAPP(c_Int_ORep__Integ,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__cases) ).
fof(fact_InterI,axiom,
! [X149,X193,X7] :
( ! [X273] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X273),X193))
=> hBOOL(hAPP(hAPP(c_member(X7),X149),X273)) )
=> hBOOL(hAPP(hAPP(c_member(X7),X149),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X193))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterI) ).
fof(fact_lists_Osimps,axiom,
! [X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X25),c_List_Olists(X7,X149)))
<=> ( X25 = c_List_Olist_ONil(X7)
| ? [X110,X330] :
( X25 = hAPP(hAPP(c_List_Olist_OCons(X7),X110),X330)
& hBOOL(hAPP(hAPP(c_member(X7),X110),X149))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X330),c_List_Olists(X7,X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists_Osimps) ).
fof(fact_folding__one_Ounion__disjoint,axiom,
! [X155,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(X2,hAPP(X215,X149)),hAPP(X215,X155)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__disjoint) ).
fof(fact_mod__diff__eq,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Oring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),c_Divides_Odiv__class_Omod(X87,X71,X10)),c_Divides_Odiv__class_Omod(X87,X84,X10)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__eq) ).
fof(fact_mod__mult__eq,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),c_Divides_Odiv__class_Omod(X87,X71,X10)),c_Divides_Odiv__class_Omod(X87,X84,X10)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__eq) ).
fof(fact_mod__add__eq,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Divides_Odiv__class_Omod(X87,X71,X10)),c_Divides_Odiv__class_Omod(X87,X84,X10)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__eq) ).
fof(fact_div__add,axiom,
! [X98,X86,X97,X87] :
( class_Divides_Osemiring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X97),X86))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X97),X98))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X86),X98)),X97) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X86),X97)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X98),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add) ).
fof(fact_power__gt1__lemma,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X25,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X25)),c_Groups_Ozero__class_Ozero(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_even__less__0__iff,axiom,
! [X25,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X25)),c_Groups_Ozero__class_Ozero(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X25,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X25)),c_Groups_Ozero__class_Ozero(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_inj__on__diff__nat,axiom,
! [X94,X214] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X214))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X3)) )
=> c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X94),X214) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff__nat) ).
fof(fact_InterE,axiom,
! [X39,X193,X149,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X149),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X193)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X39),X193))
=> hBOOL(hAPP(hAPP(c_member(X7),X149),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterE) ).
fof(fact_InterD,axiom,
! [X39,X193,X149,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X149),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X193)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X39),X193))
=> hBOOL(hAPP(hAPP(c_member(X7),X149),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterD) ).
fof(fact_div__pos__neg__trivial,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__neg__trivial) ).
fof(fact_finite__fun__UNIVD1,axiom,
! [X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X7,X105)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X7,X105),tc_HOL_Obool))))
=> ( hAPP(c_Finite__Set_Ocard(X105),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X155)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).
fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X155)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).
fof(fact_zdiv__mono1,axiom,
! [X84,X88,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X71),X88))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X88),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
fof(fact_div__le__mono2,axiom,
! [X96,X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X96),X33)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X96),X90))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono2) ).
fof(fact_zmult__zless__mono2,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X96))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X96),X114)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X96),X113))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X96))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X114),X96)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X113),X96))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X96))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X114)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X113))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_inj__map,axiom,
! [X2,X105,X7] :
( c_Fun_Oinj__on(tc_List_Olist(X7),tc_List_Olist(X105),hAPP(c_List_Omap(X7,X105),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X7),tc_HOL_Obool)))
<=> c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__map) ).
fof(fact_inj__mapD,axiom,
! [X2,X105,X7] :
( c_Fun_Oinj__on(tc_List_Olist(X7),tc_List_Olist(X105),hAPP(c_List_Omap(X7,X105),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X7),tc_HOL_Obool)))
=> c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__mapD) ).
fof(fact_subset__insertI2,axiom,
! [X24,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X24),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(fact_INT__insert,axiom,
! [X155,X149,X25,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X105),X25),X149)),X155) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(X155,X25)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert) ).
fof(fact_UN__insert,axiom,
! [X155,X149,X25,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X105),X25),X149)),X155) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(X155,X25)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert) ).
fof(fact_strict__below__fold1__iff,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),hAPP(c_Finite__Set_Ofold1(X7,c_Orderings_Oord__class_Omin(X7)),X149)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__below__fold1__iff) ).
fof(fact_min__max_Obelow__fold1__iff,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),hAPP(c_Finite__Set_Ofold1(X7,c_Orderings_Oord__class_Omin(X7)),X149)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).
fof(fact_below__fold1__iff,axiom,
! [X6,X149,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),hAPP(c_Finite__Set_Ofold1(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),X149)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__fold1__iff) ).
fof(fact_le__iff__diff__le__0,axiom,
! [X24,X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X25),X24)),c_Groups_Ozero__class_Ozero(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_less__iff__diff__less__0,axiom,
! [X24,X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X25),X24)),c_Groups_Ozero__class_Ozero(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_zdiv__mono1__neg,axiom,
! [X84,X88,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X71),X88))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X88),X84)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
fof(fact_nth__mem,axiom,
! [X292,X7,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_List_Onth(X7),X292),X44)),hAPP(c_List_Oset(X7),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__mem) ).
fof(fact_n__less__n__mult__m,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X90))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X90))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_n__less__m__mult__n,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X90))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_card_Oeq__fold__g,axiom,
! [X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ocard(X7),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X7),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).
fof(fact_divide__diff__eq__iff,axiom,
! [X98,X86,X97,X87] :
( class_Fields_Ofield(X87)
=> ( X97 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X97)),X98) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),X98))),X97) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).
fof(fact_divide__add__eq__iff,axiom,
! [X98,X86,X97,X87] :
( class_Fields_Ofield(X87)
=> ( X97 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X97)),X98) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),X98))),X97) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
fof(fact_add__frac__num,axiom,
! [X97,X86,X98,X87] :
( class_Fields_Ofield__inverse__zero(X87)
=> ( X98 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)),X97) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),X98))),X98) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__num) ).
fof(fact_in__set__conv__nth,axiom,
! [X292,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
<=> ? [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X147),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
& hAPP(hAPP(c_List_Onth(X7),X292),X147) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__nth) ).
fof(fact_mult__le__mono,axiom,
! [X115,X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X115))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X114),X96)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X113),X115))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(fact_add__le__mono,axiom,
! [X115,X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X115))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X115))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_zadd__zless__mono,axiom,
! [X97,X140,X128,X143] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X143),X128))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X140),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X143),X140)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X128),X97))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_diff__less__mono,axiom,
! [X10,X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X71),X10)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X84),X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(fact_diff__less__mono2,axiom,
! [X115,X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X115))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X115),X33)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X115),X90))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_add__less__mono,axiom,
! [X115,X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),X115))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X115))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X132,X133,X135,X134,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),X135)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X133),X132)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X133),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),X135)),X132)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_lessThan__subset__iff,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X6)),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__subset__iff) ).
fof(fact_atMost__subset__iff,axiom,
! [X127,X6,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X7),X6)),hAPP(c_SetInterval_Oord__class_OatMost(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__subset__iff) ).
fof(fact_greaterThan__subset__iff,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X6)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).
fof(fact_atLeast__subset__iff,axiom,
! [X127,X6,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X6)),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__subset__iff) ).
fof(fact_lessThan__strict__subset__iff,axiom,
! [X44,X95,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X95)),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X95),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__strict__subset__iff) ).
fof(fact_divide__nonpos__pos,axiom,
! [X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).
fof(fact_divide__nonneg__neg,axiom,
! [X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [X84,X71,X87] :
( class_Rings_Oordered__cancel__semiring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_split__mult__neg__le,axiom,
! [X84,X71,X87] :
( class_Rings_Oordered__cancel__semiring(X87)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),c_Groups_Ozero__class_Ozero(X87))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84)) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),c_Groups_Ozero__class_Ozero(X87))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [X84,X71,X87] :
( class_Rings_Oordered__cancel__semiring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [X84,X71,X87] :
( class_Rings_Oordered__cancel__semiring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X71)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_divide__neg__pos,axiom,
! [X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__pos) ).
fof(fact_divide__pos__neg,axiom,
! [X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__neg) ).
fof(fact_mult__neg__pos,axiom,
! [X84,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__pos__neg,axiom,
! [X84,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [X84,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X71)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_set__subset__Cons,axiom,
! [X6,X292,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X292)),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__subset__Cons) ).
fof(fact_transpose__map__map,axiom,
! [X292,X2,X105,X7] : c_List_Otranspose(X7,hAPP(hAPP(c_List_Omap(tc_List_Olist(X105),tc_List_Olist(X7)),hAPP(c_List_Omap(X105,X7),X2)),X292)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X105),tc_List_Olist(X7)),hAPP(c_List_Omap(X105,X7),X2)),c_List_Otranspose(X105,X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__map__map) ).
fof(fact_dvd__mult__left,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
fof(fact_dvd__mult__right,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X84),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
fof(fact_le__sup__iff,axiom,
! [X26,X127,X6,X7] :
( class_Lattices_Osemilattice__sup(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6),X127)),X26))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X26)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__sup__iff) ).
fof(fact_min__max_Ole__sup__iff,axiom,
! [X26,X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),X127)),X26))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X26)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__sup__iff) ).
fof(fact_max__less__iff__conj,axiom,
! [X26,X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),X127)),X26))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X127),X26)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__less__iff__conj) ).
fof(fact_nth__eq__iff__index__eq,axiom,
! [X158,X107,X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X158),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> ( hAPP(hAPP(c_List_Onth(X7),X292),X107) = hAPP(hAPP(c_List_Onth(X7),X292),X158)
<=> X107 = X158 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__eq__iff__index__eq) ).
fof(fact_distinct__conv__nth,axiom,
! [X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),X292))
<=> ! [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X147),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> ! [X117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X117),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> ( X147 != X117
=> hAPP(hAPP(c_List_Onth(X7),X292),X147) != hAPP(hAPP(c_List_Onth(X7),X292),X117) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).
fof(fact_distinct__map,axiom,
! [X292,X2,X105,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)))
<=> ( hBOOL(hAPP(c_List_Odistinct(X105),X292))
& c_Fun_Oinj__on(X105,X7,X2,hAPP(c_List_Oset(X105),X292)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__map) ).
fof(fact_min__max_OInf__le__Sup,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__le__Sup) ).
fof(fact_inj__on__diff,axiom,
! [X155,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> c_Fun_Oinj__on(X7,X105,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff) ).
fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
! [X6,X26,X149,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm__idem(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),hAPP(hAPP(X2,X6),X26)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).
fof(fact_insert__Diff,axiom,
! [X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff) ).
fof(fact_finite__Prod__UNIV,axiom,
! [X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X105)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X7,X105)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X7,X105),tc_HOL_Obool))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X105),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_setsum__head__Suc,axiom,
! [X2,X44,X95,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(X2,X95)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X95),X44))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__Suc) ).
fof(fact_vimageI2,axiom,
! [X105,X149,X25,X2,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X25)),X149))
=> hBOOL(hAPP(hAPP(c_member(X105),X25),hAPP(c_Set_Ovimage(X105,X7,X2),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageI2) ).
fof(fact_sorted__insort,axiom,
! [X292,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7)),X6),X292))
<=> c_List_Olinorder__class_Osorted(X7,X292) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort) ).
fof(fact_setsum__head__upt__Suc,axiom,
! [X2,X44,X95,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X44)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(X2,X95)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X95)),X44))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).
fof(fact_set__eq__subset,axiom,
! [X7,X155,X149] :
( X149 = X155
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> X149 = X155 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_rev__nth,axiom,
! [X300,X87,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Onth(X87),hAPP(c_List_Orev(X87),X300)),X33) = hAPP(hAPP(c_List_Onth(X87),X300),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),hAPP(c_Nat_OSuc,X33))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__nth) ).
fof(fact_INT__absorb,axiom,
! [X149,X105,X211,X94,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X94),X211))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,tc_HOL_Obool)),hAPP(X149,X94)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X211),X149)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X211),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__absorb) ).
fof(fact_UN__absorb,axiom,
! [X149,X105,X211,X94,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X94),X211))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,tc_HOL_Obool)),hAPP(X149,X94)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X211),X149)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X211),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__absorb) ).
fof(fact_list__update__overwrite,axiom,
! [X98,X86,X114,X300,X87] : hAPP(hAPP(c_List_Olist__update(X87,hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X86)),X114),X98) = hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X98),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__overwrite) ).
fof(fact_negative__zless,axiom,
! [X90,X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X33)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zless) ).
fof(fact_Ints__diff,axiom,
! [X24,X25,X7] :
( class_Rings_Oring__1(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Int_Oring__1__class_OInts(X7)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X24),c_Int_Oring__1__class_OInts(X7)))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X25),X24)),c_Int_Oring__1__class_OInts(X7))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__diff) ).
fof(fact_Ints__mult,axiom,
! [X24,X25,X7] :
( class_Rings_Oring__1(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Int_Oring__1__class_OInts(X7)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X24),c_Int_Oring__1__class_OInts(X7)))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X24)),c_Int_Oring__1__class_OInts(X7))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__mult) ).
fof(fact_Nats__mult,axiom,
! [X24,X25,X7] :
( class_Rings_Osemiring__1(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Nat_Osemiring__1__class_ONats(X7)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X24),c_Nat_Osemiring__1__class_ONats(X7)))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X24)),c_Nat_Osemiring__1__class_ONats(X7))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__mult) ).
fof(fact_Ints__add,axiom,
! [X24,X25,X7] :
( class_Rings_Oring__1(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Int_Oring__1__class_OInts(X7)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X24),c_Int_Oring__1__class_OInts(X7)))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X24)),c_Int_Oring__1__class_OInts(X7))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__add) ).
fof(fact_Nats__add,axiom,
! [X24,X25,X7] :
( class_Rings_Osemiring__1(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Nat_Osemiring__1__class_ONats(X7)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X24),c_Nat_Osemiring__1__class_ONats(X7)))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X24)),c_Nat_Osemiring__1__class_ONats(X7))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__add) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__neg__nonpos,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__neg,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__neg,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),c_Groups_Ozero__class_Ozero(X87))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_list__size__conv__listsum,axiom,
! [X292,X2,X7] : c_List_Olist_Olist__size(X7,X2,X292) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X7,tc_Nat_Onat),X2),X292))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__conv__listsum) ).
fof(fact_dom__restrict,axiom,
! [X149,X95,X105,X7] : c_Map_Odom(X7,X105,c_Map_Orestrict__map(X7,X105,X95,X149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Map_Odom(X7,X105,X95)),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__restrict) ).
fof(fact_map__of__eq__dom,axiom,
! [X293,X292,X105,X7] :
( c_Map_Omap__of(X7,X105,X292) = c_Map_Omap__of(X7,X105,X293)
=> hAPP(c_Set_Oimage(tc_prod(X7,X105),X7,c_Product__Type_Ofst(X7,X105)),hAPP(c_List_Oset(tc_prod(X7,X105)),X292)) = hAPP(c_Set_Oimage(tc_prod(X7,X105),X7,c_Product__Type_Ofst(X7,X105)),hAPP(c_List_Oset(tc_prod(X7,X105)),X293)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__eq__dom) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [X2,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))
=> ( c_Fun_Oinj__on(X7,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(X7,X7,X2),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_listsum__triv,axiom,
! [X292,X172,X105,X7] :
( class_Rings_Osemiring__1(X7)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),hAPP(c_COMBK(X7,X105),X172)),X292)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X292))),X172) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__triv) ).
fof(fact_power__minus,axiom,
! [X33,X71,X87] :
( class_Rings_Oring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Oone__class_Oone(X87))),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus) ).
fof(fact_rangeI,axiom,
! [X105,X6,X2,X7] : hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X6)),hAPP(c_Set_Oimage(X105,X7,X2),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_left__diff__distrib__number__of,axiom,
! [X139,X84,X71,X7] :
( ( class_Int_Onumber(X7)
& class_Rings_Oring(X7) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X71),X84)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X71),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X84),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).
fof(fact_left__distrib__number__of,axiom,
! [X139,X84,X71,X7] :
( ( class_Int_Onumber(X7)
& class_Rings_Osemiring(X7) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X71),X84)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X71),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X84),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).
fof(fact_map__add__SomeD,axiom,
! [X6,X94,X44,X95,X7,X105] :
( hAPP(c_Map_Omap__add(X105,X7,X95,X44),X94) = hAPP(c_Option_Ooption_OSome(X7),X6)
=> ( hAPP(X44,X94) = hAPP(c_Option_Ooption_OSome(X7),X6)
| ( hAPP(X44,X94) = c_Option_Ooption_ONone(X7)
& hAPP(X95,X94) = hAPP(c_Option_Ooption_OSome(X7),X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__SomeD) ).
fof(fact_map__add__Some__iff,axiom,
! [X6,X94,X44,X95,X7,X105] :
( hAPP(c_Map_Omap__add(X105,X7,X95,X44),X94) = hAPP(c_Option_Ooption_OSome(X7),X6)
<=> ( hAPP(X44,X94) = hAPP(c_Option_Ooption_OSome(X7),X6)
| ( hAPP(X44,X94) = c_Option_Ooption_ONone(X7)
& hAPP(X95,X94) = hAPP(c_Option_Ooption_OSome(X7),X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__Some__iff) ).
fof(fact_Inf__fin_Ounion__disjoint,axiom,
! [X155,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)),c_Big__Operators_Olattice__class_OInf__fin(X7,X155)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).
fof(fact_Min_Ounion__disjoint,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),c_Big__Operators_Olinorder__class_OMin(X7,X149)),c_Big__Operators_Olinorder__class_OMin(X7,X155)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ounion__disjoint) ).
fof(fact_Max_Ounion__disjoint,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),c_Big__Operators_Olinorder__class_OMax(X7,X149)),c_Big__Operators_Olinorder__class_OMax(X7,X155)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ounion__disjoint) ).
fof(fact_Sup__fin_Ounion__disjoint,axiom,
! [X155,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)),c_Big__Operators_Olattice__class_OSup__fin(X7,X155)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).
fof(fact_dvd__power__same,axiom,
! [X33,X98,X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X86),X98))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power__same) ).
fof(fact_add__right__mono,axiom,
! [X10,X84,X71,X87] :
( class_Groups_Oordered__ab__semigroup__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X10,X84,X71,X87] :
( class_Groups_Oordered__ab__semigroup__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X71)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__strict__right__mono,axiom,
! [X10,X84,X71,X87] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X10,X84,X71,X87] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X71)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_fold1__Un2,axiom,
! [X155,X149,X7] :
( class_Lattices_Oab__semigroup__idem__mult(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),X149)),hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),X155)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__Un2) ).
fof(fact_rev__drop,axiom,
! [X300,X114,X87] : hAPP(c_List_Orev(X87),hAPP(hAPP(c_List_Odrop(X87),X114),X300)) = hAPP(hAPP(c_List_Otake(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X114)),hAPP(c_List_Orev(X87),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__drop) ).
fof(fact_rev__take,axiom,
! [X300,X114,X87] : hAPP(c_List_Orev(X87),hAPP(hAPP(c_List_Otake(X87),X114),X300)) = hAPP(hAPP(c_List_Odrop(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X114)),hAPP(c_List_Orev(X87),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__take) ).
fof(fact_ivl__disj__un_I5_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X157),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X160)) = c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I5_J) ).
fof(fact_subset__Compl__self__eq,axiom,
! [X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)))
<=> X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Compl__self__eq) ).
fof(fact_map__upd__eqD1,axiom,
! [X127,X44,X6,X25,X95,X105,X7] :
( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X95),X25),hAPP(c_Option_Ooption_OSome(X105),X6)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X44),X25),hAPP(c_Option_Ooption_OSome(X105),X127))
=> X6 = X127 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__eqD1) ).
fof(fact_pdivmod__def,axiom,
! [X115,X96] : c_Divides_Opdivmod(X96,X115) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X96)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X115))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X96),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X115))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__def) ).
fof(fact_Union__upper,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__upper) ).
fof(fact_fold__image__def,axiom,
! [X1,X2,X105,X7] : hAPP(c_Finite__Set_Ofold__image(X7,X105,X2),X1) = c_Finite__Set_Ofold(X105,X7,hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X105),X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__def) ).
fof(fact_max__Suc1,axiom,
! [X95,X44] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X95) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X44),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X44)),X95),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc1) ).
fof(fact_Field__Union,axiom,
! [X191,X7] : hAPP(c_Relation_OField(X7),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),X191)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),c_Relation_OField(X7)),X191)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Union) ).
fof(fact_dvd__mult__cancel2,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X95))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X95)),X95))
<=> X44 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
fof(fact_dvd__mult__cancel1,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X95))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X44)),X95))
<=> X44 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
fof(fact_Diff__partition,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X155),X149)) = X155 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__partition) ).
fof(fact_inj__mapI,axiom,
! [X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> c_Fun_Oinj__on(tc_List_Olist(X7),tc_List_Olist(X105),hAPP(c_List_Omap(X7,X105),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X7),tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__mapI) ).
fof(fact_Compl__Int,axiom,
! [X155,X149,X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Int) ).
fof(fact_Compl__Un,axiom,
! [X155,X149,X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Un) ).
fof(fact_peek__and__def,axiom,
! [X45,X166,X161,X38,X7] :
( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X7,X38,X161),X166),X45))
<=> ( hBOOL(hAPP(hAPP(X38,X166),X45))
& hBOOL(hAPP(X161,X45)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_peek__and__def) ).
fof(fact_vimage__code,axiom,
! [X6,X149,X2,X105,X7] :
( hBOOL(hAPP(hAPP(c_Set_Ovimage(X7,X105,X2),X149),X6))
<=> hBOOL(hAPP(X149,hAPP(X2,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__code) ).
fof(fact_Inf__less__iff,axiom,
! [X25,X209,X7] :
( ( class_Complete__Lattice_Ocomplete__lattice(X7)
& class_Orderings_Olinorder(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Complete__Lattice_OInf__class_OInf(X7,X209)),X25))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X209))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X3),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__less__iff) ).
fof(fact_mult__number__of__left,axiom,
! [X97,X128,X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)),X97)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X139),X128))),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__number__of__left) ).
fof(fact_add__number__of__diff1,axiom,
! [X10,X128,X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)),X10)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),X128))),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).
fof(fact_add__number__of__left,axiom,
! [X97,X128,X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)),X97)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),X128))),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__left) ).
fof(fact_Option_Omap__def,axiom,
! [X2,X105,X7] : hAPP(c_Option_Omap(X7,X105),X2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(X105),X7,c_Option_Ooption_ONone(X105),hAPP(hAPP(c_COMBB(X105,tc_Option_Ooption(X105),X7),c_Option_Ooption_OSome(X105)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap__def) ).
fof(fact_ivl__disj__un_I3_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X157),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X160)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I3_J) ).
fof(fact_nth__map,axiom,
! [X2,X105,X292,X7,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> hAPP(hAPP(c_List_Onth(X105),hAPP(hAPP(c_List_Omap(X7,X105),X2),X292)),X44) = hAPP(X2,hAPP(hAPP(c_List_Onth(X7),X292),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__map) ).
fof(fact_le__imp__power__dvd,axiom,
! [X71,X33,X90,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X90)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).
fof(fact_nat__gcd_Opsimps,axiom,
! [X127,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X127)))
=> ( ( X127 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(X6,X127) = X6 )
& ( X127 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(X6,X127) = c_Nitpick_Onat__gcd(X127,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6,X127)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Opsimps) ).
fof(fact_UnionI,axiom,
! [X149,X193,X39,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X39),X193))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X149),X39))
=> hBOOL(hAPP(hAPP(c_member(X7),X149),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X193))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionI) ).
fof(fact_zero__less__mult__pos2,axiom,
! [X71,X84,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X71)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [X84,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_card__Un__disjoint,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X7),X155)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__disjoint) ).
fof(fact_min__Suc1,axiom,
! [X95,X44] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X95) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X44)),X95),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc1) ).
fof(fact_sorted__list__of__set__remove,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_List_Olinorder__class_Osorted__list__of__set(X7,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = c_List_Oremove1(X7,X6,c_List_Olinorder__class_Osorted__list__of__set(X7,X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__remove) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X7,X105)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X7,X105),tc_HOL_Obool))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_PowD,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Set_OPow(X7),X155)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowD) ).
fof(fact_Pow__iff,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Set_OPow(X7),X155)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__iff) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [X44,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X6)),X44)))
<=> ( X6 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_ivl__disj__un_I19_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X157),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X95),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X95)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X95,X160)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X160) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I19_J) ).
fof(fact_ivl__disj__un_I16_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X95),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X95)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X95,X160)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X160) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I16_J) ).
fof(fact_ivl__disj__un_I20_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X95),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X95)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X95,X160)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X160) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I20_J) ).
fof(fact_ivl__disj__un_I22_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X95),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X95)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X95,X160)) = c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X160) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I22_J) ).
fof(fact_Un__upper1,axiom,
! [X155,X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
fof(fact_Un__upper2,axiom,
! [X149,X155,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
fof(fact_r__into__rtrancl,axiom,
! [X172,X161,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),X172))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X161),c_Transitive__Closure_Ortrancl(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_card__Plus,axiom,
! [X155,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155))
=> hAPP(c_Finite__Set_Ocard(tc_sum(X7,X105)),c_Sum__Type_OPlus(X7,X105,X149,X155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X105),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).
fof(fact_card__Plus__conv__if,axiom,
! [X155,X105,X149,X7] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155)) )
=> hAPP(c_Finite__Set_Ocard(tc_sum(X7,X105)),c_Sum__Type_OPlus(X7,X105,X149,X155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X105),X155)) )
& ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X155)) )
=> hAPP(c_Finite__Set_Ocard(tc_sum(X7,X105)),c_Sum__Type_OPlus(X7,X105,X149,X155)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
fof(fact_le__supI,axiom,
! [X84,X86,X71,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84)),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI) ).
fof(fact_sup__least,axiom,
! [X97,X86,X98,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X97),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),X97)),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__least) ).
fof(fact_min__max_Ole__supI,axiom,
! [X84,X86,X71,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84)),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI) ).
fof(fact_min__max_Osup__least,axiom,
! [X97,X86,X98,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X97),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X98),X97)),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__least) ).
fof(fact_Int__left__commute,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).
fof(fact_Un__left__commute,axiom,
! [X193,X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X193)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).
fof(fact_Un__Diff__cancel2,axiom,
! [X149,X155,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X155),X149)),X149) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).
fof(fact_Diff__idemp,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)),X155) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__idemp) ).
fof(fact_imageI,axiom,
! [X2,X105,X149,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_member(X105),hAPP(X2,X6)),hAPP(c_Set_Oimage(X7,X105,X2),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact_hoare__derivs_Oinsert,axiom,
! [X223,X46,X216,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),X46),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,X223)
=> c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),X46),X223)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oinsert) ).
fof(fact_dvd__int__iff,axiom,
! [X95,X26] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26))),X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__int__iff) ).
fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
! [X1,X119,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> c_Finite__Set_Ofun__left__comm(X119,X105,hAPP(hAPP(c_COMBB(X7,tc_fun(X105,X105),X119),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).
fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
! [X1,X119,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm__idem(X7,X105,X2)
=> c_Finite__Set_Ofun__left__comm__idem(X119,X105,hAPP(hAPP(c_COMBB(X7,tc_fun(X105,X105),X119),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).
fof(fact_Int__insert__left__if1,axiom,
! [X155,X193,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X193))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)),X193) = hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).
fof(fact_inj__image__eq__iff,axiom,
! [X155,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> ( hAPP(c_Set_Oimage(X7,X105,X2),X149) = hAPP(c_Set_Oimage(X7,X105,X2),X155)
<=> X149 = X155 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_o__eq__dest__lhs,axiom,
! [X163,X23,X24,X25,X7,X105,X119] :
( hAPP(c_Fun_Ocomp(X119,X105,X7,X25),X24) = X23
=> hAPP(X25,hAPP(X24,X163)) = hAPP(X23,X163) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
fof(fact_negative__zless__0,axiom,
! [X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X33)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zless__0) ).
fof(fact_nth__drop_H,axiom,
! [X300,X87,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Olist_OCons(X87),hAPP(hAPP(c_List_Onth(X87),X300),X114)),hAPP(hAPP(c_List_Odrop(X87),hAPP(c_Nat_OSuc,X114)),X300)) = hAPP(hAPP(c_List_Odrop(X87),X114),X300) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__drop_H) ).
fof(fact_image__vimage__eq,axiom,
! [X149,X2,X7,X105] : hAPP(c_Set_Oimage(X105,X7,X2),hAPP(c_Set_Ovimage(X105,X7,X2),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Set_Oimage(X105,X7,X2),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__eq) ).
fof(fact_add1__zle__eq,axiom,
! [X26,X125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X125),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_ivl__disj__un_I18_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X95),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X95)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X95,X160)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X160) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I18_J) ).
fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
! [X149] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X149))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).
fof(fact_card__mono,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X7),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
fof(fact_psubset__card__mono,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X7),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
fof(fact_dom__minus,axiom,
! [X149,X105,X7,X6,X2] :
( hAPP(X2,X6) = c_Option_Ooption_ONone(X7)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),c_Map_Odom(X105,X7,X2)),hAPP(hAPP(c_Set_Oinsert(X105),X6),X149)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,tc_HOL_Obool)),c_Map_Odom(X105,X7,X2)),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__minus) ).
fof(fact_UnI1,axiom,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI1) ).
fof(fact_UnI2,axiom,
! [X149,X155,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),X155))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI2) ).
fof(fact_finite__UNIV__surj__inj,axiom,
! [X2,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))
=> ( hAPP(c_Set_Oimage(X7,X7,X2),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))
=> c_Fun_Oinj__on(X7,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
fof(fact_abs__le__iff,axiom,
! [X24,X25,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Groups_Oabs__class_Oabs(X7),X25)),X24))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__iff) ).
fof(fact_abs__leI,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__leI) ).
fof(fact_abs__less__iff,axiom,
! [X24,X25,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Groups_Oabs__class_Oabs(X7),X25)),X24))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__less__iff) ).
fof(fact_lists__accI,axiom,
! [X172,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X292),c_Wellfounded_Oacc(tc_List_Olist(X7),c_List_Olistrel1(X7,X172))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X292),c_List_Olists(X7,c_Wellfounded_Oacc(X7,X172)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accI) ).
fof(fact_inj__vimage__image__eq,axiom,
! [X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(c_Set_Oimage(X7,X105,X2),X149)) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__vimage__image__eq) ).
fof(fact_ivl__disj__un_I15_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X157),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X95),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X95)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X95),X160)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X160) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I15_J) ).
fof(fact_div__mult__self2,axiom,
! [X10,X71,X84,X87] :
( class_Divides_Osemiring__div(X87)
=> ( X84 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10))),X84) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2) ).
fof(fact_div__mult__self1,axiom,
! [X10,X71,X84,X87] :
( class_Divides_Osemiring__div(X87)
=> ( X84 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84))),X84) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1) ).
fof(fact_add__num__frac,axiom,
! [X86,X97,X98,X87] :
( class_Fields_Ofield__inverse__zero(X87)
=> ( X98 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X97),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),X98))),X98) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__num__frac) ).
fof(fact_setprod__reindex__id,axiom,
! [X155,X2,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( c_Fun_Oinj__on(X7,X105,X2,X155)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X155) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X105),c_Fun_Oid(X105)),hAPP(c_Set_Oimage(X7,X105,X2),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex__id) ).
fof(fact_setsum__reindex__id,axiom,
! [X155,X2,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( c_Fun_Oinj__on(X7,X105,X2,X155)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X155) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X105),c_Fun_Oid(X105)),hAPP(c_Set_Oimage(X7,X105,X2),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__id) ).
fof(fact_wf__comp__self,axiom,
! [X191,X7] :
( c_Wellfounded_Owf(X7,X191)
<=> c_Wellfounded_Owf(X7,hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X191),X191)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__comp__self) ).
fof(fact_less__by__empty,axiom,
! [X155,X7,X149] :
( X149 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X149),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).
fof(fact_distinct__append,axiom,
! [X293,X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Oappend(X7),X292),X293)))
<=> ( hBOOL(hAPP(c_List_Odistinct(X7),X292))
& hBOOL(hAPP(c_List_Odistinct(X7),X293))
& hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X292)),hAPP(c_List_Oset(X7),X293)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__append) ).
fof(fact_min__max_OInf__fin__set__fold,axiom,
! [X292,X6,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292))) = hAPP(c_List_Ofoldl(X7,X7,c_Orderings_Oord__class_Omin(X7),X6),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).
fof(fact_min__max_OSup__fin__set__fold,axiom,
! [X292,X6,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292))) = hAPP(c_List_Ofoldl(X7,X7,c_Orderings_Oord__class_Omax(X7),X6),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).
fof(fact_setsum__head,axiom,
! [X38,X44,X95,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X38),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(X38,X95)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X38),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X95,X44))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head) ).
fof(fact_funpow_Osimps_I2_J,axiom,
! [X2,X44,X7] : hAPP(hAPP(c_Nat_Ocompow(X7,X7),hAPP(c_Nat_OSuc,X44)),X2) = hAPP(c_Fun_Ocomp(X7,X7,X7,X2),hAPP(hAPP(c_Nat_Ocompow(X7,X7),X44),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I2_J) ).
fof(fact_list__size__estimation_H,axiom,
! [X2,X127,X292,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X127),hAPP(X2,X6)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X127),c_List_Olist_Olist__size(X7,X2,X292))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__estimation_H) ).
fof(fact_list__size__estimation,axiom,
! [X2,X127,X292,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X127),hAPP(X2,X6)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X127),c_List_Olist_Olist__size(X7,X2,X292))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__estimation) ).
fof(fact_elem__le__listsum__nat,axiom,
! [X311,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X311)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X311),X96)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X311))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__le__listsum__nat) ).
fof(fact_map__of__append,axiom,
! [X293,X292,X105,X7] : c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Oappend(tc_prod(X7,X105)),X292),X293)) = c_Map_Omap__add(X7,X105,c_Map_Omap__of(X7,X105,X293),c_Map_Omap__of(X7,X105,X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__append) ).
fof(fact_le__div__geq,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__div__geq) ).
fof(fact_lists__accD,axiom,
! [X172,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X292),c_List_Olists(X7,c_Wellfounded_Oacc(X7,X172))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X292),c_Wellfounded_Oacc(tc_List_Olist(X7),c_List_Olistrel1(X7,X172)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accD) ).
fof(fact_dvd__diffD,axiom,
! [X33,X90,X96] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X96),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X96),X90)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD) ).
fof(fact_dvd__diffD1,axiom,
! [X33,X90,X96] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X96),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X96),X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
fof(fact_semiring__1__class_Oof__nat__code,axiom,
! [X44,X7] :
( class_Rings_Osemiring__1(X7)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X44) = c_Nat_Osemiring__1__class_Oof__nat__aux(X7,hAPP(hAPP(c_COMBC(X7,X7,X7),c_Groups_Oplus__class_Oplus(X7)),c_Groups_Oone__class_Oone(X7)),X44,c_Groups_Ozero__class_Ozero(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).
fof(fact_impossible__Cons,axiom,
! [X86,X301,X300,X87] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X301)))
=> X300 != hAPP(hAPP(c_List_Olist_OCons(X87),X86),X301) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_impossible__Cons) ).
fof(fact_PowI,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Set_OPow(X7),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowI) ).
fof(fact_power_Opower_Opower__Suc,axiom,
! [X44,X25,X167,X168,X7] : hAPP(hAPP(c_Power_Opower_Opower(X7,X168,X167),X25),hAPP(c_Nat_OSuc,X44)) = hAPP(hAPP(X167,X25),hAPP(hAPP(c_Power_Opower_Opower(X7,X168,X167),X25),X44)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(fact_map__add__None,axiom,
! [X94,X44,X95,X7,X105] :
( hAPP(c_Map_Omap__add(X105,X7,X95,X44),X94) = c_Option_Ooption_ONone(X7)
<=> ( hAPP(X44,X94) = c_Option_Ooption_ONone(X7)
& hAPP(X95,X94) = c_Option_Ooption_ONone(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__None) ).
fof(fact_Min__antimono,axiom,
! [X214,X210,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X210),X214))
=> ( X210 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Big__Operators_Olinorder__class_OMin(X7,X214)),c_Big__Operators_Olinorder__class_OMin(X7,X210))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__antimono) ).
fof(fact_Max__mono,axiom,
! [X214,X210,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X210),X214))
=> ( X210 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X214))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Big__Operators_Olinorder__class_OMax(X7,X210)),c_Big__Operators_Olinorder__class_OMax(X7,X214))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__mono) ).
fof(fact_less__bin__lemma,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X157))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X94),X157)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_singletonE,axiom,
! [X25,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))
=> X24 = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
fof(fact_singleton__iff,axiom,
! [X25,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))
<=> X24 = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
fof(fact_range__eqI,axiom,
! [X105,X7,X6,X2,X24] :
( X24 = hAPP(X2,X6)
=> hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(c_Set_Oimage(X105,X7,X2),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_snd__image__times,axiom,
! [X155,X105,X7,X149] :
( ( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(X7,X105),X105,c_Product__Type_Osnd(X7,X105)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X155))) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) )
& ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(X7,X105),X105,c_Product__Type_Osnd(X7,X105)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X155))) = X155 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__image__times) ).
fof(fact_fst__image__times,axiom,
! [X149,X105,X7,X155] :
( ( X155 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(X105,X7),X105,c_Product__Type_Ofst(X105,X7)),hAPP(hAPP(c_Product__Type_OSigma(X105,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X105),X155))) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) )
& ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(X105,X7),X105,c_Product__Type_Ofst(X105,X7)),hAPP(hAPP(c_Product__Type_OSigma(X105,X7),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X105),X155))) = X149 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__image__times) ).
fof(fact_doubleton__eq__iff,axiom,
! [X136,X23,X24,X25,X7] :
( hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X7),X23),hAPP(hAPP(c_Set_Oinsert(X7),X136),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
<=> ( ( X25 = X23
& X24 = X136 )
| ( X25 = X136
& X24 = X23 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
fof(fact_dvd__setprod,axiom,
! [X2,X107,X149,X7,X105] :
( class_Rings_Ocomm__semiring__1(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X107),X149))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X105),hAPP(X2,X107)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__setprod) ).
fof(fact_nth__list__update,axiom,
! [X86,X113,X300,X87,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> ( ( X114 = X113
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X86)),X113) = X86 )
& ( X114 != X113
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X86)),X113) = hAPP(hAPP(c_List_Onth(X87),X300),X113) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update) ).
fof(fact_dvd_OmonoD,axiom,
! [X127,X6,X2,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oorder_Omono(tc_Nat_Onat,X7,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X2,X6)),hAPP(X2,X127))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OmonoD) ).
fof(fact_add__leD1,axiom,
! [X33,X96,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X96)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X33,X96,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X96)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_add__lessD1,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X113)),X96))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X96)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_diff__Suc__less,axiom,
! [X114,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),hAPP(c_Nat_OSuc,X114))),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_evaln_Oequations_I9_J,axiom,
! [X47,X41,X43,X42] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X42),X43,hAPP(c_Nat_OSuc,X41),X47)
<=> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X42)),X43,X41,X47) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I9_J) ).
fof(fact_evaln_OBody,axiom,
! [X51,X33,X52,X78] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X78)),X52,X33,X51)
=> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X78),X52,hAPP(c_Nat_OSuc,X33),X51) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OBody) ).
fof(fact_ran__map__upd,axiom,
! [X24,X105,X7,X25,X95] :
( hAPP(X95,X25) = c_Option_Ooption_ONone(X7)
=> c_Map_Oran(X105,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,tc_Option_Ooption(X7)),X95),X25),hAPP(c_Option_Ooption_OSome(X7),X24))) = hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Map_Oran(X105,X7,X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__map__upd) ).
fof(fact_ivl__disj__un_I21_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X95),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X95)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X95,X160)) = c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X160) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I21_J) ).
fof(fact_atLeastLessThan__add__Un,axiom,
! [X94,X158,X107] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X158))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X107),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X158),X94)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X107),X158)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X158),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X158),X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__add__Un) ).
fof(fact_insert__Diff__single,axiom,
! [X149,X25,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X7),X25),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__single) ).
fof(fact_card__insert__le,axiom,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).
fof(fact_zadd__int__left,axiom,
! [X97,X33,X90] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)),X97)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33))),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int__left) ).
fof(fact_less__Sup__iff,axiom,
! [X209,X25,X7] :
( ( class_Complete__Lattice_Ocomplete__lattice(X7)
& class_Orderings_Olinorder(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Complete__Lattice_OSup__class_OSup(X7,X209)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X209))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Sup__iff) ).
fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
! [X149] :
( c_Nat__Transfer_Onat__set(X149)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X149))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I1_J) ).
fof(fact_transfer__nat__int__relations_I4_J,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X127))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X6)),hAPP(c_Int_Onat,X127)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X6),X127)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I4_J) ).
fof(fact_transfer__nat__int__relations_I3_J,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X127))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X6)),hAPP(c_Int_Onat,X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),X127)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).
fof(fact_transfer__nat__int__relations_I2_J,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X127))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X6)),hAPP(c_Int_Onat,X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X127)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).
fof(fact_ivl__disj__un_I4_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X160)),hAPP(hAPP(c_Set_Oinsert(X7),X160),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I4_J) ).
fof(fact_evaln_OIfTrue,axiom,
! [X57,X58,X44,X59,X45,X24] :
( hBOOL(hAPP(X24,X45))
=> ( c_Natural_Oevaln(X59,X45,X44,X58)
=> c_Natural_Oevaln(c_Com_Ocom_OCond(X24,X59,X57),X45,X44,X58) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OIfTrue) ).
fof(fact_Min__eqI,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ! [X82] :
( hBOOL(hAPP(hAPP(c_member(X7),X82),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X82)) )
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olinorder__class_OMin(X7,X149) = X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__eqI) ).
fof(fact_map__append,axiom,
! [X293,X292,X2,X7,X105] : hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(hAPP(c_List_Oappend(X105),X292),X293)) = hAPP(hAPP(c_List_Oappend(X7),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)),hAPP(hAPP(c_List_Omap(X105,X7),X2),X293)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__append) ).
fof(fact_finite__Union,axiom,
! [X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X7,tc_HOL_Obool)),X149))
=> ( ! [X272] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X272),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X272)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Union) ).
fof(fact_div__power,axiom,
! [X33,X86,X98,X87] :
( class_Divides_Osemiring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X98),X86))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X86),X98)),X33) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__power) ).
fof(fact_int__div__less__self,axiom,
! [X96,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X96))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X86),X96)),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__div__less__self) ).
fof(fact_diff__less,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),X90)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
fof(fact_div__less__dividend,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33)),X90)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less__dividend) ).
fof(fact_insert__inter__insert,axiom,
! [X155,X149,X25,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
fof(fact_div__nonpos__pos__le0,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).
fof(fact_div__nonneg__neg__le0,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).
fof(fact_div__neg__pos__less0,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
fof(fact_evaln__nonstrict,axiom,
! [X90,X35,X33,X9,X10] :
( c_Natural_Oevaln(X10,X9,X33,X35)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> c_Natural_Oevaln(X10,X9,X90,X35) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__nonstrict) ).
fof(fact_dvd__mod__imp__dvd,axiom,
! [X33,X90,X96,X87] :
( class_Divides_Osemiring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X96),c_Divides_Odiv__class_Omod(X87,X90,X33)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X96),X33))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X96),X90)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod__imp__dvd) ).
fof(fact_dvd__mod__iff,axiom,
! [X95,X44,X94,X7] :
( class_Divides_Osemiring__div(X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X94),X44))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X94),c_Divides_Odiv__class_Omod(X7,X95,X44)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X94),X95)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod__iff) ).
fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
! [X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Divides_Odiv__class_Omod(X87,X71,X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84)),X84)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).
fof(fact_zero__le__divide__iff,axiom,
! [X24,X25,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X25),X24)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X24)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),c_Groups_Ozero__class_Ozero(X7)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [X24,X25,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X24)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X24)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),c_Groups_Ozero__class_Ozero(X7)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zero__less__divide__iff,axiom,
! [X24,X25,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X25),X24)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X24)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).
fof(fact_zadd__left__mono,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X114),X113))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X114)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X113))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_diff__le__mono,axiom,
! [X115,X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X115)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),X115))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [X115,X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X115),X33)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X115),X90))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_div__le__mono,axiom,
! [X96,X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X96)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X33),X96))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono) ).
fof(fact_mult__le__mono1,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X114),X96)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X113),X96))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X114)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X113))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_add__le__mono1,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X96))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_zadd__strict__right__mono,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X114),X113))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X114),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X113),X96))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__less__mono1,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X96))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_Inf__fin__set__fold,axiom,
! [X292,X6,X7] :
( class_Lattices_Olattice(X7)
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292))) = hAPP(c_List_Ofoldl(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7),X6),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin__set__fold) ).
fof(fact_Min__fin__set__fold,axiom,
! [X292,X6,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292))) = hAPP(c_List_Ofoldl(X7,X7,c_Orderings_Oord__class_Omin(X7),X6),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__fin__set__fold) ).
fof(fact_Max__fin__set__fold,axiom,
! [X292,X6,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292))) = hAPP(c_List_Ofoldl(X7,X7,c_Orderings_Oord__class_Omax(X7),X6),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__fin__set__fold) ).
fof(fact_Sup__fin__set__fold,axiom,
! [X292,X6,X7] :
( class_Lattices_Olattice(X7)
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292))) = hAPP(c_List_Ofoldl(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7),X6),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin__set__fold) ).
fof(fact_diff__Suc__diff__eq2,axiom,
! [X90,X113,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X113))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X113),X96))),X90) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(fact_mod__div__equality2,axiom,
! [X71,X84,X87] :
( class_Divides_Osemiring__div(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84))),c_Divides_Odiv__class_Omod(X87,X71,X84)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__equality2) ).
fof(fact_list__update__code_I3_J,axiom,
! [X98,X114,X300,X86,X87] : hAPP(hAPP(c_List_Olist__update(X87,hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)),hAPP(c_Nat_OSuc,X114)),X98) = hAPP(hAPP(c_List_Olist_OCons(X87),X86),hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X98)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I3_J) ).
fof(fact_pair__box_Oinject,axiom,
! [X112,X89,X24,X25,X105,X7] :
( c_Nitpick_Opair__box_OPairBox(X7,X105,X25,X24) = c_Nitpick_Opair__box_OPairBox(X7,X105,X89,X112)
<=> ( X25 = X89
& X24 = X112 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
fof(fact_Sumr__inject,axiom,
! [X1,X2,X7,X119,X105] :
( c_Sum__Type_OSumr(X105,X119,X7,X2) = c_Sum__Type_OSumr(X105,X119,X7,X1)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sumr__inject) ).
fof(fact_Suml__inject,axiom,
! [X1,X2,X105,X119,X7] :
( c_Sum__Type_OSuml(X7,X119,X105,X2) = c_Sum__Type_OSuml(X7,X119,X105,X1)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suml__inject) ).
fof(fact_vimageI,axiom,
! [X105,X155,X7,X24,X25,X2] :
( hAPP(X2,X25) = X24
=> ( hBOOL(hAPP(hAPP(c_member(X7),X24),X155))
=> hBOOL(hAPP(hAPP(c_member(X105),X25),hAPP(c_Set_Ovimage(X105,X7,X2),X155))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageI) ).
fof(fact_image__eqI,axiom,
! [X7,X149,X105,X6,X2,X24] :
( X24 = hAPP(X2,X6)
=> ( hBOOL(hAPP(hAPP(c_member(X105),X6),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(c_Set_Oimage(X105,X7,X2),X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X105,X2,X24,X149,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X24 = hAPP(X2,X6)
=> hBOOL(hAPP(hAPP(c_member(X105),X24),hAPP(c_Set_Oimage(X7,X105,X2),X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_inj__on__iff,axiom,
! [X127,X6,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X127),X149))
=> ( hAPP(X2,X6) = hAPP(X2,X127)
<=> X6 = X127 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__onD,axiom,
! [X127,X6,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( hAPP(X2,X6) = hAPP(X2,X127)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X127),X149))
=> X6 = X127 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
fof(fact_inj__on__contraD,axiom,
! [X127,X6,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( X6 != X127
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X127),X149))
=> hAPP(X2,X6) != hAPP(X2,X127) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
! [X24,X25] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X24)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(fact_folding__one__idem_Osubset__idem,axiom,
! [X155,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one__idem(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(X2,hAPP(X215,X155)),hAPP(X215,X149)) = hAPP(X215,X149) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
fof(fact_comp__equivI,axiom,
! [X149,X172,X7] :
( hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),hAPP(c_Relation_Oconverse(X7,X7),X172)),X172) = X172
=> ( hAPP(c_Relation_ODomain(X7,X7),X172) = X149
=> c_Equiv__Relations_Oequiv(X7,X149,X172) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__equivI) ).
fof(fact_com_Osize_I13_J,axiom,
! [X54,X55,X13] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X13,X55,X54)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X55)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X54))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I13_J) ).
fof(fact_le__funD,axiom,
! [X6,X1,X2,X7,X105] :
( class_Orderings_Oord(X105)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X105)),X2),X1))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(X2,X6)),hAPP(X1,X6))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [X6,X1,X2,X7,X105] :
( class_Orderings_Oord(X105)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X105)),X2),X1))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(X2,X6)),hAPP(X1,X6))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_inj__map__eq__map,axiom,
! [X293,X292,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> ( hAPP(hAPP(c_List_Omap(X7,X105),X2),X292) = hAPP(hAPP(c_List_Omap(X7,X105),X2),X293)
<=> X292 = X293 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__map__eq__map) ).
fof(fact_map__injective,axiom,
! [X293,X292,X2,X7,X105] :
( hAPP(hAPP(c_List_Omap(X105,X7),X2),X292) = hAPP(hAPP(c_List_Omap(X105,X7),X2),X293)
=> ( c_Fun_Oinj__on(X105,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)))
=> X292 = X293 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__injective) ).
fof(fact_nth__list__update__eq,axiom,
! [X86,X300,X87,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X86)),X114) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update__eq) ).
fof(fact_setsum__atMost__Suc,axiom,
! [X44,X2,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X44))),hAPP(X2,hAPP(c_Nat_OSuc,X44))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__atMost__Suc) ).
fof(fact_ivl__disj__un_I17_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X95),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X95)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X95),X160)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X160) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I17_J) ).
fof(fact_butlast__conv__take,axiom,
! [X300,X87] : c_List_Obutlast(X87,X300) = hAPP(hAPP(c_List_Otake(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__conv__take) ).
fof(fact_fold1__belowI,axiom,
! [X25,X149,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Finite__Set_Ofold1(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),X149)),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__belowI) ).
fof(fact_min__max_Ofold1__belowI,axiom,
! [X25,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Finite__Set_Ofold1(X7,c_Orderings_Oord__class_Omin(X7)),X149)),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold1__belowI) ).
fof(fact_sorted_Oequations_I2_J,axiom,
! [X42,X43,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Olist_OCons(X7),X43),X42))
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X42)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X43),X3)) )
& c_List_Olinorder__class_Osorted(X7,X42) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_Oequations_I2_J) ).
fof(fact_sorted__Cons,axiom,
! [X292,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292))
<=> ( c_List_Olinorder__class_Osorted(X7,X292)
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X292)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__Cons) ).
fof(fact_evalc_Oequations_I2_J,axiom,
! [X41,X43,X42] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X42,X43)),X41),hAPP(hAPP(hAPP(c_Natural_Oupdate,X41),X42),hAPP(X43,X41)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I2_J) ).
fof(fact_evalc_OAssign,axiom,
! [X45,X25,X39] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X39,X25)),X45),hAPP(hAPP(hAPP(c_Natural_Oupdate,X45),X39),hAPP(X25,X45)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OAssign) ).
fof(fact_int__power__div__base,axiom,
! [X96,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X96))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X96),X90)),X96) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power__div__base) ).
fof(fact_divide__nonneg__pos,axiom,
! [X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).
fof(fact_split__mult__pos__le,axiom,
! [X84,X71,X87] :
( class_Rings_Oordered__ring(X87)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),c_Groups_Ozero__class_Ozero(X87))) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [X84,X71,X87] :
( class_Rings_Oordered__cancel__semiring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_less__1__mult,axiom,
! [X33,X90,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X90),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(fact_divide__pos__pos,axiom,
! [X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__pos) ).
fof(fact_mult__pos__pos,axiom,
! [X84,X71,X87] :
( class_Rings_Olinordered__semiring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__pos,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__pos,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [X2,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hAPP(c_Finite__Set_Ocard(X105),hAPP(c_Set_Oimage(X7,X105,X2),X149)) = hAPP(c_Finite__Set_Ocard(X7),X149)
=> c_Fun_Oinj__on(X7,X105,X2,X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [X2,X105,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( c_Fun_Oinj__on(X7,X105,X2,X149)
<=> hAPP(c_Finite__Set_Ocard(X105),hAPP(c_Set_Oimage(X7,X105,X2),X149)) = hAPP(c_Finite__Set_Ocard(X7),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(fact_Compl__Diff__eq,axiom,
! [X155,X149,X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Diff__eq) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [X84,X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X84),X33)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> X71 = X84 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_card__cartesian__product,axiom,
! [X155,X149,X105,X7] : hAPP(c_Finite__Set_Ocard(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X155))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),hAPP(c_Finite__Set_Ocard(X105),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product) ).
fof(fact_Int__insert__right__if1,axiom,
! [X155,X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).
fof(fact_list__eq__iff__nth__eq,axiom,
! [X7,X293,X292] :
( X292 = X293
<=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X293)
& ! [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X147),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> hAPP(hAPP(c_List_Onth(X7),X292),X147) = hAPP(hAPP(c_List_Onth(X7),X293),X147) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__eq__iff__nth__eq) ).
fof(fact_folding_Oeq__fold,axiom,
! [X45,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(X215,X149),X45) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X45),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oeq__fold) ).
fof(fact_weaken,axiom,
! [X223,X224,X216,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,X224)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)),X223),X224))
=> c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,X223) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weaken) ).
fof(fact_le__SUPI,axiom,
! [X210,X149,X107,X7,X105] :
( class_Complete__Lattice_Ocomplete__lattice(X105)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X107),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X105),hAPP(X210,X107)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X105),X149),X210))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SUPI) ).
fof(fact_zmod__simps_I4_J,axiom,
! [X84,X10,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),c_Divides_Odiv__class_Omod(X87,X71,X10)),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).
fof(fact_zmod__simps_I1_J,axiom,
! [X84,X10,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Divides_Odiv__class_Omod(X87,X71,X10)),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).
fof(fact_mod__diff__left__eq,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Oring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),c_Divides_Odiv__class_Omod(X87,X71,X10)),X84),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).
fof(fact_mod__mult__left__eq,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),c_Divides_Odiv__class_Omod(X87,X71,X10)),X84),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).
fof(fact_mod__add__left__eq,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Divides_Odiv__class_Omod(X87,X71,X10)),X84),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155))
| X149 = X155 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_psubset__eq,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
& X149 != X155 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(fact_finite__UnI,axiom,
! [X216,X215,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X215))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X216))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X215),X216))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnI) ).
fof(fact_Pow__Int__eq,axiom,
! [X155,X149,X7] : hAPP(c_Set_OPow(X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X7),X149)),hAPP(c_Set_OPow(X7),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__Int__eq) ).
fof(fact_setprod_Oeq__fold,axiom,
! [X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),c_Groups_Oone__class_Oone(X105)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oeq__fold) ).
fof(fact_setsum_Oeq__fold,axiom,
! [X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Oplus__class_Oplus(X105)),X1),c_Groups_Ozero__class_Ozero(X105)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oeq__fold) ).
fof(fact_psubset__imp__subset,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_mod__pos__neg,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg) ).
fof(fact_ex__nat__less,axiom,
! [X38,X44] :
( ? [X116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X116),X44))
& hBOOL(hAPP(X38,X116)) )
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)))
& hBOOL(hAPP(X38,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less) ).
fof(fact_restrict__map__empty,axiom,
! [X6,X192,X7,X105] : hAPP(c_Map_Orestrict__map(X105,X7,hAPP(c_COMBK(tc_Option_Ooption(X7),X105),c_Option_Ooption_ONone(X7)),X192),X6) = c_Option_Ooption_ONone(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__empty) ).
fof(fact_drop__Cons__number__of,axiom,
! [X300,X86,X87,X139] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_List_Odrop(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X300) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons__number__of) ).
fof(fact_Abs__Integ__induct,axiom,
! [X6,X38] :
( ! [X82] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X82),c_Int_OInteg))
=> hBOOL(hAPP(X38,hAPP(c_Int_OAbs__Integ,X82))) )
=> hBOOL(hAPP(X38,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__induct) ).
fof(fact_zdvd__mult__cancel1,axiom,
! [X44,X95] :
( X95 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X95),X44)),X95))
<=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X44) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mult__cancel1) ).
fof(fact_wf__Int1,axiom,
! [X247,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> c_Wellfounded_Owf(X7,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X172),X247)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int1) ).
fof(fact_wf__Int2,axiom,
! [X247,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> c_Wellfounded_Owf(X7,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X247),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int2) ).
fof(fact_div__pos__neg,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__neg) ).
fof(fact_fold1__set,axiom,
! [X292,X7] :
( class_Lattices_Oab__semigroup__idem__mult(X7)
=> ( X292 != c_List_Olist_ONil(X7)
=> hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),hAPP(c_List_Oset(X7),X292)) = hAPP(c_List_Ofoldl(X7,X7,c_Groups_Otimes__class_Otimes(X7),hAPP(c_List_Ohd(X7),X292)),hAPP(c_List_Otl(X7),X292)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__set) ).
fof(fact_drop__zip,axiom,
! [X301,X300,X33,X7,X87] : hAPP(hAPP(c_List_Odrop(tc_prod(X87,X7)),X33),hAPP(hAPP(c_List_Ozip(X87,X7),X300),X301)) = hAPP(hAPP(c_List_Ozip(X87,X7),hAPP(hAPP(c_List_Odrop(X87),X33),X300)),hAPP(hAPP(c_List_Odrop(X7),X33),X301)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__zip) ).
fof(fact_take__zip,axiom,
! [X301,X300,X33,X7,X87] : hAPP(hAPP(c_List_Otake(tc_prod(X87,X7)),X33),hAPP(hAPP(c_List_Ozip(X87,X7),X300),X301)) = hAPP(hAPP(c_List_Ozip(X87,X7),hAPP(hAPP(c_List_Otake(X87),X33),X300)),hAPP(hAPP(c_List_Otake(X7),X33),X301)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__zip) ).
fof(fact_ivl__disj__un_I6_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X160)),hAPP(hAPP(c_Set_Oinsert(X7),X160),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I6_J) ).
fof(fact_mod__neg__neg,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg) ).
fof(fact_single__valued__rel__comp,axiom,
! [X45,X119,X172,X105,X7] :
( c_Relation_Osingle__valued(X7,X105,X172)
=> ( c_Relation_Osingle__valued(X105,X119,X45)
=> c_Relation_Osingle__valued(X7,X119,hAPP(hAPP(c_Relation_Orel__comp(X7,X105,X119),X172),X45)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__rel__comp) ).
fof(fact_sorted__transpose,axiom,
! [X292,X7] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X7))),c_List_Otranspose(X7,X292)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__transpose) ).
fof(fact_Int__atLeastLessThan,axiom,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X25),X24)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X23),X136)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X25),X23)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X24),X136)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastLessThan) ).
fof(fact_Int__greaterThanLessThan,axiom,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X25,X24)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X23,X136)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X7,hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X25),X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X24),X136)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greaterThanLessThan) ).
fof(fact_Int__greaterThanAtMost,axiom,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X25,X24)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X23,X136)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X7,hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X25),X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X24),X136)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greaterThanAtMost) ).
fof(fact_Int__atLeastAtMost,axiom,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X23,X136)) = c_SetInterval_Oord__class_OatLeastAtMost(X7,hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X25),X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X24),X136)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMost) ).
fof(fact_set__rev__mp,axiom,
! [X155,X149,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_in__mono,axiom,
! [X6,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_set__mp,axiom,
! [X6,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_subsetD,axiom,
! [X23,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_psubsetD,axiom,
! [X23,X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
fof(fact_nth__append__length,axiom,
! [X301,X86,X300,X87] : hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Oappend(X87),X300),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X301))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append__length) ).
fof(fact_div__neg__neg,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg) ).
fof(fact_inj__on__add__nat,axiom,
! [X214,X94] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X94),X214),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
! [X25,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X24)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
fof(fact_times__divide__times__eq,axiom,
! [X128,X97,X98,X86,X87] :
( class_Fields_Ofield__inverse__zero(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X97),X128)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X97)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X98),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X132,X133,X135,X134,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),X135)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X133),X132)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),X133)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X135),X132)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X106,X10,X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X106)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X106)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [X132,X133,X135,X134,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),X135)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X133),X132)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X135),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X133),X132))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_sorted__map__remove1,axiom,
! [X6,X292,X2,X105,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),X292))
=> c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),c_List_Oremove1(X105,X6,X292))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__map__remove1) ).
fof(fact_Domain__Union,axiom,
! [X209,X105,X7] : hAPP(c_Relation_ODomain(X7,X105),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),X209)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X7,X105),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X209),c_Relation_ODomain(X7,X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Union) ).
fof(fact_Range__Union,axiom,
! [X209,X7,X105] : hAPP(c_Relation_ORange(X105,X7),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X105,X7),tc_HOL_Obool),X209)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X105,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X209),c_Relation_ORange(X105,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Union) ).
fof(fact_all__nat__less,axiom,
! [X38,X44] :
( ! [X116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X116),X44))
=> hBOOL(hAPP(X38,X116)) )
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)))
=> hBOOL(hAPP(X38,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less) ).
fof(fact_Ints__power,axiom,
! [X44,X25,X7] :
( class_Rings_Oring__1(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Int_Oring__1__class_OInts(X7)))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X25),X44)),c_Int_Oring__1__class_OInts(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__power) ).
fof(fact_Collect__mem__eq,axiom,
! [X149,X7] : hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149)) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).
fof(fact_nat__one__le__power,axiom,
! [X33,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X114))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X114),X33))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
fof(fact_zdvd__zmod__imp__zdvd,axiom,
! [X33,X90,X96] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X96),c_Divides_Odiv__class_Omod(tc_Int_Oint,X90,X33)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X96),X33))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X96),X90)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zmod__imp__zdvd) ).
fof(fact_one__less__power,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(fact_divide__nonpos__neg,axiom,
! [X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [X84,X71,X87] :
( class_Rings_Oordered__ring(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_divide__neg__neg,axiom,
! [X98,X86,X87] :
( class_Fields_Olinordered__field(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__neg) ).
fof(fact_mult__neg__neg,axiom,
! [X84,X71,X87] :
( class_Rings_Olinordered__ring__strict(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),c_Groups_Ozero__class_Ozero(X87)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_setsum__lessThan__Suc,axiom,
! [X44,X2,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X44))),hAPP(X2,X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__lessThan__Suc) ).
fof(fact_dom__map__of__zip,axiom,
! [X293,X105,X292,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)
=> ( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> c_Map_Odom(X7,X105,c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293))) = hAPP(c_List_Oset(X7),X292) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__map__of__zip) ).
fof(fact_posDivAlg__div__mod,axiom,
! [X115,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X96))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115))
=> c_Divides_OposDivAlg(X96,X115) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),X115)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X115)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__div__mod) ).
fof(fact_pos__imp__zdiv__pos__iff,axiom,
! [X107,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X107),X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),X107)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
fof(fact_lex__def,axiom,
! [X172,X7] : c_List_Olex(X7,X172) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X7,X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lex__def) ).
fof(fact_le__max__iff__disj,axiom,
! [X127,X6,X26,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),X127)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X26),X6))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X26),X127)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__max__iff__disj) ).
fof(fact_less__max__iff__disj,axiom,
! [X127,X6,X26,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),X127)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X26),X6))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X26),X127)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__max__iff__disj) ).
fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
! [X25,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X24)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
fof(fact_select__weigth__select,axiom,
! [X7,X292] :
( X292 != c_List_Olist_ONil(X7)
=> c_Random_Oselect__weight(X7,hAPP(hAPP(c_List_Omap(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,X7)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X7),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X292)) = c_Random_Oselect(X7,X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weigth__select) ).
fof(fact_finite__Inter,axiom,
! [X210,X7] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X3),X210))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X210))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Inter) ).
fof(fact_abs__eq__mult,axiom,
! [X84,X71,X87] :
( class_Rings_Oordered__ring__abs(X87)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),c_Groups_Ozero__class_Ozero(X87))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),c_Groups_Ozero__class_Ozero(X87))) ) )
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__mult) ).
fof(fact_butlast__take,axiom,
! [X300,X87,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> c_List_Obutlast(X87,hAPP(hAPP(c_List_Otake(X87),X33),X300)) = hAPP(hAPP(c_List_Otake(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X300) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__take) ).
fof(fact_single__Diff__lessThan,axiom,
! [X94,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X94),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X94)) = hAPP(hAPP(c_Set_Oinsert(X7),X94),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__Diff__lessThan) ).
fof(fact_disjoint__iff__not__equal,axiom,
! [X155,X149,X7] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> ! [X206] :
( hBOOL(hAPP(hAPP(c_member(X7),X206),X155))
=> X3 != X206 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
fof(fact_insort__remove1,axiom,
! [X292,X25,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_List_Oset(X7),X292)))
=> ( c_List_Olinorder__class_Osorted(X7,X292)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7)),X25),c_List_Oremove1(X7,X25,X292)) = X292 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__remove1) ).
fof(fact_negDivAlg__div__mod,axiom,
! [X115,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115))
=> c_Divides_OnegDivAlg(X96,X115) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),X115)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X115)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__div__mod) ).
fof(fact_Inf__fin_Osubset__idem,axiom,
! [X155,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),c_Big__Operators_Olattice__class_OInf__fin(X7,X155)),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)) = c_Big__Operators_Olattice__class_OInf__fin(X7,X149) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Osubset__idem) ).
fof(fact_Sup__fin_Osubset__idem,axiom,
! [X155,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),c_Big__Operators_Olattice__class_OSup__fin(X7,X155)),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)) = c_Big__Operators_Olattice__class_OSup__fin(X7,X149) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Osubset__idem) ).
fof(fact_Max_Osubset__idem,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),c_Big__Operators_Olinorder__class_OMax(X7,X155)),c_Big__Operators_Olinorder__class_OMax(X7,X149)) = c_Big__Operators_Olinorder__class_OMax(X7,X149) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Osubset__idem) ).
fof(fact_Min_Osubset__idem,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),c_Big__Operators_Olinorder__class_OMin(X7,X155)),c_Big__Operators_Olinorder__class_OMin(X7,X149)) = c_Big__Operators_Olinorder__class_OMin(X7,X149) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Osubset__idem) ).
fof(fact_zpower__zmod,axiom,
! [X98,X90,X86] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X86,X90)),X98),X90) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X86),X98),X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zmod) ).
fof(fact_zdiff__zmod__left,axiom,
! [X98,X90,X86] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X86,X90)),X98),X90) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X86),X98),X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).
fof(fact_le__Inf__iff,axiom,
! [X149,X24,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),c_Complete__Lattice_OInf__class_OInf(X7,X149)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Inf__iff) ).
fof(fact_take__Cons_H,axiom,
! [X300,X86,X87,X33] :
( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(X87),X33),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = c_List_Olist_ONil(X87) )
& ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(X87),X33),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_List_Olist_OCons(X87),X86),hAPP(hAPP(c_List_Otake(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X300)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons_H) ).
fof(fact_inf1I,axiom,
! [X7,X155,X6,X149] :
( hBOOL(hAPP(X149,X6))
=> ( hBOOL(hAPP(X155,X6))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
fof(fact_Rep__Integ,axiom,
! [X6] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X6)),c_Int_OInteg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ) ).
fof(fact_folding__one__idem_Ounion__idem,axiom,
! [X155,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one__idem(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(X2,hAPP(X215,X149)),hAPP(X215,X155)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).
fof(fact_add__increasing,axiom,
! [X10,X84,X71,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X71,X84,X10,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_pos__add__strict,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__strict__increasing,axiom,
! [X10,X84,X71,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__strict__increasing2,axiom,
! [X10,X84,X71,X87] :
( class_Groups_Oordered__comm__monoid__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_zmod__zdiv__equality,axiom,
! [X84,X71] : X71 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).
fof(fact_le__infI1,axiom,
! [X84,X86,X71,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84)),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI1) ).
fof(fact_le__infI2,axiom,
! [X71,X86,X84,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84)),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI2) ).
fof(fact_min__max_Ole__infI1,axiom,
! [X84,X86,X71,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84)),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI1) ).
fof(fact_min__max_Ole__infI2,axiom,
! [X71,X86,X84,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84)),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI2) ).
fof(fact_less__infI1,axiom,
! [X84,X86,X71,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84)),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI1) ).
fof(fact_less__infI2,axiom,
! [X71,X86,X84,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84)),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI2) ).
fof(fact_min__max_Oless__infI1,axiom,
! [X84,X86,X71,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84)),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__infI1) ).
fof(fact_min__max_Oless__infI2,axiom,
! [X71,X86,X84,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84)),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__infI2) ).
fof(fact_listrel__Nil,axiom,
! [X172,X7] : hAPP(c_Relation_OImage(tc_List_Olist(X7),tc_List_Olist(X7),c_List_Olistrel(X7,X172)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X7)),c_List_Olist_ONil(X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X7),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X7)),c_List_Olist_ONil(X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X7),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil) ).
fof(fact_setprod__eq__1__iff,axiom,
! [X2,X215,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X215))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,tc_Nat_Onat),X2),X215) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X215))
=> hAPP(X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__eq__1__iff) ).
fof(fact_setsum__eq__0__iff,axiom,
! [X2,X215,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X215))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X215) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X215))
=> hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__0__iff) ).
fof(fact_restrict__in,axiom,
! [X95,X105,X149,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Map_Orestrict__map(X7,X105,X95,X149),X6) = hAPP(X95,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__in) ).
fof(fact_nat__diff__split,axiom,
! [X24,X25,X38] :
( hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X24)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X24))
=> hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X159] :
( X25 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X159)
=> hBOOL(hAPP(X38,X159)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(fact_dvd__div__mult,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X84))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X84),X71)),X10) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10)),X71) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__mult) ).
fof(fact_finite__compl,axiom,
! [X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__compl) ).
fof(fact_less__nat__number__of,axiom,
! [X169,X163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X163),X169))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X169)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X163),X169)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__number__of) ).
fof(fact_Un__insert__left,axiom,
! [X193,X155,X25,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)),X193) = hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__left) ).
fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
! [X6,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm__idem(X7,X105,X2)
=> hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X2,X6)),hAPP(X2,X6)) = hAPP(X2,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).
fof(fact_finite__dom__map__of,axiom,
! [X157,X105,X7] : hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Map_Odom(X7,X105,c_Map_Omap__of(X7,X105,X157)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__dom__map__of) ).
fof(fact_com_Osize_I12_J,axiom,
! [X73,X74] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X74,X73)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X74)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X73))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I12_J) ).
fof(fact_divmod__int__rel__mod,axiom,
! [X138,X144,X84,X71] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),X138)))
=> ( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = X138 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod) ).
fof(fact_snd__def,axiom,
! [X161,X7,X105] : hAPP(c_Product__Type_Osnd(X105,X7),X161) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X7,X7),hAPP(c_COMBK(tc_fun(X7,X7),X105),c_COMBI(X7))),X161),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__def) ).
fof(fact_Ints__odd__nonzero,axiom,
! [X25,X7] :
( class_Int_Oring__char__0(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Int_Oring__1__class_OInts(X7)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),c_Groups_Oone__class_Oone(X7)),X25)),X25) != c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).
fof(fact_finite__Int,axiom,
! [X216,X215,X7] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X215))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X216)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X215),X216))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Int) ).
fof(fact_finite__Diff,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff) ).
fof(fact_sorted__many__eq,axiom,
! [X302,X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Olist_OCons(X7),X6),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X302)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
& c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Olist_OCons(X7),X127),X302)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__many__eq) ).
fof(fact_sorted__many,axiom,
! [X299,X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> ( c_List_Olinorder__class_Osorted(X87,hAPP(hAPP(c_List_Olist_OCons(X87),X98),X299))
=> c_List_Olinorder__class_Osorted(X87,hAPP(hAPP(c_List_Olist_OCons(X87),X86),hAPP(hAPP(c_List_Olist_OCons(X87),X98),X299))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__many) ).
fof(fact_mod__eq,axiom,
! [X138,X144,X33,X90] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X90,X33),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X144),X138)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33) = X138 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq) ).
fof(fact_zmod__le__nonneg__dividend,axiom,
! [X96,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X90,X96)),X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
fof(fact_mod__le__divisor,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__le__divisor) ).
fof(fact_pos__mod__conj,axiom,
! [X71,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__conj) ).
fof(fact_pos__mod__bound,axiom,
! [X71,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
fof(fact_mod__less__divisor,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
fof(fact_card__length,axiom,
! [X292,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),hAPP(c_List_Oset(X7),X292))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__length) ).
fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
! [X127,X6,X7] :
( ( class_Divides_Osemiring__div(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X6)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X127)))
<=> c_Divides_Odiv__class_Omod(X7,hAPP(c_Int_Onumber__class_Onumber__of(X7),X127),hAPP(c_Int_Onumber__class_Onumber__of(X7),X6)) = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0__number__of) ).
fof(fact_image__Pow__surj,axiom,
! [X155,X149,X2,X7,X105] :
( hAPP(c_Set_Oimage(X105,X7,X2),X149) = X155
=> hAPP(c_Set_Oimage(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X105,X7,X2)),hAPP(c_Set_OPow(X105),X149)) = hAPP(c_Set_OPow(X7),X155) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__surj) ).
fof(fact_surj__image__vimage__eq,axiom,
! [X149,X2,X7,X105] :
( hAPP(c_Set_Oimage(X105,X7,X2),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(X105,X7,X2),hAPP(c_Set_Ovimage(X105,X7,X2),X149)) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__image__vimage__eq) ).
fof(fact_zdvd__zdiffD,axiom,
! [X33,X90,X96] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X90),X33)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X96),X33))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X96),X90)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
fof(fact_divmod__int__rel__div,axiom,
! [X138,X144,X84,X71] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),X138)))
=> ( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84) = X144 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div) ).
fof(fact_abs__le__D2,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D2) ).
fof(fact_minus__le__iff,axiom,
! [X24,X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)),X24))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X24)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__iff) ).
fof(fact_minus__less__iff,axiom,
! [X24,X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)),X24))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X24)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(fact_neg__mod__conj,axiom,
! [X71,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__conj) ).
fof(fact_neg__mod__sign,axiom,
! [X71,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__sign) ).
fof(fact_vimage__Collect__eq,axiom,
! [X38,X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(c_Set_OCollect(X105),X38)) = hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(X105,tc_HOL_Obool,X7),X38),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
fof(fact_div__eq,axiom,
! [X138,X144,X33,X90] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X90,X33),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X144),X138)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) = X144 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__eq) ).
fof(fact_card__image,axiom,
! [X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> hAPP(c_Finite__Set_Ocard(X105),hAPP(c_Set_Oimage(X7,X105,X2),X149)) = hAPP(c_Finite__Set_Ocard(X7),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
fof(fact_take__drop,axiom,
! [X300,X90,X33,X87] : hAPP(hAPP(c_List_Otake(X87),X33),hAPP(hAPP(c_List_Odrop(X87),X90),X300)) = hAPP(hAPP(c_List_Odrop(X87),X90),hAPP(hAPP(c_List_Otake(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X90)),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__drop) ).
fof(fact_sorted__filter,axiom,
! [X38,X292,X2,X105,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),X292))
=> c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(c_List_Ofilter(X105,X38),X292))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__filter) ).
fof(fact_nat__mod__eq__lemma,axiom,
! [X98,X33,X86] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X33) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X98,X33)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X86))
=> ? [X148] : X86 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X148)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mod__eq__lemma) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X25,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X25,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_add__gr__0,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X44)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X95))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_asm,axiom,
! [X216,X223,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)),X223),X216))
=> c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,X223) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_asm) ).
fof(fact_mod__diff__cong,axiom,
! [X124,X84,X88,X10,X71,X87] :
( class_Divides_Oring__div(X87)
=> ( c_Divides_Odiv__class_Omod(X87,X71,X10) = c_Divides_Odiv__class_Omod(X87,X88,X10)
=> ( c_Divides_Odiv__class_Omod(X87,X84,X10) = c_Divides_Odiv__class_Omod(X87,X124,X10)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X88),X124),X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__cong) ).
fof(fact_mod__mult__cong,axiom,
! [X124,X84,X88,X10,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> ( c_Divides_Odiv__class_Omod(X87,X71,X10) = c_Divides_Odiv__class_Omod(X87,X88,X10)
=> ( c_Divides_Odiv__class_Omod(X87,X84,X10) = c_Divides_Odiv__class_Omod(X87,X124,X10)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X88),X124),X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__cong) ).
fof(fact_mod__add__cong,axiom,
! [X124,X84,X88,X10,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> ( c_Divides_Odiv__class_Omod(X87,X71,X10) = c_Divides_Odiv__class_Omod(X87,X88,X10)
=> ( c_Divides_Odiv__class_Omod(X87,X84,X10) = c_Divides_Odiv__class_Omod(X87,X124,X10)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X88),X124),X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__cong) ).
fof(fact_dvd__mod,axiom,
! [X33,X90,X96,X87] :
( class_Divides_Osemiring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X96),X90))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X96),X33))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X96),c_Divides_Odiv__class_Omod(X87,X90,X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod) ).
fof(fact_power__diff,axiom,
! [X90,X33,X71,X87] :
( class_Fields_Ofield(X87)
=> ( X71 != c_Groups_Ozero__class_Ozero(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X90)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__diff) ).
fof(fact_divmod__int__rel__neg,axiom,
! [X180,X84,X71] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)),X180))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),hAPP(c_Divides_OnegateSnd,X180))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__neg) ).
fof(fact_evaln__Suc,axiom,
! [X83,X33,X9,X10] :
( c_Natural_Oevaln(X10,X9,X33,X83)
=> c_Natural_Oevaln(X10,X9,hAPP(c_Nat_OSuc,X33),X83) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__Suc) ).
fof(fact_insert__Diff1,axiom,
! [X149,X155,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),X155) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff1) ).
fof(fact_dom__const,axiom,
! [X2,X105,X7] : c_Map_Odom(X7,X105,hAPP(hAPP(c_COMBB(X105,tc_Option_Ooption(X105),X7),c_Option_Ooption_OSome(X105)),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__const) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [X33,X90,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X33))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X96)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),X96)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_ex__nat__less__eq,axiom,
! [X38,X44] :
( ? [X116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X116),X44))
& hBOOL(hAPP(X38,X116)) )
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)))
& hBOOL(hAPP(X38,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
fof(fact_Suc__diff__diff,axiom,
! [X96,X33,X90] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X33)),hAPP(c_Nat_OSuc,X96)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
fof(fact_power__inject__base,axiom,
! [X84,X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Nat_OSuc,X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X84),hAPP(c_Nat_OSuc,X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X84))
=> X71 = X84 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__base) ).
fof(fact_int__zle__neg,axiom,
! [X95,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95))))
<=> ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__zle__neg) ).
fof(fact_wf,axiom,
! [X7] :
( class_Orderings_Owellorder(X7)
=> c_Wellfounded_Owf(X7,hAPP(c_Set_OCollect(tc_prod(X7,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X7)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf) ).
fof(fact_dvd__diff,axiom,
! [X97,X98,X86,X87] :
( class_Rings_Ocomm__ring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X86),X97))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X86),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X98),X97))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff) ).
fof(fact_dvd__add,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__add) ).
fof(fact_inf__greatest,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),X97))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__greatest) ).
fof(fact_le__infI,axiom,
! [X84,X71,X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI) ).
fof(fact_le__inf__iff,axiom,
! [X26,X127,X6,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X127),X26)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X26)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__inf__iff) ).
fof(fact_min__max_Ole__inf__iff,axiom,
! [X26,X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X127),X26)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X26)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__inf__iff) ).
fof(fact_min__max_Ole__infI,axiom,
! [X84,X71,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI) ).
fof(fact_min__max_Oinf__greatest,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X98),X97))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__greatest) ).
fof(fact_min__less__iff__conj,axiom,
! [X127,X6,X26,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),X127)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X26),X6))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X26),X127)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__conj) ).
fof(fact_self__quotient__aux2,axiom,
! [X144,X138,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( X71 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X138),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X144))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X138))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X144),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_filter__id__conv,axiom,
! [X292,X38,X7] :
( hAPP(c_List_Ofilter(X7,X38),X292) = X292
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X292)))
=> hBOOL(hAPP(X38,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__id__conv) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X86,X98))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_evalc_OSemi,axiom,
! [X50,X49,X51,X52,X53] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X53),X52),X51))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X49),X51),X50))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X53,X49)),X52),X50)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OSemi) ).
fof(fact_nth__append__length__plus,axiom,
! [X33,X301,X300,X87] : hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X33)) = hAPP(hAPP(c_List_Onth(X87),X301),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append__length__plus) ).
fof(fact_list_Osimps_I5_J,axiom,
! [X294,X25,X21,X22,X105,X7] : hAPP(c_List_Olist_Olist__case(X7,X105,X22,X21),hAPP(hAPP(c_List_Olist_OCons(X105),X25),X294)) = hAPP(hAPP(X21,X25),X294),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).
fof(fact_sup1I1,axiom,
! [X155,X7,X6,X149] :
( hBOOL(hAPP(X149,X6))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).
fof(fact_sup1I2,axiom,
! [X149,X7,X6,X155] :
( hBOOL(hAPP(X155,X6))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
fof(fact_zero__le__power__abs,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),X33))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
fof(fact_diff__Suc__diff__eq1,axiom,
! [X90,X113,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X113))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X113),X96))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X96)),hAPP(c_Nat_OSuc,X113)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(fact_subset__empty,axiom,
! [X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
<=> X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
fof(fact_wfP__acyclicP,axiom,
! [X172,X7] :
( c_Wellfounded_OwfP(X7,X172)
=> c_Wellfounded_Oacyclic(X7,hAPP(c_Set_OCollect(tc_prod(X7,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__acyclicP) ).
fof(fact_int__dvd__iff,axiom,
! [X26,X95] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95)),X26))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X95),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__dvd__iff) ).
fof(fact_rel__comp__empty1,axiom,
! [X191,X105,X119,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X119),tc_HOL_Obool))),X191) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__empty1) ).
fof(fact_zdiv__zminus1__eq__if,axiom,
! [X71,X84] :
( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71)),X84) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71)),X84) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus1__eq__if) ).
fof(fact_compl__le__compl__iff,axiom,
! [X127,X6,X7] :
( class_Lattices_Oboolean__algebra(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X6)),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_neg__le__iff__le,axiom,
! [X25,X24,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X24)),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_neg__less__iff__less,axiom,
! [X25,X24,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X24)),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_all__nat__less__eq,axiom,
! [X38,X44] :
( ! [X116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X116),X44))
=> hBOOL(hAPP(X38,X116)) )
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)))
=> hBOOL(hAPP(X38,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
fof(fact_power__gt1,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Nat_OSuc,X33)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1) ).
fof(fact_self__quotient__aux1,axiom,
! [X144,X138,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( X71 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X138),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X144))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X138),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X144)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_le__number__of,axiom,
! [X127,X6,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Rings_Olinordered__idom(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X6)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of) ).
fof(fact_less__number__of,axiom,
! [X127,X6,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Rings_Olinordered__idom(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X6)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of) ).
fof(fact_zdvd__antisym__nonneg,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X90),X33))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X33),X90))
=> X90 = X33 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).
fof(fact_list__update__beyond,axiom,
! [X86,X114,X300,X87] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X114))
=> hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X86) = X300 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__beyond) ).
fof(fact_le__cube,axiom,
! [X90] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X90)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
fof(fact_in__set__butlastD,axiom,
! [X292,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),c_List_Obutlast(X7,X292))))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__butlastD) ).
fof(fact_insert__image,axiom,
! [X2,X105,X149,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Set_Oinsert(X105),hAPP(X2,X6)),hAPP(c_Set_Oimage(X7,X105,X2),X149)) = hAPP(c_Set_Oimage(X7,X105,X2),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).
fof(fact_self__quotient,axiom,
! [X138,X144,X71] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X71),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),X138)))
=> ( X71 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> X144 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient) ).
fof(fact_self__remainder,axiom,
! [X138,X144,X71] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X71),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),X138)))
=> ( X71 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> X138 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__remainder) ).
fof(fact_wf__exp,axiom,
! [X191,X44,X7] :
( c_Wellfounded_Owf(X7,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191))
=> c_Wellfounded_Owf(X7,X191) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__exp) ).
fof(fact_of__int__le__iff,axiom,
! [X26,X125,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Oring__1__class_Oof__int(X7),X125)),hAPP(c_Int_Oring__1__class_Oof__int(X7),X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X125),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__le__iff) ).
fof(fact_of__nat__le__iff,axiom,
! [X44,X95,X7] :
( class_Rings_Olinordered__semidom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X95)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__le__iff) ).
fof(fact_of__int__less__iff,axiom,
! [X26,X125,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Oring__1__class_Oof__int(X7),X125)),hAPP(c_Int_Oring__1__class_Oof__int(X7),X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__less__iff) ).
fof(fact_of__nat__less__imp__less,axiom,
! [X33,X90,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X90)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X33)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).
fof(fact_of__nat__less__iff,axiom,
! [X44,X95,X7] :
( class_Rings_Olinordered__semidom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X95)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).
fof(fact_nonzero__power__divide,axiom,
! [X33,X71,X84,X87] :
( class_Fields_Ofield(X87)
=> ( X84 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X84)),X33) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X84),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
fof(fact_zless__imp__add1__zle,axiom,
! [X97,X128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X128),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X128),c_Groups_Oone__class_Oone(tc_Int_Oint))),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_Inf__fin_Ounion__idem,axiom,
! [X155,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)),c_Big__Operators_Olattice__class_OInf__fin(X7,X155)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__idem) ).
fof(fact_Min__Un,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),c_Big__Operators_Olinorder__class_OMin(X7,X149)),c_Big__Operators_Olinorder__class_OMin(X7,X155)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__Un) ).
fof(fact_Max__Un,axiom,
! [X155,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),c_Big__Operators_Olinorder__class_OMax(X7,X149)),c_Big__Operators_Olinorder__class_OMax(X7,X155)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__Un) ).
fof(fact_Sup__fin_Ounion__idem,axiom,
! [X155,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( X155 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)),c_Big__Operators_Olattice__class_OSup__fin(X7,X155)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__idem) ).
fof(fact_code__numeral_Oof__nat__inject,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X6),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X127),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> ( hAPP(c_Code__Numeral_Oof__nat,X6) = hAPP(c_Code__Numeral_Oof__nat,X127)
<=> X6 = X127 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Oof__nat__inject) ).
fof(fact_nat__le__eq__zle,axiom,
! [X26,X125] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X125))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X125)),hAPP(c_Int_Onat,X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X125),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__eq__zle) ).
fof(fact_nat__less__eq__zless,axiom,
! [X26,X125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X125))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X125)),hAPP(c_Int_Onat,X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__eq__zless) ).
fof(fact_nat__mono__iff,axiom,
! [X125,X26] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X125)),hAPP(c_Int_Onat,X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mono__iff) ).
fof(fact_funpow__swap1,axiom,
! [X6,X44,X7,X2] : hAPP(X2,hAPP(hAPP(hAPP(c_Nat_Ocompow(X7,X7),X44),X2),X6)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X7,X7),X44),X2),hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__swap1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X84,X90,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X90)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_inf__sup__distrib2,axiom,
! [X86,X97,X98,X87] :
( class_Lattices_Odistrib__lattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),X97)),X86) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),X86)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X97),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib2) ).
fof(fact_sup__inf__distrib2,axiom,
! [X86,X97,X98,X87] :
( class_Lattices_Odistrib__lattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),X97)),X86) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),X86)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X97),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib2) ).
fof(fact_min__max_Osup__inf__distrib2,axiom,
! [X86,X97,X98,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X98),X97)),X86) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X98),X86)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X97),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib2) ).
fof(fact_min__max_Oinf__sup__distrib2,axiom,
! [X86,X97,X98,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X98),X97)),X86) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X98),X86)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X97),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__distrib2) ).
fof(fact_diff__divide__distrib,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Odivision__ring(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84)),X10) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).
fof(fact_add__divide__distrib,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Odivision__ring(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
fof(fact_power__divide,axiom,
! [X33,X84,X71,X87] :
( class_Fields_Ofield__inverse__zero(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X84)),X33) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X84),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__divide) ).
fof(fact_power__mult__distrib,axiom,
! [X33,X84,X71,X87] :
( class_Groups_Ocomm__monoid__mult(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X84),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X144,X98,X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X98)),X144) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X144)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),X144)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_max__diff__distrib__left,axiom,
! [X97,X98,X86,X87] :
( class_Groups_Oordered__ab__group__add(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98)),X97) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X86),X97)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X98),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__diff__distrib__left) ).
fof(fact_min__diff__distrib__left,axiom,
! [X97,X98,X86,X87] :
( class_Groups_Oordered__ab__group__add(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98)),X97) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X86),X97)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X98),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__diff__distrib__left) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Ocomm__semiring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_max__add__distrib__left,axiom,
! [X97,X98,X86,X87] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98)),X97) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X86),X97)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X98),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__add__distrib__left) ).
fof(fact_min__add__distrib__left,axiom,
! [X97,X98,X86,X87] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98)),X97) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X86),X97)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X98),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__add__distrib__left) ).
fof(fact_set__insort,axiom,
! [X292,X6,X2,X7,X105] :
( class_Orderings_Olinorder(X105)
=> hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X105,X2),X6),X292)) = hAPP(hAPP(c_Set_Oinsert(X7),X6),hAPP(c_List_Oset(X7),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__insort) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X86),X98))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X86),X98))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X86),X98))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X44)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X95))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_dvd__div__div__eq__mult,axiom,
! [X136,X24,X23,X25,X7] :
( class_Divides_Osemiring__div(X7)
=> ( X25 != c_Groups_Ozero__class_Ozero(X7)
=> ( X23 != c_Groups_Ozero__class_Ozero(X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X25),X24))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X23),X136))
=> ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7),X24),X25) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7),X136),X23)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X136) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__div__eq__mult) ).
fof(fact_ivl__disj__un_I1_J,axiom,
! [X157,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X157),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X157)) = hAPP(c_SetInterval_Oord__class_OatLeast(X7),X157) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I1_J) ).
fof(fact_finite__converse,axiom,
! [X172,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X105)),hAPP(c_Relation_Oconverse(X105,X7),X172)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X105,X7)),X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__converse) ).
fof(fact_finite__UNIV__card__ge__0,axiom,
! [X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(fact_set__remove1__eq,axiom,
! [X6,X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> hAPP(c_List_Oset(X7),c_List_Oremove1(X7,X6,X292)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X292)),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remove1__eq) ).
fof(fact_Int__Union,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X155),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union) ).
fof(fact_Un__Inter,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X155),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Inter) ).
fof(fact_length__insort,axiom,
! [X292,X6,X2,X7,X105] :
( class_Orderings_Olinorder(X105)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X105,X2),X6),X292)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__insort) ).
fof(fact_nat__less__iff,axiom,
! [X95,X125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X125))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X125)),X95))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__iff) ).
fof(fact_remove1__insort,axiom,
! [X292,X6,X7] :
( class_Orderings_Olinorder(X7)
=> c_List_Oremove1(X7,X6,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7)),X6),X292)) = X292 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__insort) ).
fof(fact_Powp__def,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(c_Predicate_OPowp(X7,X149),X155))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X155))
=> hBOOL(hAPP(X149,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__def) ).
fof(fact_restrict__map__to__empty,axiom,
! [X6,X95,X7,X105] : hAPP(c_Map_Orestrict__map(X105,X7,X95,c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))),X6) = c_Option_Ooption_ONone(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__to__empty) ).
fof(fact_split__curry,axiom,
! [X2,X119,X105,X7] : hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,X119),c_Product__Type_Ocurry(X7,X105,X119,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__curry) ).
fof(fact_eq__number__of__eq,axiom,
! [X127,X6,X7] :
( class_Int_Onumber__ring(X7)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X7),X6) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X127)
<=> c_Int_Oiszero(X7,hAPP(c_Int_Onumber__class_Onumber__of(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X127)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__eq) ).
fof(fact_append__eq__conv__conj,axiom,
! [X302,X293,X292,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X292),X293) = X302
<=> ( X292 = hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)),X302)
& X293 = hAPP(hAPP(c_List_Odrop(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)),X302) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__conv__conj) ).
fof(fact_zdiv__zminus2__eq__if,axiom,
! [X71,X84] :
( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2__eq__if) ).
fof(fact_singleton__conv,axiom,
! [X25,X7] : hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv) ).
fof(fact_insert__is__Un,axiom,
! [X149,X25,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X25),X149) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__is__Un) ).
fof(fact_evalc__elim__cases_I2_J,axiom,
! [X46,X45,X25,X39] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X39,X25)),X45),X46))
=> X46 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X45),X39),hAPP(X25,X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I2_J) ).
fof(fact_less__imp__diff__less,axiom,
! [X33,X96,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),X96))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X113),X33)),X96)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_add__diff__assoc2,axiom,
! [X114,X113,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X113))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X113),X96)),X114) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X114)),X96) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc2,axiom,
! [X114,X113,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X113))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X114)),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X113),X96)),X114) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_Int__absorb2,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb2) ).
fof(fact_Int__absorb1,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = X155 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).
fof(fact_Un__absorb1,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155) = X155 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).
fof(fact_subset__Un__eq,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155) = X155 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
fof(fact_Un__absorb2,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).
fof(fact_zdvd__zmod,axiom,
! [X33,X90,X205] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X205),X90))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X205),X33))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X205),c_Divides_Odiv__class_Omod(tc_Int_Oint,X90,X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zmod) ).
fof(fact_Collect__neg__eq,axiom,
! [X38,X7] : hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),X38)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_Sumr_Osimps,axiom,
! [X6,X2,X119,X7,X105] : hAPP(c_Sum__Type_OSumr(X105,X7,X119,X2),hAPP(c_Sum__Type_OInr(X105,X119),X6)) = hAPP(X2,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sumr_Osimps) ).
fof(fact_Suml_Osimps,axiom,
! [X6,X2,X119,X7,X105] : hAPP(c_Sum__Type_OSuml(X105,X7,X119,X2),hAPP(c_Sum__Type_OInl(X105,X119),X6)) = hAPP(X2,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suml_Osimps) ).
fof(fact_drop__all,axiom,
! [X33,X300,X87] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X33))
=> hAPP(hAPP(c_List_Odrop(X87),X33),X300) = c_List_Olist_ONil(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__all) ).
fof(fact_drop__eq__Nil,axiom,
! [X292,X44,X7] :
( hAPP(hAPP(c_List_Odrop(X7),X44),X292) = c_List_Olist_ONil(X7)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__eq__Nil) ).
fof(fact_insert__iff,axiom,
! [X149,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(hAPP(c_Set_Oinsert(X7),X24),X149)))
<=> ( X25 = X24
| hBOOL(hAPP(hAPP(c_member(X7),X25),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
fof(fact_insertE,axiom,
! [X149,X24,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(hAPP(c_Set_Oinsert(X7),X24),X149)))
=> ( X25 != X24
=> hBOOL(hAPP(hAPP(c_member(X7),X25),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
fof(fact_take__all,axiom,
! [X33,X300,X87] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X33))
=> hAPP(hAPP(c_List_Otake(X87),X33),X300) = X300 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__all) ).
fof(fact_ivl__diff,axiom,
! [X95,X44,X107,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X107),X44))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X107),X95)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X107),X44)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X44),X95) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__diff) ).
fof(fact_accp_Oequations,axiom,
! [X25,X172,X7] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X172),X25))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X172,X3),X25))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X172),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).
fof(fact_accp_Osimps,axiom,
! [X25,X172,X7] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X172),X25))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X172,X3),X25))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X172),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).
fof(fact_Times__empty,axiom,
! [X155,X149,X105,X7] :
( hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X155)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X105),tc_HOL_Obool))
<=> ( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
| X155 = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__empty) ).
fof(fact_ivl__disj__un_I12_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X160)),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X160)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X157) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I12_J) ).
fof(fact_ivl__disj__un_I11_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X160)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X160)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X157) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I11_J) ).
fof(fact_ivl__disj__un_I13_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X160)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X160)) = hAPP(c_SetInterval_Oord__class_OatLeast(X7),X157) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I13_J) ).
fof(fact_Sup__set__fold,axiom,
! [X292,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OSup__class_OSup(X7,hAPP(c_List_Oset(X7),X292)) = hAPP(c_List_Ofoldl(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7),c_Orderings_Obot__class_Obot(X7)),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__set__fold) ).
fof(fact_Inf__set__fold,axiom,
! [X292,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OInf__class_OInf(X7,hAPP(c_List_Oset(X7),X292)) = hAPP(c_List_Ofoldl(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7),c_Orderings_Otop__class_Otop(X7)),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__set__fold) ).
fof(fact_card__atLeastAtMost__int,axiom,
! [X160,X157] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X157,X160)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X160),X157)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastAtMost__int) ).
fof(fact_finite__imageI,axiom,
! [X200,X105,X215,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X215))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(c_Set_Oimage(X7,X105,X200),X215))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(fact_dvd_OatMost__iff,axiom,
! [X94,X107] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X107),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X107),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatMost__iff) ).
fof(fact_dvd_OatLeast__iff,axiom,
! [X94,X107] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X107),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),X107)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeast__iff) ).
fof(fact_Sup__binary,axiom,
! [X24,X25,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OSup__class_OSup(X7,hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X25),X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__binary) ).
fof(fact_Inf__binary,axiom,
! [X24,X25,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OInf__class_OInf(X7,hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X25),X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__binary) ).
fof(fact_div__mult__swap,axiom,
! [X71,X84,X10,X87] :
( class_Divides_Osemiring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X10),X84))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X84),X10)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__swap) ).
fof(fact_ord_OatMost__iff,axiom,
! [X94,X218,X107,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X107),c_SetInterval_Oord_OatMost(X7,X218,X94)))
<=> hBOOL(hAPP(hAPP(X218,X107),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
fof(fact_ord_OlessThan__iff,axiom,
! [X94,X219,X107,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X107),c_SetInterval_Oord_OlessThan(X7,X219,X94)))
<=> hBOOL(hAPP(hAPP(X219,X107),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
fof(fact_ord_OatLeast__iff,axiom,
! [X94,X218,X107,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X107),c_SetInterval_Oord_OatLeast(X7,X218,X94)))
<=> hBOOL(hAPP(hAPP(X218,X94),X107)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
fof(fact_ord_OgreaterThan__iff,axiom,
! [X94,X219,X107,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X107),c_SetInterval_Oord_OgreaterThan(X7,X219,X94)))
<=> hBOOL(hAPP(hAPP(X219,X94),X107)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
fof(fact_partition__set,axiom,
! [X332,X333,X292,X38,X7] :
( c_List_Opartition(X7,X38,X292) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X333),X332)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X333)),hAPP(c_List_Oset(X7),X332)) = hAPP(c_List_Oset(X7),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__set) ).
fof(fact_nth__Cons__number__of,axiom,
! [X300,X86,X87,X139] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = X86 )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(hAPP(c_List_Onth(X87),X300),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__number__of) ).
fof(fact_r__comp__rtrancl__eq,axiom,
! [X172,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X172),c_Transitive__Closure_Ortrancl(X7,X172)) = hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),c_Transitive__Closure_Ortrancl(X7,X172)),X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__comp__rtrancl__eq) ).
fof(help_c__COMBS__1,axiom,
! [X191,X194,X38,X7,X119,X105] : hAPP(hAPP(hAPP(c_COMBS(X105,X119,X7),X38),X194),X191) = hAPP(hAPP(X38,X191),hAPP(X194,X191)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_abs__minus__le__zero,axiom,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71))),c_Groups_Ozero__class_Ozero(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).
fof(fact_Un__insert__right,axiom,
! [X155,X25,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__right) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [X127,X6,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X127),X127)) = c_Groups_Ozero__class_Ozero(X7)
<=> ( X6 = c_Groups_Ozero__class_Ozero(X7)
& X127 = c_Groups_Ozero__class_Ozero(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_map__add__find__right,axiom,
! [X95,X105,X282,X7,X94,X44] :
( hAPP(X44,X94) = hAPP(c_Option_Ooption_OSome(X7),X282)
=> hAPP(c_Map_Omap__add(X105,X7,X95,X44),X94) = hAPP(c_Option_Ooption_OSome(X7),X282) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__find__right) ).
fof(fact_union__fold__insert,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155) = hAPP(hAPP(c_Finite__Set_Ofold(X7,tc_fun(X7,tc_HOL_Obool),c_Set_Oinsert(X7)),X155),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__fold__insert) ).
fof(fact_eq__special_I3_J,axiom,
! [X6,X7] :
( class_Int_Onumber__ring(X7)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X7),X6) = c_Groups_Ozero__class_Ozero(X7)
<=> c_Int_Oiszero(X7,hAPP(c_Int_Onumber__class_Onumber__of(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I3_J) ).
fof(fact_eq__special_I1_J,axiom,
! [X127,X7] :
( class_Int_Onumber__ring(X7)
=> ( c_Groups_Ozero__class_Ozero(X7) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X127)
<=> c_Int_Oiszero(X7,hAPP(c_Int_Onumber__class_Onumber__of(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X127)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I1_J) ).
fof(fact_wf__lex__prod,axiom,
! [X265,X105,X266,X7] :
( c_Wellfounded_Owf(X7,X266)
=> ( c_Wellfounded_Owf(X105,X265)
=> c_Wellfounded_Owf(tc_prod(X7,X105),c_Wellfounded_Olex__prod(X7,X105,X266,X265)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex__prod) ).
fof(fact_distinct__zipI1,axiom,
! [X301,X7,X300,X87] :
( hBOOL(hAPP(c_List_Odistinct(X87),X300))
=> hBOOL(hAPP(c_List_Odistinct(tc_prod(X87,X7)),hAPP(hAPP(c_List_Ozip(X87,X7),X300),X301))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__zipI1) ).
fof(fact_distinct__zipI2,axiom,
! [X300,X7,X301,X87] :
( hBOOL(hAPP(c_List_Odistinct(X87),X301))
=> hBOOL(hAPP(c_List_Odistinct(tc_prod(X7,X87)),hAPP(hAPP(c_List_Ozip(X7,X87),X300),X301))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__zipI2) ).
fof(fact_vimage__Union,axiom,
! [X149,X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X105,tc_HOL_Obool),X149)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X149),c_Set_Ovimage(X7,X105,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Union) ).
fof(fact_image__Union,axiom,
! [X209,X2,X7,X105] : hAPP(c_Set_Oimage(X105,X7,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X105,tc_HOL_Obool),X209)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X105,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X209),c_Set_Oimage(X105,X7,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Union) ).
fof(fact_Pow__bottom,axiom,
! [X155,X7] : hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),hAPP(c_Set_OPow(X7),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__bottom) ).
fof(fact_listsum__0,axiom,
! [X292,X105,X7] :
( class_Groups_Omonoid__add(X7)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X105,X7),hAPP(c_COMBK(X7,X105),c_Groups_Ozero__class_Ozero(X7))),X292)) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__0) ).
fof(fact_Int__left__absorb,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
fof(fact_Un__left__absorb,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
fof(fact_Un__Diff__cancel,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X155),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).
fof(fact_rotate1__length01,axiom,
! [X300,X87] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
=> hAPP(c_List_Orotate1(X87),X300) = X300 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__length01) ).
fof(fact_fold__image__empty,axiom,
! [X26,X1,X2,X105,X7] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X105,X2),X1),X26),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__empty) ).
fof(fact_dvd__diff__nat,axiom,
! [X33,X90,X96] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X96),X90))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X96),X33))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
fof(fact_mult__eq__if,axiom,
! [X33,X90] :
( ( X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X90 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X6)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X127)))
<=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X127),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X6)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__iff__zmod__eq__0__number__of) ).
fof(fact_triple_Osimps_I2_J,axiom,
! [X228,X66,X229,X22,X7,X105] : c_Hoare__Mirabelle_Otriple_Otriple__case(X105,X7,X22,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X105),X229),X66),X228)) = hAPP(hAPP(hAPP(X22,X229),X66),X228),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osimps_I2_J) ).
fof(fact_triple_Orecs,axiom,
! [X228,X66,X229,X22,X7,X105] : c_Hoare__Mirabelle_Otriple_Otriple__rec(X105,X7,X22,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X105),X229),X66),X228)) = hAPP(hAPP(hAPP(X22,X229),X66),X228),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Orecs) ).
fof(fact_RangeP_Oequations,axiom,
! [X43,X172,X105,X7] :
( hBOOL(hAPP(c_Predicate_ORangeP(X7,X105,X172),X43))
<=> ? [X110] : hBOOL(hAPP(hAPP(X172,X110),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
fof(fact_nat__mult__distrib__neg,axiom,
! [X140,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X97),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),X140)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X97))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X140))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib__neg) ).
fof(fact_pair__box_Osize_I2_J,axiom,
! [X84,X71,X7,X87] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X87,X7)),c_Nitpick_Opair__box_OPairBox(X87,X7,X71,X84)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osize_I2_J) ).
fof(fact_butlast__list__update,axiom,
! [X86,X300,X87,X96] :
( ( X96 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Obutlast(X87,hAPP(hAPP(c_List_Olist__update(X87,X300),X96),X86)) = c_List_Obutlast(X87,X300) )
& ( X96 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Obutlast(X87,hAPP(hAPP(c_List_Olist__update(X87,X300),X96),X86)) = hAPP(hAPP(c_List_Olist__update(X87,c_List_Obutlast(X87,X300)),X96),X86) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__list__update) ).
fof(fact_image__insert,axiom,
! [X155,X25,X2,X7,X105] : hAPP(c_Set_Oimage(X105,X7,X2),hAPP(hAPP(c_Set_Oinsert(X105),X25),X155)) = hAPP(hAPP(c_Set_Oinsert(X7),hAPP(X2,X25)),hAPP(c_Set_Oimage(X105,X7,X2),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).
fof(fact_finite__subset,axiom,
! [X155,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(fact_rev__finite__subset,axiom,
! [X149,X155,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X155))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_neg__le__0__iff__le,axiom,
! [X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)),c_Groups_Ozero__class_Ozero(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_neg__less__0__iff__less,axiom,
! [X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)),c_Groups_Ozero__class_Ozero(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_zip__rev,axiom,
! [X301,X7,X300,X87] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X301)
=> hAPP(hAPP(c_List_Ozip(X87,X7),hAPP(c_List_Orev(X87),X300)),hAPP(c_List_Orev(X7),X301)) = hAPP(c_List_Orev(tc_prod(X87,X7)),hAPP(hAPP(c_List_Ozip(X87,X7),X300),X301)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__rev) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [X44,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X6),X44)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6))
| X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_Int__atLeastAtMostL2,axiom,
! [X23,X24,X25,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24)),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X23)) = c_SetInterval_Oord__class_OatLeastAtMost(X7,hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X25),X23),X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL2) ).
fof(fact_Int__atLeastAtMostL1,axiom,
! [X136,X24,X25,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24)),hAPP(c_SetInterval_Oord__class_OatMost(X7),X136)) = c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X24),X136)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL1) ).
fof(fact_list__update__code_I2_J,axiom,
! [X98,X300,X86,X87] : hAPP(hAPP(c_List_Olist__update(X87,hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98) = hAPP(hAPP(c_List_Olist_OCons(X87),X98),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I2_J) ).
fof(help_c__COMBC__1,axiom,
! [X191,X194,X38,X7,X119,X105] : hAPP(hAPP(hAPP(c_COMBC(X105,X119,X7),X38),X194),X191) = hAPP(hAPP(X38,X191),X194),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__COMBB__1,axiom,
! [X191,X194,X38,X119,X7,X105] : hAPP(hAPP(hAPP(c_COMBB(X105,X7,X119),X38),X194),X191) = hAPP(X38,hAPP(X194,X191)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_option_Osimps_I5_J,axiom,
! [X25,X21,X22,X105,X7] : hAPP(c_Option_Ooption_Ooption__case(X7,X105,X22,X21),hAPP(c_Option_Ooption_OSome(X105),X25)) = hAPP(X21,X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I5_J) ).
fof(fact_vimage__Compl,axiom,
! [X149,X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X105,tc_HOL_Obool)),X149)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7,X105,X2),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Compl) ).
fof(fact_mod__mult__self3,axiom,
! [X90,X33,X96] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X33)),X90),X33) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X86)),hAPP(c_Int_Onat,X98)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X86)),hAPP(c_Int_Onat,X98)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X86)),hAPP(c_Int_Onat,X98)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).
fof(fact_nat__add__distrib,axiom,
! [X140,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X140))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),X140)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X97)),hAPP(c_Int_Onat,X140)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__distrib) ).
fof(fact_length__zip,axiom,
! [X301,X300,X7,X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X87,X7))),hAPP(hAPP(c_List_Ozip(X87,X7),X300),X301)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X301)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__zip) ).
fof(fact_Union__image__eq,axiom,
! [X149,X155,X105,X7] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_Oimage(X105,tc_fun(X7,tc_HOL_Obool),X155),X149)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__image__eq) ).
fof(fact_Inter__image__eq,axiom,
! [X149,X155,X105,X7] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_Oimage(X105,tc_fun(X7,tc_HOL_Obool),X155),X149)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__image__eq) ).
fof(fact_INTER__eq__Inter__image,axiom,
! [X155,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_Oimage(X105,tc_fun(X7,tc_HOL_Obool),X155),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__eq__Inter__image) ).
fof(fact_UNION__eq__Union__image,axiom,
! [X155,X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_Oimage(X105,tc_fun(X7,tc_HOL_Obool),X155),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__eq__Union__image) ).
fof(fact_of__nat__aux_Osimps_I2_J,axiom,
! [X107,X44,X108,X7] :
( class_Rings_Osemiring__1(X7)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X7,X108,hAPP(c_Nat_OSuc,X44),X107) = c_Nat_Osemiring__1__class_Oof__nat__aux(X7,X108,X44,hAPP(X108,X107)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X86),hAPP(c_Int_Onat,X98)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X86,X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I2_J) ).
fof(fact_nat__mod__distrib,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
=> hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X86,X98)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X86),hAPP(c_Int_Onat,X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mod__distrib) ).
fof(fact_zmod__zdiv__equality_H,axiom,
! [X33,X90] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X90,X33) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X90),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X90),X33)),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).
fof(fact_Divides_Omod__div__equality_H,axiom,
! [X33,X90] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33)),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Omod__div__equality_H) ).
fof(fact_one__le__power,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Oone__class_Oone(X87)),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Oone__class_Oone(X87)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(fact_zero__le__power,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(fact_zero__less__power,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(fact_image__constant,axiom,
! [X23,X105,X149,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Set_Oimage(X7,X105,hAPP(c_COMBK(X105,X7),X23)),X149) = hAPP(hAPP(c_Set_Oinsert(X105),X23),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant) ).
fof(fact_zless__nat__conj,axiom,
! [X26,X125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X125)),hAPP(c_Int_Onat,X26)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__nat__conj) ).
fof(fact_UNIV__Times__UNIV,axiom,
! [X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Times__UNIV) ).
fof(fact_zless__add1__eq,axiom,
! [X26,X125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X26))
| X125 = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_minus__le__self__iff,axiom,
! [X25,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)),X25))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__less__nonneg,axiom,
! [X25,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)),X25))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_funpow__mult,axiom,
! [X2,X95,X44,X7] : hAPP(hAPP(c_Nat_Ocompow(X7,X7),X44),hAPP(hAPP(c_Nat_Ocompow(X7,X7),X95),X2)) = hAPP(hAPP(c_Nat_Ocompow(X7,X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X44)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__mult) ).
fof(fact_transfer__int__nat__relations_I4_J,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X127)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I4_J) ).
fof(fact_zdvd__int,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X127))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__int) ).
fof(fact_less__eq__number__of__int__code,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X94)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X157)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).
fof(fact_transfer__int__nat__relations_I3_J,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I3_J) ).
fof(fact_zle__int,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__int) ).
fof(fact_less__number__of__int__code,axiom,
! [X157,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X94)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X157)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).
fof(fact_transfer__int__nat__relations_I2_J,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I2_J) ).
fof(fact_zless__int,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__int) ).
fof(fact_zero__less__diff,axiom,
! [X95,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),X95)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_zle__add1__eq__le,axiom,
! [X26,X125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X125),X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_zle__diff1__eq,axiom,
! [X26,X125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X125),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_minus__number__of__mult,axiom,
! [X97,X128,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128))),X97) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128))),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X90,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X90)),X90) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),c_Groups_Oone__class_Oone(X87))),X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_list__update__same__conv,axiom,
! [X6,X292,X7,X107] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
=> ( hAPP(hAPP(c_List_Olist__update(X7,X292),X107),X6) = X292
<=> hAPP(hAPP(c_List_Onth(X7),X292),X107) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__same__conv) ).
fof(fact_evaln__elim__cases_I2_J,axiom,
! [X46,X44,X45,X25,X39] :
( c_Natural_Oevaln(c_Com_Ocom_OAss(X39,X25),X45,X44,X46)
=> X46 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X45),X39),hAPP(X25,X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I2_J) ).
fof(fact_negative__zle,axiom,
! [X90,X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zle) ).
fof(fact_zero__le__zpower__abs,axiom,
! [X33,X86] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X86)),X33))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).
fof(fact_min__diff,axiom,
! [X33,X114,X90] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X114)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),X114)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X90),X33)),X114),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__diff) ).
fof(fact_zdiff__zmult__distrib,axiom,
! [X128,X130,X131] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X131),X130)),X128) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X131),X128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X130),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(fact_zadd__zmult__distrib,axiom,
! [X128,X130,X131] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X131),X130)),X128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X131),X128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X130),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_diff__mult__distrib,axiom,
! [X96,X33,X90] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),X96) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X96)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [X96,X33,X90] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33)),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X96)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_nth_Osimps,axiom,
! [X44,X292,X6,X7] : hAPP(hAPP(c_List_Onth(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)),X44) = c_Nat_Onat_Onat__case(X7,X6,hAPP(c_List_Onth(X7),X292),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth_Osimps) ).
fof(fact_Plus__eq__empty__conv,axiom,
! [X155,X149,X105,X7] :
( c_Sum__Type_OPlus(X7,X105,X149,X155) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X7,X105),tc_HOL_Obool))
<=> ( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
& X155 = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).
fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
! [X23,X24,X25] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
<=> ( X25 = X24
& X24 = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton__iff) ).
fof(fact_Union__insert,axiom,
! [X155,X25,X7] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),X25),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X25),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__insert) ).
fof(fact_Inter__insert,axiom,
! [X155,X25,X7] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),X25),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X25),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__insert) ).
fof(fact_zmod__eq__dvd__iff,axiom,
! [X127,X44,X6] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X6,X44) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X127,X44)
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X44),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6),X127))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__dvd__iff) ).
fof(fact_wf__no__loop,axiom,
! [X191,X7] :
( hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),X191),X191) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))
=> c_Wellfounded_Owf(X7,X191) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__no__loop) ).
fof(fact_add__eq__if,axiom,
! [X33,X90] :
( ( X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33) = X33 )
& ( X90 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).
fof(fact_map__upd__nonempty,axiom,
! [X6,X94,X46,X105,X7] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X46),X94),hAPP(c_Option_Ooption_OSome(X105),X6)) != hAPP(c_COMBK(tc_Option_Ooption(X105),X7),c_Option_Ooption_ONone(X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__nonempty) ).
fof(fact_setsum__constant,axiom,
! [X149,X127,X105,X7] :
( class_Rings_Osemiring__1(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(c_COMBK(X7,X105),X127)),X149) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),hAPP(c_Finite__Set_Ocard(X105),X149))),X127) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__constant) ).
fof(fact_of__int__le__0__iff,axiom,
! [X26,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Oring__1__class_Oof__int(X7),X26)),c_Groups_Ozero__class_Ozero(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__le__0__iff) ).
fof(fact_of__int__less__0__iff,axiom,
! [X26,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Oring__1__class_Oof__int(X7),X26)),c_Groups_Ozero__class_Ozero(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__less__0__iff) ).
fof(fact_zmod__simps_I2_J,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),c_Divides_Odiv__class_Omod(X87,X84,X10)),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).
fof(fact_mod__diff__right__eq,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Oring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),c_Divides_Odiv__class_Omod(X87,X84,X10)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).
fof(fact_mod__mult__right__eq,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),c_Divides_Odiv__class_Omod(X87,X84,X10)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).
fof(fact_mod__add__right__eq,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84),X10) = c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),c_Divides_Odiv__class_Omod(X87,X84,X10)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).
fof(fact_predicate1D,axiom,
! [X6,X194,X38,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X38),X194))
=> ( hBOOL(hAPP(X38,X6))
=> hBOOL(hAPP(X194,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X194,X7,X6,X38] :
( hBOOL(hAPP(X38,X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X38),X194))
=> hBOOL(hAPP(X194,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_nat__diff__distrib,axiom,
! [X97,X140] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X140))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X140),X97))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X97),X140)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X97)),hAPP(c_Int_Onat,X140)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__distrib) ).
fof(fact_ivl__disj__un_I14_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X160)),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X160)) = hAPP(c_SetInterval_Oord__class_OatLeast(X7),X157) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I14_J) ).
fof(fact_le__special_I3_J,axiom,
! [X6,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Rings_Olinordered__idom(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X6)),c_Groups_Ozero__class_Ozero(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Int_OPls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I3_J) ).
fof(fact_less__special_I3_J,axiom,
! [X6,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Rings_Olinordered__idom(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X6)),c_Groups_Ozero__class_Ozero(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),c_Int_OPls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I3_J) ).
fof(fact_domIff,axiom,
! [X95,X105,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Map_Odom(X7,X105,X95)))
<=> hAPP(X95,X25) != c_Option_Ooption_ONone(X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_domIff) ).
fof(fact_map__fst__zip,axiom,
! [X293,X105,X292,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)
=> hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X7),c_Product__Type_Ofst(X7,X105)),hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293)) = X292 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__fst__zip) ).
fof(fact_map__snd__zip,axiom,
! [X293,X105,X292,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)
=> hAPP(hAPP(c_List_Omap(tc_prod(X7,X105),X105),c_Product__Type_Osnd(X7,X105)),hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293)) = X293 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__snd__zip) ).
fof(fact_div__add__self1,axiom,
! [X71,X84,X87] :
( class_Divides_Osemiring__div(X87)
=> ( X84 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X71)),X84) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84)),c_Groups_Oone__class_Oone(X87)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self1) ).
fof(fact_div__add__self2,axiom,
! [X71,X84,X87] :
( class_Divides_Osemiring__div(X87)
=> ( X84 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),X84) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84)),c_Groups_Oone__class_Oone(X87)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self2) ).
fof(fact_mod__mult__mult2,axiom,
! [X84,X10,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),c_Divides_Odiv__class_Omod(X87,X71,X84)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).
fof(fact_nat__abs__mult__distrib,axiom,
! [X97,X128] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X97))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X128))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__abs__mult__distrib) ).
fof(fact_nat__mult__div__cancel1,axiom,
! [X33,X90,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X96))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X33)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).
fof(fact_zdiv__zmult2__eq,axiom,
! [X84,X71,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X10)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
fof(fact_dom__map__of__conv__image__fst,axiom,
! [X288,X105,X7] : c_Map_Odom(X7,X105,c_Map_Omap__of(X7,X105,X288)) = hAPP(c_Set_Oimage(tc_prod(X7,X105),X7,c_Product__Type_Ofst(X7,X105)),hAPP(c_List_Oset(tc_prod(X7,X105)),X288)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__map__of__conv__image__fst) ).
fof(fact_split__def,axiom,
! [X161,X23,X7,X119,X105] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,X7),X23),X161) = hAPP(hAPP(X23,hAPP(c_Product__Type_Ofst(X105,X119),X161)),hAPP(c_Product__Type_Osnd(X105,X119),X161)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__def) ).
fof(fact_split__beta,axiom,
! [X26,X38,X7,X119,X105] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,X7),X38),X26) = hAPP(hAPP(X38,hAPP(c_Product__Type_Ofst(X105,X119),X26)),hAPP(c_Product__Type_Osnd(X105,X119),X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__beta) ).
fof(fact_prod__case__beta,axiom,
! [X161,X2,X7,X119,X105] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,X7),X2),X161) = hAPP(hAPP(X2,hAPP(c_Product__Type_Ofst(X105,X119),X161)),hAPP(c_Product__Type_Osnd(X105,X119),X161)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__case__beta) ).
fof(fact_append1__eq__conv,axiom,
! [X127,X293,X6,X292,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X292),hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7))) = hAPP(hAPP(c_List_Oappend(X7),X293),hAPP(hAPP(c_List_Olist_OCons(X7),X127),c_List_Olist_ONil(X7)))
<=> ( X292 = X293
& X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append1__eq__conv) ).
fof(fact_dvd__reduce,axiom,
! [X44,X94] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X94)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__reduce) ).
fof(fact_hd__drop__conv__nth,axiom,
! [X33,X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(c_List_Ohd(X87),hAPP(hAPP(c_List_Odrop(X87),X33),X300)) = hAPP(hAPP(c_List_Onth(X87),X300),X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__drop__conv__nth) ).
fof(fact_abs__add__abs,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__abs) ).
fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
! [X25,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one__idem(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,X2),X25),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
fof(fact_inf__le1,axiom,
! [X98,X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le1) ).
fof(fact_inf__sup__ord_I1_J,axiom,
! [X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
fof(fact_inf__le2,axiom,
! [X98,X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le2) ).
fof(fact_inf__sup__ord_I2_J,axiom,
! [X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
fof(fact_min__max_Oinf__le1,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98)),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le1) ).
fof(fact_min__max_Oinf__le2,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98)),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le2) ).
fof(fact_expand__Suc,axiom,
! [X139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expand__Suc) ).
fof(fact_evalc__evaln,axiom,
! [X35,X9,X10] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X10),X9),X35))
=> ? [X70] : c_Natural_Oevaln(X10,X9,X70,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__evaln) ).
fof(fact_eval__eq,axiom,
! [X46,X45,X23] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X45),X46))
<=> ? [X70] : c_Natural_Oevaln(X23,X45,X70,X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eval__eq) ).
fof(fact_ivl__disj__un_I7_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X7),X157)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X160)) = hAPP(c_SetInterval_Oord__class_OlessThan(X7),X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I7_J) ).
fof(fact_ivl__disj__un_I9_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X7),X157)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X160)) = hAPP(c_SetInterval_Oord__class_OatMost(X7),X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I9_J) ).
fof(fact_ivl__disj__un_I10_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X157)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X160)) = hAPP(c_SetInterval_Oord__class_OatMost(X7),X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I10_J) ).
fof(fact_minus__dvd__iff,axiom,
! [X127,X6,X7] :
( class_Rings_Ocomm__ring__1(X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X6)),X127))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
fof(fact_abs__dvd__iff,axiom,
! [X94,X95,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),hAPP(c_Groups_Oabs__class_Oabs(X7),X95)),X94))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X95),X94)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__dvd__iff) ).
fof(fact_abs__le__D1,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D1) ).
fof(fact_inf__sup__distrib1,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Odistrib__lattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),X97)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib1) ).
fof(fact_sup__inf__distrib1,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Odistrib__lattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),X97)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib1) ).
fof(fact_min__max_Osup__inf__distrib1,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X98),X97)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib1) ).
fof(fact_min__max_Oinf__sup__distrib1,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X98),X97)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__distrib1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X97,X98,X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X98),X97)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X133,X135,X134,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),X135)),X133) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),X133)),X135) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_UNIV__option__conv,axiom,
! [X7] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X7),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X7)),c_Option_Ooption_ONone(X7)),hAPP(c_Set_Oimage(X7,tc_Option_Ooption(X7),c_Option_Ooption_OSome(X7)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__option__conv) ).
fof(fact_id__o,axiom,
! [X1,X7,X105] : hAPP(c_Fun_Ocomp(X105,X105,X7,c_Fun_Oid(X105)),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__o) ).
fof(fact_length__pos__if__in__set,axiom,
! [X292,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__pos__if__in__set) ).
fof(fact_single__valued__rel__pow,axiom,
! [X44,X191,X7] :
( c_Relation_Osingle__valued(X7,X7,X191)
=> c_Relation_Osingle__valued(X7,X7,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__rel__pow) ).
fof(fact_Random__Sequence_Osingle__def,axiom,
! [X198,X199,X6,X7] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X7),X6),X199),X198) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X7),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Random__Sequence_Osingle__def) ).
fof(fact_DomainP_Oequations,axiom,
! [X42,X172,X105,X7] :
( hBOOL(hAPP(c_Predicate_ODomainP(X7,X105,X172),X42))
<=> ? [X142] : hBOOL(hAPP(hAPP(X172,X42),X142)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
fof(fact_inj__eq,axiom,
! [X127,X6,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> ( hAPP(X2,X6) = hAPP(X2,X127)
<=> X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
fof(fact_injD,axiom,
! [X127,X6,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> ( hAPP(X2,X6) = hAPP(X2,X127)
=> X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).
fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
! [X25,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omin(X7)),X25),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).
fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
! [X25,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omax(X7)),X25),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).
fof(fact_foldl__Nil,axiom,
! [X25,X2,X105,X7] : hAPP(c_List_Ofoldl(X7,X105,X2,X25),c_List_Olist_ONil(X105)) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__Nil) ).
fof(fact_list_Osimps_I4_J,axiom,
! [X21,X22,X105,X7] : hAPP(c_List_Olist_Olist__case(X7,X105,X22,X21),c_List_Olist_ONil(X105)) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
fof(fact_o__id,axiom,
! [X2,X105,X7] : hAPP(c_Fun_Ocomp(X7,X105,X7,X2),c_Fun_Oid(X7)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__id) ).
fof(fact_option_Osimps_I4_J,axiom,
! [X21,X22,X105,X7] : hAPP(c_Option_Ooption_Ooption__case(X7,X105,X22,X21),c_Option_Ooption_ONone(X105)) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I4_J) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X127,X6,X7] :
( class_Groups_Oordered__comm__monoid__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X127))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X6),X127) = c_Groups_Ozero__class_Ozero(X7)
<=> ( X6 = c_Groups_Ozero__class_Ozero(X7)
& X127 = c_Groups_Ozero__class_Ozero(X7) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_diff__add__assoc,axiom,
! [X114,X113,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X113))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X113)),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X113),X96)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_diff__diff__right,axiom,
! [X114,X113,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X113))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X114),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X113),X96)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X96)),X113) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).
fof(fact_add__diff__assoc,axiom,
! [X114,X113,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X113))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X113),X96)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X113)),X96) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_compl__mono,axiom,
! [X98,X86,X87] :
( class_Lattices_Oboolean__algebra(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X98)),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__mono) ).
fof(fact_le__imp__neg__le,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__ab__group__add(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_one__less__nat__eq,axiom,
! [X26] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__nat__eq) ).
fof(fact_mod__less__eq__dividend,axiom,
! [X33,X90] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)),X90)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
fof(fact_greaterThan__Suc,axiom,
! [X94] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X94)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__Suc) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X144,X162,X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X162)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X144)) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X162),X144)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [X33,X90,X71,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X90)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__add) ).
fof(fact_fold1__eq__fold__idem,axiom,
! [X25,X149,X7] :
( class_Lattices_Oab__semigroup__idem__mult(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Groups_Otimes__class_Otimes(X7)),X25),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__eq__fold__idem) ).
fof(fact_add__scale__eq__noteq,axiom,
! [X106,X10,X84,X71,X138,X87] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X87)
=> ( X138 != c_Groups_Ozero__class_Ozero(X87)
=> ( ( X71 = X84
& X10 != X106 )
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X138),X10)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X138),X106)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_some__eq__trivial,axiom,
! [X6,X7] : c_Hilbert__Choice_OEps(X7,hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X6)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__trivial) ).
fof(fact_the__eq__trivial,axiom,
! [X25,X7] : c_HOL_OThe(X7,hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25)) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__eq__trivial) ).
fof(fact_diff__less__Suc,axiom,
! [X33,X90] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),hAPP(c_Nat_OSuc,X90))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_less__add__Suc1,axiom,
! [X90,X114] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X90)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X90,X114] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X114)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_ivl__disj__int_I13_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X95)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X95,X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I13_J) ).
fof(fact_ivl__disj__int_I10_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X95)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X95,X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I10_J) ).
fof(fact_ivl__disj__int_I14_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X95)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X95,X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I14_J) ).
fof(fact_ivl__disj__int_I12_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X95)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X95,X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I12_J) ).
fof(fact_ivl__disj__int_I16_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X95)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X95,X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I16_J) ).
fof(fact_empty__subsetI,axiom,
! [X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
fof(fact_equiv__comp__eq,axiom,
! [X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),hAPP(c_Relation_Oconverse(X7,X7),X172)),X172) = X172 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__comp__eq) ).
fof(fact_evaln__evalc,axiom,
! [X35,X33,X9,X10] :
( c_Natural_Oevaln(X10,X9,X33,X35)
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(X10),X9),X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__evalc) ).
fof(fact_evaln_Oequations_I2_J,axiom,
! [X47,X41,X43,X42] : c_Natural_Oevaln(c_Com_Ocom_OAss(X42,X43),X41,X47,hAPP(hAPP(hAPP(c_Natural_Oupdate,X41),X42),hAPP(X43,X41))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I2_J) ).
fof(fact_evaln_OAssign,axiom,
! [X44,X45,X25,X39] : c_Natural_Oevaln(c_Com_Ocom_OAss(X39,X25),X45,X44,hAPP(hAPP(hAPP(c_Natural_Oupdate,X45),X39),hAPP(X25,X45))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OAssign) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X86,X98))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_subset__insertI,axiom,
! [X25,X155,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(fact_zdiff__zmod__right,axiom,
! [X90,X98,X86] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X86),c_Divides_Odiv__class_Omod(tc_Int_Oint,X98,X90)),X90) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X86),X98),X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).
fof(fact_zmod__simps_I3_J,axiom,
! [X10,X84,X71] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X10)),X10) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X84),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
fof(fact_zmod__zmult1__eq,axiom,
! [X10,X84,X71] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X84),X10) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X10)),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
fof(fact_ivl__disj__un_I8_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X157)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X160)) = hAPP(c_SetInterval_Oord__class_OlessThan(X7),X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I8_J) ).
fof(fact_atLeastAtMostSuc__conv,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X44)))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(c_Nat_OSuc,X44)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMostSuc__conv) ).
fof(fact_finite__option__UNIV,axiom,
! [X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X7)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X7),tc_HOL_Obool))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_less__imp__of__nat__less,axiom,
! [X33,X90,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X90)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).
fof(fact_Int__atLeastAtMostR2,axiom,
! [X136,X23,X25,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X25)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X23,X136)) = c_SetInterval_Oord__class_OatLeastAtMost(X7,hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X25),X23),X136) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR2) ).
fof(fact_Int__atLeastAtMostR1,axiom,
! [X136,X23,X24,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X7),X24)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X23,X136)) = c_SetInterval_Oord__class_OatLeastAtMost(X7,X23,hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X24),X136)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR1) ).
fof(fact_zless__nat__eq__int__zless,axiom,
! [X26,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Int_Onat,X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95)),X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__nat__eq__int__zless) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X86)),hAPP(c_Int_Onat,X98)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X86,X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).
fof(fact_drop__take,axiom,
! [X300,X90,X33,X87] : hAPP(hAPP(c_List_Odrop(X87),X33),hAPP(hAPP(c_List_Otake(X87),X90),X300)) = hAPP(hAPP(c_List_Otake(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),hAPP(hAPP(c_List_Odrop(X87),X33),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__take) ).
fof(fact_rel__comp__empty2,axiom,
! [X191,X105,X119,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),X191),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X119,X105),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__empty2) ).
fof(fact_curry__split,axiom,
! [X2,X119,X105,X7] : c_Product__Type_Ocurry(X7,X105,X119,hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,X119),X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__split) ).
fof(fact_mod__pos__pos__1__number__of,axiom,
! [X128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__1__number__of) ).
fof(fact_mod__mult__distrib,axiom,
! [X96,X33,X90] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)),X96) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X96),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).
fof(fact_dvd__power,axiom,
! [X86,X33,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
| X86 = c_Groups_Oone__class_Oone(X87) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X86),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power) ).
fof(fact_dvd__mult2,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X84))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult2) ).
fof(fact_dvd__mult,axiom,
! [X84,X10,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult) ).
fof(fact_le__supI1,axiom,
! [X84,X71,X86,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI1) ).
fof(fact_le__supI2,axiom,
! [X71,X84,X86,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI2) ).
fof(fact_min__max_Ole__supI1,axiom,
! [X84,X71,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI1) ).
fof(fact_min__max_Ole__supI2,axiom,
! [X71,X84,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI2) ).
fof(fact_less__supI1,axiom,
! [X84,X71,X86,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__supI1) ).
fof(fact_less__supI2,axiom,
! [X71,X84,X86,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__supI2) ).
fof(fact_min__max_Oless__supI1,axiom,
! [X84,X71,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__supI1) ).
fof(fact_min__max_Oless__supI2,axiom,
! [X71,X84,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__supI2) ).
fof(fact_negative__zle__0,axiom,
! [X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zle__0) ).
fof(fact_transpose__empty,axiom,
! [X292,X7] :
( c_List_Otranspose(X7,X292) = c_List_Olist_ONil(tc_List_Olist(X7))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),X3),hAPP(c_List_Oset(tc_List_Olist(X7)),X292)))
=> X3 = c_List_Olist_ONil(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__empty) ).
fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
! [X94,X2,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X94)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).
fof(fact_UN__empty2,axiom,
! [X149,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X105,tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X105),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__empty2) ).
fof(fact_less__trans__Suc,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),X96))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X114)),X96)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_div__pos__pos__1__number__of,axiom,
! [X128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__1__number__of) ).
fof(fact_pos__mod__sign,axiom,
! [X71,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__sign) ).
fof(fact_greaterThanLessThan__upto,axiom,
! [X158,X107] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X107,X158) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X158),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__upto) ).
fof(fact_map_Osimps_I2_J,axiom,
! [X292,X6,X2,X7,X105] : hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(hAPP(c_List_Olist_OCons(X105),X6),X292)) = hAPP(hAPP(c_List_Olist_OCons(X7),hAPP(X2,X6)),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I2_J) ).
fof(fact_power__one__over,axiom,
! [X33,X71,X87] :
( class_Fields_Ofield__inverse__zero(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),c_Groups_Oone__class_Oone(X87)),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),c_Groups_Oone__class_Oone(X87)),X71)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__over) ).
fof(fact_le__imp__0__less,axiom,
! [X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_insertI2,axiom,
! [X24,X155,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X155))
=> hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(hAPP(c_Set_Oinsert(X7),X24),X155))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
fof(fact_le__minus__iff,axiom,
! [X24,X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X24)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__iff) ).
fof(fact_less__minus__iff,axiom,
! [X24,X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X24)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).
fof(fact_last__list__update,axiom,
! [X86,X96,X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> ( ( X96 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Olast(X87,hAPP(hAPP(c_List_Olist__update(X87,X300),X96),X86)) = X86 )
& ( X96 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Olast(X87,hAPP(hAPP(c_List_Olist__update(X87,X300),X96),X86)) = c_List_Olast(X87,X300) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__list__update) ).
fof(fact_sgn__less,axiom,
! [X25,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Osgn__class_Osgn(X7,X25)),c_Groups_Ozero__class_Ozero(X7)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__less) ).
fof(fact_take__butlast,axiom,
! [X300,X87,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Otake(X87),X33),c_List_Obutlast(X87,X300)) = hAPP(hAPP(c_List_Otake(X87),X33),X300) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__butlast) ).
fof(fact_last__drop,axiom,
! [X300,X87,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> c_List_Olast(X87,hAPP(hAPP(c_List_Odrop(X87),X33),X300)) = c_List_Olast(X87,X300) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__drop) ).
fof(fact_prod_Osimps_I2_J,axiom,
! [X24,X25,X22,X7,X119,X105] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,X7),X22),hAPP(hAPP(c_Product__Type_OPair(X105,X119),X25),X24)) = hAPP(hAPP(X22,X25),X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).
fof(fact_split__conv,axiom,
! [X24,X25,X2,X7,X119,X105] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,X7),X2),hAPP(hAPP(c_Product__Type_OPair(X105,X119),X25),X24)) = hAPP(hAPP(X2,X25),X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__conv) ).
fof(fact_min__max_OSup__fin_Oin__idem,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)) = c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).
fof(fact_min__max_OInf__fin_Oin__idem,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)) = c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).
fof(fact_atLeastLessThan__eq__iff,axiom,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),X136))
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X25),X24) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X23),X136)
<=> ( X25 = X23
& X24 = X136 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
fof(fact_atLeastLessThan__inj_I1_J,axiom,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Olinorder(X7)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X25),X24) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X23),X136)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),X136))
=> X25 = X23 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
fof(fact_atLeastLessThan__inj_I2_J,axiom,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Olinorder(X7)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X25),X24) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X23),X136)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),X136))
=> X24 = X136 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
fof(fact_posDivAlg__correct,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),c_Divides_OposDivAlg(X71,X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__correct) ).
fof(fact_nth__list__update__neq,axiom,
! [X86,X300,X87,X113,X114] :
( X114 != X113
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X86)),X113) = hAPP(hAPP(c_List_Onth(X87),X300),X113) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update__neq) ).
fof(fact_ivl__disj__int_I9_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X95)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X95),X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I9_J) ).
fof(fact_converse__inv__image,axiom,
! [X2,X191,X105,X7] : hAPP(c_Relation_Oconverse(X7,X7),hAPP(hAPP(c_Relation_Oinv__image(X105,X7),X191),X2)) = hAPP(hAPP(c_Relation_Oinv__image(X105,X7),hAPP(c_Relation_Oconverse(X105,X105),X191)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__inv__image) ).
fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
! [X25,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),X25),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).
fof(fact_Min_Oeq__fold__idem_H,axiom,
! [X25,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omin(X7)),X25),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).
fof(fact_Max_Oeq__fold__idem_H,axiom,
! [X25,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omax(X7)),X25),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).
fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
! [X25,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7)),X25),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).
fof(fact_log_Osimps,axiom,
! [X114,X84] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X84),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X114),X84)) )
=> c_Random_Olog(X84,X114) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
& ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X84),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X114),X84)) )
=> c_Random_Olog(X84,X114) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X84,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X114),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_log_Osimps) ).
fof(fact_Ints__minus,axiom,
! [X25,X7] :
( class_Rings_Oring__1(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Int_Oring__1__class_OInts(X7)))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)),c_Int_Oring__1__class_OInts(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__minus) ).
fof(fact_bot__empty__eq,axiom,
! [X6,X7] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X6))
<=> hBOOL(hAPP(hAPP(c_member(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
fof(fact_abs__div__pos,axiom,
! [X86,X98,X87] :
( class_Fields_Olinordered__field__inverse__zero(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X98))
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X86)),X98) = hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__div__pos) ).
fof(fact_abs__mult__pos,axiom,
! [X98,X86,X87] :
( class_Rings_Olinordered__idom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X98)),X86) = hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X98),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
fof(fact_Pow__empty,axiom,
! [X7] : hAPP(c_Set_OPow(X7),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__empty) ).
fof(fact_setsum__shift__lb__Suc0__0,axiom,
! [X94,X2] :
( hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).
fof(fact_inf__fun__def,axiom,
! [X6,X1,X2,X105,X7] :
( class_Lattices_Olattice(X7)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,X7)),X2),X1),X6) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),hAPP(X2,X6)),hAPP(X1,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__fun__def) ).
fof(fact_inf__apply,axiom,
! [X6,X1,X2,X105,X7] :
( class_Lattices_Olattice(X7)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X105,X7)),X2),X1),X6) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),hAPP(X2,X6)),hAPP(X1,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__apply) ).
fof(fact_sup__fun__def,axiom,
! [X6,X1,X2,X105,X7] :
( class_Lattices_Olattice(X7)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,X7)),X2),X1),X6) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),hAPP(X2,X6)),hAPP(X1,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__fun__def) ).
fof(fact_sup__apply,axiom,
! [X6,X1,X2,X105,X7] :
( class_Lattices_Olattice(X7)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X105,X7)),X2),X1),X6) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),hAPP(X2,X6)),hAPP(X1,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__apply) ).
fof(fact_fun__diff__def,axiom,
! [X6,X155,X149,X105,X7] :
( class_Groups_Ominus(X7)
=> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,X7)),X149),X155),X6) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(X149,X6)),hAPP(X155,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__diff__def) ).
fof(fact_minus__apply,axiom,
! [X6,X155,X149,X105,X7] :
( class_Groups_Ominus(X7)
=> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X105,X7)),X149),X155),X6) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(X149,X6)),hAPP(X155,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__apply) ).
fof(fact_negDivAlg__correct,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),c_Divides_OnegDivAlg(X71,X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__correct) ).
fof(fact_neg__mod__bound,axiom,
! [X71,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
fof(fact_folding_Oempty,axiom,
! [X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> hAPP(X215,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Fun_Oid(X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oempty) ).
fof(fact_less__eq__code__numeral__def,axiom,
! [X95,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X44),X95))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X44)),hAPP(c_Code__Numeral_Onat__of,X95))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__code__numeral__def) ).
fof(fact_less__eq__code__numeral__code,axiom,
! [X95,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X44)),hAPP(c_Code__Numeral_Oof__nat,X95)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__code__numeral__code) ).
fof(fact_Suc__le__mono,axiom,
! [X95,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),hAPP(c_Nat_OSuc,X95)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_less__code__numeral__def,axiom,
! [X95,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X44),X95))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X44)),hAPP(c_Code__Numeral_Onat__of,X95))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__code__numeral__def) ).
fof(fact_less__code__numeral__code,axiom,
! [X95,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X44)),hAPP(c_Code__Numeral_Oof__nat,X95)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__code__numeral__code) ).
fof(fact_Suc__less__eq,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X95)),hAPP(c_Nat_OSuc,X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_Suc__less__SucD,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),hAPP(c_Nat_OSuc,X33)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_nth__take,axiom,
! [X300,X87,X33,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X33))
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Otake(X87),X33),X300)),X114) = hAPP(hAPP(c_List_Onth(X87),X300),X114) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__take) ).
fof(fact_Diff__disjoint,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X155),X149)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__disjoint) ).
fof(fact_rev__eq__Cons__iff,axiom,
! [X293,X127,X292,X7] :
( hAPP(c_List_Orev(X7),X292) = hAPP(hAPP(c_List_Olist_OCons(X7),X127),X293)
<=> X292 = hAPP(hAPP(c_List_Oappend(X7),hAPP(c_List_Orev(X7),X293)),hAPP(hAPP(c_List_Olist_OCons(X7),X127),c_List_Olist_ONil(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__eq__Cons__iff) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [X33,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X86),X33))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_diff__le__self,axiom,
! [X33,X90] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),X90)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(fact_div__le__dividend,axiom,
! [X33,X90] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33)),X90)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__dividend) ).
fof(fact_ivl__disj__un_I2_J,axiom,
! [X160,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X160)),hAPP(hAPP(c_Set_Oinsert(X7),X160),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X7),X160) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I2_J) ).
fof(fact_Min__le,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Big__Operators_Olinorder__class_OMin(X7,X149)),X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__le) ).
fof(fact_zpower__zadd__distrib,axiom,
! [X97,X98,X86] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X86),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X86),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_zdiff__zmult__distrib2,axiom,
! [X130,X131,X128] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X131),X130)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X131)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X130)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [X130,X131,X128] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X131),X130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X131)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X130)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_diff__mult__distrib2,axiom,
! [X33,X90,X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
fof(fact_add__mult__distrib2,axiom,
! [X33,X90,X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_diff__commute,axiom,
! [X96,X113,X114] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X114),X113)),X96) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X114),X96)),X113),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(fact_neg__0__le__iff__le,axiom,
! [X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_neg__0__less__iff__less,axiom,
! [X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_WT_Oequations_I8_J,axiom,
! [X41,X42,X43] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X43,X42,X41)))
<=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I8_J) ).
fof(fact_WTs__elim__cases_I8_J,axiom,
! [X25,X38,X39] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X39,X38,X25)))
=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I8_J) ).
fof(fact_dvd__trans,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X84),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__trans) ).
fof(fact_order__trans,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X97,X86,X98,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X97),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X97),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_order__less__le__trans,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__trans,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I7_J,axiom,
! [X97,X86,X98,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X97),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X97),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_xt1_I8_J,axiom,
! [X97,X86,X98,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X97),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X97),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I10_J,axiom,
! [X97,X86,X98,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X97),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X97),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_divmod__int__rel__0,axiom,
! [X84] :
( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__0) ).
fof(fact_mod__pos__pos,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X71,X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [X136,X23,X24,X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X25),X24) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X23),X136)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X23),X136)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_diff__eq__diff__less,axiom,
! [X136,X23,X24,X25,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X25),X24) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X23),X136)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),X136)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_eq__diff__iff,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X44))
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X94) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),X94)
<=> X95 = X44 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_uminus__dvd__conv_I1_J,axiom,
! [X46,X136] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),X46))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X136)),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
fof(fact_Sigma__empty2,axiom,
! [X149,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty2) ).
fof(fact_numeral__1__eq__Suc__0,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X71,X90,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X90),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X90)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),c_Groups_Oone__class_Oone(X87))),X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_div__pos__pos,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X71,X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos) ).
fof(fact_ivl__disj__int_I15_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X95)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X95,X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I15_J) ).
fof(fact_of__int__0__le__iff,axiom,
! [X26,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Oring__1__class_Oof__int(X7),X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__le__iff) ).
fof(fact_of__int__0__less__iff,axiom,
! [X26,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Oring__1__class_Oof__int(X7),X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__less__iff) ).
fof(fact_of__nat__0__less__iff,axiom,
! [X44,X7] :
( class_Rings_Olinordered__semidom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0__less__iff) ).
fof(fact_com_Osize_I5_J,axiom,
! [X54,X55,X13] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X13,X55,X54)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X55)),c_Com_Ocom_Ocom__size(X54))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I5_J) ).
fof(fact_abs__le__zero__iff,axiom,
! [X25,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Groups_Oabs__class_Oabs(X7),X25)),c_Groups_Ozero__class_Ozero(X7)))
<=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).
fof(fact_dvd__imp__le__int,axiom,
! [X106,X114] :
( X114 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X106),X114))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X106)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X114))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__le__int) ).
fof(fact_mod__neg__pos,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X71,X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__pos) ).
fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).
fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).
fof(fact_dvd__div__mult__self,axiom,
! [X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X84))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X84),X71)),X71) = X84 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__mult__self) ).
fof(fact_of__nat__diff,axiom,
! [X90,X33,X87] :
( class_Rings_Oring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X90)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__diff) ).
fof(fact_div__neg__pos,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X71,X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos) ).
fof(fact_finite__insert,axiom,
! [X149,X25,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).
fof(fact_inf__Inf__fold__inf,axiom,
! [X155,X149,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X155),c_Complete__Lattice_OInf__class_OInf(X7,X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),X155),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Inf__fold__inf) ).
fof(fact_sup__Sup__fold__sup,axiom,
! [X155,X149,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X155),c_Complete__Lattice_OSup__class_OSup(X7,X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7)),X155),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Sup__fold__sup) ).
fof(fact_nat__numeral__1__eq__1,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).
fof(fact_one__code__numeral__code,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__code__numeral__code) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__num__one) ).
fof(fact_Numeral1__eq1__nat,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).
fof(fact_Compl__disjoint2,axiom,
! [X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)),X149) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint2) ).
fof(fact_Compl__partition2,axiom,
! [X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)),X149) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition2) ).
fof(fact_UNIV__Plus__UNIV,axiom,
! [X105,X7] : c_Sum__Type_OPlus(X7,X105,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X7,X105),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_ivl__disj__int_I6_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X160)),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I6_J) ).
fof(fact_ivl__disj__int_I5_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X160)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I5_J) ).
fof(fact_ivl__disj__int_I7_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X160)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I7_J) ).
fof(fact_le__special_I1_J,axiom,
! [X127,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Rings_Olinordered__idom(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I1_J) ).
fof(fact_less__special_I1_J,axiom,
! [X127,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Rings_Olinordered__idom(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I1_J) ).
fof(fact_finite__Domain,axiom,
! [X172,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X105)),X172))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Relation_ODomain(X7,X105),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Domain) ).
fof(fact_finite__Range,axiom,
! [X172,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X105)),X172))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(c_Relation_ORange(X7,X105),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Range) ).
fof(fact_fold1Set__nonempty,axiom,
! [X6,X149,X2,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,X2,X149),X6))
=> X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__nonempty) ).
fof(fact_Nitpick_Oint__gcd__def,axiom,
! [X98,X86] : hAPP(hAPP(c_Nitpick_Oint__gcd,X86),X98) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X86)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X98)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oint__gcd__def) ).
fof(fact_drop__map,axiom,
! [X292,X2,X105,X44,X7] : hAPP(hAPP(c_List_Odrop(X7),X44),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)) = hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(hAPP(c_List_Odrop(X105),X44),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__map) ).
fof(fact_take__map,axiom,
! [X292,X2,X105,X44,X7] : hAPP(hAPP(c_List_Otake(X7),X44),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)) = hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(hAPP(c_List_Otake(X105),X44),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__map) ).
fof(fact_filter__append,axiom,
! [X293,X292,X38,X7] : hAPP(c_List_Ofilter(X7,X38),hAPP(hAPP(c_List_Oappend(X7),X292),X293)) = hAPP(hAPP(c_List_Oappend(X7),hAPP(c_List_Ofilter(X7,X38),X292)),hAPP(c_List_Ofilter(X7,X38),X293)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__append) ).
fof(fact_wf__acc__iff,axiom,
! [X172,X7] :
( c_Wellfounded_Owf(X7,X172)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(X7),X3),c_Wellfounded_Oacc(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
fof(fact_minus__Min__eq__Max,axiom,
! [X209,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( X209 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Groups_Ouminus__class_Ouminus(X7),c_Big__Operators_Olinorder__class_OMin(X7,X209)) = c_Big__Operators_Olinorder__class_OMax(X7,hAPP(c_Set_Oimage(X7,X7,c_Groups_Ouminus__class_Ouminus(X7)),X209)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Min__eq__Max) ).
fof(fact_minus__Max__eq__Min,axiom,
! [X209,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( X209 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Groups_Ouminus__class_Ouminus(X7),c_Big__Operators_Olinorder__class_OMax(X7,X209)) = c_Big__Operators_Olinorder__class_OMin(X7,hAPP(c_Set_Oimage(X7,X7,c_Groups_Ouminus__class_Ouminus(X7)),X209)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Max__eq__Min) ).
fof(fact_finite__UnionD,axiom,
! [X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X149)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X7,tc_HOL_Obool)),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnionD) ).
fof(fact_Suc__times__mod__eq,axiom,
! [X90,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X96))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X90)),X96) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__times__mod__eq) ).
fof(fact_sgn__greater,axiom,
! [X25,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),c_Groups_Osgn__class_Osgn(X7,X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__greater) ).
fof(fact_dvd__neg__div,axiom,
! [X86,X98,X87] :
( class_Divides_Oring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X98),X86))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86)),X98) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__neg__div) ).
fof(fact_mod__mult__mult1,axiom,
! [X84,X71,X10,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),c_Divides_Odiv__class_Omod(X87,X71,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).
fof(fact_INT__constant,axiom,
! [X23,X105,X7,X149] :
( ( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X23)) = c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)) )
& ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X23)) = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__constant) ).
fof(fact_UN__constant,axiom,
! [X23,X105,X7,X149] :
( ( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X23)) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) )
& ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X105,tc_HOL_Obool)),X149),hAPP(c_COMBK(tc_fun(X105,tc_HOL_Obool),X7),X23)) = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__constant) ).
fof(fact_Random__Sequence_Oempty__def,axiom,
! [X198,X199,X7] : c_Random__Sequence_Oempty(X7,X199,X198) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Random__Sequence_Oempty__def) ).
fof(fact_div__mult__mult1__if,axiom,
! [X84,X71,X10,X87] :
( class_Divides_Osemiring__div(X87)
=> ( ( X10 = c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84)) = c_Groups_Ozero__class_Ozero(X87) )
& ( X10 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).
fof(fact_mult__divide__mult__cancel__left,axiom,
! [X84,X71,X10,X87] :
( class_Fields_Ofield__inverse__zero(X87)
=> ( X10 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(fact_mult__divide__mult__cancel__right,axiom,
! [X84,X71,X10,X87] :
( class_Fields_Ofield__inverse__zero(X87)
=> ( X10 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
fof(fact_div__mult__mult1,axiom,
! [X84,X71,X10,X87] :
( class_Divides_Osemiring__div(X87)
=> ( X10 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1) ).
fof(fact_div__mult__mult2,axiom,
! [X84,X71,X10,X87] :
( class_Divides_Osemiring__div(X87)
=> ( X10 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult2) ).
fof(fact_nat__rec__Suc,axiom,
! [X103,X21,X22,X7] : hAPP(c_Nat_Onat_Onat__rec(X7,X22,X21),hAPP(c_Nat_OSuc,X103)) = hAPP(hAPP(X21,X103),hAPP(c_Nat_Onat_Onat__rec(X7,X22,X21),X103)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).
fof(fact_trans__le__add1,axiom,
! [X90,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X90))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X97,X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add2,axiom,
! [X90,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X113))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X98,X97,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X97,X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add1,axiom,
! [X90,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X90))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X98,X97,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__less__add2,axiom,
! [X90,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X113))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_mod__mult__self2,axiom,
! [X10,X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10)),X84) = c_Divides_Odiv__class_Omod(X87,X71,X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2) ).
fof(fact_mod__mult__self1,axiom,
! [X84,X10,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X10),X84)),X84) = c_Divides_Odiv__class_Omod(X87,X71,X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X44)))
<=> ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X117] :
( X95 = hAPP(c_Nat_OSuc,X117)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X117),X44)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_rotate1__hd__tl,axiom,
! [X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> hAPP(c_List_Orotate1(X87),X300) = hAPP(hAPP(c_List_Oappend(X87),hAPP(c_List_Otl(X87),X300)),hAPP(hAPP(c_List_Olist_OCons(X87),hAPP(c_List_Ohd(X87),X300)),c_List_Olist_ONil(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__hd__tl) ).
fof(fact_fun__upd__def,axiom,
! [X24,X2,X105,X7,X25,X6] :
( ( X6 = X25
=> hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X25),X24),X6) = X24 )
& ( X6 != X25
=> hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X25),X24),X6) = hAPP(X2,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__def) ).
fof(fact_fun__upd__other,axiom,
! [X127,X2,X105,X7,X6,X26] :
( X26 != X6
=> hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X127),X26) = hAPP(X2,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__other) ).
fof(fact_fun__upd__apply,axiom,
! [X127,X2,X105,X7,X6,X26] :
( ( X26 = X6
=> hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X127),X26) = X127 )
& ( X26 != X6
=> hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X127),X26) = hAPP(X2,X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
fof(fact_setsum__set__upto__conv__listsum__int,axiom,
! [X158,X107,X2,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X7),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X107,X158))) = hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X7),X2),c_List_Oupto(X107,X158))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).
fof(fact_interv__listsum__conv__setsum__set__int,axiom,
! [X157,X94,X2,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X7),X2),c_List_Oupto(X94,X157))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X7),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X94,X157))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).
fof(fact_inf_Oassoc,axiom,
! [X10,X84,X71,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84)),X10) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
fof(fact_inf__assoc,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)),X97) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__assoc) ).
fof(fact_inf__sup__aci_I2_J,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)),X97) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
fof(fact_sup_Oassoc,axiom,
! [X10,X84,X71,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84)),X10) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oassoc) ).
fof(fact_sup__assoc,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98)),X97) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__assoc) ).
fof(fact_inf__sup__aci_I6_J,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98)),X97) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).
fof(fact_min__max_Osup__assoc,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98)),X97) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X98),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__assoc) ).
fof(fact_min__max_Osup_Oassoc,axiom,
! [X10,X84,X71,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84)),X10) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oassoc) ).
fof(fact_min__max_Oinf__assoc,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98)),X97) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X98),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__assoc) ).
fof(fact_min__max_Oinf_Oassoc,axiom,
! [X10,X84,X71,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84)),X10) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oassoc) ).
fof(fact_power__commutes,axiom,
! [X33,X71,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),X71) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X10,X84,X71,X87] :
( class_Groups_Oab__semigroup__mult(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X133,X135,X134,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),X135)),X133) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X135),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X10,X84,X71,X87] :
( class_Groups_Oab__semigroup__add(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_times__divide__eq__right,axiom,
! [X10,X84,X71,X87] :
( class_Rings_Odivision__ring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X84),X10)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X132,X133,X134,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X133),X132)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),X133)),X132) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X106,X10,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X106)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)),X106) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_last__conv__nth,axiom,
! [X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> c_List_Olast(X87,X300) = hAPP(hAPP(c_List_Onth(X87),X300),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__conv__nth) ).
fof(fact_Nats__number__of,axiom,
! [X125,X7] :
( class_Int_Onumber__ring(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X125))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Nat_Osemiring__1__class_ONats(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__number__of) ).
fof(fact_card__Pow,axiom,
! [X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ocard(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_OPow(X7),X149)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X7),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Pow) ).
fof(fact_atLeast__Suc,axiom,
! [X94] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X94)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X94),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc) ).
fof(fact_Diff__Compl,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Compl) ).
fof(fact_Diff__eq,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__eq) ).
fof(fact_zero__less__two,axiom,
! [X87] :
( class_Rings_Olinordered__semidom(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Oone__class_Oone(X87)),c_Groups_Oone__class_Oone(X87)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_card__greaterThanLessThan__int,axiom,
! [X160,X157] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X157,X160)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X160),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X157),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanLessThan__int) ).
fof(fact_min__max_Osup__Inf__absorb,axiom,
! [X25,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X25),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)) = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).
fof(fact_min__max_Oinf__Sup__absorb,axiom,
! [X25,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X25),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)) = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).
fof(fact_le__minus__self__iff,axiom,
! [X25,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_less__minus__self__iff,axiom,
! [X25,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_Diff__triv,axiom,
! [X155,X149,X7] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__triv) ).
fof(fact_insort__not__Nil,axiom,
! [X292,X25,X2,X7,X105] :
( class_Orderings_Olinorder(X105)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X105,X2),X25),X292) != c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__not__Nil) ).
fof(fact_setprod__constant,axiom,
! [X127,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(c_COMBK(X105,X7),X127)),X149) = hAPP(hAPP(c_Power_Opower__class_Opower(X105),X127),hAPP(c_Finite__Set_Ocard(X7),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__constant) ).
fof(fact_fold1__insert__idem,axiom,
! [X6,X149,X7] :
( class_Lattices_Oab__semigroup__idem__mult(X7)
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__insert__idem) ).
fof(fact_ivl__disj__int_I11_J,axiom,
! [X160,X95,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X95)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X95),X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I11_J) ).
fof(fact_diff__Suc,axiom,
! [X44,X95] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X44)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X44)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc) ).
fof(fact_append__assoc,axiom,
! [X299,X301,X300,X87] : hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)),X299) = hAPP(hAPP(c_List_Oappend(X87),X300),hAPP(hAPP(c_List_Oappend(X87),X301),X299)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__assoc) ).
fof(fact_append__Cons,axiom,
! [X301,X300,X86,X87] : hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)),X301) = hAPP(hAPP(c_List_Olist_OCons(X87),X86),hAPP(hAPP(c_List_Oappend(X87),X300),X301)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Cons) ).
fof(fact_zdvd__imp__le,axiom,
! [X33,X97] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X97),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X97),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).
fof(fact_dvd__imp__le,axiom,
! [X33,X96] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X96),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
fof(fact_take__Suc,axiom,
! [X33,X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> hAPP(hAPP(c_List_Otake(X87),hAPP(c_Nat_OSuc,X33)),X300) = hAPP(hAPP(c_List_Olist_OCons(X87),hAPP(c_List_Ohd(X87),X300)),hAPP(hAPP(c_List_Otake(X87),X33),hAPP(c_List_Otl(X87),X300))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc) ).
fof(fact_image__atLeastZeroLessThan__int,axiom,
! [X160] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X160))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X160) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__atLeastZeroLessThan__int) ).
fof(fact_nth__Cons_H,axiom,
! [X300,X86,X87,X33] :
( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)),X33) = X86 )
& ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)),X33) = hAPP(hAPP(c_List_Onth(X87),X300),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons_H) ).
fof(fact_image__constant__conv,axiom,
! [X23,X105,X7,X149] :
( ( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(X7,X105,hAPP(c_COMBK(X105,X7),X23)),X149) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) )
& ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(X7,X105,hAPP(c_COMBK(X105,X7),X23)),X149) = hAPP(hAPP(c_Set_Oinsert(X105),X23),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant__conv) ).
fof(fact_WT_Oequations_I5_J,axiom,
! [X43,X42,X41] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X41,X42,X43)))
<=> ( hBOOL(hAPP(c_Com_OWT,X42))
& hBOOL(hAPP(c_Com_OWT,X43)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I5_J) ).
fof(fact_WT_Oequations_I3_J,axiom,
! [X42,X41,X43] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X43,X41,X42)))
<=> hBOOL(hAPP(c_Com_OWT,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I3_J) ).
fof(fact_WTs__elim__cases_I3_J,axiom,
! [X23,X25,X60] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X60,X25,X23)))
=> hBOOL(hAPP(c_Com_OWT,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I3_J) ).
fof(fact_listsum__distinct__conv__setsum__set,axiom,
! [X2,X292,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> hAPP(c_List_Omonoid__add__class_Olistsum(X105),hAPP(hAPP(c_List_Omap(X7,X105),X2),X292)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(c_List_Oset(X7),X292)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).
fof(fact_power__mult,axiom,
! [X33,X90,X71,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X90)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X144,X162,X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X162)),X144) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X162),X144)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_mod__minus__eq,axiom,
! [X84,X71,X87] :
( class_Divides_Oring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71),X84) = c_Divides_Odiv__class_Omod(X87,hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Divides_Odiv__class_Omod(X87,X71,X84)),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__eq) ).
fof(fact_tl__take,axiom,
! [X300,X33,X87] : hAPP(c_List_Otl(X87),hAPP(hAPP(c_List_Otake(X87),X33),X300)) = hAPP(hAPP(c_List_Otake(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X87),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__take) ).
fof(fact_abs__power__minus,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),X33)) = hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power__minus) ).
fof(fact_fun__upd__same,axiom,
! [X127,X6,X2,X7,X105] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,X7),X2),X6),X127),X6) = X127,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))
=> ( hAPP(c_Finite__Set_Ocard(X7),X149) = hAPP(c_Finite__Set_Ocard(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> X149 = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_drop__Cons_H,axiom,
! [X300,X86,X87,X33] :
( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(X87),X33),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300) )
& ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(X87),X33),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_List_Odrop(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X300) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons_H) ).
fof(fact_neg__zminus__int,axiom,
! [X33] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X33))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zminus__int) ).
fof(fact_insert__code,axiom,
! [X6,X149,X127,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X7),X127),X149),X6))
<=> ( X127 = X6
| hBOOL(hAPP(X149,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_dvd__minus__iff,axiom,
! [X127,X6,X7] :
( class_Rings_Ocomm__ring__1(X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X127)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X6),X127)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
fof(fact_dvd__abs__iff,axiom,
! [X94,X95,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X95),hAPP(c_Groups_Oabs__class_Oabs(X7),X94)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X95),X94)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__abs__iff) ).
fof(fact_atMost__iff,axiom,
! [X94,X107,X7] :
( class_Orderings_Oord(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X107),hAPP(c_SetInterval_Oord__class_OatMost(X7),X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X107),X94)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__iff) ).
fof(fact_atLeast__iff,axiom,
! [X94,X107,X7] :
( class_Orderings_Oord(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X107),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X94),X107)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__iff) ).
fof(fact_lessThan__iff,axiom,
! [X94,X107,X7] :
( class_Orderings_Oord(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X107),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X107),X94)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__iff) ).
fof(fact_greaterThan__iff,axiom,
! [X94,X107,X7] :
( class_Orderings_Oord(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X107),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X94)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X94),X107)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__iff) ).
fof(fact_image__uminus__greaterThanAtMost,axiom,
! [X127,X6,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> hAPP(c_Set_Oimage(X7,X7,c_Groups_Ouminus__class_Ouminus(X7)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X6,X127)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,hAPP(c_Groups_Ouminus__class_Ouminus(X7),X127)),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).
fof(fact_folding__one__idem_Oin__idem,axiom,
! [X6,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one__idem(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(X2,X6),hAPP(X215,X149)) = hAPP(X215,X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
fof(fact_Max__ge,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),c_Big__Operators_Olinorder__class_OMax(X7,X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__ge) ).
fof(fact_listsum__setsum__nth,axiom,
! [X292,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X7),X292) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(c_List_Onth(X7),X292)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__setsum__nth) ).
fof(fact_zdiff__int,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__int) ).
fof(fact_abs__div,axiom,
! [X86,X98] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X98),X86))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X86),X98)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X86)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__div) ).
fof(fact_odd__nonzero,axiom,
! [X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X97)),X97) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(fact_Field__def,axiom,
! [X172,X7] : hAPP(c_Relation_OField(X7),X172) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X7,X7),X172)),hAPP(c_Relation_ORange(X7,X7),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__def) ).
fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
! [X44,X95] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).
fof(fact_div__mult__self1__is__m,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X90)),X33) = X90 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).
fof(fact_div__mult__self__is__m,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33)),X33) = X90 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).
fof(fact_zmod__zminus2__eq__if,axiom,
! [X84,X71] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2__eq__if) ).
fof(fact_subset__UNIV,axiom,
! [X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_dvd_Oorder__trans,axiom,
! [X97,X98,X86] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X97))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X97)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
fof(fact_zle__trans,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X113),X96))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X114),X96)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(fact_le__trans,axiom,
! [X96,X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X113),X96))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X96)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_mod__mod__cancel,axiom,
! [X71,X84,X10,X87] :
( class_Divides_Osemiring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X10),X84))
=> c_Divides_Odiv__class_Omod(X87,c_Divides_Odiv__class_Omod(X87,X71,X84),X10) = c_Divides_Odiv__class_Omod(X87,X71,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mod__cancel) ).
fof(fact_evaln__elim__cases_I1_J,axiom,
! [X35,X33,X9] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,X9,X33,X35)
=> X35 = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X90,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X90),X90) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Oone__class_Oone(X87)),c_Groups_Oone__class_Oone(X87))),X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_less__add__eq__less,axiom,
! [X33,X90,X115,X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),X115))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X115) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X33)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_dvd__div__neg,axiom,
! [X86,X98,X87] :
( class_Divides_Oring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X98),X86))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X86),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X98)) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__neg) ).
fof(fact_Suc__leD,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_less__eq__Suc__le,axiom,
! [X95,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X95))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__le__eq,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X95)),X44))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_Suc__le__lessD,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_Suc__lessD,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_drop__drop,axiom,
! [X300,X90,X33,X87] : hAPP(hAPP(c_List_Odrop(X87),X33),hAPP(hAPP(c_List_Odrop(X87),X90),X300)) = hAPP(hAPP(c_List_Odrop(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X90)),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__drop) ).
fof(fact_take__take,axiom,
! [X300,X90,X33,X87] : hAPP(hAPP(c_List_Otake(X87),X33),hAPP(hAPP(c_List_Otake(X87),X90),X300)) = hAPP(hAPP(c_List_Otake(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X33),X90)),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__take) ).
fof(fact_Inf__lower,axiom,
! [X149,X6,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Complete__Lattice_OInf__class_OInf(X7,X149)),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__lower) ).
fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
! [X38] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
=> hBOOL(hAPP(X38,X3)) )
<=> ! [X3] : hBOOL(hAPP(X38,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).
fof(fact_nat__div__distrib,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X86),X98)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X86)),hAPP(c_Int_Onat,X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__div__distrib) ).
fof(fact_nat__mult__distrib,axiom,
! [X140,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),X140)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X97)),hAPP(c_Int_Onat,X140)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib) ).
fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
! [X44,X95] :
( c_Nat__Transfer_Ois__nat(X95)
=> ( c_Nat__Transfer_Ois__nat(X44)
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X95,X44) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,X95),hAPP(c_Int_Onat,X44))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__functions) ).
fof(fact_transpose_Opsimps_I1_J,axiom,
! [X7] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X7)),c_List_Otranspose__rel(X7)),c_List_Olist_ONil(tc_List_Olist(X7))))
=> c_List_Otranspose(X7,c_List_Olist_ONil(tc_List_Olist(X7))) = c_List_Olist_ONil(tc_List_Olist(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I1_J) ).
fof(fact_mod__mult__distrib2,axiom,
! [X33,X90,X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X90),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).
fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
! [X155,X149] :
( X149 = X155
<=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X149) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X155) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I3_J) ).
fof(fact_set__append,axiom,
! [X293,X292,X7] : hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Oappend(X7),X292),X293)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X292)),hAPP(c_List_Oset(X7),X293)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__append) ).
fof(fact_Suc__mono,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),hAPP(c_Nat_OSuc,X33))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_power__inject__exp,axiom,
! [X44,X95,X25,X7] :
( class_Rings_Olinordered__semidom(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Oone__class_Oone(X7)),X25))
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X7),X25),X95) = hAPP(hAPP(c_Power_Opower__class_Opower(X7),X25),X44)
<=> X95 = X44 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(fact_listset_Osimps_I2_J,axiom,
! [X310,X149,X7] : c_List_Olistset(X7,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X7,tc_HOL_Obool)),X149),X310)) = c_List_Oset__Cons(X7,X149,c_List_Olistset(X7,X310)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listset_Osimps_I2_J) ).
fof(fact_Sup__fold__sup,axiom,
! [X149,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Complete__Lattice_OSup__class_OSup(X7,X149) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7)),c_Orderings_Obot__class_Obot(X7)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fold__sup) ).
fof(fact_Inf__fold__inf,axiom,
! [X149,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Complete__Lattice_OInf__class_OInf(X7,X149) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),c_Orderings_Otop__class_Otop(X7)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fold__inf) ).
fof(fact_power__eq__if,axiom,
! [X162,X90] :
( ( X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X162),X90) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X90 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X162),X90) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X162),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X162),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(fact_image__uminus__greaterThanLessThan,axiom,
! [X127,X6,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> hAPP(c_Set_Oimage(X7,X7,c_Groups_Ouminus__class_Ouminus(X7)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X6,X127)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X7,hAPP(c_Groups_Ouminus__class_Ouminus(X7),X127),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).
fof(fact_image__uminus__atLeastAtMost,axiom,
! [X127,X6,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> hAPP(c_Set_Oimage(X7,X7,c_Groups_Ouminus__class_Ouminus(X7)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X6,X127)) = c_SetInterval_Oord__class_OatLeastAtMost(X7,hAPP(c_Groups_Ouminus__class_Ouminus(X7),X127),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeastAtMost) ).
fof(fact_lessThan__Suc__eq__insert__0,axiom,
! [X44] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X44))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).
fof(fact_div__mod__code__numeral__def,axiom,
! [X90,X33] : c_Code__Numeral_Odiv__mod__code__numeral(X33,X90) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X33),X90)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X33,X90)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__code__numeral__def) ).
fof(fact_divmod__int__mod__div,axiom,
! [X144,X162] : c_Divides_Odivmod__int(X162,X144) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X162),X144)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X162,X144)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__mod__div) ).
fof(fact_zminus__zmod,axiom,
! [X90,X86] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X86,X90)),X90) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X86),X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zmod) ).
fof(fact_transfer__nat__int__relations_I1_J,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X127))
=> ( hAPP(c_Int_Onat,X6) = hAPP(c_Int_Onat,X127)
<=> X6 = X127 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).
fof(fact_eq__nat__nat__iff,axiom,
! [X141,X26] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X141))
=> ( hAPP(c_Int_Onat,X26) = hAPP(c_Int_Onat,X141)
<=> X26 = X141 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__nat__iff) ).
fof(fact_zless__iff__Suc__zadd,axiom,
! [X26,X125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X26))
<=> ? [X70] : X26 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X125),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X70))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).
fof(fact_div__mod__equality_H,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33)),X33) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality_H) ).
fof(fact_le__add__diff__inverse2,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),X33) = X90 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_zero__less__int__conv,axiom,
! [X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__int__conv) ).
fof(fact_int__eq__iff__number__of,axiom,
! [X163,X95] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X163)
<=> ( X95 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X163))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X163))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__iff__number__of) ).
fof(fact_ranI,axiom,
! [X105,X24,X7,X25,X95] :
( hAPP(X95,X25) = hAPP(c_Option_Ooption_OSome(X7),X24)
=> hBOOL(hAPP(hAPP(c_member(X7),X24),c_Map_Oran(X105,X7,X95))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ranI) ).
fof(fact_domI,axiom,
! [X105,X24,X7,X25,X95] :
( hAPP(X95,X25) = hAPP(c_Option_Ooption_OSome(X7),X24)
=> hBOOL(hAPP(hAPP(c_member(X105),X25),c_Map_Odom(X105,X7,X95))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_domI) ).
fof(fact_finite__Pow__iff,axiom,
! [X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_OPow(X7),X149)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Pow__iff) ).
fof(fact_DomainP_Ointros,axiom,
! [X105,X7,X24,X25,X172] :
( hBOOL(hAPP(hAPP(X172,X25),X24))
=> hBOOL(hAPP(c_Predicate_ODomainP(X7,X105,X172),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_RangeP_Ointros,axiom,
! [X105,X7,X24,X25,X172] :
( hBOOL(hAPP(hAPP(X172,X25),X24))
=> hBOOL(hAPP(c_Predicate_ORangeP(X7,X105,X172),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_length__greater__0__conv,axiom,
! [X292,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)))
<=> X292 != c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__greater__0__conv) ).
fof(fact_ivl__disj__int_I8_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X160)),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I8_J) ).
fof(fact_le__less__Suc__eq,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X95)))
<=> X44 = X95 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_mod__pos__pos__trivial,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),X84))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).
fof(fact_atMost__Int__atLeast,axiom,
! [X44,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X7),X44)),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X44)) = hAPP(hAPP(c_Set_Oinsert(X7),X44),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__Int__atLeast) ).
fof(fact_length__append,axiom,
! [X301,X300,X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X301)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__append) ).
fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
! [X155,X149] :
( c_Nat__Transfer_Onat__set(X149)
=> ( c_Nat__Transfer_Onat__set(X155)
=> ( X149 = X155
<=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X149) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X155) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I3_J) ).
fof(fact_triple_Oinject,axiom,
! [X226,X68,X227,X228,X66,X229,X7] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X229),X66),X228) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X227),X68),X226)
<=> ( X229 = X227
& X66 = X68
& X228 = X226 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Oinject) ).
fof(fact_setprod__zero,axiom,
! [X2,X149,X7,X105] :
( class_Rings_Ocomm__semiring__1(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X105) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149) = c_Groups_Ozero__class_Ozero(X105) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__zero) ).
fof(fact_nat__mult__div__cancel__disj,axiom,
! [X33,X90,X96] :
( ( X96 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X33)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X96 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X33)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
fof(fact_Pow__top,axiom,
! [X149,X7] : hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Set_OPow(X7),X149))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__top) ).
fof(fact_rev_Osimps_I2_J,axiom,
! [X300,X86,X87] : hAPP(c_List_Orev(X87),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_List_Oappend(X87),hAPP(c_List_Orev(X87),X300)),hAPP(hAPP(c_List_Olist_OCons(X87),X86),c_List_Olist_ONil(X87))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I2_J) ).
fof(fact_div__pos__pos__trivial,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),X84))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).
fof(fact_zdiv__eq__0__iff,axiom,
! [X94,X107] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X107),X94) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( X94 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X107))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X107),X94)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X107),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X107)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(fact_Inf__le__Sup,axiom,
! [X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)),c_Big__Operators_Olattice__class_OSup__fin(X7,X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__le__Sup) ).
fof(fact_equivp__transp,axiom,
! [X26,X127,X6,X191,X7] :
( c_Equiv__Relations_Oequivp(X7,X191)
=> ( hBOOL(hAPP(hAPP(X191,X6),X127))
=> ( hBOOL(hAPP(hAPP(X191,X127),X26))
=> hBOOL(hAPP(hAPP(X191,X6),X26)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__transp) ).
fof(fact_folding__one__idem_Oinsert__idem,axiom,
! [X6,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one__idem(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(X2,X6),hAPP(X215,X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).
fof(fact_mod__minus__cong,axiom,
! [X88,X84,X71,X87] :
( class_Divides_Oring__div(X87)
=> ( c_Divides_Odiv__class_Omod(X87,X71,X84) = c_Divides_Odiv__class_Omod(X87,X88,X84)
=> c_Divides_Odiv__class_Omod(X87,hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71),X84) = c_Divides_Odiv__class_Omod(X87,hAPP(c_Groups_Ouminus__class_Ouminus(X87),X88),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__cong) ).
fof(fact_Union__def,axiom,
! [X209,X7] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X209) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X209),c_COMBI(tc_fun(X7,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__def) ).
fof(fact_Inter__def,axiom,
! [X209,X7] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),X209) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X209),c_COMBI(tc_fun(X7,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__def) ).
fof(fact_zabs__less__one__iff,axiom,
! [X26] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> X26 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
fof(fact_int__le__0__conv,axiom,
! [X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__le__0__conv) ).
fof(fact_empty__map__add,axiom,
! [X95,X105,X7] : c_Map_Omap__add(X7,X105,hAPP(c_COMBK(tc_Option_Ooption(X105),X7),c_Option_Ooption_ONone(X105)),X95) = X95,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__map__add) ).
fof(fact_map__add__empty,axiom,
! [X95,X105,X7] : c_Map_Omap__add(X7,X105,X95,hAPP(c_COMBK(tc_Option_Ooption(X105),X7),c_Option_Ooption_ONone(X105))) = X95,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__empty) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
! [X33,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X86))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X86)),X33) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X86),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).
fof(fact_nat__power__eq,axiom,
! [X33,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X97),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X97)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq) ).
fof(fact_diff__cancel,axiom,
! [X33,X90,X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [X33,X96,X90] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X96)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(fact_zpower__zpower,axiom,
! [X97,X98,X86] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X86),X98)),X97) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X86),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(fact_diff__diff__left,axiom,
! [X96,X113,X114] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X114),X113)),X96) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X114),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_zmult__assoc,axiom,
! [X129,X130,X131] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X131),X130)),X129) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X130),X129)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(fact_nat__mult__assoc,axiom,
! [X96,X33,X90] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33)),X96) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_zadd__assoc,axiom,
! [X129,X130,X131] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X131),X130)),X129) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X130),X129)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_nat__add__assoc,axiom,
! [X96,X33,X90] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33)),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_div__mult2__eq,axiom,
! [X10,X84,X71] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X10)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X71),X84)),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult2__eq) ).
fof(fact_ball__empty,axiom,
! [X38,X7,X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> hBOOL(hAPP(X38,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__empty) ).
fof(fact_ivl__disj__int_I1_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X7),X157)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X157,X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I1_J) ).
fof(fact_ivl__disj__int_I3_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X7),X157)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X157,X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I3_J) ).
fof(fact_ivl__disj__int_I4_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X157)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X157,X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I4_J) ).
fof(fact_mod__neg__neg__trivial,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X71))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).
fof(fact_set__map,axiom,
! [X292,X2,X105,X7] : hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)) = hAPP(c_Set_Oimage(X105,X7,X2),hAPP(c_List_Oset(X105),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__map) ).
fof(fact_append__take__drop__id,axiom,
! [X300,X33,X87] : hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Otake(X87),X33),X300)),hAPP(hAPP(c_List_Odrop(X87),X33),X300)) = X300,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__take__drop__id) ).
fof(fact_mod__Suc__eq__Suc__mod,axiom,
! [X33,X90] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X90),X33) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
fof(fact_com_Osize_I4_J,axiom,
! [X73,X74] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X74,X73)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X74)),c_Com_Ocom_Ocom__size(X73))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I4_J) ).
fof(fact_less__0__number__of,axiom,
! [X163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X163)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__0__number__of) ).
fof(fact_WT_OCall,axiom,
! [X25,X39,X40] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X40)))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X39,X40,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OCall) ).
fof(fact_div__neg__neg__trivial,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X71))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).
fof(fact_take__Suc__Cons,axiom,
! [X300,X86,X33,X87] : hAPP(hAPP(c_List_Otake(X87),hAPP(c_Nat_OSuc,X33)),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_List_Olist_OCons(X87),X86),hAPP(hAPP(c_List_Otake(X87),X33),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc__Cons) ).
fof(fact_map__eq__imp__length__eq,axiom,
! [X293,X1,X119,X292,X2,X7,X105] :
( hAPP(hAPP(c_List_Omap(X105,X7),X2),X292) = hAPP(hAPP(c_List_Omap(X119,X7),X1),X293)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X119)),X293) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__eq__imp__length__eq) ).
fof(fact_transfer__int__nat__set__return__embed,axiom,
! [X149] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X149)) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__return__embed) ).
fof(fact_fst__eqD,axiom,
! [X71,X98,X86,X7,X87] :
( hAPP(c_Product__Type_Ofst(X87,X7),hAPP(hAPP(c_Product__Type_OPair(X87,X7),X86),X98)) = X71
=> X86 = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__eqD) ).
fof(fact_snd__eqD,axiom,
! [X71,X98,X86,X87,X7] :
( hAPP(c_Product__Type_Osnd(X7,X87),hAPP(hAPP(c_Product__Type_OPair(X7,X87),X86),X98)) = X71
=> X98 = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__eqD) ).
fof(fact_transfer__nat__int__set__return__embed,axiom,
! [X149] :
( c_Nat__Transfer_Onat__set(X149)
=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X149)) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__return__embed) ).
fof(fact_finite__Field,axiom,
! [X172,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X7)),X172))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Relation_OField(X7),X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Field) ).
fof(fact_image__uminus__atLeastLessThan,axiom,
! [X127,X6,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> hAPP(c_Set_Oimage(X7,X7,c_Groups_Ouminus__class_Ouminus(X7)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X6),X127)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X7,hAPP(c_Groups_Ouminus__class_Ouminus(X7),X127),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeastLessThan) ).
fof(fact_Suc__lessI,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> ( hAPP(c_Nat_OSuc,X90) != X33
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X214] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X214))
<=> ? [X116] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X214))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X116)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X214] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X214))
<=> ? [X116] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X214))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X116)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(fact_diff__number__of__eq,axiom,
! [X128,X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__number__of__eq) ).
fof(fact_zero__less__nat__eq,axiom,
! [X26] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__nat__eq) ).
fof(fact_butlast__snoc,axiom,
! [X86,X300,X87] : c_List_Obutlast(X87,hAPP(hAPP(c_List_Oappend(X87),X300),hAPP(hAPP(c_List_Olist_OCons(X87),X86),c_List_Olist_ONil(X87)))) = X300,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__snoc) ).
fof(fact_last__snoc,axiom,
! [X86,X300,X87] : c_List_Olast(X87,hAPP(hAPP(c_List_Oappend(X87),X300),hAPP(hAPP(c_List_Olist_OCons(X87),X86),c_List_Olist_ONil(X87)))) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__snoc) ).
fof(fact_rtrancl__idemp__self__comp,axiom,
! [X191,X7] : hAPP(hAPP(c_Relation_Orel__comp(X7,X7,X7),c_Transitive__Closure_Ortrancl(X7,X191)),c_Transitive__Closure_Ortrancl(X7,X191)) = c_Transitive__Closure_Ortrancl(X7,X191),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp__self__comp) ).
fof(fact_fst__def,axiom,
! [X161,X105,X7] : hAPP(c_Product__Type_Ofst(X7,X105),X161) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,X7),c_COMBK(X7,X105)),X161),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__def) ).
fof(fact_finite__acyclic__wf__converse,axiom,
! [X172,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X7)),X172))
=> ( c_Wellfounded_Oacyclic(X7,X172)
=> c_Wellfounded_Owf(X7,hAPP(c_Relation_Oconverse(X7,X7),X172)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__acyclic__wf__converse) ).
fof(fact_order__eq__iff,axiom,
! [X127,X6,X7] :
( class_Orderings_Oorder(X7)
=> ( X6 = X127
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__antisym__conv,axiom,
! [X6,X127,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
<=> X6 = X127 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__antisym,axiom,
! [X98,X86,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> X86 = X98 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X86,X98,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> X86 = X98 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_le__mod__geq,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mod__geq) ).
fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
! [X24,X25] :
( X25 = X24
=> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X25),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton_H) ).
fof(fact_uminus__dvd__conv_I2_J,axiom,
! [X46,X136] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),X46))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X46))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
fof(fact_Suc__diff__le,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X33) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
fof(fact_abs__ge__minus__self,axiom,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X71))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).
fof(fact_zero__le__square,axiom,
! [X71,X87] :
( class_Rings_Olinordered__ring(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X71))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(fact_less__add__one,axiom,
! [X71,X87] :
( class_Rings_Olinordered__semidom(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),c_Groups_Oone__class_Oone(X87)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_zero__less__abs__iff,axiom,
! [X25,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Groups_Oabs__class_Oabs(X7),X25)))
<=> X25 != c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
fof(fact_accp__downward,axiom,
! [X25,X24,X172,X7] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X172),X24))
=> ( hBOOL(hAPP(hAPP(X172,X25),X24))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X172),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__downward) ).
fof(fact_hd__in__set,axiom,
! [X7,X292] :
( X292 != c_List_Olist_ONil(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_List_Ohd(X7),X292)),hAPP(c_List_Oset(X7),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__in__set) ).
fof(fact_dvd_OatLeastAtMost__singleton,axiom,
! [X25] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X25) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X25),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
! [X144,X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X144)),X86) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Nat_OSuc,X144)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(fact_power__Suc2,axiom,
! [X33,X71,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Nat_OSuc,X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc2) ).
fof(fact_com__det,axiom,
! [X63,X35,X9,X10] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X10),X9),X35))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X10),X9),X63))
=> X63 = X35 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com__det) ).
fof(fact_map__upd__triv,axiom,
! [X105,X6,X7,X94,X46] :
( hAPP(X46,X94) = hAPP(c_Option_Ooption_OSome(X7),X6)
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,tc_Option_Ooption(X7)),X46),X94),hAPP(c_Option_Ooption_OSome(X7),X6)) = X46 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__triv) ).
fof(fact_semigroup_Oassoc,axiom,
! [X23,X24,X25,X2,X7] :
( c_Groups_Osemigroup(X7,X2)
=> hAPP(hAPP(X2,hAPP(hAPP(X2,X25),X24)),X23) = hAPP(hAPP(X2,X25),hAPP(hAPP(X2,X24),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semigroup_Oassoc) ).
fof(fact_list_Osize_I4_J,axiom,
! [X305,X71,X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),hAPP(hAPP(c_List_Olist_OCons(X87),X71),X305)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X305)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I4_J) ).
fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
! [X38] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
& hBOOL(hAPP(X38,X3)) )
<=> ? [X3] : hBOOL(hAPP(X38,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).
fof(fact_Suc__leI,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_Inf__fin_Oin__idem,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X6),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)) = c_Big__Operators_Olattice__class_OInf__fin(X7,X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oin__idem) ).
fof(fact_Sup__fin_Oin__idem,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)) = c_Big__Operators_Olattice__class_OSup__fin(X7,X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oin__idem) ).
fof(fact_Max_Oin__idem,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olinorder__class_OMax(X7,X149)) = c_Big__Operators_Olinorder__class_OMax(X7,X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oin__idem) ).
fof(fact_Min_Oin__idem,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olinorder__class_OMin(X7,X149)) = c_Big__Operators_Olinorder__class_OMin(X7,X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oin__idem) ).
fof(fact_Sup__upper,axiom,
! [X149,X6,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),c_Complete__Lattice_OSup__class_OSup(X7,X149))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__upper) ).
fof(fact_ivl__disj__int_I2_J,axiom,
! [X160,X157,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X157)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X157),X160)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I2_J) ).
fof(fact_card__gt__0__iff,axiom,
! [X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X7),X149)))
<=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
fof(fact_nth__Cons__Suc,axiom,
! [X33,X300,X86,X87] : hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)),hAPP(c_Nat_OSuc,X33)) = hAPP(hAPP(c_List_Onth(X87),X300),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__Suc) ).
fof(fact_map__tl,axiom,
! [X292,X2,X7,X105] : hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(c_List_Otl(X105),X292)) = hAPP(c_List_Otl(X7),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__tl) ).
fof(fact_rev__map,axiom,
! [X292,X2,X105,X7] : hAPP(c_List_Orev(X7),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)) = hAPP(hAPP(c_List_Omap(X105,X7),X2),hAPP(c_List_Orev(X105),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__map) ).
fof(fact_zdvd__antisym__abs,axiom,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X84),X71))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X71) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__antisym__abs) ).
fof(fact_dvd__mult__div__cancel,axiom,
! [X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X84))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X84),X71)) = X84 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__div__cancel) ).
fof(fact_ex__nat,axiom,
! [X38] :
( ? [X142] : hBOOL(hAPP(X38,X142))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
& hBOOL(hAPP(X38,hAPP(c_Int_Onat,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat) ).
fof(fact_card__ge__0__finite,axiom,
! [X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X7),X149)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
fof(fact_Suc__pred,axiom,
! [X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X33 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).
fof(fact_singleton__inject,axiom,
! [X24,X25,X7] :
( hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))
=> X25 = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
fof(fact_of__nat__inverse,axiom,
! [X127] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X127),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X127)) = X127 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__inverse) ).
fof(fact_divide__eq__eq__number__of,axiom,
! [X125,X23,X24,X7] :
( ( class_Fields_Ofield__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)
<=> ( ( X23 != c_Groups_Ozero__class_Ozero(X7)
=> X24 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23) )
& ( X23 = c_Groups_Ozero__class_Ozero(X7)
=> hAPP(c_Int_Onumber__class_Onumber__of(X7),X125) = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).
fof(fact_eq__divide__eq__number__of,axiom,
! [X23,X24,X125,X7] :
( ( class_Fields_Ofield__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X7),X125) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)
<=> ( ( X23 != c_Groups_Ozero__class_Ozero(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23) = X24 )
& ( X23 = c_Groups_Ozero__class_Ozero(X7)
=> hAPP(c_Int_Onumber__class_Onumber__of(X7),X125) = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).
fof(fact_le__Suc__eq,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X44)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
| X95 = hAPP(c_Nat_OSuc,X44) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_append__butlast__last__id,axiom,
! [X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> hAPP(hAPP(c_List_Oappend(X87),c_List_Obutlast(X87,X300)),hAPP(hAPP(c_List_Olist_OCons(X87),c_List_Olast(X87,X300)),c_List_Olist_ONil(X87))) = X300 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).
fof(fact_WT_OIf,axiom,
! [X24,X57,X59] :
( hBOOL(hAPP(c_Com_OWT,X59))
=> ( hBOOL(hAPP(c_Com_OWT,X57))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X24,X59,X57))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OIf) ).
fof(fact_pair__collapse,axiom,
! [X162,X7,X87] : hAPP(hAPP(c_Product__Type_OPair(X87,X7),hAPP(c_Product__Type_Ofst(X87,X7),X162)),hAPP(c_Product__Type_Osnd(X87,X7),X162)) = X162,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__collapse) ).
fof(fact_surjective__pairing,axiom,
! [X7,X87,X35] : X35 = hAPP(hAPP(c_Product__Type_OPair(X87,X7),hAPP(c_Product__Type_Ofst(X87,X7),X35)),hAPP(c_Product__Type_Osnd(X87,X7),X35)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surjective__pairing) ).
fof(fact_insort__key_Osimps_I1_J,axiom,
! [X6,X2,X7,X105] :
( class_Orderings_Olinorder(X105)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X105,X2),X6),c_List_Olist_ONil(X7)) = hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key_Osimps_I1_J) ).
fof(fact_fun__upd__idem__iff,axiom,
! [X127,X6,X2,X105,X7] :
( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X127) = X2
<=> hAPP(X2,X6) = X127 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
fof(fact_distinct__sublistI,axiom,
! [X211,X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> hBOOL(hAPP(c_List_Odistinct(X7),c_List_Osublist(X7,X292,X211))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__sublistI) ).
fof(fact_distinct__remove1,axiom,
! [X86,X300,X87] :
( hBOOL(hAPP(c_List_Odistinct(X87),X300))
=> hBOOL(hAPP(c_List_Odistinct(X87),c_List_Oremove1(X87,X86,X300))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remove1) ).
fof(fact_remove1__commute,axiom,
! [X299,X98,X86,X87] : c_List_Oremove1(X87,X86,c_List_Oremove1(X87,X98,X299)) = c_List_Oremove1(X87,X98,c_List_Oremove1(X87,X86,X299)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__commute) ).
fof(fact_fun__left__comm_Ofun__left__comm,axiom,
! [X26,X127,X6,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> hAPP(hAPP(X2,X6),hAPP(hAPP(X2,X127),X26)) = hAPP(hAPP(X2,X127),hAPP(hAPP(X2,X6),X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
fof(fact_inf__Sup__absorb,axiom,
! [X25,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X25),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)) = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup__absorb) ).
fof(fact_sup__Inf__absorb,axiom,
! [X25,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X25),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)) = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf__absorb) ).
fof(fact_wfP__empty,axiom,
! [X7] : c_Wellfounded_OwfP(X7,hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X7),hAPP(c_COMBK(tc_HOL_Obool,X7),c_fFalse))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__empty) ).
fof(fact_dvd__triv__left,axiom,
! [X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
fof(fact_dvd__triv__right,axiom,
! [X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X71))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(fact_sup__ge1,axiom,
! [X98,X86,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge1) ).
fof(fact_inf__sup__ord_I3_J,axiom,
! [X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).
fof(fact_sup__ge2,axiom,
! [X86,X98,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge2) ).
fof(fact_inf__sup__ord_I4_J,axiom,
! [X86,X98,X87] :
( class_Lattices_Olattice(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).
fof(fact_le__maxI1,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__maxI1) ).
fof(fact_le__maxI2,axiom,
! [X86,X98,X87] :
( class_Orderings_Olinorder(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__maxI2) ).
fof(fact_mem__Collect__eq,axiom,
! [X38,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Set_OCollect(X7),X38)))
<=> hBOOL(hAPP(X38,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Collect__eq) ).
fof(fact_CollectD,axiom,
! [X38,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Set_OCollect(X7),X38)))
=> hBOOL(hAPP(X38,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectD) ).
fof(fact_CollectE,axiom,
! [X38,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Set_OCollect(X7),X38)))
=> hBOOL(hAPP(X38,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectE) ).
fof(fact_Suc__nat__eq__nat__zadd1,axiom,
! [X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X97)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).
fof(fact_remove1_Osimps_I2_J,axiom,
! [X300,X87,X98,X86] :
( ( X86 = X98
=> c_List_Oremove1(X87,X86,hAPP(hAPP(c_List_Olist_OCons(X87),X98),X300)) = X300 )
& ( X86 != X98
=> c_List_Oremove1(X87,X86,hAPP(hAPP(c_List_Olist_OCons(X87),X98),X300)) = hAPP(hAPP(c_List_Olist_OCons(X87),X98),c_List_Oremove1(X87,X86,X300)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I2_J) ).
fof(fact_dvd__div__eq__mult,axiom,
! [X23,X24,X25,X7] :
( class_Divides_Osemiring__div(X7)
=> ( X25 != c_Groups_Ozero__class_Ozero(X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X25),X24))
=> ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7),X24),X25) = X23
<=> X24 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X23),X25) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__eq__mult) ).
fof(fact_less__Suc__eq,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X44)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44))
| X95 = X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Image__Id__on,axiom,
! [X155,X149,X7] : hAPP(c_Relation_OImage(X7,X7,c_Relation_OId__on(X7,X149)),X155) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id__on) ).
fof(fact_inf_Oleft__commute,axiom,
! [X10,X71,X84,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X84),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X10)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
fof(fact_inf__left__commute,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),X97)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__commute) ).
fof(fact_inf__sup__aci_I3_J,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),X97)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
fof(fact_sup_Oleft__commute,axiom,
! [X10,X71,X84,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X84),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X10)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__commute) ).
fof(fact_sup__left__commute,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),X97)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__commute) ).
fof(fact_inf__sup__aci_I7_J,axiom,
! [X97,X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),X97)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).
fof(fact_min__max_Osup__left__commute,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X98),X97)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X98),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__left__commute) ).
fof(fact_min__max_Osup_Oleft__commute,axiom,
! [X10,X71,X84,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X84),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X10)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__commute) ).
fof(fact_min__max_Oinf__left__commute,axiom,
! [X97,X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X98),X97)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X98),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__left__commute) ).
fof(fact_min__max_Oinf_Oleft__commute,axiom,
! [X10,X71,X84,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X84),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X10)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X84),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__commute) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X132,X133,X134,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X133),X132)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X133),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X134),X132)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X106,X10,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X106)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X106)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_add__minus__cancel,axiom,
! [X84,X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),X84)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [X44,X95,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X95) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X44)
<=> X95 = X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_less__Suc__eq__le,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X44)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_one__div__nat__number__of,axiom,
! [X165] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__div__nat__number__of) ).
fof(fact_split__nat,axiom,
! [X107,X38] :
( hBOOL(hAPP(X38,hAPP(c_Int_Onat,X107)))
<=> ( ! [X70] :
( X107 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X70)
=> hBOOL(hAPP(X38,X70)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X107),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__nat) ).
fof(fact_distinct__drop,axiom,
! [X114,X300,X87] :
( hBOOL(hAPP(c_List_Odistinct(X87),X300))
=> hBOOL(hAPP(c_List_Odistinct(X87),hAPP(hAPP(c_List_Odrop(X87),X114),X300))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__drop) ).
fof(fact_distinct__take,axiom,
! [X114,X300,X87] :
( hBOOL(hAPP(c_List_Odistinct(X87),X300))
=> hBOOL(hAPP(c_List_Odistinct(X87),hAPP(hAPP(c_List_Otake(X87),X114),X300))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__take) ).
fof(fact_finite_OinsertI,axiom,
! [X25,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
fof(fact_image__Suc__atLeastAtMost,axiom,
! [X158,X107] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X107,X158)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X107),hAPP(c_Nat_OSuc,X158)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastAtMost) ).
fof(fact_INT__empty,axiom,
! [X155,X7,X105] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))),X155) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__empty) ).
fof(fact_minus__numeral__code_I6_J,axiom,
! [X128,X139] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__numeral__code_I6_J) ).
fof(fact_Compl__eq__Diff__UNIV,axiom,
! [X149,X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).
fof(fact_map__butlast,axiom,
! [X292,X2,X7,X105] : hAPP(hAPP(c_List_Omap(X105,X7),X2),c_List_Obutlast(X105,X292)) = c_List_Obutlast(X7,hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__butlast) ).
fof(fact_Min__in,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(X7),c_Big__Operators_Olinorder__class_OMin(X7,X149)),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__in) ).
fof(fact_Max__in,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(X7),c_Big__Operators_Olinorder__class_OMax(X7,X149)),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__in) ).
fof(fact_all__nat,axiom,
! [X38] :
( ! [X142] : hBOOL(hAPP(X38,X142))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
=> hBOOL(hAPP(X38,hAPP(c_Int_Onat,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat) ).
fof(fact_insertI1,axiom,
! [X155,X25,X7] : hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(fact_mod__Suc,axiom,
! [X33,X90] :
( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)) = X33
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X90),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)) != X33
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X90),X33) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc) ).
fof(fact_insert__commute,axiom,
! [X149,X127,X6,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X6),hAPP(hAPP(c_Set_Oinsert(X7),X127),X149)) = hAPP(hAPP(c_Set_Oinsert(X7),X127),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
fof(fact_folding__one_Osingleton,axiom,
! [X6,X215,X2,X7] :
( c_Finite__Set_Ofolding__one(X7,X2,X215)
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Osingleton) ).
fof(fact_diff__Suc__eq__diff__pred,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
fof(fact_less__imp__add__positive,axiom,
! [X113,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> ? [X118] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X118))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X118) = X113 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__add__positive) ).
fof(fact_fold__empty,axiom,
! [X26,X2,X7,X105] : hAPP(hAPP(c_Finite__Set_Ofold(X105,X7,X2),X26),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__empty) ).
fof(fact_length__drop,axiom,
! [X300,X33,X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),hAPP(hAPP(c_List_Odrop(X87),X33),X300)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__drop) ).
fof(fact_length__take,axiom,
! [X300,X33,X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),hAPP(hAPP(c_List_Otake(X87),X33),X300)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__take) ).
fof(fact_inj__of__nat,axiom,
! [X7] :
( class_Nat_Osemiring__char__0(X7)
=> c_Fun_Oinj__on(tc_Nat_Onat,X7,c_Nat_Osemiring__1__class_Oof__nat(X7),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__of__nat) ).
fof(fact_take__tl,axiom,
! [X300,X33,X87] : hAPP(hAPP(c_List_Otake(X87),X33),hAPP(c_List_Otl(X87),X300)) = hAPP(c_List_Otl(X87),hAPP(hAPP(c_List_Otake(X87),hAPP(c_Nat_OSuc,X33)),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__tl) ).
fof(fact_less__imp__Suc__add,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> ? [X118] : X33 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X118)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__Suc__add) ).
fof(fact_less__iff__Suc__add,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44))
<=> ? [X118] : X44 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X118)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
! [X44] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X44) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) ).
fof(fact_nonzero__abs__divide,axiom,
! [X71,X84,X87] :
( class_Fields_Olinordered__field(X87)
=> ( X84 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X84)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).
fof(fact_card_Oneutral,axiom,
! [X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(X7),X149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oneutral) ).
fof(fact_Compl__disjoint,axiom,
! [X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint) ).
fof(fact_Compl__partition,axiom,
! [X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition) ).
fof(fact_inj__Inl,axiom,
! [X149,X105,X7] : c_Fun_Oinj__on(X7,tc_sum(X7,X105),c_Sum__Type_OInl(X7,X105),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Inl) ).
fof(fact_inj__Inr,axiom,
! [X149,X105,X7] : c_Fun_Oinj__on(X7,tc_sum(X105,X7),c_Sum__Type_OInr(X7,X105),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Inr) ).
fof(fact_inj__on__empty,axiom,
! [X2,X105,X7] : c_Fun_Oinj__on(X7,X105,X2,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).
fof(fact_dvd_Oeq__iff,axiom,
! [X127,X6] :
( X6 = X127
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X127),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
fof(fact_dvd_Oantisym__conv,axiom,
! [X6,X127] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X127),X6))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
<=> X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
fof(fact_dvd__antisym,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X90),X33))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X90))
=> X90 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__antisym) ).
fof(fact_dvd_Oantisym,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X86))
=> X86 = X98 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
fof(fact_zle__antisym,axiom,
! [X128,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X97),X128))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X128),X97))
=> X97 = X128 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(fact_le__antisym,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> X90 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_zmod__minus1,axiom,
! [X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X84) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X84),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__minus1) ).
fof(fact_Inf__fin_Oinsert__idem,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X6),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).
fof(fact_Min__insert,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olinorder__class_OMin(X7,X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__insert) ).
fof(fact_Max__insert,axiom,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olinorder__class_OMax(X7,X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__insert) ).
fof(fact_Sup__fin_Oinsert__idem,axiom,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).
fof(fact_Un__empty,axiom,
! [X155,X149,X7] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
& X155 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).
fof(fact_listsum__append,axiom,
! [X301,X300,X87] :
( class_Groups_Omonoid__add(X87)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_List_Omonoid__add__class_Olistsum(X87),X300)),hAPP(c_List_Omonoid__add__class_Olistsum(X87),X301)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__append) ).
fof(fact_abs__divide,axiom,
! [X84,X71,X87] :
( class_Fields_Olinordered__field__inverse__zero(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X84)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__divide) ).
fof(fact_abs__mult,axiom,
! [X84,X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult) ).
fof(fact_compl__inf,axiom,
! [X98,X86,X87] :
( class_Lattices_Oboolean__algebra(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86)),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__inf) ).
fof(fact_compl__sup,axiom,
! [X98,X86,X87] :
( class_Lattices_Oboolean__algebra(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86)),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__sup) ).
fof(fact_minus__max__eq__min,axiom,
! [X98,X86,X87] :
( class_Groups_Olinordered__ab__group__add(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86)),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__max__eq__min) ).
fof(fact_minus__min__eq__max,axiom,
! [X98,X86,X87] :
( class_Groups_Olinordered__ab__group__add(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86)),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__min__eq__max) ).
fof(fact_minus__add__distrib,axiom,
! [X84,X71,X87] :
( class_Groups_Oab__group__add(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_minus__add,axiom,
! [X84,X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add) ).
fof(fact_Cantors__paradox,axiom,
! [X149,X7] :
~ ? [X240] : hAPP(c_Set_Oimage(X7,tc_fun(X7,tc_HOL_Obool),X240),X149) = hAPP(c_Set_OPow(X7),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cantors__paradox) ).
fof(fact_equalityD1,axiom,
! [X7,X155,X149] :
( X149 = X155
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X7,X155,X149] :
( X149 = X155
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_last__in__set,axiom,
! [X7,X322] :
( X322 != c_List_Olist_ONil(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),c_List_Olast(X7,X322)),hAPP(c_List_Oset(X7),X322))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__in__set) ).
fof(fact_Suc__mult__cancel1,axiom,
! [X44,X95,X94] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)),X95) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)),X44)
<=> X95 = X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_Pair__eq,axiom,
! [X112,X89,X24,X25,X105,X7] :
( hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24) = hAPP(hAPP(c_Product__Type_OPair(X7,X105),X89),X112)
<=> ( X25 = X89
& X24 = X112 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
fof(fact_Pair__inject,axiom,
! [X124,X88,X84,X71,X7,X87] :
( hAPP(hAPP(c_Product__Type_OPair(X87,X7),X71),X84) = hAPP(hAPP(c_Product__Type_OPair(X87,X7),X88),X124)
=> ~ ( X71 = X88
=> X84 != X124 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
fof(fact_zmod__zminus1__eq__if,axiom,
! [X84,X71] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),X84) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),X84) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus1__eq__if) ).
fof(fact_subset__refl,axiom,
! [X149,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_image__Suc__atLeastLessThan,axiom,
! [X158,X107] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X107),X158)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X107)),hAPP(c_Nat_OSuc,X158)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
fof(fact_rev__append,axiom,
! [X301,X300,X87] : hAPP(c_List_Orev(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = hAPP(hAPP(c_List_Oappend(X87),hAPP(c_List_Orev(X87),X301)),hAPP(c_List_Orev(X87),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__append) ).
fof(fact_rotate__simps,axiom,
! [X300,X86,X7,X87] :
( hAPP(c_List_Orotate1(X87),c_List_Olist_ONil(X87)) = c_List_Olist_ONil(X87)
& hAPP(c_List_Orotate1(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X86),X300)) = hAPP(hAPP(c_List_Oappend(X7),X300),hAPP(hAPP(c_List_Olist_OCons(X7),X86),c_List_Olist_ONil(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__simps) ).
fof(fact_le__SucI,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,X33))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_le__imp__less__Suc,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,X33))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_less__SucI,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,X33))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_greaterThanAtMost__upto,axiom,
! [X158,X107] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X107,X158) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint)),X158)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__upto) ).
fof(fact_Ints__double__eq__0__iff,axiom,
! [X25,X7] :
( class_Int_Oring__char__0(X7)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),c_Int_Oring__1__class_OInts(X7)))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X25) = c_Groups_Ozero__class_Ozero(X7)
<=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).
fof(fact_div__eq__minus1,axiom,
! [X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X84) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__eq__minus1) ).
fof(fact_Int__commute,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).
fof(fact_Un__commute,axiom,
! [X155,X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X155),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).
fof(fact_triple_Osize_I1_J,axiom,
! [X228,X66,X229,X85,X7] : c_Hoare__Mirabelle_Otriple_Otriple__size(X7,X85,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X229),X66),X228)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osize_I1_J) ).
fof(fact_zero__less__imp__eq__int,axiom,
! [X96] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X96))
=> ? [X70] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X70))
& X96 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X70) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__imp__eq__int) ).
fof(fact_frac__eq__eq,axiom,
! [X125,X6,X26,X127,X7] :
( class_Fields_Ofield(X7)
=> ( X127 != c_Groups_Ozero__class_Ozero(X7)
=> ( X26 != c_Groups_Ozero__class_Ozero(X7)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X6),X127) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X125),X26)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X125),X127) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
fof(fact_zmult__div__cancel,axiom,
! [X90,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X90),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X90),c_Divides_Odiv__class_Omod(tc_Int_Oint,X90,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).
fof(fact_mult__div__cancel,axiom,
! [X90,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__div__cancel) ).
fof(fact_minus__code__numeral__def,axiom,
! [X90,X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33),X90) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X33)),hAPP(c_Code__Numeral_Onat__of,X90))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__code__numeral__def) ).
fof(fact_div__code__numeral__def,axiom,
! [X90,X33] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X33),X90) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X33)),hAPP(c_Code__Numeral_Onat__of,X90))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__code__numeral__def) ).
fof(fact_times__code__numeral__def,axiom,
! [X90,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X33),X90) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X33)),hAPP(c_Code__Numeral_Onat__of,X90))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__code__numeral__def) ).
fof(fact_plus__code__numeral__def,axiom,
! [X90,X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X33),X90) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X33)),hAPP(c_Code__Numeral_Onat__of,X90))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__code__numeral__def) ).
fof(fact_diff__diff__cancel,axiom,
! [X33,X114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X33))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),X114)) = X114 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_zdvd__mult__div__cancel,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X33),X90))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X90),X33)) = X90 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mult__div__cancel) ).
fof(fact_le__add__diff__inverse,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)) = X90 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_nat__case__Suc,axiom,
! [X103,X21,X22,X7] : c_Nat_Onat_Onat__case(X7,X22,X21,hAPP(c_Nat_OSuc,X103)) = hAPP(X21,X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
fof(fact_listsum__eq__0__nat__iff__nat,axiom,
! [X308] :
( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X308) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_List_Oset(tc_Nat_Onat),X308)))
=> X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__eq__0__nat__iff__nat) ).
fof(fact_WT_OLocal,axiom,
! [X25,X60,X23] :
( hBOOL(hAPP(c_Com_OWT,X23))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X60,X25,X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OLocal) ).
fof(fact_xt1_I11_J,axiom,
! [X71,X84,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X71))
=> ( X71 != X84
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X71)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X84,X71,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> ( X71 != X84
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X98,X86,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
| X86 = X98 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X84,X71,X87] :
( class_Orderings_Oorder(X87)
=> ( X71 != X84
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__less,axiom,
! [X127,X6,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
| X6 = X127 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__le,axiom,
! [X127,X6,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
& X6 != X127 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_xt1_I12_J,axiom,
! [X84,X71,X87] :
( class_Orderings_Oorder(X87)
=> ( X71 != X84
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X71))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X71)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_arith__simps_I32_J,axiom,
! [X128,X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X139),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).
fof(fact_add__number__of__eq,axiom,
! [X128,X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__eq) ).
fof(fact_number__of__diff,axiom,
! [X128,X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X139),X128)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__diff) ).
fof(fact_number__of__mult,axiom,
! [X128,X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X139),X128)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__mult) ).
fof(fact_number__of__add,axiom,
! [X128,X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),X128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__add) ).
fof(fact_of__int__diff,axiom,
! [X97,X128,X87] :
( class_Rings_Oring__1(X87)
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X128),X97)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(c_Int_Oring__1__class_Oof__int(X87),X128)),hAPP(c_Int_Oring__1__class_Oof__int(X87),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__diff) ).
fof(fact_of__int__mult,axiom,
! [X97,X128,X87] :
( class_Rings_Oring__1(X87)
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X97)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Oring__1__class_Oof__int(X87),X128)),hAPP(c_Int_Oring__1__class_Oof__int(X87),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__mult) ).
fof(fact_of__int__add,axiom,
! [X97,X128,X87] :
( class_Rings_Oring__1(X87)
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X128),X97)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Int_Oring__1__class_Oof__int(X87),X128)),hAPP(c_Int_Oring__1__class_Oof__int(X87),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__add) ).
fof(fact_of__nat__mult,axiom,
! [X33,X90,X87] :
( class_Rings_Osemiring__1(X87)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X90)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__mult) ).
fof(fact_of__nat__add,axiom,
! [X33,X90,X87] :
( class_Rings_Osemiring__1(X87)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X90)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__add) ).
fof(fact_minus1__divide,axiom,
! [X86,X87] :
( ( class_Fields_Ofield__inverse__zero(X87)
& class_Int_Onumber__ring(X87) )
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin)),X86) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),c_Groups_Oone__class_Oone(X87)),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus1__divide) ).
fof(fact_setprod__1,axiom,
! [X149,X105,X7] :
( class_Groups_Ocomm__monoid__mult(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X7),hAPP(c_COMBK(X7,X105),c_Groups_Oone__class_Oone(X7))),X149) = c_Groups_Oone__class_Oone(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__1) ).
fof(fact_setsum__0,axiom,
! [X149,X105,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),hAPP(c_COMBK(X7,X105),c_Groups_Ozero__class_Ozero(X7))),X149) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__0) ).
fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
! [X160,X157] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X157),c_Groups_Oone__class_Oone(tc_Int_Oint))),X160) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X157,X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).
fof(fact_order__less__imp__le,axiom,
! [X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_negateSnd__eq,axiom,
! [X138,X144] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),X138)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X138)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negateSnd__eq) ).
fof(fact_abs__power__minus__one,axiom,
! [X33,X87] :
( ( class_Int_Onumber__ring(X87)
& class_Rings_Olinordered__idom(X87) )
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin)),X33)) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power__minus__one) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
! [X155,X149] :
( c_Nat__Transfer_Onat__set(X149)
=> ( c_Nat__Transfer_Onat__set(X155)
=> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X149),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
! [X155,X149] :
( c_Nat__Transfer_Onat__set(X149)
=> ( c_Nat__Transfer_Onat__set(X155)
=> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X149),X155)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).
fof(fact_zle__iff__zadd,axiom,
! [X26,X125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X125),X26))
<=> ? [X70] : X26 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X125),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X70)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__iff__zadd) ).
fof(fact_filter__remove1,axiom,
! [X292,X6,X194,X7] : hAPP(c_List_Ofilter(X7,X194),c_List_Oremove1(X7,X6,X292)) = c_List_Oremove1(X7,X6,hAPP(c_List_Ofilter(X7,X194),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__remove1) ).
fof(fact_snoc__eq__iff__butlast,axiom,
! [X293,X6,X292,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X292),hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7))) = X293
<=> ( X293 != c_List_Olist_ONil(X7)
& c_List_Obutlast(X7,X293) = X292
& c_List_Olast(X7,X293) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).
fof(fact_negD,axiom,
! [X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X86),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ? [X70] : X86 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X70))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negD) ).
fof(fact_Ints__number__of,axiom,
! [X125,X7] :
( class_Int_Onumber__ring(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Int_Oring__1__class_OInts(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__number__of) ).
fof(fact_Ints__of__int,axiom,
! [X26,X7] :
( class_Rings_Oring__1(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Int_Oring__1__class_Oof__int(X7),X26)),c_Int_Oring__1__class_OInts(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__of__int) ).
fof(fact_Ints__of__nat,axiom,
! [X44,X7] :
( class_Rings_Oring__1(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X44)),c_Int_Oring__1__class_OInts(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__of__nat) ).
fof(fact_of__nat__in__Nats,axiom,
! [X44,X7] :
( class_Rings_Osemiring__1(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X44)),c_Nat_Osemiring__1__class_ONats(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__in__Nats) ).
fof(fact_Suc__diff__1,axiom,
! [X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X33 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
fof(fact_Suc__pred_H,axiom,
! [X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> X33 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
fof(fact_nat__of,axiom,
! [X6] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X6)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of) ).
fof(fact_mod__div__trivial,axiom,
! [X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),c_Divides_Odiv__class_Omod(X87,X71,X84)),X84) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__trivial) ).
fof(fact_negDivAlg__minus1,axiom,
! [X84] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X84) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X84),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__minus1) ).
fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X6,X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).
fof(fact_min__max_OInf__fin_Osingleton,axiom,
! [X6,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).
fof(fact_min__max_OSup__fin_Osingleton,axiom,
! [X6,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [X26] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_Int__empty__left,axiom,
! [X155,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X155) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__left) ).
fof(fact_Un__UNIV__left,axiom,
! [X155,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),X155) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__left) ).
fof(fact_empty__Diff,axiom,
! [X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X149) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Diff) ).
fof(fact_Sigma__empty1,axiom,
! [X155,X105,X7] : hAPP(hAPP(c_Product__Type_OSigma(X7,X105),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X155) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty1) ).
fof(fact_le__square,axiom,
! [X90] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X90))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
fof(fact_le__add1,axiom,
! [X90,X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X90))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X90,X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_divide__eq__eq__number__of1,axiom,
! [X25,X125,X24,X7] :
( ( class_Fields_Ofield__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)) = X25
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X7),X125) != c_Groups_Ozero__class_Ozero(X7)
=> X24 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X7),X125) = c_Groups_Ozero__class_Ozero(X7)
=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).
fof(fact_eq__divide__eq__number__of1,axiom,
! [X125,X24,X25,X7] :
( ( class_Fields_Ofield__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( X25 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X7),X125) != c_Groups_Ozero__class_Ozero(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)) = X24 )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X7),X125) = c_Groups_Ozero__class_Ozero(X7)
=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).
fof(fact_nat__less__cases,axiom,
! [X38,X44,X95] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44))
=> hBOOL(hAPP(hAPP(X38,X44),X95)) )
=> ( ( X95 = X44
=> hBOOL(hAPP(hAPP(X38,X44),X95)) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X95))
=> hBOOL(hAPP(hAPP(X38,X44),X95)) )
=> hBOOL(hAPP(hAPP(X38,X44),X95)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
! [X149] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X149) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).
fof(fact_append__eq__appendI,axiom,
! [X316,X301,X299,X318,X300,X87] :
( hAPP(hAPP(c_List_Oappend(X87),X300),X318) = X299
=> ( X301 = hAPP(hAPP(c_List_Oappend(X87),X318),X316)
=> hAPP(hAPP(c_List_Oappend(X87),X300),X301) = hAPP(hAPP(c_List_Oappend(X87),X299),X316) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
fof(fact_Cons__eq__appendI,axiom,
! [X299,X300,X301,X318,X86,X87] :
( hAPP(hAPP(c_List_Olist_OCons(X87),X86),X318) = X301
=> ( X300 = hAPP(hAPP(c_List_Oappend(X87),X318),X299)
=> hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300) = hAPP(hAPP(c_List_Oappend(X87),X301),X299) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).
fof(fact_zadd__left__commute,axiom,
! [X97,X98,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),X97)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X86),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X97,X98,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_atLeastLessThan__upto,axiom,
! [X158,X107] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X107),X158) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X107,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X158),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__upto) ).
fof(fact_nat__minus__add__max,axiom,
! [X90,X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),X90)),X90) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X33),X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__minus__add__max) ).
fof(fact_dual__max,axiom,
! [X7] :
( class_Orderings_Olinorder(X7)
=> c_Orderings_Oord_Omax(X7,hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X7))) = c_Orderings_Oord__class_Omin(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dual__max) ).
fof(fact_dual__min,axiom,
! [X7] :
( class_Orderings_Olinorder(X7)
=> c_Orderings_Oord_Omin(X7,hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X7))) = c_Orderings_Oord__class_Omax(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dual__min) ).
fof(fact_listsum__foldl,axiom,
! [X7] :
( class_Groups_Omonoid__add(X7)
=> c_List_Omonoid__add__class_Olistsum(X7) = c_List_Ofoldl(X7,X7,c_Groups_Oplus__class_Oplus(X7),c_Groups_Ozero__class_Ozero(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__foldl) ).
fof(fact_elem__set,axiom,
! [X217,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Option_Oset(X7,X217)))
<=> X217 = hAPP(c_Option_Ooption_OSome(X7),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__set) ).
fof(fact_div__mult__self1__is__id,axiom,
! [X71,X84,X87] :
( class_Divides_Osemiring__div(X87)
=> ( X84 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X71)),X84) = X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).
fof(fact_div__mult__self2__is__id,axiom,
! [X71,X84,X87] :
( class_Divides_Osemiring__div(X87)
=> ( X84 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)),X84) = X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).
fof(fact_le__imp__diff__is__add,axiom,
! [X94,X158,X107] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X158))
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X158),X107) = X94
<=> X158 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X107) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_zmod__zminus2,axiom,
! [X84,X71] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),X84)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2) ).
fof(fact_vname_Orecs_I1_J,axiom,
! [X100,X21,X22,X7] : c_Com_Ovname_Ovname__rec(X7,X22,X21,c_Com_Ovname_OGlb(X100)) = hAPP(X22,X100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Orecs_I1_J) ).
fof(fact_vname_Orecs_I2_J,axiom,
! [X67,X21,X22,X7] : c_Com_Ovname_Ovname__rec(X7,X22,X21,c_Com_Ovname_OLoc(X67)) = hAPP(X21,X67),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Orecs_I2_J) ).
fof(fact_vname_Osimps_I5_J,axiom,
! [X100,X21,X22,X7] : c_Com_Ovname_Ovname__case(X7,X22,X21,c_Com_Ovname_OGlb(X100)) = hAPP(X22,X100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I5_J) ).
fof(fact_vname_Osimps_I6_J,axiom,
! [X67,X21,X22,X7] : c_Com_Ovname_Ovname__case(X7,X22,X21,c_Com_Ovname_OLoc(X67)) = hAPP(X21,X67),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I6_J) ).
fof(fact_insert__dom,axiom,
! [X105,X127,X7,X6,X2] :
( hAPP(X2,X6) = hAPP(c_Option_Ooption_OSome(X7),X127)
=> hAPP(hAPP(c_Set_Oinsert(X105),X6),c_Map_Odom(X105,X7,X2)) = c_Map_Odom(X105,X7,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__dom) ).
fof(fact_Nitpick_Owf_H__def,axiom,
! [X172,X7] :
( c_Nitpick_Owf_H(X7,X172)
<=> ( c_Wellfounded_Oacyclic(X7,X172)
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X7)),X172))
| c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Owf_H__def) ).
fof(fact_wf__iff__acyclic__if__finite,axiom,
! [X172,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X7)),X172))
=> ( c_Wellfounded_Owf(X7,X172)
<=> c_Wellfounded_Oacyclic(X7,X172) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).
fof(fact_finite__acyclic__wf,axiom,
! [X172,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X7)),X172))
=> ( c_Wellfounded_Oacyclic(X7,X172)
=> c_Wellfounded_Owf(X7,X172) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__acyclic__wf) ).
fof(fact_inj__on__rev,axiom,
! [X149,X7] : c_Fun_Oinj__on(tc_List_Olist(X7),tc_List_Olist(X7),c_List_Orev(X7),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__rev) ).
fof(fact_distinct__filter,axiom,
! [X38,X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> hBOOL(hAPP(c_List_Odistinct(X7),hAPP(c_List_Ofilter(X7,X38),X292))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__filter) ).
fof(fact_triple_Osize_I2_J,axiom,
! [X228,X66,X229,X7] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X229),X66),X228)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osize_I2_J) ).
fof(fact_equivp__def,axiom,
! [X191,X7] :
( c_Equiv__Relations_Oequivp(X7,X191)
<=> ! [X3,X82] :
( hBOOL(hAPP(hAPP(X191,X3),X82))
<=> hAPP(X191,X3) = hAPP(X191,X82) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__def) ).
fof(fact_add__diff__cancel,axiom,
! [X84,X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)),X84) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X84,X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84)),X84) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_fst__eq__Domain,axiom,
! [X191,X105,X7] : hAPP(c_Set_Oimage(tc_prod(X7,X105),X7,c_Product__Type_Ofst(X7,X105)),X191) = hAPP(c_Relation_ODomain(X7,X105),X191),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__eq__Domain) ).
fof(fact_snd__eq__Range,axiom,
! [X191,X7,X105] : hAPP(c_Set_Oimage(tc_prod(X105,X7),X7,c_Product__Type_Osnd(X105,X7)),X191) = hAPP(c_Relation_ORange(X105,X7),X191),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__eq__Range) ).
fof(fact_zero__induct,axiom,
! [X94,X38] :
( hBOOL(hAPP(X38,X94))
=> ( ! [X70] :
( hBOOL(hAPP(X38,hAPP(c_Nat_OSuc,X70)))
=> hBOOL(hAPP(X38,X70)) )
=> hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__induct) ).
fof(fact_total__on__converse,axiom,
! [X172,X149,X7] :
( c_Relation_Ototal__on(X7,X149,hAPP(c_Relation_Oconverse(X7,X7),X172))
<=> c_Relation_Ototal__on(X7,X149,X172) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__converse) ).
fof(fact_refl__on__converse,axiom,
! [X172,X149,X7] :
( c_Relation_Orefl__on(X7,X149,hAPP(c_Relation_Oconverse(X7,X7),X172))
<=> c_Relation_Orefl__on(X7,X149,X172) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__converse) ).
fof(fact_com_Osize_I11_J,axiom,
! [X66,X13,X67] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X67,X13,X66)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X66)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I11_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
! [X149] :
( c_Nat__Transfer_Onat__set(X149)
=> hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X149) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
! [X6,X149] :
( c_Nat__Transfer_Onat__set(X149)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).
fof(fact_nat__set__def,axiom,
! [X209] :
( c_Nat__Transfer_Onat__set(X209)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X209))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__set__def) ).
fof(fact_refl__on__empty,axiom,
! [X7] : c_Relation_Orefl__on(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__empty) ).
fof(fact_card__eq__setsum,axiom,
! [X149,X7] : hAPP(c_Finite__Set_Ocard(X7),X149) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X7),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__setsum) ).
fof(fact_divmod__nat__rel__unique,axiom,
! [X179,X180,X33,X90] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X90,X33),X180))
=> ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X90,X33),X179))
=> X180 = X179 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
fof(fact_inj__uminus,axiom,
! [X149,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> c_Fun_Oinj__on(X7,X7,c_Groups_Ouminus__class_Ouminus(X7),X149) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__uminus) ).
fof(fact_mod__code__numeral__def,axiom,
! [X90,X33] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X33,X90) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X33),hAPP(c_Code__Numeral_Onat__of,X90))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__code__numeral__def) ).
fof(fact_nth__Cons__0,axiom,
! [X300,X86,X87] : hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__0) ).
fof(fact_image__is__empty,axiom,
! [X149,X2,X7,X105] :
( hAPP(c_Set_Oimage(X105,X7,X2),X149) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> X149 = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__is__empty) ).
fof(fact_empty__is__image,axiom,
! [X149,X2,X105,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X105,X7,X2),X149)
<=> X149 = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__is__image) ).
fof(fact_inj__Some,axiom,
! [X149,X7] : c_Fun_Oinj__on(X7,tc_Option_Ooption(X7),c_Option_Ooption_OSome(X7),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Some) ).
fof(fact_listrelp_Oequations_I1_J,axiom,
! [X172,X7] : c_List_Olistrelp(X7,X172,c_List_Olist_ONil(X7),c_List_Olist_ONil(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
fof(fact_listrelp_ONil,axiom,
! [X172,X7] : c_List_Olistrelp(X7,X172,c_List_Olist_ONil(X7),c_List_Olist_ONil(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_ONil) ).
fof(fact_hd__map,axiom,
! [X2,X105,X7,X292] :
( X292 != c_List_Olist_ONil(X7)
=> hAPP(c_List_Ohd(X105),hAPP(hAPP(c_List_Omap(X7,X105),X2),X292)) = hAPP(X2,hAPP(c_List_Ohd(X7),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__map) ).
fof(fact_of__nat__aux_Osimps_I1_J,axiom,
! [X107,X108,X7] :
( class_Rings_Osemiring__1(X7)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X7,X108,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X107) = X107 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
fof(fact_atLeastAtMost__singleton__iff,axiom,
! [X23,X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24) = hAPP(hAPP(c_Set_Oinsert(X7),X23),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))
<=> ( X25 = X24
& X24 = X23 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).
fof(fact_neg__single__def,axiom,
! [X197,X198,X199,X6,X7] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X7),X6),X199),X198),X197) = c_New__DSequence_Oneg__single(X7,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__single__def) ).
fof(fact_pos__single__def,axiom,
! [X197,X198,X199,X6,X7] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X7),X6),X199),X198),X197) = c_New__DSequence_Opos__single(X7,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__single__def) ).
fof(fact_power__abs,axiom,
! [X33,X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__abs) ).
fof(fact_minus__divide__left,axiom,
! [X84,X71,X87] :
( class_Rings_Odivision__ring(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X84)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__left) ).
fof(fact_minus__mult__left,axiom,
! [X84,X71,X87] :
( class_Rings_Oring(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__left) ).
fof(fact_power_Opower_Opower__0,axiom,
! [X25,X167,X168,X7] : hAPP(hAPP(c_Power_Opower_Opower(X7,X168,X167),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X168,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_map__filter__simps_I2_J,axiom,
! [X2,X7,X105] : c_List_Omap__filter(X105,X7,X2,c_List_Olist_ONil(X105)) = c_List_Olist_ONil(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__filter__simps_I2_J) ).
fof(fact_greaterThanLessThan__empty,axiom,
! [X94,X157,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X94))
=> c_SetInterval_Oord__class_OgreaterThanLessThan(X7,X94,X157) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__empty) ).
fof(fact_greaterThanAtMost__empty,axiom,
! [X94,X157,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X157),X94))
=> c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X94,X157) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty) ).
fof(fact_atLeastatMost__empty,axiom,
! [X25,X24,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),X25))
=> c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty) ).
fof(fact_dvd__1__iff__1,axiom,
! [X95] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X95 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
fof(fact_tl__append2,axiom,
! [X301,X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> hAPP(c_List_Otl(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = hAPP(hAPP(c_List_Oappend(X87),hAPP(c_List_Otl(X87),X300)),X301) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__append2) ).
fof(fact_zmod__zdiv__trivial,axiom,
! [X84,X71] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)),X84) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
fof(fact_prod__eqI,axiom,
! [X144,X162,X7,X87] :
( hAPP(c_Product__Type_Ofst(X87,X7),X162) = hAPP(c_Product__Type_Ofst(X87,X7),X144)
=> ( hAPP(c_Product__Type_Osnd(X87,X7),X162) = hAPP(c_Product__Type_Osnd(X87,X7),X144)
=> X162 = X144 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__eqI) ).
fof(fact_Pair__fst__snd__eq,axiom,
! [X105,X7,X46,X45] :
( X45 = X46
<=> ( hAPP(c_Product__Type_Ofst(X7,X105),X45) = hAPP(c_Product__Type_Ofst(X7,X105),X46)
& hAPP(c_Product__Type_Osnd(X7,X105),X45) = hAPP(c_Product__Type_Osnd(X7,X105),X46) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__fst__snd__eq) ).
fof(fact_inj__on__id,axiom,
! [X149,X7] : c_Fun_Oinj__on(X7,X7,c_Fun_Oid(X7),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id) ).
fof(fact_inj__on__id2,axiom,
! [X149,X7] : c_Fun_Oinj__on(X7,X7,c_COMBI(X7),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).
fof(fact_sgn__times,axiom,
! [X84,X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> c_Groups_Osgn__class_Osgn(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),c_Groups_Osgn__class_Osgn(X87,X71)),c_Groups_Osgn__class_Osgn(X87,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__times) ).
fof(fact_sorted__distinct__set__unique,axiom,
! [X293,X292,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,X292)
=> ( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> ( c_List_Olinorder__class_Osorted(X7,X293)
=> ( hBOOL(hAPP(c_List_Odistinct(X7),X293))
=> ( hAPP(c_List_Oset(X7),X292) = hAPP(c_List_Oset(X7),X293)
=> X292 = X293 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__distinct__set__unique) ).
fof(fact_drop__Suc__Cons,axiom,
! [X300,X86,X33,X87] : hAPP(hAPP(c_List_Odrop(X87),hAPP(c_Nat_OSuc,X33)),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_List_Odrop(X87),X33),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Suc__Cons) ).
fof(fact_less__than__def,axiom,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__than__def) ).
fof(fact_abs__minus__commute,axiom,
! [X84,X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84)) = hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X84),X71)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__commute) ).
fof(fact_nat__case__0,axiom,
! [X21,X22,X7] : c_Nat_Onat_Onat__case(X7,X22,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).
fof(fact_code__numeral_Orecs_I1_J,axiom,
! [X21,X22,X7] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X7,X22,X21,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).
fof(fact_code__numeral_Osimps_I4_J,axiom,
! [X21,X22,X7] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X7,X22,X21,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).
fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
! [X98,X86] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X86),X98)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).
fof(fact_times__numeral__code_I5_J,axiom,
! [X128,X139] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X139),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
! [X98,X86] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),X98)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
fof(fact_zmult__int,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__int) ).
fof(fact_plus__numeral__code_I9_J,axiom,
! [X128,X139] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
! [X98,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X98)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
fof(fact_zadd__int,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int) ).
fof(fact_zminus__zadd__distrib,axiom,
! [X128,X97] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),X128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X97)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_zdiv__int,axiom,
! [X84,X71] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X71),X84)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X71)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X84)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__int) ).
fof(fact_int__mult,axiom,
! [X33,X90] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__mult) ).
fof(fact_Int__UNIV__left,axiom,
! [X155,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),X155) = X155,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__left) ).
fof(fact_Un__empty__left,axiom,
! [X155,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X155) = X155,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X95))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X95),X44) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X95 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X44 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_succ__Pls,axiom,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Pls) ).
fof(fact_fold1__singleton,axiom,
! [X25,X2,X7] : hAPP(c_Finite__Set_Ofold1(X7,X2),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton) ).
fof(fact_length__list__update,axiom,
! [X86,X114,X300,X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),hAPP(hAPP(c_List_Olist__update(X87,X300),X114),X86)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__list__update) ).
fof(fact_length__map,axiom,
! [X292,X2,X105,X7] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__map) ).
fof(fact_evaln_Oequations_I1_J,axiom,
! [X36,X37] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X37,X36,X37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I1_J) ).
fof(fact_evaln_OSkip,axiom,
! [X33,X9] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X9,X33,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSkip) ).
fof(fact_of__int__power,axiom,
! [X33,X97,X87] :
( class_Rings_Oring__1(X87)
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X97),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Int_Oring__1__class_Oof__int(X87),X97)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__power) ).
fof(fact_of__nat__power,axiom,
! [X33,X90,X87] :
( class_Rings_Osemiring__1(X87)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X90)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__power) ).
fof(fact_zless__le,axiom,
! [X125,X26] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),X125))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),X125))
& X26 != X125 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
fof(fact_nat__less__le,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
& X95 != X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44))
| X95 = X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_le__neq__implies__less,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> ( X90 != X33
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_fold1__singleton__def,axiom,
! [X25,X2,X7,X1] :
( X1 = c_Finite__Set_Ofold1(X7,X2)
=> hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton__def) ).
fof(fact_length__tl,axiom,
! [X300,X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),hAPP(c_List_Otl(X87),X300)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__tl) ).
fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
! [X26,X6,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm__idem(X7,X105,X2)
=> hAPP(hAPP(X2,X6),hAPP(hAPP(X2,X6),X26)) = hAPP(hAPP(X2,X6),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
! [X193] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X193)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).
fof(fact_finite__greaterThanLessThan__int,axiom,
! [X160,X157] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X157,X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan__int) ).
fof(fact_finite__greaterThanAtMost__int,axiom,
! [X160,X157] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X157,X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost__int) ).
fof(fact_finite__atLeastAtMost__int,axiom,
! [X160,X157] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X157,X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost__int) ).
fof(fact_finite__greaterThanLessThan,axiom,
! [X160,X157] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X157,X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).
fof(fact_finite__greaterThanAtMost,axiom,
! [X160,X157] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X157,X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).
fof(fact_finite__atLeastAtMost,axiom,
! [X160,X157] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X157,X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).
fof(fact_less__Suc0,axiom,
! [X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_inj__Suc,axiom,
! [X214] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X214),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(fact_less__imp__le__nat,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X33,X90] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
| X90 = X33 )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_atLeastLessThan__empty,axiom,
! [X25,X24,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),X25))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X25),X24) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).
fof(fact_eq__mem,axiom,
! [X127,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_fequal,X127)))
<=> X6 = X127 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_last__map,axiom,
! [X2,X105,X7,X292] :
( X292 != c_List_Olist_ONil(X7)
=> c_List_Olast(X105,hAPP(hAPP(c_List_Omap(X7,X105),X2),X292)) = hAPP(X2,c_List_Olast(X7,X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__map) ).
fof(fact_map__of__Cons__code_I1_J,axiom,
! [X96,X87,X7] : hAPP(c_Map_Omap__of(X7,X87,c_List_Olist_ONil(tc_prod(X7,X87))),X96) = c_Option_Ooption_ONone(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__Cons__code_I1_J) ).
fof(fact_map__of_Osimps_I1_J,axiom,
! [X264,X7,X87] : hAPP(c_Map_Omap__of(X87,X7,c_List_Olist_ONil(tc_prod(X87,X7))),X264) = c_Option_Ooption_ONone(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of_Osimps_I1_J) ).
fof(fact_minus__add__cancel,axiom,
! [X84,X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_ex__in__conv,axiom,
! [X149,X7] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
<=> X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
fof(fact_of__nat__nat,axiom,
! [X97,X87] :
( class_Rings_Oring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onat,X97)) = hAPP(c_Int_Oring__1__class_Oof__int(X87),X97) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__nat) ).
fof(fact_zmod__zminus__zminus,axiom,
! [X84,X71] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).
fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
! [X98,X86] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X98)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).
fof(fact_zmod__int,axiom,
! [X84,X71] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X71,X84)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X71),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X84)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__int) ).
fof(fact_distinct__listsum__conv__Setsum,axiom,
! [X292,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> hAPP(c_List_Omonoid__add__class_Olistsum(X7),X292) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X7),c_COMBI(X7)),hAPP(c_List_Oset(X7),X292)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
! [X144,X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X144)) = hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Nat_OSuc,X144)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(fact_power__Suc,axiom,
! [X33,X71,X87] :
( class_Power_Opower(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Nat_OSuc,X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
! [X144,X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Nat_OSuc,X144)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),X144)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
fof(fact_image__uminus__atLeast,axiom,
! [X6,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> hAPP(c_Set_Oimage(X7,X7,c_Groups_Ouminus__class_Ouminus(X7)),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X6)) = hAPP(c_SetInterval_Oord__class_OatMost(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeast) ).
fof(fact_image__uminus__atMost,axiom,
! [X6,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> hAPP(c_Set_Oimage(X7,X7,c_Groups_Ouminus__class_Ouminus(X7)),hAPP(c_SetInterval_Oord__class_OatMost(X7),X6)) = hAPP(c_SetInterval_Oord__class_OatLeast(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atMost) ).
fof(fact_image__uminus__greaterThan,axiom,
! [X6,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> hAPP(c_Set_Oimage(X7,X7,c_Groups_Ouminus__class_Ouminus(X7)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X6)) = hAPP(c_SetInterval_Oord__class_OlessThan(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThan) ).
fof(fact_image__uminus__lessThan,axiom,
! [X6,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> hAPP(c_Set_Oimage(X7,X7,c_Groups_Ouminus__class_Ouminus(X7)),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X6)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),hAPP(c_Groups_Ouminus__class_Ouminus(X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__lessThan) ).
fof(fact_abs__of__nonneg,axiom,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),X71) = X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_abs__of__pos,axiom,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),X71) = X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__pos) ).
fof(fact_abs__of__nonpos,axiom,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),X71) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).
fof(fact_abs__of__neg,axiom,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),X71) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__neg) ).
fof(fact_sgn__1__neg,axiom,
! [X25,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( c_Groups_Osgn__class_Osgn(X7,X25) = hAPP(c_Groups_Ouminus__class_Ouminus(X7),c_Groups_Oone__class_Oone(X7))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__neg) ).
fof(fact_sgn__neg,axiom,
! [X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> c_Groups_Osgn__class_Osgn(X87,X71) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Oone__class_Oone(X87)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__neg) ).
fof(fact_equivp__symp,axiom,
! [X127,X6,X191,X7] :
( c_Equiv__Relations_Oequivp(X7,X191)
=> ( hBOOL(hAPP(hAPP(X191,X6),X127))
=> hBOOL(hAPP(hAPP(X191,X127),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__symp) ).
fof(fact_dvd__eq__mod__eq__0,axiom,
! [X24,X25,X7] :
( class_Divides_Osemiring__div(X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X7),X25),X24))
<=> c_Divides_Odiv__class_Omod(X7,X24,X25) = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
fof(fact_dvd__imp__mod__0,axiom,
! [X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X84))
=> c_Divides_Odiv__class_Omod(X87,X84,X71) = c_Groups_Ozero__class_Ozero(X87) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__mod__0) ).
fof(fact_length__butlast,axiom,
! [X300,X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),c_List_Obutlast(X87,X300)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__butlast) ).
fof(fact_lists_ONil,axiom,
! [X149,X7] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7)),c_List_Olist_ONil(X7)),c_List_Olists(X7,X149))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists_ONil) ).
fof(fact_sgn__pos,axiom,
! [X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> c_Groups_Osgn__class_Osgn(X87,X71) = c_Groups_Oone__class_Oone(X87) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__pos) ).
fof(fact_sgn__1__pos,axiom,
! [X25,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( c_Groups_Osgn__class_Osgn(X7,X25) = c_Groups_Oone__class_Oone(X7)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__pos) ).
fof(fact_nonzero__minus__divide__divide,axiom,
! [X71,X84,X87] :
( class_Rings_Odivision__ring(X87)
=> ( X84 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).
fof(fact_lists__empty,axiom,
! [X7] : c_List_Olists(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X7)),c_List_Olist_ONil(X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X7),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__empty) ).
fof(fact_listset_Osimps_I1_J,axiom,
! [X7] : c_List_Olistset(X7,c_List_Olist_ONil(tc_fun(X7,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X7)),c_List_Olist_ONil(X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X7),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listset_Osimps_I1_J) ).
fof(fact_CollectI,axiom,
! [X7,X25,X38] :
( hBOOL(hAPP(X38,X25))
=> hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Set_OCollect(X7),X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectI) ).
fof(fact_distinct__rev,axiom,
! [X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(c_List_Orev(X7),X292)))
<=> hBOOL(hAPP(c_List_Odistinct(X7),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__rev) ).
fof(fact_distinct1__rotate,axiom,
! [X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(c_List_Orotate1(X7),X292)))
<=> hBOOL(hAPP(c_List_Odistinct(X7),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct1__rotate) ).
fof(fact_quotient__empty,axiom,
! [X172,X7] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X172) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__empty) ).
fof(fact_split__Pair,axiom,
! [X105,X7] : hAPP(c_Product__Type_Oprod_Oprod__case(X7,X105,tc_prod(X7,X105)),c_Product__Type_OPair(X7,X105)) = c_Fun_Oid(tc_prod(X7,X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__Pair) ).
fof(fact_inf__absorb1,axiom,
! [X98,X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98) = X86 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb1) ).
fof(fact_le__iff__inf,axiom,
! [X127,X6,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
<=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X6),X127) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__inf) ).
fof(fact_inf__absorb2,axiom,
! [X86,X98,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98) = X98 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb2) ).
fof(fact_le__iff__sup,axiom,
! [X127,X6,X7] :
( class_Lattices_Osemilattice__sup(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6),X127) = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__sup) ).
fof(fact_sup__absorb2,axiom,
! [X98,X86,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98) = X98 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb2) ).
fof(fact_sup__absorb1,axiom,
! [X86,X98,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98) = X86 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb1) ).
fof(fact_min__max_Ole__iff__sup,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
<=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),X127) = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__iff__sup) ).
fof(fact_min__max_Osup__absorb2,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98) = X98 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__absorb2) ).
fof(fact_min__max_Osup__absorb1,axiom,
! [X86,X98,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98) = X86 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__absorb1) ).
fof(fact_min__max_Ole__iff__inf,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
<=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),X127) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__iff__inf) ).
fof(fact_min__max_Oinf__absorb1,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98) = X86 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb1) ).
fof(fact_min__max_Oinf__absorb2,axiom,
! [X86,X98,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98) = X98 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb2) ).
fof(fact_Sup__singleton,axiom,
! [X25,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OSup__class_OSup(X7,hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__singleton) ).
fof(fact_Inf__singleton,axiom,
! [X25,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OInf__class_OInf(X7,hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__singleton) ).
fof(fact_Inf__fin_Osingleton,axiom,
! [X6,X7] :
( class_Lattices_Olattice(X7)
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Osingleton) ).
fof(fact_Min_Osingleton,axiom,
! [X6,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Osingleton) ).
fof(fact_Max_Osingleton,axiom,
! [X6,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Osingleton) ).
fof(fact_Sup__fin_Osingleton,axiom,
! [X6,X7] :
( class_Lattices_Olattice(X7)
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Osingleton) ).
fof(fact_mult__Suc,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
fof(fact_cut,axiom,
! [X216,X223,X225,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X7,X225,X223)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,X225)
=> c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,X223) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut) ).
fof(fact_diff__add__inverse,axiom,
! [X90,X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X90)),X33) = X90,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33)),X33) = X90,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_Union__quotient,axiom,
! [X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__quotient) ).
fof(fact_minus__divide__divide,axiom,
! [X84,X71,X87] :
( class_Fields_Ofield__inverse__zero(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__divide) ).
fof(fact_abs__mult__self,axiom,
! [X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__self) ).
fof(fact_minus__mult__minus,axiom,
! [X84,X71,X87] :
( class_Rings_Oring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_minus__mult__commute,axiom,
! [X84,X71,X87] :
( class_Rings_Oring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),X84) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_wfP__accp__iff,axiom,
! [X172,X7] :
( c_Wellfounded_OwfP(X7,X172)
<=> ! [X142] : hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X172),X142)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
fof(fact_nonzero__minus__divide__right,axiom,
! [X71,X84,X87] :
( class_Rings_Odivision__ring(X87)
=> ( X84 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X84)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).
fof(fact_quotient__is__empty2,axiom,
! [X172,X149,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)
<=> X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).
fof(fact_quotient__is__empty,axiom,
! [X172,X149,X7] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))
<=> X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty) ).
fof(fact_card__greaterThanAtMost__int,axiom,
! [X160,X157] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X157,X160)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X160),X157)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanAtMost__int) ).
fof(fact_linorder__neq__iff,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( X6 != X127
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X127),X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
| X86 = X98
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_mod__mod__trivial,axiom,
! [X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,c_Divides_Odiv__class_Omod(X87,X71,X84),X84) = c_Divides_Odiv__class_Omod(X87,X71,X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
fof(fact_Int__empty__right,axiom,
! [X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__right) ).
fof(fact_Un__UNIV__right,axiom,
! [X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__right) ).
fof(fact_Diff__UNIV,axiom,
! [X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__UNIV) ).
fof(fact_Domain__empty,axiom,
! [X105,X7] : hAPP(c_Relation_ODomain(X7,X105),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X105),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty) ).
fof(fact_Range__empty,axiom,
! [X7,X105] : hAPP(c_Relation_ORange(X105,X7),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X105,X7),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty) ).
fof(fact_fun__upd__triv,axiom,
! [X6,X2,X105,X7] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),hAPP(X2,X6)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
fof(fact_fst__conv,axiom,
! [X84,X71,X7,X87] : hAPP(c_Product__Type_Ofst(X87,X7),hAPP(hAPP(c_Product__Type_OPair(X87,X7),X71),X84)) = X71,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__conv) ).
fof(fact_snd__conv,axiom,
! [X84,X71,X87,X7] : hAPP(c_Product__Type_Osnd(X7,X87),hAPP(hAPP(c_Product__Type_OPair(X7,X87),X71),X84)) = X84,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__conv) ).
fof(fact_minus__Min,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Min) ).
fof(fact_le__iff__add,axiom,
! [X44,X95] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
<=> ? [X118] : X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X118) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_insert__absorb,axiom,
! [X149,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Set_Oinsert(X7),X25),X149) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_the__elem__eq,axiom,
! [X6,X7] : c_Set_Othe__elem(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__eq) ).
fof(fact_linorder__linear,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_linorder__le__less__linear,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_fun__upd__idem,axiom,
! [X7,X105,X127,X6,X2] :
( hAPP(X2,X6) = X127
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,X7),X2),X6),X127) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
fof(fact_listsum__simps_I2_J,axiom,
! [X300,X86,X87] :
( class_Groups_Omonoid__add(X87)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X87),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X86),hAPP(c_List_Omonoid__add__class_Olistsum(X87),X300)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__simps_I2_J) ).
fof(fact_minus__divide__right,axiom,
! [X84,X71,X87] :
( class_Fields_Ofield__inverse__zero(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X84)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__right) ).
fof(fact_minus__mult__right,axiom,
! [X84,X71,X87] :
( class_Rings_Oring(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__right) ).
fof(fact_option_Osize_I2_J,axiom,
! [X25,X85,X7] : c_Option_Ooption_Ooption__size(X7,X85,hAPP(c_Option_Ooption_OSome(X7),X25)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X85,X25)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osize_I2_J) ).
fof(fact_partition_Osimps_I1_J,axiom,
! [X38,X7] : c_List_Opartition(X7,X38,c_List_Olist_ONil(X7)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_ONil(X7)),c_List_Olist_ONil(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I1_J) ).
fof(fact_take__1__Cons,axiom,
! [X300,X86,X87] : hAPP(hAPP(c_List_Otake(X87),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_List_Olist_OCons(X87),X86),c_List_Olist_ONil(X87)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__1__Cons) ).
fof(fact_wf__inv__image,axiom,
! [X2,X105,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> c_Wellfounded_Owf(X105,hAPP(hAPP(c_Relation_Oinv__image(X7,X105),X172),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__inv__image) ).
fof(fact_rp__inv__image__rp,axiom,
! [X2,X105,X38,X7] :
( c_FunDef_Oreduction__pair(X7,X38)
=> c_FunDef_Oreduction__pair(X105,hAPP(hAPP(c_FunDef_Orp__inv__image(X7,X105),X38),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
fof(fact_dvd__0__left,axiom,
! [X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),c_Groups_Ozero__class_Ozero(X87)),X71))
=> X71 = c_Groups_Ozero__class_Ozero(X87) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__left) ).
fof(fact_mod__add__self1,axiom,
! [X71,X84,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X71),X84) = c_Divides_Odiv__class_Omod(X87,X71,X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self1) ).
fof(fact_mod__add__self2,axiom,
! [X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84),X84) = c_Divides_Odiv__class_Omod(X87,X71,X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self2) ).
fof(fact_nth__via__drop,axiom,
! [X301,X98,X300,X33,X87] :
( hAPP(hAPP(c_List_Odrop(X87),X33),X300) = hAPP(hAPP(c_List_Olist_OCons(X87),X98),X301)
=> hAPP(hAPP(c_List_Onth(X87),X300),X33) = X98 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__via__drop) ).
fof(fact_max__Suc__Suc,axiom,
! [X33,X90] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),hAPP(c_Nat_OSuc,X33)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X90),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc__Suc) ).
fof(fact_min__Suc__Suc,axiom,
! [X33,X90] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),hAPP(c_Nat_OSuc,X33)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X90),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc__Suc) ).
fof(fact_times__code__numeral__code,axiom,
! [X90,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X33)),hAPP(c_Code__Numeral_Oof__nat,X90)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X90)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__code__numeral__code) ).
fof(fact_plus__code__numeral__code,axiom,
! [X90,X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X33)),hAPP(c_Code__Numeral_Oof__nat,X90)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X90)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__code__numeral__code) ).
fof(fact_zpower__int,axiom,
! [X33,X90] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)),X33) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X90),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__int) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
! [X33,X86] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86)),X33) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X86),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
fof(fact_zmult__zminus,axiom,
! [X128,X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X97)),X128) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zminus) ).
fof(fact_int__power,axiom,
! [X33,X90] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X90),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power) ).
fof(fact_abs__ge__zero,axiom,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(c_Groups_Oabs__class_Oabs(X87),X71))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_of__nat__0__le__iff,axiom,
! [X33,X87] :
( class_Rings_Olinordered__semidom(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X33))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0__le__iff) ).
fof(fact_zero__le__imp__of__nat,axiom,
! [X90,X87] :
( class_Rings_Olinordered__semidom(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X90))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__imp__of__nat) ).
fof(fact_inf_Oleft__idem,axiom,
! [X84,X71,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
fof(fact_inf__left__idem,axiom,
! [X98,X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__idem) ).
fof(fact_inf__sup__aci_I4_J,axiom,
! [X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
fof(fact_sup_Oleft__idem,axiom,
! [X84,X71,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).
fof(fact_sup__left__idem,axiom,
! [X98,X86,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__idem) ).
fof(fact_inf__sup__aci_I8_J,axiom,
! [X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).
fof(fact_min__max_Osup__left__idem,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__left__idem) ).
fof(fact_min__max_Osup_Oleft__idem,axiom,
! [X84,X71,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__idem) ).
fof(fact_min__max_Oinf__left__idem,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__left__idem) ).
fof(fact_min__max_Oinf_Oleft__idem,axiom,
! [X84,X71,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__idem) ).
fof(fact_mult__left__idem,axiom,
! [X84,X71,X87] :
( class_Lattices_Oab__semigroup__idem__mult(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__idem) ).
fof(fact_drop__tl,axiom,
! [X300,X33,X87] : hAPP(hAPP(c_List_Odrop(X87),X33),hAPP(c_List_Otl(X87),X300)) = hAPP(c_List_Otl(X87),hAPP(hAPP(c_List_Odrop(X87),X33),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__tl) ).
fof(fact_tl__drop,axiom,
! [X300,X33,X87] : hAPP(c_List_Otl(X87),hAPP(hAPP(c_List_Odrop(X87),X33),X300)) = hAPP(hAPP(c_List_Odrop(X87),X33),hAPP(c_List_Otl(X87),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__drop) ).
fof(fact_List_Oset_Osimps_I2_J,axiom,
! [X292,X6,X7] : hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)) = hAPP(hAPP(c_Set_Oinsert(X7),X6),hAPP(c_List_Oset(X7),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).
fof(fact_card__atLeastAtMost,axiom,
! [X160,X157] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X157,X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X160)),X157),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastAtMost) ).
fof(fact_surj__id,axiom,
! [X7] : hAPP(c_Set_Oimage(X7,X7,c_Fun_Oid(X7)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__id) ).
fof(fact_some__eq__ex,axiom,
! [X7,X38] :
( hBOOL(hAPP(X38,c_Hilbert__Choice_OEps(X7,X38)))
<=> ? [X142] : hBOOL(hAPP(X38,X142)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__ex) ).
fof(fact_partition__filter1,axiom,
! [X292,X38,X7] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Opartition(X7,X38,X292)) = hAPP(c_List_Ofilter(X7,X38),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter1) ).
fof(fact_dvd__1__left,axiom,
! [X96] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__left) ).
fof(fact_iso__tuple__UNIV__I,axiom,
! [X6,X7] : hBOOL(hAPP(hAPP(c_member(X7),X6),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(fact_UNIV__I,axiom,
! [X6,X7] : hBOOL(hAPP(hAPP(c_member(X7),X6),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(fact_Compl__eq__Compl__iff,axiom,
! [X155,X149,X7] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X155)
<=> X149 = X155 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).
fof(fact_fun__Compl__def,axiom,
! [X6,X149,X105,X7] :
( class_Groups_Ouminus(X7)
=> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X105,X7)),X149),X6) = hAPP(c_Groups_Ouminus__class_Ouminus(X7),hAPP(X149,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__Compl__def) ).
fof(fact_uminus__apply,axiom,
! [X6,X149,X105,X7] :
( class_Groups_Ouminus(X7)
=> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X105,X7)),X149),X6) = hAPP(c_Groups_Ouminus__class_Ouminus(X7),hAPP(X149,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__apply) ).
fof(fact_nat__0__le,axiom,
! [X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X97)) = X97 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__le) ).
fof(fact_tsub__eq,axiom,
! [X86,X98] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X86))
=> c_Nat__Transfer_Otsub(X86,X98) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X86),X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__eq) ).
fof(fact_subtract__code__numeral__code,axiom,
! [X90,X33] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X33)),hAPP(c_Code__Numeral_Oof__nat,X90)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),X90)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subtract__code__numeral__code) ).
fof(fact_full__small__int__def,axiom,
! [X136,X2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X2,X136) = c_Smallcheck_Ofull__small_H(X2,hAPP(c_Code__Numeral_Oint__of,X136),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X136))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_full__small__int__def) ).
fof(fact_int__eq__iff,axiom,
! [X26,X95] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) = X26
<=> ( X95 = hAPP(c_Int_Onat,X26)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__iff) ).
fof(fact_semilattice__big_OF__eq,axiom,
! [X149,X215,X2,X7] :
( c_Big__Operators_Osemilattice__big(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(X215,X149) = hAPP(c_Finite__Set_Ofold1(X7,X2),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).
fof(fact_folding__one_Oeq__fold,axiom,
! [X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(X215,X149) = hAPP(c_Finite__Set_Ofold1(X7,X2),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold) ).
fof(fact_Union__empty,axiom,
! [X7] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__empty) ).
fof(fact_Union__UNIV,axiom,
! [X7] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__UNIV) ).
fof(fact_Inter__empty,axiom,
! [X7] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__empty) ).
fof(fact_Inter__UNIV,axiom,
! [X7] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X7,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__UNIV) ).
fof(fact_insert__absorb2,axiom,
! [X149,X6,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X6),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Set_Oinsert(X7),X6),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
fof(fact_Bit1__Min,axiom,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__Min) ).
fof(fact_INF__const,axiom,
! [X210,X7,X149,X105] :
( class_Complete__Lattice_Ocomplete__lattice(X105)
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X105),X149),hAPP(c_COMBK(X105,X7),X210)) = X210 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__const) ).
fof(fact_SUP__const,axiom,
! [X210,X7,X149,X105] :
( class_Complete__Lattice_Ocomplete__lattice(X105)
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X105),X149),hAPP(c_COMBK(X105,X7),X210)) = X210 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__const) ).
fof(fact_compl__unique,axiom,
! [X98,X86,X87] :
( class_Lattices_Oboolean__algebra(X87)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98) = c_Orderings_Obot__class_Obot(X87)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98) = c_Orderings_Otop__class_Otop(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86) = X98 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__unique) ).
fof(fact_mult__Suc__right,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_finite__atLeastZeroLessThan__int,axiom,
! [X160] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).
fof(fact_transpose_Osimps_I2_J,axiom,
! [X334,X87] : c_List_Otranspose(X87,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X87)),c_List_Olist_ONil(X87)),X334)) = c_List_Otranspose(X87,X334),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I2_J) ).
fof(fact_Field__empty,axiom,
! [X7] : hAPP(c_Relation_OField(X7),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__empty) ).
fof(fact_mod__less,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33) = X90 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less) ).
fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
! [X160,X157] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X157),c_Groups_Oone__class_Oone(tc_Int_Oint)),X160) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X157,X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).
fof(fact_Sup__insert,axiom,
! [X149,X25,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OSup__class_OSup(X7,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X25),c_Complete__Lattice_OSup__class_OSup(X7,X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__insert) ).
fof(fact_Inf__insert,axiom,
! [X149,X25,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OInf__class_OInf(X7,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X25),c_Complete__Lattice_OInf__class_OInf(X7,X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__insert) ).
fof(fact_infinite__UNIV__int,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__int) ).
fof(fact_infinite__UNIV__nat,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).
fof(fact_small__int__def,axiom,
! [X136,X2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X2),X136) = c_Smallcheck_Osmall_H(X2,hAPP(c_Code__Numeral_Oint__of,X136),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X136))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__int__def) ).
fof(fact_butlast__append,axiom,
! [X300,X87,X301] :
( ( X301 = c_List_Olist_ONil(X87)
=> c_List_Obutlast(X87,hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = c_List_Obutlast(X87,X300) )
& ( X301 != c_List_Olist_ONil(X87)
=> c_List_Obutlast(X87,hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = hAPP(hAPP(c_List_Oappend(X87),X300),c_List_Obutlast(X87,X301)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__append) ).
fof(fact_butlast_Osimps_I2_J,axiom,
! [X86,X87,X300] :
( ( X300 = c_List_Olist_ONil(X87)
=> c_List_Obutlast(X87,hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = c_List_Olist_ONil(X87) )
& ( X300 != c_List_Olist_ONil(X87)
=> c_List_Obutlast(X87,hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = hAPP(hAPP(c_List_Olist_OCons(X87),X86),c_List_Obutlast(X87,X300)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).
fof(fact_vimage__empty,axiom,
! [X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__empty) ).
fof(fact_vimage__UNIV,axiom,
! [X2,X105,X7] : hAPP(c_Set_Ovimage(X7,X105,X2),c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UNIV) ).
fof(fact_Image__empty,axiom,
! [X191,X7,X105] : hAPP(c_Relation_OImage(X105,X7,X191),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__empty) ).
fof(fact_image__empty,axiom,
! [X2,X7,X105] : hAPP(c_Set_Oimage(X105,X7,X2),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).
fof(fact_listrel__refl__on,axiom,
! [X172,X149,X7] :
( c_Relation_Orefl__on(X7,X149,X172)
=> c_Relation_Orefl__on(tc_List_Olist(X7),c_List_Olists(X7,X149),c_List_Olistrel(X7,X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__refl__on) ).
fof(fact_equiv__listrel,axiom,
! [X172,X149,X7] :
( c_Equiv__Relations_Oequiv(X7,X149,X172)
=> c_Equiv__Relations_Oequiv(tc_List_Olist(X7),c_List_Olists(X7,X149),c_List_Olistrel(X7,X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__listrel) ).
fof(fact_mem__def,axiom,
! [X149,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
<=> hBOOL(hAPP(X149,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_com_Osize_I3_J,axiom,
! [X66,X13,X67] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X67,X13,X66)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X66)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I3_J) ).
fof(fact_dvdI,axiom,
! [X96,X84,X71,X87] :
( class_Rings_Odvd(X87)
=> ( X71 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X96)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X84),X71)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvdI) ).
fof(fact_diff__is__0__eq,axiom,
! [X44,X95] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X44) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_diff__is__0__eq_H,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_div__less,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less) ).
fof(fact_Int__UNIV__right,axiom,
! [X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__right) ).
fof(fact_Un__empty__right,axiom,
! [X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).
fof(fact_Diff__empty,axiom,
! [X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__empty) ).
fof(fact_double__complement,axiom,
! [X149,X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_rel__pow__1,axiom,
! [X191,X7] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X191) = X191,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__1) ).
fof(fact_dom__empty,axiom,
! [X105,X7] : c_Map_Odom(X7,X105,hAPP(c_COMBK(tc_Option_Ooption(X105),X7),c_Option_Ooption_ONone(X105))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__empty) ).
fof(fact_ran__empty,axiom,
! [X7,X105] : c_Map_Oran(X105,X7,hAPP(c_COMBK(tc_Option_Ooption(X7),X105),c_Option_Ooption_ONone(X7))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__empty) ).
fof(fact_list__update__id,axiom,
! [X114,X300,X87] : hAPP(hAPP(c_List_Olist__update(X87,X300),X114),hAPP(hAPP(c_List_Onth(X87),X300),X114)) = X300,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__id) ).
fof(fact_square__eq__iff,axiom,
! [X24,X25,X7] :
( class_Rings_Oidom(X7)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X24),X24)
<=> ( X25 = X24
| X25 = hAPP(c_Groups_Ouminus__class_Ouminus(X7),X24) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__iff) ).
fof(fact_add__Suc,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X33) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_drop__butlast,axiom,
! [X300,X33,X87] : hAPP(hAPP(c_List_Odrop(X87),X33),c_List_Obutlast(X87,X300)) = c_List_Obutlast(X87,hAPP(hAPP(c_List_Odrop(X87),X33),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__butlast) ).
fof(fact_butlast__drop,axiom,
! [X300,X33,X87] : c_List_Obutlast(X87,hAPP(hAPP(c_List_Odrop(X87),X33),X300)) = hAPP(hAPP(c_List_Odrop(X87),X33),c_List_Obutlast(X87,X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__drop) ).
fof(fact_code__numeral__not__eq__zero,axiom,
! [X107] :
( X107 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X107)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__not__eq__zero) ).
fof(fact_Domain__empty__iff,axiom,
! [X172,X105,X7] :
( hAPP(c_Relation_ODomain(X7,X105),X172) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> X172 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X105),tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
fof(fact_Range__empty__iff,axiom,
! [X172,X7,X105] :
( hAPP(c_Relation_ORange(X105,X7),X172) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> X172 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X105,X7),tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty__iff) ).
fof(fact_abs__zmult__eq__1,axiom,
! [X33,X90] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X33)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X90) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).
fof(fact_zless__linear,axiom,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X86),X98))
| X86 = X98
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(fact_nat__neq__iff,axiom,
! [X44,X95] :
( X95 != X44
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X95)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_card__atLeastLessThan__int,axiom,
! [X160,X157] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X157),X160)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X160),X157)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastLessThan__int) ).
fof(fact_abs__ge__self,axiom,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),hAPP(c_Groups_Oabs__class_Oabs(X87),X71))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__self) ).
fof(fact_card__greaterThanLessThan,axiom,
! [X160,X157] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X157,X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X160),hAPP(c_Nat_OSuc,X157)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanLessThan) ).
fof(fact_zle__linear,axiom,
! [X128,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X97),X128))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X128),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(fact_nat__le__linear,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_zdiv__zminus__zminus,axiom,
! [X84,X71] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).
fof(fact_zdiv__zminus2,axiom,
! [X84,X71] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71)),X84),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).
fof(fact_drop__Suc,axiom,
! [X300,X33,X87] : hAPP(hAPP(c_List_Odrop(X87),hAPP(c_Nat_OSuc,X33)),X300) = hAPP(hAPP(c_List_Odrop(X87),X33),hAPP(c_List_Otl(X87),X300)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Suc) ).
fof(fact_dom__eq__empty__conv,axiom,
! [X2,X105,X7] :
( c_Map_Odom(X7,X105,X2) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> X2 = hAPP(c_COMBK(tc_Option_Ooption(X105),X7),c_Option_Ooption_ONone(X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__eq__empty__conv) ).
fof(fact_gr0__implies__Suc,axiom,
! [X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ? [X116] : X33 = hAPP(c_Nat_OSuc,X116) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__implies__Suc) ).
fof(fact_gr0__conv__Suc,axiom,
! [X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44))
<=> ? [X116] : X44 = hAPP(c_Nat_OSuc,X116) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_min__max_OInf__fin_OF__eq,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149) = hAPP(c_Finite__Set_Ofold1(X7,c_Orderings_Oord__class_Omin(X7)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).
fof(fact_min__max_OSup__fin_OF__eq,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149) = hAPP(c_Finite__Set_Ofold1(X7,c_Orderings_Oord__class_Omax(X7)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).
fof(fact_fun__left__comm__insort,axiom,
! [X7] :
( class_Orderings_Olinorder(X7)
=> c_Finite__Set_Ofun__left__comm(X7,tc_List_Olist(X7),c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__insort) ).
fof(fact_distinct__tl,axiom,
! [X300,X87] :
( hBOOL(hAPP(c_List_Odistinct(X87),X300))
=> hBOOL(hAPP(c_List_Odistinct(X87),hAPP(c_List_Otl(X87),X300))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__tl) ).
fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
! [X160,X157] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X160),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X157,X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).
fof(fact_neg__def,axiom,
! [X166] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X166))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X166),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__def) ).
fof(fact_card__distinct,axiom,
! [X292,X7] :
( hAPP(c_Finite__Set_Ocard(X7),hAPP(c_List_Oset(X7),X292)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)
=> hBOOL(hAPP(c_List_Odistinct(X7),X292)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__distinct) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
! [X98,X86] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X86),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X86),X98)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).
fof(fact_singleton__rev__conv,axiom,
! [X292,X6,X7] :
( hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7)) = hAPP(c_List_Orev(X7),X292)
<=> X292 = hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__rev__conv) ).
fof(fact_rev__singleton__conv,axiom,
! [X6,X292,X7] :
( hAPP(c_List_Orev(X7),X292) = hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7))
<=> X292 = hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__singleton__conv) ).
fof(fact_com_Osize_I14_J,axiom,
! [X66,X13] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X13,X66)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X66)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I14_J) ).
fof(fact_listrel1__converse,axiom,
! [X172,X7] : c_List_Olistrel1(X7,hAPP(c_Relation_Oconverse(X7,X7),X172)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olistrel1(X7,X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__converse) ).
fof(fact_minus__diff__eq,axiom,
! [X84,X71,X87] :
( class_Groups_Oab__group__add(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X84),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_acc__wfD,axiom,
! [X6,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> hBOOL(hAPP(hAPP(c_member(X7),X6),c_Wellfounded_Oacc(X7,X172))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__wfD) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [X86,X87] :
( class_Rings_Ocomm__ring__1(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Oone__class_Oone(X87))),X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(fact_finite__atLeastLessThan__int,axiom,
! [X160,X157] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X157),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan__int) ).
fof(fact_finite__atLeastLessThan,axiom,
! [X160,X157] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X157),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
fof(fact_nat_Osize_I4_J,axiom,
! [X104] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X104)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X98,X86,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> X98 != X86 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X98,X86,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> X86 != X98 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X98,X86,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> X86 != X98 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_zdvd1__eq,axiom,
! [X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X6),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X6) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd1__eq) ).
fof(fact_dvd__if__abs__eq,axiom,
! [X96,X115,X87] :
( class_Rings_Olinordered__idom(X87)
=> ( hAPP(c_Groups_Oabs__class_Oabs(X87),X115) = hAPP(c_Groups_Oabs__class_Oabs(X87),X96)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X115),X96)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__if__abs__eq) ).
fof(fact_diff__eq__diff__eq,axiom,
! [X136,X23,X24,X25,X7] :
( class_Groups_Oab__group__add(X7)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X25),X24) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X23),X136)
=> ( X25 = X24
<=> X23 = X136 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_option__map__Some,axiom,
! [X6,X2,X7,X105] : hAPP(hAPP(c_Option_Omap(X105,X7),X2),hAPP(c_Option_Ooption_OSome(X105),X6)) = hAPP(c_Option_Ooption_OSome(X7),hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__Some) ).
fof(fact_rev__filter,axiom,
! [X292,X38,X7] : hAPP(c_List_Orev(X7),hAPP(c_List_Ofilter(X7,X38),X292)) = hAPP(c_List_Ofilter(X7,X38),hAPP(c_List_Orev(X7),X292)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__filter) ).
fof(fact_zmod__zminus1__not__zero,axiom,
! [X115,X96] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96),X115) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X115) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus1__not__zero) ).
fof(fact_zmod__zminus2__not__zero,axiom,
! [X115,X96] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X115)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X115) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2__not__zero) ).
fof(fact_neq0__conv,axiom,
! [X44] :
( X44 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_add__right__imp__eq,axiom,
! [X10,X71,X84,X87] :
( class_Groups_Ocancel__semigroup__add(X87)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X84),X71) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X71)
=> X84 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [X23,X25,X24,X7] :
( class_Groups_Ocancel__semigroup__add(X7)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X24),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X23),X25)
<=> X24 = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__imp__eq,axiom,
! [X10,X84,X71,X87] :
( class_Groups_Ocancel__ab__semigroup__add(X87)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)
=> X84 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X10,X84,X71,X87] :
( class_Groups_Ocancel__semigroup__add(X87)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10)
=> X84 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X23,X24,X25,X7] :
( class_Groups_Ocancel__semigroup__add(X7)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X23)
<=> X24 = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_com_Osimps_I2_J,axiom,
! [X68,X27,X69,X66,X13,X67] :
( c_Com_Ocom_OLocal(X67,X13,X66) = c_Com_Ocom_OLocal(X69,X27,X68)
<=> ( X67 = X69
& X13 = X27
& X66 = X68 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I2_J) ).
fof(fact_com_Osimps_I4_J,axiom,
! [X64,X65,X27,X54,X55,X13] :
( c_Com_Ocom_OCond(X13,X55,X54) = c_Com_Ocom_OCond(X27,X65,X64)
<=> ( X13 = X27
& X55 = X65
& X54 = X64 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I4_J) ).
fof(fact_com_Osimps_I7_J,axiom,
! [X27,X4,X28,X13,X5,X14] :
( c_Com_Ocom_OCall(X14,X5,X13) = c_Com_Ocom_OCall(X28,X4,X27)
<=> ( X14 = X28
& X5 = X4
& X13 = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I7_J) ).
fof(fact_nat__le__0,axiom,
! [X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X97),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Onat,X97) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__0) ).
fof(fact_nat__0__iff,axiom,
! [X107] :
( hAPP(c_Int_Onat,X107) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X107),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__iff) ).
fof(fact_is__nat__def,axiom,
! [X6] :
( c_Nat__Transfer_Ois__nat(X6)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__nat__def) ).
fof(fact_add__Suc__right,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,X33)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_com_Osimps_I36_J,axiom,
! [X64,X65,X27,X66,X13,X67] : c_Com_Ocom_OLocal(X67,X13,X66) != c_Com_Ocom_OCond(X27,X65,X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I36_J) ).
fof(fact_com_Osimps_I42_J,axiom,
! [X27,X4,X28,X66,X13,X67] : c_Com_Ocom_OLocal(X67,X13,X66) != c_Com_Ocom_OCall(X28,X4,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I42_J) ).
fof(fact_com_Osimps_I37_J,axiom,
! [X66,X13,X67,X64,X65,X27] : c_Com_Ocom_OCond(X27,X65,X64) != c_Com_Ocom_OLocal(X67,X13,X66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I37_J) ).
fof(fact_com_Osimps_I43_J,axiom,
! [X66,X13,X67,X27,X4,X28] : c_Com_Ocom_OCall(X28,X4,X27) != c_Com_Ocom_OLocal(X67,X13,X66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I43_J) ).
fof(fact_com_Osimps_I56_J,axiom,
! [X27,X4,X28,X54,X55,X13] : c_Com_Ocom_OCond(X13,X55,X54) != c_Com_Ocom_OCall(X28,X4,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I56_J) ).
fof(fact_com_Osimps_I57_J,axiom,
! [X54,X55,X13,X27,X4,X28] : c_Com_Ocom_OCall(X28,X4,X27) != c_Com_Ocom_OCond(X13,X55,X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I57_J) ).
fof(fact_lexn_Osimps_I1_J,axiom,
! [X172,X7] : hAPP(c_List_Olexn(X7,X172),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7)),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn_Osimps_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
! [X97] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(fact_zero__zle__int,axiom,
! [X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__zle__int) ).
fof(fact_Diff__cancel,axiom,
! [X149,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X149) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__cancel) ).
fof(fact_wf__empty,axiom,
! [X7] : c_Wellfounded_Owf(X7,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__empty) ).
fof(fact_atLeastAtMost__singleton_H,axiom,
! [X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( X25 = X24
=> c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24) = hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton_H) ).
fof(fact_sorted__list__of__set,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hAPP(c_List_Oset(X7),c_List_Olinorder__class_Osorted__list__of__set(X7,X149)) = X149
& c_List_Olinorder__class_Osorted(X7,c_List_Olinorder__class_Osorted__list__of__set(X7,X149))
& hBOOL(hAPP(c_List_Odistinct(X7),c_List_Olinorder__class_Osorted__list__of__set(X7,X149))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set) ).
fof(fact_mod__mult__self1__is__0,axiom,
! [X71,X84,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X71),X84) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).
fof(fact_mod__mult__self2__is__0,axiom,
! [X84,X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84),X84) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).
fof(fact_distinct__butlast,axiom,
! [X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> ( hBOOL(hAPP(c_List_Odistinct(X87),X300))
=> hBOOL(hAPP(c_List_Odistinct(X87),c_List_Obutlast(X87,X300))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__butlast) ).
fof(fact_card__greaterThanAtMost,axiom,
! [X160,X157] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X157,X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X160),X157),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanAtMost) ).
fof(fact_list_Oinject,axiom,
! [X303,X89,X294,X25,X7] :
( hAPP(hAPP(c_List_Olist_OCons(X7),X25),X294) = hAPP(hAPP(c_List_Olist_OCons(X7),X89),X303)
<=> ( X25 = X89
& X294 = X303 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Oinject) ).
fof(fact_append__same__eq,axiom,
! [X302,X292,X293,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X293),X292) = hAPP(hAPP(c_List_Oappend(X7),X302),X292)
<=> X293 = X302 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__same__eq) ).
fof(fact_same__append__eq,axiom,
! [X302,X293,X292,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X292),X293) = hAPP(hAPP(c_List_Oappend(X7),X292),X302)
<=> X293 = X302 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__append__eq) ).
fof(fact_char_Osimps_I2_J,axiom,
! [X31,X32,X22,X7] : c_String_Ochar_Ochar__case(X7,X22,hAPP(hAPP(c_String_Ochar_OChar,X32),X31)) = hAPP(hAPP(X22,X32),X31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_char_Osimps_I2_J) ).
fof(fact_char_Orecs,axiom,
! [X31,X32,X22,X7] : c_String_Ochar_Ochar__rec(X7,X22,hAPP(hAPP(c_String_Ochar_OChar,X32),X31)) = hAPP(hAPP(X22,X32),X31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_char_Orecs) ).
fof(fact_atLeastAtMost__singleton,axiom,
! [X25,X7] :
( class_Orderings_Oorder(X7)
=> c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X25) = hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton) ).
fof(fact_WT_OSemi,axiom,
! [X49,X53] :
( hBOOL(hAPP(c_Com_OWT,X53))
=> ( hBOOL(hAPP(c_Com_OWT,X49))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X53,X49))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OSemi) ).
fof(fact_WT_Oequations_I4_J,axiom,
! [X43,X42] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X42,X43)))
<=> ( hBOOL(hAPP(c_Com_OWT,X42))
& hBOOL(hAPP(c_Com_OWT,X43)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I4_J) ).
fof(fact_upto__empty,axiom,
! [X114,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X113),X114))
=> c_List_Oupto(X114,X113) = c_List_Olist_ONil(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto__empty) ).
fof(fact_atMost__Suc,axiom,
! [X94] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X94)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__Suc) ).
fof(fact_eq__number__of__0,axiom,
! [X163] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X163),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__0) ).
fof(fact_neg__imp__number__of__eq__0,axiom,
! [X139] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__number__of__eq__0) ).
fof(fact_eq__0__number__of,axiom,
! [X163] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X163),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__0__number__of) ).
fof(fact_inf__sup__absorb,axiom,
! [X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98)) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__absorb) ).
fof(fact_sup__inf__absorb,axiom,
! [X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98)) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__absorb) ).
fof(fact_min__max_Osup__inf__absorb,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98)) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__absorb) ).
fof(fact_min__max_Oinf__sup__absorb,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98)) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__absorb) ).
fof(fact_nat__dvd__1__iff__1,axiom,
! [X95] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X95),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> X95 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(fact_le__0__eq,axiom,
! [X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_drop__1__Cons,axiom,
! [X300,X86,X87] : hAPP(hAPP(c_List_Odrop(X87),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = X300,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__1__Cons) ).
fof(fact_diff__Suc__Suc,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),hAPP(c_Nat_OSuc,X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
fof(fact_add__Suc__shift,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_fold1__def,axiom,
! [X149,X2,X7] : hAPP(c_Finite__Set_Ofold1(X7,X2),X149) = c_HOL_OThe(X7,c_Finite__Set_Ofold1Set(X7,X2,X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__def) ).
fof(fact_zmod__eq__0__iff,axiom,
! [X136,X95] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X95,X136) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ? [X148] : X95 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X136),X148) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
fof(fact_mod__eq__0__iff,axiom,
! [X136,X95] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X95,X136) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ? [X148] : X95 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X136),X148) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
! [X6,X149] :
( c_Nat__Transfer_Onat__set(X149)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X6),X149))
=> c_Nat__Transfer_Ois__nat(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).
fof(fact_acyclic__converse,axiom,
! [X172,X7] :
( c_Wellfounded_Oacyclic(X7,hAPP(c_Relation_Oconverse(X7,X7),X172))
<=> c_Wellfounded_Oacyclic(X7,X172) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__converse) ).
fof(fact_distinct__card,axiom,
! [X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(c_List_Oset(X7),X292)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__card) ).
fof(fact_Domain__converse,axiom,
! [X172,X105,X7] : hAPP(c_Relation_ODomain(X7,X105),hAPP(c_Relation_Oconverse(X105,X7),X172)) = hAPP(c_Relation_ORange(X105,X7),X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__converse) ).
fof(fact_Range__converse,axiom,
! [X172,X7,X105] : hAPP(c_Relation_ORange(X105,X7),hAPP(c_Relation_Oconverse(X7,X105),X172)) = hAPP(c_Relation_ODomain(X7,X105),X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__converse) ).
fof(fact_rtrancl__converse,axiom,
! [X172,X7] : c_Transitive__Closure_Ortrancl(X7,hAPP(c_Relation_Oconverse(X7,X7),X172)) = hAPP(c_Relation_Oconverse(X7,X7),c_Transitive__Closure_Ortrancl(X7,X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converse) ).
fof(fact_Range__def,axiom,
! [X172,X7,X105] : hAPP(c_Relation_ORange(X105,X7),X172) = hAPP(c_Relation_ODomain(X7,X105),hAPP(c_Relation_Oconverse(X105,X7),X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__def) ).
fof(fact_list__update__nonempty,axiom,
! [X6,X94,X292,X7] :
( hAPP(hAPP(c_List_Olist__update(X7,X292),X94),X6) = c_List_Olist_ONil(X7)
<=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__nonempty) ).
fof(fact_map__is__Nil__conv,axiom,
! [X292,X2,X7,X105] :
( hAPP(hAPP(c_List_Omap(X105,X7),X2),X292) = c_List_Olist_ONil(X7)
<=> X292 = c_List_Olist_ONil(X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__is__Nil__conv) ).
fof(fact_option__map__is__None,axiom,
! [X295,X2,X7,X105] :
( hAPP(hAPP(c_Option_Omap(X105,X7),X2),X295) = c_Option_Ooption_ONone(X7)
<=> X295 = c_Option_Ooption_ONone(X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__is__None) ).
fof(fact_Nil__is__map__conv,axiom,
! [X292,X2,X105,X7] :
( c_List_Olist_ONil(X7) = hAPP(hAPP(c_List_Omap(X105,X7),X2),X292)
<=> X292 = c_List_Olist_ONil(X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__map__conv) ).
fof(fact_Option_Oset_Osimps_I2_J,axiom,
! [X6,X7] : c_Option_Oset(X7,hAPP(c_Option_Ooption_OSome(X7),X6)) = hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Oset_Osimps_I2_J) ).
fof(fact_diffs0__imp__equal,axiom,
! [X33,X90] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),X90) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X90 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_setprod__empty,axiom,
! [X2,X105,X7] :
( class_Groups_Ocomm__monoid__mult(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X7),X2),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__empty) ).
fof(fact_setprod_Oempty,axiom,
! [X1,X105,X7] :
( class_Groups_Ocomm__monoid__mult(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X105,X7),X1),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oempty) ).
fof(fact_setsum__empty,axiom,
! [X2,X105,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X2),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__empty) ).
fof(fact_setsum_Oempty,axiom,
! [X1,X105,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X105,X7),X1),c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oempty) ).
fof(fact_gr__implies__not0,axiom,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_finite__UNIV,axiom,
! [X7] :
( class_Finite__Set_Ofinite(X7)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV) ).
fof(fact_divide__eq__eq,axiom,
! [X25,X23,X24,X7] :
( class_Fields_Ofield__inverse__zero(X7)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23) = X25
<=> ( ( X23 != c_Groups_Ozero__class_Ozero(X7)
=> X24 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23) )
& ( X23 = c_Groups_Ozero__class_Ozero(X7)
=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
fof(fact_eq__divide__eq,axiom,
! [X23,X24,X25,X7] :
( class_Fields_Ofield__inverse__zero(X7)
=> ( X25 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)
<=> ( ( X23 != c_Groups_Ozero__class_Ozero(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23) = X24 )
& ( X23 = c_Groups_Ozero__class_Ozero(X7)
=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
fof(fact_of__nat__Suc,axiom,
! [X90,X87] :
( class_Rings_Osemiring__1(X87)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Nat_OSuc,X90)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Oone__class_Oone(X87)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__Suc) ).
fof(fact_zero__less__Suc,axiom,
! [X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X33))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_sum_Osize_I3_J,axiom,
! [X71,X7,X87] : hAPP(c_Nat_Osize__class_Osize(tc_sum(X87,X7)),hAPP(c_Sum__Type_OInl(X87,X7),X71)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osize_I3_J) ).
fof(fact_sum_Osize_I4_J,axiom,
! [X84,X7,X87] : hAPP(c_Nat_Osize__class_Osize(tc_sum(X87,X7)),hAPP(c_Sum__Type_OInr(X7,X87),X84)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osize_I4_J) ).
fof(fact_less__not__refl3,axiom,
! [X35,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X35))
=> X9 != X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X90))
=> X90 != X33 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_WT_Oequations_I6_J,axiom,
! [X42,X43] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X43,X42)))
<=> hBOOL(hAPP(c_Com_OWT,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I6_J) ).
fof(fact_WTs__elim__cases_I6_J,axiom,
! [X23,X24] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X24,X23)))
=> hBOOL(hAPP(c_Com_OWT,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I6_J) ).
fof(fact_atLeastLessThan__singleton,axiom,
! [X95] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X95)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X95),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__singleton) ).
fof(fact_sorted__remove1,axiom,
! [X71,X300,X87] :
( class_Orderings_Olinorder(X87)
=> ( c_List_Olinorder__class_Osorted(X87,X300)
=> c_List_Olinorder__class_Osorted(X87,c_List_Oremove1(X87,X71,X300)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__remove1) ).
fof(fact_mult__cancel2,axiom,
! [X44,X94,X95] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X94) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X94)
<=> ( X95 = X44
| X94 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [X44,X95,X94] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X95) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X44)
<=> ( X94 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X95 = X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_mult__cancel1,axiom,
! [X44,X95,X94] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X95) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X44)
<=> ( X95 = X44
| X94 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(fact_hd__append,axiom,
! [X301,X87,X300] :
( ( X300 = c_List_Olist_ONil(X87)
=> hAPP(c_List_Ohd(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = hAPP(c_List_Ohd(X87),X301) )
& ( X300 != c_List_Olist_ONil(X87)
=> hAPP(c_List_Ohd(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = hAPP(c_List_Ohd(X87),X300) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__append) ).
fof(fact_WTs__elim__cases_I7_J,axiom,
! [X79] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X79)))
=> ~ ! [X82] : hAPP(c_Com_Obody,X79) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X82) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I7_J) ).
fof(fact_WT_Oequations_I7_J,axiom,
! [X25] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X25)))
<=> ? [X82] : hAPP(c_Com_Obody,X25) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X82) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I7_J) ).
fof(fact_evalc__elim__cases_I1_J,axiom,
! [X35,X9] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X9),X35))
=> X35 = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I1_J) ).
fof(fact_mult__sgn__abs,axiom,
! [X86,X87] :
( class_Rings_Olinordered__idom(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),c_Groups_Osgn__class_Osgn(X87,X86)),hAPP(c_Groups_Oabs__class_Oabs(X87),X86)) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).
fof(fact_Ints__1,axiom,
! [X7] :
( class_Rings_Oring__1(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),c_Groups_Oone__class_Oone(X7)),c_Int_Oring__1__class_OInts(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__1) ).
fof(fact_Nats__1,axiom,
! [X7] :
( class_Rings_Osemiring__1(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),c_Groups_Oone__class_Oone(X7)),c_Nat_Osemiring__1__class_ONats(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__1) ).
fof(fact_Ints__0,axiom,
! [X7] :
( class_Rings_Oring__1(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),c_Groups_Ozero__class_Ozero(X7)),c_Int_Oring__1__class_OInts(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__0) ).
fof(fact_Nats__0,axiom,
! [X7] :
( class_Rings_Osemiring__1(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),c_Groups_Ozero__class_Ozero(X7)),c_Nat_Osemiring__1__class_ONats(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__0) ).
fof(fact_zero__le__one,axiom,
! [X87] :
( class_Rings_Olinordered__semidom(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Ozero__class_Ozero(X87)),c_Groups_Oone__class_Oone(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_zero__less__one,axiom,
! [X87] :
( class_Rings_Olinordered__semidom(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),c_Groups_Oone__class_Oone(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_divide__eq__imp,axiom,
! [X71,X84,X10,X87] :
( class_Rings_Odivision__ring(X87)
=> ( X10 != c_Groups_Ozero__class_Ozero(X87)
=> ( X84 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X84),X10) = X71 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
fof(fact_nonzero__divide__eq__eq,axiom,
! [X25,X24,X23,X7] :
( class_Rings_Odivision__ring(X7)
=> ( X23 != c_Groups_Ozero__class_Ozero(X7)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23) = X25
<=> X24 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [X24,X25,X23,X7] :
( class_Rings_Odivision__ring(X7)
=> ( X23 != c_Groups_Ozero__class_Ozero(X7)
=> ( X25 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23) = X24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
fof(fact_eq__divide__imp,axiom,
! [X84,X71,X10,X87] :
( class_Rings_Odivision__ring(X87)
=> ( X10 != c_Groups_Ozero__class_Ozero(X87)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X10) = X84
=> X71 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X84),X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
fof(fact_diff__minus__eq__add,axiom,
! [X84,X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_diff__eq,axiom,
! [X98,X86,X87] :
( class_Lattices_Oboolean__algebra(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X86),X98) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq) ).
fof(fact_ab__diff__minus,axiom,
! [X84,X71,X87] :
( class_Groups_Oab__group__add(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_diff__def,axiom,
! [X84,X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X84) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__def) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
! [X98,X86,X87] :
( class_Rings_Ocomm__ring__1(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X86),X98) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X86),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_mult__minus1,axiom,
! [X97,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin)),X97) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__minus1) ).
fof(fact_bin__less__0__simps_I1_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
fof(fact_hd__append2,axiom,
! [X301,X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> hAPP(c_List_Ohd(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = hAPP(c_List_Ohd(X87),X300) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__append2) ).
fof(fact_nat__add__right__cancel,axiom,
! [X44,X94,X95] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X94) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X94)
<=> X95 = X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X44,X95,X94] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X95) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X44)
<=> X95 = X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_singleton__conv2,axiom,
! [X25,X7] : hAPP(c_Set_OCollect(X7),hAPP(c_fequal,X25)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv2) ).
fof(fact_sorted__drop,axiom,
! [X33,X300,X87] :
( class_Orderings_Olinorder(X87)
=> ( c_List_Olinorder__class_Osorted(X87,X300)
=> c_List_Olinorder__class_Osorted(X87,hAPP(hAPP(c_List_Odrop(X87),X33),X300)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__drop) ).
fof(fact_sorted__take,axiom,
! [X33,X300,X87] :
( class_Orderings_Olinorder(X87)
=> ( c_List_Olinorder__class_Osorted(X87,X300)
=> c_List_Olinorder__class_Osorted(X87,hAPP(hAPP(c_List_Otake(X87),X33),X300)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__take) ).
fof(fact_finite_Oequations_I1_J,axiom,
! [X7] : hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
fof(fact_finite_OemptyI,axiom,
! [X7] : hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OemptyI) ).
fof(fact_Pow__not__empty,axiom,
! [X149,X7] : hAPP(c_Set_OPow(X7),X149) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__not__empty) ).
fof(fact_Compl__empty__eq,axiom,
! [X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_Pow__UNIV,axiom,
! [X7] : hAPP(c_Set_OPow(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__UNIV) ).
fof(fact_Id__on__empty,axiom,
! [X7] : c_Relation_OId__on(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__empty) ).
fof(fact_Int__absorb,axiom,
! [X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X149) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
fof(fact_Un__absorb,axiom,
! [X149,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X149) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
fof(fact_wf__in__rel,axiom,
! [X191,X7] :
( c_Wellfounded_Owf(X7,X191)
=> c_Wellfounded_OwfP(X7,c_FunDef_Oin__rel(X7,X7,X191)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__in__rel) ).
fof(fact_wf__mlex,axiom,
! [X2,X191,X7] :
( c_Wellfounded_Owf(X7,X191)
=> c_Wellfounded_Owf(X7,c_Wellfounded_Omlex__prod(X7,X2,X191)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__mlex) ).
fof(fact_Inf__fin_OF__eq,axiom,
! [X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,X149) = hAPP(c_Finite__Set_Ofold1(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_OF__eq) ).
fof(fact_Min_OF__eq,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olinorder__class_OMin(X7,X149) = hAPP(c_Finite__Set_Ofold1(X7,c_Orderings_Oord__class_Omin(X7)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_OF__eq) ).
fof(fact_Max_OF__eq,axiom,
! [X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olinorder__class_OMax(X7,X149) = hAPP(c_Finite__Set_Ofold1(X7,c_Orderings_Oord__class_Omax(X7)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_OF__eq) ).
fof(fact_Sup__fin_OF__eq,axiom,
! [X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,X149) = hAPP(c_Finite__Set_Ofold1(X7,c_Lattices_Osemilattice__sup__class_Osup(X7)),X149) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_OF__eq) ).
fof(fact_lessI,axiom,
! [X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_OSuc,X33))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_compl__inf__bot,axiom,
! [X86,X87] :
( class_Lattices_Oboolean__algebra(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86)),X86) = c_Orderings_Obot__class_Obot(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__inf__bot) ).
fof(fact_compl__sup__top,axiom,
! [X86,X87] :
( class_Lattices_Oboolean__algebra(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86)),X86) = c_Orderings_Otop__class_Otop(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__sup__top) ).
fof(fact_ab__left__minus,axiom,
! [X71,X87] :
( class_Groups_Oab__group__add(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),X71) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(fact_left__minus,axiom,
! [X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)),X71) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__minus) ).
fof(fact_last__append,axiom,
! [X300,X87,X301] :
( ( X301 = c_List_Olist_ONil(X87)
=> c_List_Olast(X87,hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = c_List_Olast(X87,X300) )
& ( X301 != c_List_Olist_ONil(X87)
=> c_List_Olast(X87,hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = c_List_Olast(X87,X301) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__append) ).
fof(fact_last__appendL,axiom,
! [X300,X87,X301] :
( X301 = c_List_Olist_ONil(X87)
=> c_List_Olast(X87,hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = c_List_Olast(X87,X300) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendL) ).
fof(fact_diff__add__0,axiom,
! [X90,X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X90)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(fact_sublist__upt__eq__take,axiom,
! [X44,X157,X7] : c_List_Osublist(X7,X157,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X44)) = hAPP(hAPP(c_List_Otake(X7),X44),X157),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__upt__eq__take) ).
fof(fact_one__dvd,axiom,
! [X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),c_Groups_Oone__class_Oone(X87)),X71)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(fact_bot__least,axiom,
! [X86,X87] :
( class_Orderings_Obot(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Orderings_Obot__class_Obot(X87)),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
fof(fact_divmod__int__correct,axiom,
! [X71,X84] :
( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),c_Divides_Odivmod__int(X71,X84))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__correct) ).
fof(fact_pdivmod__posDivAlg,axiom,
! [X96,X115] :
( ( X115 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Opdivmod(X96,X115) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X96)) )
& ( X115 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Opdivmod(X96,X115) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X96),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X115)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__posDivAlg) ).
fof(fact_sorted__single,axiom,
! [X86,X87] :
( class_Orderings_Olinorder(X87)
=> c_List_Olinorder__class_Osorted(X87,hAPP(hAPP(c_List_Olist_OCons(X87),X86),c_List_Olist_ONil(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__single) ).
fof(fact_last__appendR,axiom,
! [X300,X87,X301] :
( X301 != c_List_Olist_ONil(X87)
=> c_List_Olast(X87,hAPP(hAPP(c_List_Oappend(X87),X300),X301)) = c_List_Olast(X87,X301) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendR) ).
fof(fact_last_Osimps,axiom,
! [X86,X87,X300] :
( ( X300 = c_List_Olist_ONil(X87)
=> c_List_Olast(X87,hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = X86 )
& ( X300 != c_List_Olist_ONil(X87)
=> c_List_Olast(X87,hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = c_List_Olast(X87,X300) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last_Osimps) ).
fof(fact_last__ConsR,axiom,
! [X86,X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> c_List_Olast(X87,hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = c_List_Olast(X87,X300) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsR) ).
fof(fact_nat__gcd_Osimps,axiom,
! [X86,X98] :
( ( X98 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(X86,X98) = X86 )
& ( X98 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(X86,X98) = c_Nitpick_Onat__gcd(X98,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X86,X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Osimps) ).
fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
! [X160,X157] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X157)),X160) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X157,X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).
fof(fact_card__atLeastLessThan,axiom,
! [X160,X157] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X157),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X160),X157),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastLessThan) ).
fof(fact_rel__simps_I20_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I20_J) ).
fof(fact_rel__simps_I2_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).
fof(fact_rel__simps_I3_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I3_J) ).
fof(fact_rel__simps_I7_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I7_J) ).
fof(fact_not__neg__number__of__Pls,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__number__of__Pls) ).
fof(fact_zip__Nil,axiom,
! [X301,X7,X87] : hAPP(hAPP(c_List_Ozip(X87,X7),c_List_Olist_ONil(X87)),X301) = c_List_Olist_ONil(tc_prod(X87,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Nil) ).
fof(fact_top1I,axiom,
! [X6,X7] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_vimage__id,axiom,
! [X149,X7] : hAPP(c_Set_Ovimage(X7,X7,c_Fun_Oid(X7)),X149) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__id) ).
fof(fact_vimage__ident,axiom,
! [X60,X7] : hAPP(c_Set_Ovimage(X7,X7,c_COMBI(X7)),X60) = X60,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__ident) ).
fof(fact_image__id,axiom,
! [X60,X7] : hAPP(c_Set_Oimage(X7,X7,c_Fun_Oid(X7)),X60) = X60,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__id) ).
fof(fact_image__ident,axiom,
! [X60,X7] : hAPP(c_Set_Oimage(X7,X7,c_COMBI(X7)),X60) = X60,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
fof(fact_Projr_Osimps,axiom,
! [X86,X7,X87] : c_Sum__Type_OProjr(X87,X7,hAPP(c_Sum__Type_OInr(X7,X87),X86)) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projr_Osimps) ).
fof(fact_Projl_Osimps,axiom,
! [X86,X7,X87] : c_Sum__Type_OProjl(X87,X7,hAPP(c_Sum__Type_OInl(X87,X7),X86)) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projl_Osimps) ).
fof(fact_refl__rtrancl,axiom,
! [X172,X7] : c_Relation_Orefl__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X7,X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__rtrancl) ).
fof(fact_Compl__atLeast,axiom,
! [X94,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X7),X94)) = hAPP(c_SetInterval_Oord__class_OlessThan(X7),X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__atLeast) ).
fof(fact_Compl__atMost,axiom,
! [X94,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X7),X94)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__atMost) ).
fof(fact_Compl__greaterThan,axiom,
! [X94,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X94)) = hAPP(c_SetInterval_Oord__class_OatMost(X7),X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__greaterThan) ).
fof(fact_Compl__lessThan,axiom,
! [X94,X7] :
( class_Orderings_Olinorder(X7)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X7),X94)) = hAPP(c_SetInterval_Oord__class_OatLeast(X7),X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__lessThan) ).
fof(fact_empty,axiom,
! [X216,X7] : c_Hoare__Mirabelle_Ohoare__derivs(X7,X216,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty) ).
fof(fact_hoare__derivs_Oequations_I1_J,axiom,
! [X25,X7] : c_Hoare__Mirabelle_Ohoare__derivs(X7,X25,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).
fof(fact_Sup__fin__Sup,axiom,
! [X149,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,X149) = c_Complete__Lattice_OSup__class_OSup(X7,X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin__Sup) ).
fof(fact_Inf__fin__Inf,axiom,
! [X149,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,X149) = c_Complete__Lattice_OInf__class_OInf(X7,X149) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin__Inf) ).
fof(fact_add__numeral__0,axiom,
! [X71,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OPls)),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0) ).
fof(fact_add__is__1,axiom,
! [X44,X95] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X44) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X95 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X44 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(fact_one__is__add,axiom,
! [X44,X95] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X44)
<=> ( ( X95 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X44 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(fact_someI__ex,axiom,
! [X7,X38] :
( ? [X142] : hBOOL(hAPP(X38,X142))
=> hBOOL(hAPP(X38,c_Hilbert__Choice_OEps(X7,X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI__ex) ).
fof(fact_someI,axiom,
! [X7,X6,X38] :
( hBOOL(hAPP(X38,X6))
=> hBOOL(hAPP(X38,c_Hilbert__Choice_OEps(X7,X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI) ).
fof(fact_tfl__some,axiom,
! [X7,X267] :
( ? [X3] : hBOOL(hAPP(X267,X3))
=> hBOOL(hAPP(X267,c_Hilbert__Choice_OEps(X7,X267))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__some) ).
fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
! [X160,X157] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X157),X160) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X157,X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).
fof(fact_square__eq__1__iff,axiom,
! [X6,X7] :
( class_Rings_Oring__1__no__zero__divisors(X7)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X6) = c_Groups_Oone__class_Oone(X7)
<=> ( X6 = c_Groups_Oone__class_Oone(X7)
| X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X7),c_Groups_Oone__class_Oone(X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_Inl__inject,axiom,
! [X98,X86,X7,X87] :
( hAPP(c_Sum__Type_OInl(X87,X7),X86) = hAPP(c_Sum__Type_OInl(X87,X7),X98)
=> X86 = X98 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inl__inject) ).
fof(fact_sum_Osimps_I1_J,axiom,
! [X89,X25,X105,X7] :
( hAPP(c_Sum__Type_OInl(X7,X105),X25) = hAPP(c_Sum__Type_OInl(X7,X105),X89)
<=> X25 = X89 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I1_J) ).
fof(fact_Inr__inject,axiom,
! [X98,X86,X87,X7] :
( hAPP(c_Sum__Type_OInr(X7,X87),X86) = hAPP(c_Sum__Type_OInr(X7,X87),X98)
=> X86 = X98 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inr__inject) ).
fof(fact_sum_Osimps_I2_J,axiom,
! [X112,X24,X7,X105] :
( hAPP(c_Sum__Type_OInr(X105,X7),X24) = hAPP(c_Sum__Type_OInr(X105,X7),X112)
<=> X24 = X112 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I2_J) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_zip_Osimps_I1_J,axiom,
! [X300,X7,X87] : hAPP(hAPP(c_List_Ozip(X87,X7),X300),c_List_Olist_ONil(X7)) = c_List_Olist_ONil(tc_prod(X87,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip_Osimps_I1_J) ).
fof(fact_comm__monoid_Ocomm__neutral,axiom,
! [X25,X26,X2,X7] :
( c_Groups_Ocomm__monoid(X7,X2,X26)
=> hAPP(hAPP(X2,X25),X26) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid_Ocomm__neutral) ).
fof(fact_folding__one__idem_Oidem,axiom,
! [X6,X215,X2,X7] :
( c_Finite__Set_Ofolding__one__idem(X7,X2,X215)
=> hAPP(hAPP(X2,X6),X6) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
fof(fact_com_Osize_I16_J,axiom,
! [X13,X5,X14] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X14,X5,X13)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I16_J) ).
fof(fact_dvd__0__right,axiom,
! [X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),c_Groups_Ozero__class_Ozero(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(fact_top__greatest,axiom,
! [X86,X87] :
( class_Orderings_Otop(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),c_Orderings_Otop__class_Otop(X87))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).
fof(fact_Inl__not__Inr,axiom,
! [X84,X71,X7,X87] : hAPP(c_Sum__Type_OInl(X87,X7),X71) != hAPP(c_Sum__Type_OInr(X7,X87),X84),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inl__not__Inr) ).
fof(fact_sum_Osimps_I3_J,axiom,
! [X124,X71,X7,X87] : hAPP(c_Sum__Type_OInl(X87,X7),X71) != hAPP(c_Sum__Type_OInr(X7,X87),X124),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I3_J) ).
fof(fact_Inr__not__Inl,axiom,
! [X71,X84,X87,X7] : hAPP(c_Sum__Type_OInr(X7,X87),X84) != hAPP(c_Sum__Type_OInl(X87,X7),X71),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inr__not__Inl) ).
fof(fact_sum_Osimps_I4_J,axiom,
! [X120,X121,X122,X123] : hAPP(c_Sum__Type_OInr(X123,X122),X121) != hAPP(c_Sum__Type_OInl(X122,X123),X120),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I4_J) ).
fof(fact_last__ConsL,axiom,
! [X86,X87,X300] :
( X300 = c_List_Olist_ONil(X87)
=> c_List_Olast(X87,hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsL) ).
fof(fact_nat__rec__0,axiom,
! [X21,X22,X7] : hAPP(c_Nat_Onat_Onat__rec(X7,X22,X21),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__0) ).
fof(fact_insert__not__empty,axiom,
! [X149,X25,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X25),X149) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
fof(fact_empty__not__insert,axiom,
! [X149,X25,X7] : c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X7),X25),X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
fof(fact_int__Suc,axiom,
! [X90] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X90)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__Suc) ).
fof(fact_diff__int__def__symmetric,axiom,
! [X128,X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X97),X128),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [X128,X97] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X97),X128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).
fof(fact_tl_Osimps_I2_J,axiom,
! [X300,X86,X87] : hAPP(c_List_Otl(X87),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = X300,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I2_J) ).
fof(fact_hd_Osimps,axiom,
! [X300,X86,X87] : hAPP(c_List_Ohd(X87),hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300)) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd_Osimps) ).
fof(fact_power__eq__0__iff,axiom,
! [X44,X25,X7] :
( ( class_Power_Opower(X7)
& class_Rings_Omult__zero(X7)
& class_Rings_Ono__zero__divisors(X7)
& class_Rings_Ozero__neq__one(X7) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X7),X25),X44) = c_Groups_Ozero__class_Ozero(X7)
<=> ( X25 = c_Groups_Ozero__class_Ozero(X7)
& X44 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
! [X98,X86] :
( c_Nat__Transfer_Ois__nat(X86)
=> ( c_Nat__Transfer_Ois__nat(X98)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X86,X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).
fof(fact_While,axiom,
! [X24,X23] :
( hBOOL(hAPP(c_Com_OWT,X23))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X24,X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_While) ).
fof(fact_divide__minus1,axiom,
! [X86,X87] :
( ( class_Fields_Ofield__inverse__zero(X87)
& class_Int_Onumber__ring(X87) )
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__minus1) ).
fof(fact_wf__lexn,axiom,
! [X44,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> c_Wellfounded_Owf(tc_List_Olist(X7),hAPP(c_List_Olexn(X7,X172),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lexn) ).
fof(fact_list__update__code_I1_J,axiom,
! [X98,X114,X87] : hAPP(hAPP(c_List_Olist__update(X87,c_List_Olist_ONil(X87)),X114),X98) = c_List_Olist_ONil(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I1_J) ).
fof(fact_list__update_Osimps_I1_J,axiom,
! [X139,X114,X87] : hAPP(hAPP(c_List_Olist__update(X87,c_List_Olist_ONil(X87)),X114),X139) = c_List_Olist_ONil(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update_Osimps_I1_J) ).
fof(fact_power__Suc__0,axiom,
! [X33] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__0) ).
fof(fact_finite__set,axiom,
! [X292,X7] : hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_List_Oset(X7),X292))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__set) ).
fof(fact_converse__converse,axiom,
! [X172,X7,X105] : hAPP(c_Relation_Oconverse(X105,X7),hAPP(c_Relation_Oconverse(X7,X105),X172)) = X172,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__converse) ).
fof(fact_char_Oinject,axiom,
! [X29,X30,X31,X32] :
( hAPP(hAPP(c_String_Ochar_OChar,X32),X31) = hAPP(hAPP(c_String_Ochar_OChar,X30),X29)
<=> ( X32 = X30
& X31 = X29 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_char_Oinject) ).
fof(fact_lessThan__Suc,axiom,
! [X94] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X94),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X94)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc) ).
fof(fact_Field__converse,axiom,
! [X172,X7] : hAPP(c_Relation_OField(X7),hAPP(c_Relation_Oconverse(X7,X7),X172)) = hAPP(c_Relation_OField(X7),X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__converse) ).
fof(fact_number__of__minus,axiom,
! [X128,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__minus) ).
fof(fact_of__int__minus,axiom,
! [X97,X87] :
( class_Rings_Oring__1(X87)
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X97)) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(c_Int_Oring__1__class_Oof__int(X87),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__minus) ).
fof(fact_arith__simps_I30_J,axiom,
! [X128,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [X95,X6] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X6),X95) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X6 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_order__eq__refl,axiom,
! [X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( X86 = X98
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_com_Osize_I6_J,axiom,
! [X66,X13] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X13,X66)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X66)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I6_J) ).
fof(fact_minus__unique,axiom,
! [X84,X71,X87] :
( class_Groups_Ogroup__add(X87)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X84) = c_Groups_Ozero__class_Ozero(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71) = X84 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__unique) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [X24,X25,X7] :
( class_Groups_Ogroup__add(X7)
=> ( X25 = hAPP(c_Groups_Ouminus__class_Ouminus(X7),X24)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X24) = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_empty__def,axiom,
! [X7] : c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7),hAPP(c_COMBK(tc_HOL_Obool,X7),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_UNIV__def,axiom,
! [X7] : c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7),hAPP(c_COMBK(tc_HOL_Obool,X7),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
! [X127,X6] :
( c_Nat__Transfer_Ois__nat(X6)
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X6,X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).
fof(fact_mult__minus1__right,axiom,
! [X97,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X97),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__minus1__right) ).
fof(fact_mult__eq__1__iff,axiom,
! [X44,X95] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X44) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X95 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X44 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
fof(fact_nat_Osize_I2_J,axiom,
! [X104] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X104)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).
fof(fact_dvd__refl,axiom,
! [X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X87),X71),X71)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(fact_order__refl,axiom,
! [X86,X87] :
( class_Orderings_Opreorder(X87)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_card__atLeastZeroLessThan__int,axiom,
! [X160] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X160)) = hAPP(c_Int_Onat,X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).
fof(fact_com_Osize_I8_J,axiom,
! [X13,X5,X14] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X14,X5,X13)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I8_J) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X97)),X97) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
! [X160,X157] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X157),hAPP(c_Nat_OSuc,X160)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X157,X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).
fof(fact_mod__int__def,axiom,
! [X84,X71] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X84) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X71,X84)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__int__def) ).
fof(fact_inf_Ocommute,axiom,
! [X84,X71,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X84),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
fof(fact_inf__commute,axiom,
! [X98,X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__commute) ).
fof(fact_inf__sup__aci_I1_J,axiom,
! [X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X98) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X98),X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
fof(fact_sup_Ocommute,axiom,
! [X84,X71,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X84),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Ocommute) ).
fof(fact_sup__commute,axiom,
! [X98,X86,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__commute) ).
fof(fact_inf__sup__aci_I5_J,axiom,
! [X98,X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X98) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X98),X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).
fof(fact_min__max_Osup__commute,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X98) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X98),X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__commute) ).
fof(fact_min__max_Osup_Ocommute,axiom,
! [X84,X71,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X84),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Ocommute) ).
fof(fact_min__max_Oinf__commute,axiom,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X98) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X98),X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__commute) ).
fof(fact_min__max_Oinf_Ocommute,axiom,
! [X84,X71,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X84),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Ocommute) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X84,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X84),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X10,X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X10),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_nat__zminus__int,axiom,
! [X33] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zminus__int) ).
fof(fact_gr0I,axiom,
! [X33] :
( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
! [X98,X86] :
( c_Nat__Transfer_Ois__nat(X86)
=> ( c_Nat__Transfer_Ois__nat(X98)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
! [X98,X86] :
( c_Nat__Transfer_Ois__nat(X86)
=> ( c_Nat__Transfer_Ois__nat(X98)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
! [X98,X86] :
( c_Nat__Transfer_Ois__nat(X86)
=> ( c_Nat__Transfer_Ois__nat(X98)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X86),X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).
fof(fact_negative__eq__positive,axiom,
! [X95,X44] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95)
<=> ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__eq__positive) ).
fof(fact_com_Osimps_I38_J,axiom,
! [X68,X27,X66,X13,X67] : c_Com_Ocom_OLocal(X67,X13,X66) != c_Com_Ocom_OWhile(X27,X68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I38_J) ).
fof(fact_com_Osimps_I34_J,axiom,
! [X64,X65,X66,X13,X67] : c_Com_Ocom_OLocal(X67,X13,X66) != c_Com_Ocom_OSemi(X65,X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I34_J) ).
fof(fact_com_Osimps_I23_J,axiom,
! [X13,X14,X68,X27,X69] : c_Com_Ocom_OLocal(X69,X27,X68) != c_Com_Ocom_OAss(X14,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I23_J) ).
fof(fact_com_Osimps_I52_J,axiom,
! [X68,X27,X54,X55,X13] : c_Com_Ocom_OCond(X13,X55,X54) != c_Com_Ocom_OWhile(X27,X68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I52_J) ).
fof(fact_com_Osimps_I45_J,axiom,
! [X54,X55,X64,X65,X27] : c_Com_Ocom_OCond(X27,X65,X64) != c_Com_Ocom_OSemi(X55,X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I45_J) ).
fof(fact_com_Osimps_I27_J,axiom,
! [X13,X14,X64,X65,X27] : c_Com_Ocom_OCond(X27,X65,X64) != c_Com_Ocom_OAss(X14,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I27_J) ).
fof(fact_com_Osimps_I61_J,axiom,
! [X66,X13,X27,X4,X28] : c_Com_Ocom_OCall(X28,X4,X27) != c_Com_Ocom_OWhile(X13,X66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I61_J) ).
fof(fact_com_Osimps_I51_J,axiom,
! [X54,X55,X27,X4,X28] : c_Com_Ocom_OCall(X28,X4,X27) != c_Com_Ocom_OSemi(X55,X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I51_J) ).
fof(fact_com_Osimps_I33_J,axiom,
! [X13,X14,X27,X4,X28] : c_Com_Ocom_OCall(X28,X4,X27) != c_Com_Ocom_OAss(X14,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I33_J) ).
fof(fact_com_Osimps_I39_J,axiom,
! [X66,X13,X67,X68,X27] : c_Com_Ocom_OWhile(X27,X68) != c_Com_Ocom_OLocal(X67,X13,X66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I39_J) ).
fof(fact_com_Osimps_I53_J,axiom,
! [X54,X55,X13,X68,X27] : c_Com_Ocom_OWhile(X27,X68) != c_Com_Ocom_OCond(X13,X55,X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I53_J) ).
fof(fact_com_Osimps_I60_J,axiom,
! [X27,X4,X28,X66,X13] : c_Com_Ocom_OWhile(X13,X66) != c_Com_Ocom_OCall(X28,X4,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I60_J) ).
fof(fact_com_Osimps_I35_J,axiom,
! [X66,X13,X67,X64,X65] : c_Com_Ocom_OSemi(X65,X64) != c_Com_Ocom_OLocal(X67,X13,X66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I35_J) ).
fof(fact_com_Osimps_I44_J,axiom,
! [X64,X65,X27,X54,X55] : c_Com_Ocom_OSemi(X55,X54) != c_Com_Ocom_OCond(X27,X65,X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I44_J) ).
fof(fact_com_Osimps_I50_J,axiom,
! [X27,X4,X28,X54,X55] : c_Com_Ocom_OSemi(X55,X54) != c_Com_Ocom_OCall(X28,X4,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I50_J) ).
fof(fact_com_Osimps_I22_J,axiom,
! [X68,X27,X69,X13,X14] : c_Com_Ocom_OAss(X14,X13) != c_Com_Ocom_OLocal(X69,X27,X68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I22_J) ).
fof(fact_com_Osimps_I26_J,axiom,
! [X64,X65,X27,X13,X14] : c_Com_Ocom_OAss(X14,X13) != c_Com_Ocom_OCond(X27,X65,X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I26_J) ).
fof(fact_com_Osimps_I32_J,axiom,
! [X27,X4,X28,X13,X14] : c_Com_Ocom_OAss(X14,X13) != c_Com_Ocom_OCall(X28,X4,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I32_J) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_total__on__empty,axiom,
! [X172,X7] : c_Relation_Ototal__on(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__empty) ).
fof(fact_divisors__zero,axiom,
! [X84,X71,X87] :
( class_Rings_Ono__zero__divisors(X87)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84) = c_Groups_Ozero__class_Ozero(X87)
=> ( X71 = c_Groups_Ozero__class_Ozero(X87)
| X84 = c_Groups_Ozero__class_Ozero(X87) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(fact_no__zero__divisors,axiom,
! [X84,X71,X87] :
( class_Rings_Ono__zero__divisors(X87)
=> ( X71 != c_Groups_Ozero__class_Ozero(X87)
=> ( X84 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X84) != c_Groups_Ozero__class_Ozero(X87) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_mult__eq__0__iff,axiom,
! [X24,X25,X7] :
( class_Rings_Oring__no__zero__divisors(X7)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X24) = c_Groups_Ozero__class_Ozero(X7)
<=> ( X25 = c_Groups_Ozero__class_Ozero(X7)
| X24 = c_Groups_Ozero__class_Ozero(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_posDivAlg__0,axiom,
! [X84] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X84) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__0) ).
fof(fact_div__int__def,axiom,
! [X84,X71] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X84) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X71,X84)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__int__def) ).
fof(fact_power__0__Suc,axiom,
! [X33,X87] :
( ( class_Power_Opower(X87)
& class_Rings_Osemiring__0(X87) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),c_Groups_Ozero__class_Ozero(X87)),hAPP(c_Nat_OSuc,X33)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__Suc) ).
fof(fact_divide__Numeral0,axiom,
! [X86,X87] :
( ( class_Fields_Ofield__inverse__zero(X87)
& class_Int_Onumber__ring(X87) )
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral0) ).
fof(fact_abs__sgn,axiom,
! [X96,X87] :
( class_Rings_Olinordered__idom(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),X96) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X96),c_Groups_Osgn__class_Osgn(X87,X96)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sgn) ).
fof(fact_com_Osimps_I40_J,axiom,
! [X4,X66,X13,X67] : c_Com_Ocom_OLocal(X67,X13,X66) != hAPP(c_Com_Ocom_OBODY,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I40_J) ).
fof(fact_com_Osimps_I54_J,axiom,
! [X4,X54,X55,X13] : c_Com_Ocom_OCond(X13,X55,X54) != hAPP(c_Com_Ocom_OBODY,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I54_J) ).
fof(fact_com_Osimps_I63_J,axiom,
! [X5,X27,X4,X28] : c_Com_Ocom_OCall(X28,X4,X27) != hAPP(c_Com_Ocom_OBODY,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I63_J) ).
fof(fact_com_Osimps_I41_J,axiom,
! [X66,X13,X67,X4] : hAPP(c_Com_Ocom_OBODY,X4) != c_Com_Ocom_OLocal(X67,X13,X66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I41_J) ).
fof(fact_com_Osimps_I55_J,axiom,
! [X54,X55,X13,X4] : hAPP(c_Com_Ocom_OBODY,X4) != c_Com_Ocom_OCond(X13,X55,X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I55_J) ).
fof(fact_com_Osimps_I62_J,axiom,
! [X27,X4,X28,X5] : hAPP(c_Com_Ocom_OBODY,X5) != c_Com_Ocom_OCall(X28,X4,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I62_J) ).
fof(fact_lists__UNIV,axiom,
! [X7] : c_List_Olists(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X7),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__UNIV) ).
fof(fact_map__ident,axiom,
! [X292,X7] : hAPP(hAPP(c_List_Omap(X7,X7),c_COMBI(X7)),X292) = X292,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__ident) ).
fof(fact_accp__wfPD,axiom,
! [X6,X172,X7] :
( c_Wellfounded_OwfP(X7,X172)
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X172),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__wfPD) ).
fof(fact_reflpE,axiom,
! [X6,X172,X7] :
( c_Predicate_Oreflp(X7,X172)
=> hBOOL(hAPP(hAPP(X172,X6),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflpE) ).
fof(fact_equivp__reflp,axiom,
! [X6,X191,X7] :
( c_Equiv__Relations_Oequivp(X7,X191)
=> hBOOL(hAPP(hAPP(X191,X6),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__reflp) ).
fof(fact_sublist__empty,axiom,
! [X292,X7] : c_List_Osublist(X7,X292,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__empty) ).
fof(fact_right__inverse__eq,axiom,
! [X25,X24,X7] :
( class_Rings_Odivision__ring(X7)
=> ( X24 != c_Groups_Ozero__class_Ozero(X7)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X25),X24) = c_Groups_Oone__class_Oone(X7)
<=> X25 = X24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
fof(fact_length__rev,axiom,
! [X300,X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),hAPP(c_List_Orev(X87),X300)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rev) ).
fof(fact_length__rotate1,axiom,
! [X300,X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),hAPP(c_List_Orotate1(X87),X300)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rotate1) ).
fof(fact_exE__some,axiom,
! [X7,X23,X38] :
( ? [X142] : hBOOL(hAPP(X38,X142))
=> ( X23 = c_Hilbert__Choice_OEps(X7,X38)
=> hBOOL(hAPP(X38,X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exE__some) ).
fof(fact_funpow_Osimps_I1_J,axiom,
! [X2,X7] : hAPP(hAPP(c_Nat_Ocompow(X7,X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_Fun_Oid(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I1_J) ).
fof(fact_option__map__None,axiom,
! [X2,X7,X105] : hAPP(hAPP(c_Option_Omap(X105,X7),X2),c_Option_Ooption_ONone(X105)) = c_Option_Ooption_ONone(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__None) ).
fof(fact_map_Osimps_I1_J,axiom,
! [X2,X7,X105] : hAPP(hAPP(c_List_Omap(X105,X7),X2),c_List_Olist_ONil(X105)) = c_List_Olist_ONil(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).
fof(fact_inf__compl__bot,axiom,
! [X86,X87] :
( class_Lattices_Oboolean__algebra(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86)) = c_Orderings_Obot__class_Obot(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__compl__bot) ).
fof(fact_sup__compl__top,axiom,
! [X86,X87] :
( class_Lattices_Oboolean__algebra(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86)) = c_Orderings_Otop__class_Otop(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__compl__top) ).
fof(fact_right__minus,axiom,
! [X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
! [X33,X86] :
( c_Nat__Transfer_Ois__nat(X86)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X86),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).
fof(fact_zmult__eq__1__iff,axiom,
! [X44,X95] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X95),X44) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( ( X95 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X44 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| ( X95 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& X44 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__eq__1__iff) ).
fof(fact_sup__eq__bot__iff,axiom,
! [X127,X6,X7] :
( class_Lattices_Obounded__lattice__bot(X7)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6),X127) = c_Orderings_Obot__class_Obot(X7)
<=> ( X6 = c_Orderings_Obot__class_Obot(X7)
& X127 = c_Orderings_Obot__class_Obot(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__eq__bot__iff) ).
fof(fact_inf__eq__top__iff,axiom,
! [X127,X6,X7] :
( class_Lattices_Obounded__lattice__top(X7)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X6),X127) = c_Orderings_Otop__class_Otop(X7)
<=> ( X6 = c_Orderings_Otop__class_Otop(X7)
& X127 = c_Orderings_Otop__class_Otop(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__eq__top__iff) ).
fof(fact_field__power__not__zero,axiom,
! [X33,X71,X87] :
( class_Rings_Oring__1__no__zero__divisors(X87)
=> ( X71 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),X33) != c_Groups_Ozero__class_Ozero(X87) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_double__eq__0__iff,axiom,
! [X25,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X25) = c_Groups_Ozero__class_Ozero(X7)
<=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X25,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( c_Groups_Ozero__class_Ozero(X7) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X25),X25)
<=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_finite__atMost,axiom,
! [X94] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X94))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atMost) ).
fof(fact_finite__lessThan,axiom,
! [X94] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X94))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lessThan) ).
fof(fact_minus__numeral__code_I5_J,axiom,
! [X128] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [X24,X25,X7] :
( class_Groups_Oab__group__add(X7)
=> ( X25 = X24
<=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X25),X24) = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_right__minus__eq,axiom,
! [X24,X25,X7] :
( class_Groups_Ogroup__add(X7)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X25),X24) = c_Groups_Ozero__class_Ozero(X7)
<=> X25 = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_dvd_Oeq__refl,axiom,
! [X98,X86] :
( X86 = X98
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
fof(fact_eq__imp__le,axiom,
! [X33,X90] :
( X90 = X33
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_take__eq__Nil,axiom,
! [X292,X44,X7] :
( hAPP(hAPP(c_List_Otake(X7),X44),X292) = c_List_Olist_ONil(X7)
<=> ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X292 = c_List_Olist_ONil(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__eq__Nil) ).
fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
! [X33,X90] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X33) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> ( X90 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X90 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).
fof(fact_add__0__iff,axiom,
! [X25,X24,X7] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
=> ( X24 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X24),X25)
<=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_diff__Suc__1,axiom,
! [X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
fof(fact_set__upto,axiom,
! [X158,X107] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X107,X158)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X107,X158),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__upto) ).
fof(fact_atLeastAtMost__upto,axiom,
! [X158,X107] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X107,X158) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X107,X158)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__upto) ).
fof(fact_add__numeral__0__right,axiom,
! [X71,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OPls)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).
fof(fact_dvd_Oorder__refl,axiom,
! [X86] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X86)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
fof(fact_zle__refl,axiom,
! [X128] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X128),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(fact_le__refl,axiom,
! [X33] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_evalc_Oequations_I1_J,axiom,
! [X71] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X71),X71)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I1_J) ).
fof(fact_evalc_OSkip,axiom,
! [X9] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X9),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OSkip) ).
fof(fact_append__is__Nil__conv,axiom,
! [X293,X292,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X292),X293) = c_List_Olist_ONil(X7)
<=> ( X292 = c_List_Olist_ONil(X7)
& X293 = c_List_Olist_ONil(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).
fof(fact_Nil__is__append__conv,axiom,
! [X293,X292,X7] :
( c_List_Olist_ONil(X7) = hAPP(hAPP(c_List_Oappend(X7),X292),X293)
<=> ( X292 = c_List_Olist_ONil(X7)
& X293 = c_List_Olist_ONil(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).
fof(fact_Domain__rtrancl,axiom,
! [X191,X7] : hAPP(c_Relation_ODomain(X7,X7),c_Transitive__Closure_Ortrancl(X7,X191)) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__rtrancl) ).
fof(fact_Range__rtrancl,axiom,
! [X191,X7] : hAPP(c_Relation_ORange(X7,X7),c_Transitive__Closure_Ortrancl(X7,X191)) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__rtrancl) ).
fof(help_c__COMBK__1,axiom,
! [X338,X79,X7,X87] : hAPP(hAPP(c_COMBK(X87,X7),X79),X338) = X79,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_zdiv__minus1__right,axiom,
! [X71] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__minus1__right) ).
fof(fact_zmult__commute,axiom,
! [X128,X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),X128) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(fact_nat__mult__commute,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_zadd__commute,axiom,
! [X128,X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),X128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X128),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_nat__add__commute,axiom,
! [X33,X90] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_Nitpick_Ofrac__def,axiom,
! [X84,X71,X87] : hAPP(hAPP(c_Nitpick_Ofrac(X87),X71),X84) = c_Nitpick_OAbs__Frac(X87,c_Nitpick_Onorm__frac(X71,X84)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ofrac__def) ).
fof(fact_diff__0,axiom,
! [X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),c_Groups_Ozero__class_Ozero(X87)),X71) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0) ).
fof(fact_char_Osize_I2_J,axiom,
! [X11,X12] : hAPP(c_Nat_Osize__class_Osize(tc_String_Ochar),hAPP(hAPP(c_String_Ochar_OChar,X12),X11)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_char_Osize_I2_J) ).
fof(fact_append__self__conv2,axiom,
! [X293,X292,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X292),X293) = X293
<=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__self__conv2) ).
fof(fact_append__self__conv,axiom,
! [X293,X292,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X292),X293) = X292
<=> X293 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__self__conv) ).
fof(fact_self__append__conv,axiom,
! [X293,X7,X292] :
( X292 = hAPP(hAPP(c_List_Oappend(X7),X292),X293)
<=> X293 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__append__conv) ).
fof(fact_self__append__conv2,axiom,
! [X292,X7,X293] :
( X293 = hAPP(hAPP(c_List_Oappend(X7),X292),X293)
<=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__append__conv2) ).
fof(fact_power__0__left,axiom,
! [X33,X87] :
( ( class_Power_Opower(X87)
& class_Rings_Osemiring__0(X87) )
=> ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),c_Groups_Ozero__class_Ozero(X87)),X33) = c_Groups_Oone__class_Oone(X87) )
& ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),c_Groups_Ozero__class_Ozero(X87)),X33) = c_Groups_Ozero__class_Ozero(X87) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(fact_list_Osimps_I3_J,axiom,
! [X309,X88,X87] : hAPP(hAPP(c_List_Olist_OCons(X87),X88),X309) != c_List_Olist_ONil(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
fof(fact_list_Osimps_I2_J,axiom,
! [X309,X88,X87] : c_List_Olist_ONil(X87) != hAPP(hAPP(c_List_Olist_OCons(X87),X88),X309),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(fact_WT_OBody,axiom,
! [X78] :
( hAPP(c_Com_Obody,X78) != c_Option_Ooption_ONone(tc_Com_Ocom)
=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X78))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OBody) ).
fof(fact_distinct__upto,axiom,
! [X113,X114] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X114,X113))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__upto) ).
fof(fact_com_Osimps_I11_J,axiom,
! [X68,X27,X69] : c_Com_Ocom_OLocal(X69,X27,X68) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I11_J) ).
fof(fact_com_Osimps_I15_J,axiom,
! [X64,X65,X27] : c_Com_Ocom_OCond(X27,X65,X64) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I15_J) ).
fof(fact_com_Osimps_I21_J,axiom,
! [X27,X4,X28] : c_Com_Ocom_OCall(X28,X4,X27) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I21_J) ).
fof(fact_com_Osimps_I10_J,axiom,
! [X68,X27,X69] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X69,X27,X68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I10_J) ).
fof(fact_com_Osimps_I14_J,axiom,
! [X64,X65,X27] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X27,X65,X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I14_J) ).
fof(fact_com_Osimps_I20_J,axiom,
! [X27,X4,X28] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X28,X4,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I20_J) ).
fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
! [X172,X7] : c_List_Olistrel(X7,c_Transitive__Closure_Ortrancl(X7,X172)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X7),c_List_Olistrel1(X7,X172)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
fof(fact_max__ext__wf,axiom,
! [X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> c_Wellfounded_Owf(tc_fun(X7,tc_HOL_Obool),c_Wellfounded_Omax__ext(X7,X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__wf) ).
fof(fact_min__ext__wf,axiom,
! [X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> c_Wellfounded_Owf(tc_fun(X7,tc_HOL_Obool),c_Wellfounded_Omin__ext(X7,X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__wf) ).
fof(fact_listsum__rev,axiom,
! [X300,X87] :
( class_Groups_Ocomm__monoid__add(X87)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X87),hAPP(c_List_Orev(X87),X300)) = hAPP(c_List_Omonoid__add__class_Olistsum(X87),X300) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__rev) ).
fof(fact_abs__idempotent,axiom,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)) = hAPP(c_Groups_Oabs__class_Oabs(X87),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__idempotent) ).
fof(fact_abs__minus__cancel,axiom,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)) = hAPP(c_Groups_Oabs__class_Oabs(X87),X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_abs__of__nat,axiom,
! [X33,X87] :
( class_Rings_Olinordered__idom(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X33)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nat) ).
fof(fact_UNIV__not__empty,axiom,
! [X7] : c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
fof(fact_zmod__minus1__right,axiom,
! [X71] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__minus1__right) ).
fof(fact_mod__1,axiom,
! [X90] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__1) ).
fof(fact_mult__is__0,axiom,
! [X44,X95] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X44) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(fact_not__Cons__self2,axiom,
! [X300,X86,X87] : hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300) != X300,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
fof(fact_not__Cons__self,axiom,
! [X86,X87,X300] : X300 != hAPP(hAPP(c_List_Olist_OCons(X87),X86),X300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self) ).
fof(fact_fun__left__comm__idem__insert,axiom,
! [X7] : c_Finite__Set_Ofun__left__comm__idem(X7,tc_fun(X7,tc_HOL_Obool),c_Set_Oinsert(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).
fof(fact_bot__apply,axiom,
! [X6,X105,X7] :
( class_Orderings_Obot(X7)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X105,X7)),X6) = c_Orderings_Obot__class_Obot(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
fof(fact_bot__fun__def,axiom,
! [X6,X105,X7] :
( class_Orderings_Obot(X7)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X105,X7)),X6) = c_Orderings_Obot__class_Obot(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(fact_top__apply,axiom,
! [X6,X105,X7] :
( class_Orderings_Otop(X7)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X105,X7)),X6) = c_Orderings_Otop__class_Otop(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_minus__code__numeral__code,axiom,
! [X90,X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33),X90) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X33),X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__code__numeral__code) ).
fof(fact_sorted__tl,axiom,
! [X300,X87] :
( class_Orderings_Olinorder(X87)
=> ( c_List_Olinorder__class_Osorted(X87,X300)
=> c_List_Olinorder__class_Osorted(X87,hAPP(c_List_Otl(X87),X300)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__tl) ).
fof(fact_mult__eq__self__implies__10,axiom,
! [X33,X90] :
( X90 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X33)
=> ( X33 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X90 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(fact_hd__conv__nth,axiom,
! [X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> hAPP(c_List_Ohd(X87),X300) = hAPP(hAPP(c_List_Onth(X87),X300),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__conv__nth) ).
fof(help_c__fimplies__1,axiom,
! [X194,X38] :
( hBOOL(X38)
| hBOOL(hAPP(hAPP(c_fimplies,X38),X194)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__1) ).
fof(fact_single__valued__Id__on,axiom,
! [X149,X7] : c_Relation_Osingle__valued(X7,X7,c_Relation_OId__on(X7,X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
fof(fact_refl__on__Id__on,axiom,
! [X149,X7] : c_Relation_Orefl__on(X7,X149,c_Relation_OId__on(X7,X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [X44,X95] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X44) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X95 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X44 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(fact_add__is__0,axiom,
! [X44,X95] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X44) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [X44,X95] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X44)
<=> ( X95 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X44 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_eq__number__of,axiom,
! [X127,X6,X7] :
( ( class_Int_Onumber__ring(X7)
& class_Int_Oring__char__0(X7) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X7),X6) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X127)
<=> X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of) ).
fof(fact_converse__Id__on,axiom,
! [X149,X7] : hAPP(c_Relation_Oconverse(X7,X7),c_Relation_OId__on(X7,X149)) = c_Relation_OId__on(X7,X149),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Id__on) ).
fof(help_c__fequal__2,axiom,
! [X127,X6] :
( X6 != X127
| hBOOL(hAPP(hAPP(c_fequal,X6),X127)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_of__int__number__of__eq,axiom,
! [X139,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),X139) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__number__of__eq) ).
fof(fact_of__int__of__nat__eq,axiom,
! [X33,X87] :
( class_Rings_Oring__1(X87)
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__of__nat__eq) ).
fof(fact_set__empty2,axiom,
! [X292,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_List_Oset(X7),X292)
<=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty2) ).
fof(fact_set__empty,axiom,
! [X292,X7] :
( hAPP(c_List_Oset(X7),X292) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty) ).
fof(fact_WT_OAssign,axiom,
! [X25,X39] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X39,X25))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OAssign) ).
fof(fact_WT_Oequations_I2_J,axiom,
! [X43,X42] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X42,X43))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I2_J) ).
fof(fact_set__rev,axiom,
! [X292,X7] : hAPP(c_List_Oset(X7),hAPP(c_List_Orev(X7),X292)) = hAPP(c_List_Oset(X7),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev) ).
fof(fact_set__rotate1,axiom,
! [X292,X7] : hAPP(c_List_Oset(X7),hAPP(c_List_Orotate1(X7),X292)) = hAPP(c_List_Oset(X7),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rotate1) ).
fof(fact_power__power__power,axiom,
! [X7] :
( class_Power_Opower(X7)
=> c_Power_Opower__class_Opower(X7) = c_Power_Opower_Opower(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Otimes__class_Otimes(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(fact_add__eq__self__zero,axiom,
! [X33,X90] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X33) = X90
=> X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_hd__rev,axiom,
! [X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> hAPP(c_List_Ohd(X87),hAPP(c_List_Orev(X87),X300)) = c_List_Olast(X87,X300) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__rev) ).
fof(fact_last__rev,axiom,
! [X87,X300] :
( X300 != c_List_Olist_ONil(X87)
=> c_List_Olast(X87,hAPP(c_List_Orev(X87),X300)) = hAPP(c_List_Ohd(X87),X300) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__rev) ).
fof(fact_sorted__list__of__set__empty,axiom,
! [X7] :
( class_Orderings_Olinorder(X7)
=> c_List_Olinorder__class_Osorted__list__of__set(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__empty) ).
fof(fact_Sup__empty,axiom,
! [X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OSup__class_OSup(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__empty) ).
fof(fact_Sup__UNIV,axiom,
! [X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OSup__class_OSup(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__UNIV) ).
fof(fact_Inf__empty,axiom,
! [X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OInf__class_OInf(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__empty) ).
fof(fact_Inf__UNIV,axiom,
! [X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OInf__class_OInf(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__UNIV) ).
fof(fact_div__1,axiom,
! [X90] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X90,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__1) ).
fof(fact_Union__Pow__eq,axiom,
! [X149,X7] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_OPow(X7),X149)) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Pow__eq) ).
fof(fact_inf__bot__left,axiom,
! [X86,X87] :
( class_Lattices_Obounded__lattice__bot(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),c_Orderings_Obot__class_Obot(X87)),X86) = c_Orderings_Obot__class_Obot(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__left) ).
fof(fact_sup__top__left,axiom,
! [X86,X87] :
( class_Lattices_Obounded__lattice__top(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),c_Orderings_Otop__class_Otop(X87)),X86) = c_Orderings_Otop__class_Otop(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__top__left) ).
fof(fact_divide__zero__left,axiom,
! [X71,X87] :
( class_Rings_Odivision__ring(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),c_Groups_Ozero__class_Ozero(X87)),X71) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero__left) ).
fof(fact_power__one,axiom,
! [X33,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),c_Groups_Oone__class_Oone(X87)),X33) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_div__0,axiom,
! [X71,X87] :
( class_Divides_Osemiring__div(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),c_Groups_Ozero__class_Ozero(X87)),X71) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__0) ).
fof(fact_mult__zero__left,axiom,
! [X71,X87] :
( class_Rings_Omult__zero(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),c_Groups_Ozero__class_Ozero(X87)),X71) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),c_Groups_Ozero__class_Ozero(X87)),X71) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_sorted__butlast,axiom,
! [X300,X87] :
( class_Orderings_Olinorder(X87)
=> ( X300 != c_List_Olist_ONil(X87)
=> ( c_List_Olinorder__class_Osorted(X87,X300)
=> c_List_Olinorder__class_Osorted(X87,c_List_Obutlast(X87,X300)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__butlast) ).
fof(fact_WT__bodiesD,axiom,
! [X84,X78] :
( c_Com_OWT__bodies
=> ( hAPP(c_Com_Obody,X78) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X84)
=> hBOOL(hAPP(c_Com_OWT,X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT__bodiesD) ).
fof(fact_of__int__m1,axiom,
! [X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__m1) ).
fof(fact_card_Oempty,axiom,
! [X7] : hAPP(c_Finite__Set_Ocard(X7),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oempty) ).
fof(fact_abs__minus__one,axiom,
! [X87] :
( ( class_Int_Onumber__ring(X87)
& class_Rings_Olinordered__idom(X87) )
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin)) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__one) ).
fof(fact_option_Osize_I4_J,axiom,
! [X71,X87] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X87)),hAPP(c_Option_Ooption_OSome(X87),X71)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osize_I4_J) ).
fof(fact_atLeast0AtMost,axiom,
! [X44] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).
fof(fact_atLeast__eq__iff,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hAPP(c_SetInterval_Oord__class_OatLeast(X7),X6) = hAPP(c_SetInterval_Oord__class_OatLeast(X7),X127)
<=> X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__eq__iff) ).
fof(fact_atMost__eq__iff,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hAPP(c_SetInterval_Oord__class_OatMost(X7),X6) = hAPP(c_SetInterval_Oord__class_OatMost(X7),X127)
<=> X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__eq__iff) ).
fof(fact_greaterThan__eq__iff,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X6) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X7),X127)
<=> X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).
fof(fact_lessThan__eq__iff,axiom,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hAPP(c_SetInterval_Oord__class_OlessThan(X7),X6) = hAPP(c_SetInterval_Oord__class_OlessThan(X7),X127)
<=> X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__eq__iff) ).
fof(fact_compl__eq__compl__iff,axiom,
! [X127,X6,X7] :
( class_Lattices_Oboolean__algebra(X7)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X7),X6) = hAPP(c_Groups_Ouminus__class_Ouminus(X7),X127)
<=> X6 = X127 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [X24,X25,X7] :
( class_Groups_Ogroup__add(X7)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25) = hAPP(c_Groups_Ouminus__class_Ouminus(X7),X24)
<=> X25 = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_of__int__eq__iff,axiom,
! [X26,X125,X7] :
( class_Int_Oring__char__0(X7)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(X7),X125) = hAPP(c_Int_Oring__1__class_Oof__int(X7),X26)
<=> X125 = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__eq__iff) ).
fof(fact_of__nat__eq__iff,axiom,
! [X44,X95,X7] :
( class_Nat_Osemiring__char__0(X7)
=> ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X95) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),X44)
<=> X95 = X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).
fof(fact_inf__top__left,axiom,
! [X86,X87] :
( class_Lattices_Obounded__lattice__top(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),c_Orderings_Otop__class_Otop(X87)),X86) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__top__left) ).
fof(fact_sup__bot__left,axiom,
! [X86,X87] :
( class_Lattices_Obounded__lattice__bot(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),c_Orderings_Obot__class_Obot(X87)),X86) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__left) ).
fof(fact_mult__1,axiom,
! [X71,X87] :
( class_Groups_Ocomm__monoid__mult(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),c_Groups_Oone__class_Oone(X87)),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [X71,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),c_Groups_Oone__class_Oone(X87)),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),c_Groups_Oone__class_Oone(X87)),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Ozero__class_Ozero(X87)),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0,axiom,
! [X71,X87] :
( class_Groups_Ocomm__monoid__add(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Ozero__class_Ozero(X87)),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_add__0__left,axiom,
! [X71,X87] :
( class_Groups_Omonoid__add(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),c_Groups_Ozero__class_Ozero(X87)),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_divide__self__if,axiom,
! [X71,X87] :
( class_Rings_Odivision__ring__inverse__zero(X87)
=> ( ( X71 = c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X71) = c_Groups_Ozero__class_Ozero(X87) )
& ( X71 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X71) = c_Groups_Oone__class_Oone(X87) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self__if) ).
fof(fact_mod__0,axiom,
! [X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,c_Groups_Ozero__class_Ozero(X87),X71) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__0) ).
fof(fact_mod__by__1,axiom,
! [X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,X71,c_Groups_Oone__class_Oone(X87)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__1) ).
fof(fact_set__empty__eq,axiom,
! [X217,X7] :
( c_Option_Oset(X7,X217) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> X217 = c_Option_Ooption_ONone(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty__eq) ).
fof(fact_inf__bot__right,axiom,
! [X86,X87] :
( class_Lattices_Obounded__lattice__bot(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),c_Orderings_Obot__class_Obot(X87)) = c_Orderings_Obot__class_Obot(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__right) ).
fof(fact_sup__top__right,axiom,
! [X86,X87] :
( class_Lattices_Obounded__lattice__top(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),c_Orderings_Otop__class_Otop(X87)) = c_Orderings_Otop__class_Otop(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__top__right) ).
fof(fact_divide__zero,axiom,
! [X71,X87] :
( class_Rings_Odivision__ring__inverse__zero(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),c_Groups_Ozero__class_Ozero(X87)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero) ).
fof(fact_div__by__0,axiom,
! [X71,X87] :
( class_Divides_Osemiring__div(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),c_Groups_Ozero__class_Ozero(X87)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__0) ).
fof(fact_mult__zero__right,axiom,
! [X71,X87] :
( class_Rings_Omult__zero(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),c_Groups_Ozero__class_Ozero(X87)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),c_Groups_Ozero__class_Ozero(X87)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_wf__lex,axiom,
! [X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> c_Wellfounded_Owf(tc_List_Olist(X7),c_List_Olex(X7,X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex) ).
fof(fact_wf__lenlex,axiom,
! [X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> c_Wellfounded_Owf(tc_List_Olist(X7),c_List_Olenlex(X7,X172)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lenlex) ).
fof(fact_eq__Nil__appendI,axiom,
! [X87,X301,X300] :
( X300 = X301
=> X300 = hAPP(hAPP(c_List_Oappend(X87),c_List_Olist_ONil(X87)),X301) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).
fof(fact_divide__self,axiom,
! [X71,X87] :
( class_Rings_Odivision__ring(X87)
=> ( X71 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),X71) = c_Groups_Oone__class_Oone(X87) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self) ).
fof(fact_div__self,axiom,
! [X71,X87] :
( class_Divides_Osemiring__div(X87)
=> ( X71 != c_Groups_Ozero__class_Ozero(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),X71) = c_Groups_Oone__class_Oone(X87) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__self) ).
fof(fact_mod__by__0,axiom,
! [X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,X71,c_Groups_Ozero__class_Ozero(X87)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__0) ).
fof(fact_fun__left__comm,axiom,
! [X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> c_Finite__Set_Ofun__left__comm(X7,X7,c_Groups_Otimes__class_Otimes(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm) ).
fof(fact_fun__left__comm__idem__inf,axiom,
! [X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Finite__Set_Ofun__left__comm__idem(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__inf) ).
fof(fact_fun__left__comm__idem__sup,axiom,
! [X7] :
( class_Lattices_Osemilattice__sup(X7)
=> c_Finite__Set_Ofun__left__comm__idem(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__sup) ).
fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
! [X7] :
( class_Orderings_Olinorder(X7)
=> c_Finite__Set_Ofun__left__comm__idem(X7,X7,c_Orderings_Oord__class_Omax(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).
fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
! [X7] :
( class_Orderings_Olinorder(X7)
=> c_Finite__Set_Ofun__left__comm__idem(X7,X7,c_Orderings_Oord__class_Omin(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).
fof(fact_fun__left__comm__idem,axiom,
! [X7] :
( class_Lattices_Oab__semigroup__idem__mult(X7)
=> c_Finite__Set_Ofun__left__comm__idem(X7,X7,c_Groups_Otimes__class_Otimes(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem) ).
fof(fact_Domain__Id__on,axiom,
! [X149,X7] : hAPP(c_Relation_ODomain(X7,X7),c_Relation_OId__on(X7,X149)) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
fof(fact_Range__Id__on,axiom,
! [X149,X7] : hAPP(c_Relation_ORange(X7,X7),c_Relation_OId__on(X7,X149)) = X149,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id__on) ).
fof(fact_power__0,axiom,
! [X71,X87] :
( class_Power_Opower(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_inf__top__right,axiom,
! [X86,X87] :
( class_Lattices_Obounded__lattice__top(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),c_Orderings_Otop__class_Otop(X87)) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__top__right) ).
fof(fact_sup__bot__right,axiom,
! [X86,X87] :
( class_Lattices_Obounded__lattice__bot(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),c_Orderings_Obot__class_Obot(X87)) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__right) ).
fof(fact_divide__1,axiom,
! [X71,X87] :
( class_Rings_Odivision__ring(X87)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X87),X71),c_Groups_Oone__class_Oone(X87)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__1) ).
fof(fact_diff__0__right,axiom,
! [X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),c_Groups_Ozero__class_Ozero(X87)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(fact_div__by__1,axiom,
! [X71,X87] :
( class_Divides_Osemiring__div(X87)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X87),X71),c_Groups_Oone__class_Oone(X87)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__1) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [X71,X87] :
( class_Groups_Ocomm__monoid__mult(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),c_Groups_Oone__class_Oone(X87)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [X71,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),c_Groups_Oone__class_Oone(X87)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),c_Groups_Oone__class_Oone(X87)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X71,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),c_Groups_Ozero__class_Ozero(X87)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X71,X87] :
( class_Groups_Ocomm__monoid__add(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),c_Groups_Ozero__class_Ozero(X87)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [X71,X87] :
( class_Groups_Omonoid__add(X87)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),X71),c_Groups_Ozero__class_Ozero(X87)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_double__compl,axiom,
! [X86,X87] :
( class_Lattices_Oboolean__algebra(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X86)) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__compl) ).
fof(fact_minus__minus,axiom,
! [X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_abs__int__eq,axiom,
! [X90] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__int__eq) ).
fof(fact_of__int__int__eq,axiom,
! [X33] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__int__eq) ).
fof(fact_mod__self,axiom,
! [X71,X87] :
( class_Divides_Osemiring__div(X87)
=> c_Divides_Odiv__class_Omod(X87,X71,X71) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__self) ).
fof(fact_rev__is__rev__conv,axiom,
! [X293,X292,X7] :
( hAPP(c_List_Orev(X7),X292) = hAPP(c_List_Orev(X7),X293)
<=> X292 = X293 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).
fof(fact_option_Oinject,axiom,
! [X89,X25,X7] :
( hAPP(c_Option_Ooption_OSome(X7),X25) = hAPP(c_Option_Ooption_OSome(X7),X89)
<=> X25 = X89 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oinject) ).
fof(fact_inc__shift__def,axiom,
! [X96,X139] :
( ( X139 = X96
=> c_Random_Oinc__shift(X139,X96) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
& ( X139 != X96
=> c_Random_Oinc__shift(X139,X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X96),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inc__shift__def) ).
fof(fact_append__Nil,axiom,
! [X301,X87] : hAPP(hAPP(c_List_Oappend(X87),c_List_Olist_ONil(X87)),X301) = X301,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X33] : hAPP(c_Nat_OSuc,X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_sublist__nil,axiom,
! [X149,X7] : c_List_Osublist(X7,c_List_Olist_ONil(X7),X149) = c_List_Olist_ONil(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__nil) ).
fof(fact_remove1_Osimps_I1_J,axiom,
! [X86,X87] : c_List_Oremove1(X87,X86,c_List_Olist_ONil(X87)) = c_List_Olist_ONil(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I1_J) ).
fof(fact_atLeastLessThan0,axiom,
! [X95] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
fof(fact_power__one__right,axiom,
! [X71,X87] :
( class_Groups_Omonoid__mult(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X86,X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_diff__self,axiom,
! [X71,X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X87),X71),X71) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
fof(fact_list_Osize_I1_J,axiom,
! [X85,X7] : c_List_Olist_Olist__size(X7,X85,c_List_Olist_ONil(X7)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I1_J) ).
fof(fact_option_Osize_I1_J,axiom,
! [X85,X7] : c_Option_Ooption_Ooption__size(X7,X85,c_Option_Ooption_ONone(X7)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osize_I1_J) ).
fof(fact_take__0,axiom,
! [X300,X87] : hAPP(hAPP(c_List_Otake(X87),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X300) = c_List_Olist_ONil(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__0) ).
fof(fact_drop__Nil,axiom,
! [X33,X87] : hAPP(hAPP(c_List_Odrop(X87),X33),c_List_Olist_ONil(X87)) = c_List_Olist_ONil(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Nil) ).
fof(fact_take__Nil,axiom,
! [X33,X87] : hAPP(hAPP(c_List_Otake(X87),X33),c_List_Olist_ONil(X87)) = c_List_Olist_ONil(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Nil) ).
fof(fact_minus__equation__iff,axiom,
! [X24,X25,X7] :
( class_Groups_Ogroup__add(X7)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25) = X24
<=> hAPP(c_Groups_Ouminus__class_Ouminus(X7),X24) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_equation__minus__iff,axiom,
! [X24,X25,X7] :
( class_Groups_Ogroup__add(X7)
=> ( X25 = hAPP(c_Groups_Ouminus__class_Ouminus(X7),X24)
<=> X24 = hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_nat__list__def,axiom,
! [X157] :
( c_List_Onat__list(X157)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X157)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__list__def) ).
fof(fact_card__atMost,axiom,
! [X160] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X160)) = hAPP(c_Nat_OSuc,X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atMost) ).
fof(fact_nat__of__number,axiom,
! [X96] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X96)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__number) ).
fof(fact_nat__number__of,axiom,
! [X128] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of) ).
fof(fact_nat__number__of__def,axiom,
! [X139] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__def) ).
fof(fact_Suc__eq__plus1,axiom,
! [X33] : hAPP(c_Nat_OSuc,X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_sgn__sgn,axiom,
! [X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> c_Groups_Osgn__class_Osgn(X87,c_Groups_Osgn__class_Osgn(X87,X71)) = c_Groups_Osgn__class_Osgn(X87,X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__sgn) ).
fof(fact_inf_Oidem,axiom,
! [X71,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oidem) ).
fof(fact_inf__idem,axiom,
! [X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X86) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__idem) ).
fof(fact_Inf__fin_Oidem,axiom,
! [X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X86),X86) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oidem) ).
fof(fact_sup_Oidem,axiom,
! [X71,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oidem) ).
fof(fact_sup__idem,axiom,
! [X86,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X86) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__idem) ).
fof(fact_Sup__fin_Oidem,axiom,
! [X86,X87] :
( class_Lattices_Olattice(X87)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X86),X86) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oidem) ).
fof(fact_Max_Oidem,axiom,
! [X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X86),X86) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oidem) ).
fof(fact_min__max_Osup_Oidem,axiom,
! [X71,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oidem) ).
fof(fact_Min_Oidem,axiom,
! [X86,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X86),X86) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oidem) ).
fof(fact_min__max_Oinf_Oidem,axiom,
! [X71,X87] :
( class_Orderings_Olinorder(X87)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oidem) ).
fof(fact_mult__idem,axiom,
! [X86,X87] :
( class_Lattices_Oab__semigroup__idem__mult(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X86) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__idem) ).
fof(fact_times_Oidem,axiom,
! [X71,X87] :
( class_Lattices_Oab__semigroup__idem__mult(X87)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times_Oidem) ).
fof(fact_length__0__conv,axiom,
! [X292,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__0__conv) ).
fof(fact_mult__Min,axiom,
! [X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X96) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Min) ).
fof(fact_atLeast0LessThan,axiom,
! [X44] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).
fof(fact_drop__0,axiom,
! [X300,X87] : hAPP(hAPP(c_List_Odrop(X87),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X300) = X300,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__0) ).
fof(fact_append__Nil2,axiom,
! [X300,X87] : hAPP(hAPP(c_List_Oappend(X87),X300),c_List_Olist_ONil(X87)) = X300,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil2) ).
fof(fact_rev__rev__ident,axiom,
! [X300,X87] : hAPP(c_List_Orev(X87),hAPP(c_List_Orev(X87),X300)) = X300,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_the_Osimps,axiom,
! [X86,X87] : hAPP(c_Option_Othe(X87),hAPP(c_Option_Ooption_OSome(X87),X86)) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the_Osimps) ).
fof(fact_zmod__zero,axiom,
! [X84] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X84) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zero) ).
fof(fact_neg__nat,axiom,
! [X97] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X97))
=> hAPP(c_Int_Onat,X97) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__nat) ).
fof(fact_atLeast__Suc__greaterThan,axiom,
! [X94] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc__greaterThan) ).
fof(fact_lessThan__Suc__atMost,axiom,
! [X94] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc__atMost) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X44] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_DIVISION__BY__ZERO,axiom,
! [X71] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
fof(fact_iszero__Numeral0,axiom,
! [X87] :
( class_Int_Onumber__ring(X87)
=> c_Int_Oiszero(X87,hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).
fof(fact_Option_Omap_Oid,axiom,
! [X7] : hAPP(c_Option_Omap(X7,X7),c_Fun_Oid(X7)) = c_Fun_Oid(tc_Option_Ooption(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap_Oid) ).
fof(fact_Option_Omap_Oidentity,axiom,
! [X7] : hAPP(c_Option_Omap(X7,X7),c_COMBI(X7)) = c_Fun_Oid(tc_Option_Ooption(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap_Oidentity) ).
fof(fact_List_Omap_Oid,axiom,
! [X7] : hAPP(c_List_Omap(X7,X7),c_Fun_Oid(X7)) = c_Fun_Oid(tc_List_Olist(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oid) ).
fof(fact_List_Omap_Oidentity,axiom,
! [X7] : hAPP(c_List_Omap(X7,X7),c_COMBI(X7)) = c_Fun_Oid(tc_List_Olist(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oidentity) ).
fof(fact_transfer__int__nat__relations_I1_J,axiom,
! [X127,X6] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X127)
<=> X6 = X127 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).
fof(fact_int__int__eq,axiom,
! [X44,X95] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44)
<=> X95 = X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__int__eq) ).
fof(fact_zmod__self,axiom,
! [X71] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X71,X71) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__self) ).
fof(fact_rev__swap,axiom,
! [X293,X292,X7] :
( hAPP(c_List_Orev(X7),X292) = X293
<=> X292 = hAPP(c_List_Orev(X7),X293) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__swap) ).
fof(fact_min__0L,axiom,
! [X33] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__0L) ).
fof(fact_diff__0__eq__0,axiom,
! [X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(fact_zdiv__zero,axiom,
! [X84] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zero) ).
fof(fact_mult__0,axiom,
! [X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
fof(fact_distinct_Osimps_I1_J,axiom,
! [X87] : hBOOL(hAPP(c_List_Odistinct(X87),c_List_Olist_ONil(X87))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(fact_New__DSequence_Oneg__single__def,axiom,
! [X204,X86,X87] : hAPP(c_New__DSequence_Oneg__single(X87,X86),X204) = c_Lazy__Sequence_Ohb__single(X87,X86),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
fof(fact_New__DSequence_Opos__single__def,axiom,
! [X204,X86,X87] : hAPP(c_New__DSequence_Opos__single(X87,X86),X204) = c_Lazy__Sequence_Osingle(X87,X86),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
fof(fact_rtrancl__idemp,axiom,
! [X172,X7] : c_Transitive__Closure_Ortrancl(X7,c_Transitive__Closure_Ortrancl(X7,X172)) = c_Transitive__Closure_Ortrancl(X7,X172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
fof(fact_List_Oset_Osimps_I1_J,axiom,
! [X7] : hAPP(c_List_Oset(X7),c_List_Olist_ONil(X7)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).
fof(fact_max__0L,axiom,
! [X33] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33) = X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__0L) ).
fof(fact_zmult__1,axiom,
! [X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X97) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(fact_nat__mult__1,axiom,
! [X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33) = X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_zadd__0,axiom,
! [X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33) = X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_not__neg__1,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__1) ).
fof(fact_not__neg__0,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__0) ).
fof(fact_zdiv__self,axiom,
! [X71] :
( X71 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X71) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__self) ).
fof(fact_option_Oexhaust,axiom,
! [X87,X98] :
( X98 != c_Option_Ooption_ONone(X87)
=> ~ ! [X110] : X98 != hAPP(c_Option_Ooption_OSome(X87),X110) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oexhaust) ).
fof(fact_not__Some__eq,axiom,
! [X7,X6] :
( ! [X82] : X6 != hAPP(c_Option_Ooption_OSome(X7),X82)
<=> X6 = c_Option_Ooption_ONone(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Some__eq) ).
fof(fact_not__None__eq,axiom,
! [X7,X6] :
( X6 != c_Option_Ooption_ONone(X7)
<=> ? [X82] : X6 = hAPP(c_Option_Ooption_OSome(X7),X82) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__None__eq) ).
fof(fact_arith__simps_I31_J,axiom,
! [X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Oone__class_Oone(X87)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I31_J) ).
fof(fact_number__of__Min,axiom,
! [X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Oone__class_Oone(X87)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Min) ).
fof(fact_min__0R,axiom,
! [X33] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X33),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__0R) ).
fof(fact_mult__0__right,axiom,
! [X90] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [X25,X7] :
( class_Groups_Ogroup__add(X7)
=> ( c_Groups_Ozero__class_Ozero(X7) = hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)
<=> c_Groups_Ozero__class_Ozero(X7) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_abs__eq__0,axiom,
! [X25,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> ( hAPP(c_Groups_Oabs__class_Oabs(X7),X25) = c_Groups_Ozero__class_Ozero(X7)
<=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__0) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [X25,X7] :
( class_Groups_Ogroup__add(X7)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25) = c_Groups_Ozero__class_Ozero(X7)
<=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_max__0R,axiom,
! [X33] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X33),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__0R) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [X90] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X90,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_zmult__1__right,axiom,
! [X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_nat__mult__1__right,axiom,
! [X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_zadd__0__right,axiom,
! [X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X90] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X90,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_card__lessThan,axiom,
! [X160] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X160)) = X160,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__lessThan) ).
fof(fact_zminus__zminus,axiom,
! [X97] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X97)) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(fact_filter_Osimps_I1_J,axiom,
! [X38,X7] : hAPP(c_List_Ofilter(X7,X38),c_List_Olist_ONil(X7)) = c_List_Olist_ONil(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter_Osimps_I1_J) ).
fof(fact_finite__code,axiom,
! [X149,X7] :
( class_Finite__Set_Ofinite(X7)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
fof(fact_finite,axiom,
! [X149,X7] :
( class_Finite__Set_Ofinite(X7)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).
fof(fact_of__int__eq__0__iff,axiom,
! [X26,X7] :
( class_Int_Oring__char__0(X7)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(X7),X26) = c_Groups_Ozero__class_Ozero(X7)
<=> X26 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__eq__0__iff) ).
fof(fact_of__int__0__eq__iff,axiom,
! [X26,X7] :
( class_Int_Oring__char__0(X7)
=> ( c_Groups_Ozero__class_Ozero(X7) = hAPP(c_Int_Oring__1__class_Oof__int(X7),X26)
<=> X26 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__eq__iff) ).
fof(fact_diff__self__eq__0,axiom,
! [X90] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X90) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(fact_number__of__eq,axiom,
! [X96,X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),X96) = hAPP(c_Int_Oring__1__class_Oof__int(X87),X96) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__eq) ).
fof(fact_Option_Oset_Osimps_I1_J,axiom,
! [X7] : c_Option_Oset(X7,c_Option_Ooption_ONone(X7)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Oset_Osimps_I1_J) ).
fof(fact_com_Osimps_I5_J,axiom,
! [X68,X27,X66,X13] :
( c_Com_Ocom_OWhile(X13,X66) = c_Com_Ocom_OWhile(X27,X68)
<=> ( X13 = X27
& X66 = X68 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).
fof(fact_com_Osimps_I3_J,axiom,
! [X64,X65,X54,X55] :
( c_Com_Ocom_OSemi(X55,X54) = c_Com_Ocom_OSemi(X65,X64)
<=> ( X55 = X65
& X54 = X64 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).
fof(fact_com_Osimps_I1_J,axiom,
! [X27,X28,X13,X14] :
( c_Com_Ocom_OAss(X14,X13) = c_Com_Ocom_OAss(X28,X27)
<=> ( X14 = X28
& X13 = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I1_J) ).
fof(fact_neg__equal__zero,axiom,
! [X25,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25) = X25
<=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_equal__neg__zero,axiom,
! [X25,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( X25 = hAPP(c_Groups_Ouminus__class_Ouminus(X7),X25)
<=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_com_Osize_I10_J,axiom,
! [X13,X14] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X14,X13)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I10_J) ).
fof(fact_diff__bin__simps_I1_J,axiom,
! [X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),c_Int_OPls) = X96,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).
fof(fact_add__Pls__right,axiom,
! [X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Int_OPls) = X96,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_nat__int,axiom,
! [X33] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)) = X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__int) ).
fof(arity_prod__Smallcheck_Osmall,axiom,
! [X337,X336] :
( ( class_Smallcheck_Osmall(X336)
& class_Smallcheck_Osmall(X337) )
=> class_Smallcheck_Osmall(tc_prod(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Smallcheck_Osmall) ).
fof(arity_prod__Finite__Set_Ofinite,axiom,
! [X337,X336] :
( ( class_Finite__Set_Ofinite(X336)
& class_Finite__Set_Ofinite(X337) )
=> class_Finite__Set_Ofinite(tc_prod(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(arity_fun__Finite__Set_Ofinite,axiom,
! [X337,X336] :
( ( class_Finite__Set_Ofinite(X336)
& class_Finite__Set_Ofinite(X337) )
=> class_Finite__Set_Ofinite(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(arity_sum__Finite__Set_Ofinite,axiom,
! [X337,X336] :
( ( class_Finite__Set_Ofinite(X336)
& class_Finite__Set_Ofinite(X337) )
=> class_Finite__Set_Ofinite(tc_sum(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
! [X98,X86] :
( c_Nat__Transfer_Ois__nat(X86)
=> ( c_Nat__Transfer_Ois__nat(X98)
=> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X86,X98)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).
fof(fact_com_Osimps_I47_J,axiom,
! [X54,X55,X68,X27] : c_Com_Ocom_OWhile(X27,X68) != c_Com_Ocom_OSemi(X55,X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I47_J) ).
fof(fact_com_Osimps_I29_J,axiom,
! [X13,X14,X68,X27] : c_Com_Ocom_OWhile(X27,X68) != c_Com_Ocom_OAss(X14,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I29_J) ).
fof(fact_com_Osimps_I46_J,axiom,
! [X68,X27,X54,X55] : c_Com_Ocom_OSemi(X55,X54) != c_Com_Ocom_OWhile(X27,X68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I46_J) ).
fof(fact_com_Osimps_I28_J,axiom,
! [X68,X27,X13,X14] : c_Com_Ocom_OAss(X14,X13) != c_Com_Ocom_OWhile(X27,X68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I28_J) ).
fof(fact_com_Osimps_I25_J,axiom,
! [X13,X14,X64,X65] : c_Com_Ocom_OSemi(X65,X64) != c_Com_Ocom_OAss(X14,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I25_J) ).
fof(fact_com_Osimps_I24_J,axiom,
! [X64,X65,X13,X14] : c_Com_Ocom_OAss(X14,X13) != c_Com_Ocom_OSemi(X65,X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I24_J) ).
fof(fact_add__Pls,axiom,
! [X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X96) = X96,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(fact_rev__is__Nil__conv,axiom,
! [X292,X7] :
( hAPP(c_List_Orev(X7),X292) = c_List_Olist_ONil(X7)
<=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__Nil__conv) ).
fof(fact_rotate1__is__Nil__conv,axiom,
! [X292,X7] :
( hAPP(c_List_Orotate1(X7),X292) = c_List_Olist_ONil(X7)
<=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).
fof(fact_Nil__is__rev__conv,axiom,
! [X292,X7] :
( c_List_Olist_ONil(X7) = hAPP(c_List_Orev(X7),X292)
<=> X292 = c_List_Olist_ONil(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__rev__conv) ).
fof(fact_mult__Pls,axiom,
! [X128] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X128) = c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Pls) ).
fof(fact_wf__finite__psubset,axiom,
! [X7] : c_Wellfounded_Owf(tc_fun(X7,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__finite__psubset) ).
fof(fact_com_Osize_I15_J,axiom,
! [X8] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X8)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I15_J) ).
fof(fact_transpose_Osimps_I1_J,axiom,
! [X87] : c_List_Otranspose(X87,c_List_Olist_ONil(tc_List_Olist(X87))) = c_List_Olist_ONil(tc_List_Olist(X87)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I1_J) ).
fof(fact_com_Osimps_I59_J,axiom,
! [X66,X13,X4] : hAPP(c_Com_Ocom_OBODY,X4) != c_Com_Ocom_OWhile(X13,X66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I59_J) ).
fof(fact_com_Osimps_I49_J,axiom,
! [X73,X74,X34] : hAPP(c_Com_Ocom_OBODY,X34) != c_Com_Ocom_OSemi(X74,X73),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I49_J) ).
fof(fact_com_Osimps_I31_J,axiom,
! [X13,X14,X4] : hAPP(c_Com_Ocom_OBODY,X4) != c_Com_Ocom_OAss(X14,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I31_J) ).
fof(fact_com_Osimps_I58_J,axiom,
! [X4,X66,X13] : c_Com_Ocom_OWhile(X13,X66) != hAPP(c_Com_Ocom_OBODY,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I58_J) ).
fof(fact_com_Osimps_I48_J,axiom,
! [X34,X73,X74] : c_Com_Ocom_OSemi(X74,X73) != hAPP(c_Com_Ocom_OBODY,X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I48_J) ).
fof(fact_com_Osimps_I30_J,axiom,
! [X4,X13,X14] : c_Com_Ocom_OAss(X14,X13) != hAPP(c_Com_Ocom_OBODY,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I30_J) ).
fof(fact_succ__Min,axiom,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Min) ).
fof(fact_Bit0__Pls,axiom,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
fof(fact_pred__Pls,axiom,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Pls) ).
fof(fact_Rep__Integ__inject,axiom,
! [X127,X6] :
( hAPP(c_Int_ORep__Integ,X6) = hAPP(c_Int_ORep__Integ,X127)
<=> X6 = X127 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
fof(fact_Code__Numeral_Onat__of__inject,axiom,
! [X157,X94] :
( hAPP(c_Code__Numeral_Onat__of,X94) = hAPP(c_Code__Numeral_Onat__of,X157)
<=> X94 = X157 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).
fof(fact_code__numeral_Onat__of__inject,axiom,
! [X127,X6] :
( hAPP(c_Code__Numeral_Onat__of,X6) = hAPP(c_Code__Numeral_Onat__of,X127)
<=> X6 = X127 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
fof(fact_Code__Numeral_Oof__nat__inject,axiom,
! [X95,X44] :
( hAPP(c_Code__Numeral_Oof__nat,X44) = hAPP(c_Code__Numeral_Oof__nat,X95)
<=> X44 = X95 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
fof(fact_nat_Oinject,axiom,
! [X102,X103] :
( hAPP(c_Nat_OSuc,X103) = hAPP(c_Nat_OSuc,X102)
<=> X103 = X102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(fact_Suc__inject,axiom,
! [X98,X86] :
( hAPP(c_Nat_OSuc,X86) = hAPP(c_Nat_OSuc,X98)
=> X86 = X98 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(fact_com_Osimps_I6_J,axiom,
! [X4,X5] :
( hAPP(c_Com_Ocom_OBODY,X5) = hAPP(c_Com_Ocom_OBODY,X4)
<=> X5 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).
fof(fact_sgn__0__0,axiom,
! [X25,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( c_Groups_Osgn__class_Osgn(X7,X25) = c_Groups_Ozero__class_Ozero(X7)
<=> X25 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__0__0) ).
fof(fact_list_Osize_I3_J,axiom,
! [X87] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),c_List_Olist_ONil(X87)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I3_J) ).
fof(fact_option_Osize_I3_J,axiom,
! [X87] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X87)),c_Option_Ooption_ONone(X87)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osize_I3_J) ).
fof(fact_sorted__upto,axiom,
! [X113,X114] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X114,X113)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__upto) ).
fof(fact_option_Osimps_I3_J,axiom,
! [X88,X87] : hAPP(c_Option_Ooption_OSome(X87),X88) != c_Option_Ooption_ONone(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I3_J) ).
fof(fact_option_Osimps_I2_J,axiom,
! [X88,X87] : c_Option_Ooption_ONone(X87) != hAPP(c_Option_Ooption_OSome(X87),X88),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I2_J) ).
fof(fact_some__sym__eq__trivial,axiom,
! [X6,X7] : c_Hilbert__Choice_OEps(X7,hAPP(c_fequal,X6)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
fof(fact_the__sym__eq__trivial,axiom,
! [X6,X7] : c_HOL_OThe(X7,hAPP(c_fequal,X6)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).
fof(fact_listsum__simps_I1_J,axiom,
! [X87] :
( class_Groups_Omonoid__add(X87)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X87),c_List_Olist_ONil(X87)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__simps_I1_J) ).
fof(fact_abs__one,axiom,
! [X87] :
( class_Rings_Olinordered__idom(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),c_Groups_Oone__class_Oone(X87)) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__one) ).
fof(fact_abs__zero,axiom,
! [X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> hAPP(c_Groups_Oabs__class_Oabs(X87),c_Groups_Ozero__class_Ozero(X87)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zero) ).
fof(fact_compl__bot__eq,axiom,
! [X87] :
( class_Lattices_Oboolean__algebra(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Orderings_Obot__class_Obot(X87)) = c_Orderings_Otop__class_Otop(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__bot__eq) ).
fof(fact_compl__top__eq,axiom,
! [X87] :
( class_Lattices_Oboolean__algebra(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Orderings_Otop__class_Otop(X87)) = c_Orderings_Obot__class_Obot(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__top__eq) ).
fof(fact_minus__zero,axiom,
! [X87] :
( class_Groups_Ogroup__add(X87)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Ozero__class_Ozero(X87)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(arity_fun__Lattices_Obounded__lattice,axiom,
! [X336,X337] :
( class_Lattices_Obounded__lattice(X337)
=> class_Lattices_Obounded__lattice(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
fof(arity_fun__Lattices_Odistrib__lattice,axiom,
! [X336,X337] :
( class_Lattices_Odistrib__lattice(X337)
=> class_Lattices_Odistrib__lattice(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
fof(arity_fun__Lattices_Osemilattice__inf,axiom,
! [X336,X337] :
( class_Lattices_Olattice(X337)
=> class_Lattices_Osemilattice__inf(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
! [X336,X337] :
( class_Lattices_Obounded__lattice(X337)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(arity_fun__Orderings_Obot,axiom,
! [X336,X337] :
( class_Orderings_Obot(X337)
=> class_Orderings_Obot(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
! [X336,X337] :
( class_Lattices_Obounded__lattice(X337)
=> class_Lattices_Obounded__lattice__top(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).
fof(arity_fun__Orderings_Otop,axiom,
! [X336,X337] :
( class_Orderings_Otop(X337)
=> class_Orderings_Otop(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
! [X336,X337] :
( class_Complete__Lattice_Ocomplete__lattice(X337)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(arity_fun__Lattices_Osemilattice__sup,axiom,
! [X336,X337] :
( class_Lattices_Olattice(X337)
=> class_Lattices_Osemilattice__sup(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
fof(arity_fun__Lattices_Olattice,axiom,
! [X336,X337] :
( class_Lattices_Olattice(X337)
=> class_Lattices_Olattice(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(arity_fun__Groups_Ominus,axiom,
! [X336,X337] :
( class_Groups_Ominus(X337)
=> class_Groups_Ominus(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [X336,X337] :
( class_Groups_Ouminus(X337)
=> class_Groups_Ouminus(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [X336,X337] :
( class_Lattices_Oboolean__algebra(X337)
=> class_Lattices_Oboolean__algebra(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X336,X337] :
( class_Orderings_Oord(X337)
=> class_Orderings_Oord(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X336,X337] :
( class_Orderings_Opreorder(X337)
=> class_Orderings_Opreorder(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X336,X337] :
( class_Orderings_Oorder(X337)
=> class_Orderings_Oorder(tc_fun(X336,X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(fact_wf__acyclic,axiom,
! [X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> c_Wellfounded_Oacyclic(X7,X172) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acyclic) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
! [X97] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).
fof(fact_Rep__Integ__inverse,axiom,
! [X6] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X6)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inverse) ).
fof(fact_nat__of__of__nat,axiom,
! [X33] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X33)) = X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__of__nat) ).
fof(fact_of__nat__nat__of,axiom,
! [X96] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X96)) = X96,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__nat__of) ).
fof(fact_nat__of__inverse,axiom,
! [X86] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X86)) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__inverse) ).
fof(fact_iszero__def,axiom,
! [X26,X7] :
( class_Rings_Osemiring__1(X7)
=> ( c_Int_Oiszero(X7,X26)
<=> X26 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__def) ).
fof(fact_int__eq__0__conv,axiom,
! [X44] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
fof(fact_of__int__1,axiom,
! [X87] :
( class_Rings_Oring__1(X87)
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__1) ).
fof(fact_of__int__0,axiom,
! [X87] :
( class_Rings_Oring__1(X87)
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0) ).
fof(fact_of__nat__1,axiom,
! [X87] :
( class_Rings_Osemiring__1(X87)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__1) ).
fof(fact_of__nat__0,axiom,
! [X87] :
( class_Rings_Osemiring__1(X87)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0) ).
fof(fact_int__number__of__def,axiom,
! [X128] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X128),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__number__of__def) ).
fof(fact_com_Osize_I2_J,axiom,
! [X13,X14] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X14,X13)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I2_J) ).
fof(fact_sgn0,axiom,
! [X87] :
( class_Groups_Osgn__if(X87)
=> c_Groups_Osgn__class_Osgn(X87,c_Groups_Ozero__class_Ozero(X87)) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn0) ).
fof(fact_max__ord__max,axiom,
! [X7] :
( class_Orderings_Oord(X7)
=> c_Orderings_Oord__class_Omax(X7) = c_Orderings_Oord_Omax(X7,c_Orderings_Oord__class_Oless__eq(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ord__max) ).
fof(fact_min__ord__min,axiom,
! [X7] :
( class_Orderings_Oord(X7)
=> c_Orderings_Oord__class_Omin(X7) = c_Orderings_Oord_Omin(X7,c_Orderings_Oord__class_Oless__eq(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ord__min) ).
fof(fact_rev_Osimps_I1_J,axiom,
! [X87] : hAPP(c_List_Orev(X87),c_List_Olist_ONil(X87)) = c_List_Olist_ONil(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I1_J) ).
fof(fact_tl_Osimps_I1_J,axiom,
! [X87] : hAPP(c_List_Otl(X87),c_List_Olist_ONil(X87)) = c_List_Olist_ONil(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I1_J) ).
fof(fact_number__of__Pls,axiom,
! [X87] :
( class_Int_Onumber__ring(X87)
=> hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Pls) ).
fof(fact_semiring__norm_I112_J,axiom,
! [X87] :
( class_Int_Onumber__ring(X87)
=> c_Groups_Ozero__class_Ozero(X87) = hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(fact_com_Osize_I7_J,axiom,
! [X8] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X8)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I7_J) ).
fof(fact_is__none__def,axiom,
! [X6,X7] :
( c_Option_Ois__none(X7,X6)
<=> X6 = c_Option_Ooption_ONone(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__none__def) ).
fof(fact_sorted_Oequations_I1_J,axiom,
! [X87] :
( class_Orderings_Olinorder(X87)
=> c_List_Olinorder__class_Osorted(X87,c_List_Olist_ONil(X87)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_Oequations_I1_J) ).
fof(fact_sorted_ONil,axiom,
! [X87] :
( class_Orderings_Olinorder(X87)
=> c_List_Olinorder__class_Osorted(X87,c_List_Olist_ONil(X87)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_ONil) ).
fof(fact_iszero__0,axiom,
! [X87] :
( class_Rings_Osemiring__1(X87)
=> c_Int_Oiszero(X87,c_Groups_Ozero__class_Ozero(X87)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__0) ).
fof(fact_vname_Osize_I3_J,axiom,
! [X93] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X93)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osize_I3_J) ).
fof(fact_vname_Osize_I4_J,axiom,
! [X81] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X81)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osize_I4_J) ).
fof(fact_New__DSequence_Opos__empty__def,axiom,
! [X204,X87] : hAPP(c_New__DSequence_Opos__empty(X87),X204) = c_Lazy__Sequence_Oempty(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
fof(fact_butlast_Osimps_I1_J,axiom,
! [X87] : c_List_Obutlast(X87,c_List_Olist_ONil(X87)) = c_List_Olist_ONil(X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).
fof(fact_Suc__not__Zero,axiom,
! [X90] : hAPP(c_Nat_OSuc,X90) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [X91] : hAPP(c_Nat_OSuc,X91) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Suc__neq__Zero,axiom,
! [X90] : hAPP(c_Nat_OSuc,X90) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_Zero__not__Suc,axiom,
! [X90] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X92] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X92),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__neq__Suc,axiom,
! [X90] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_nat_Oexhaust,axiom,
! [X98] :
( X98 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ~ ! [X111] : X98 != hAPP(c_Nat_OSuc,X111) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oexhaust) ).
fof(fact_com_Osimps_I17_J,axiom,
! [X68,X27] : c_Com_Ocom_OWhile(X27,X68) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I17_J) ).
fof(fact_com_Osimps_I13_J,axiom,
! [X75,X76] : c_Com_Ocom_OSemi(X76,X75) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I13_J) ).
fof(fact_com_Osimps_I9_J,axiom,
! [X27,X28] : c_Com_Ocom_OAss(X28,X27) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I9_J) ).
fof(fact_com_Osimps_I16_J,axiom,
! [X68,X27] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X27,X68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I16_J) ).
fof(fact_com_Osimps_I12_J,axiom,
! [X75,X76] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X76,X75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).
fof(fact_com_Osimps_I8_J,axiom,
! [X27,X28] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X28,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I8_J) ).
fof(fact_inf__min,axiom,
! [X7] :
( ( class_Lattices_Osemilattice__inf(X7)
& class_Orderings_Olinorder(X7) )
=> c_Lattices_Osemilattice__inf__class_Oinf(X7) = c_Orderings_Oord__class_Omin(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__min) ).
fof(fact_sup__max,axiom,
! [X7] :
( ( class_Lattices_Osemilattice__sup(X7)
& class_Orderings_Olinorder(X7) )
=> c_Lattices_Osemilattice__sup__class_Osup(X7) = c_Orderings_Oord__class_Omax(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__max) ).
fof(fact_Suc__n__not__n,axiom,
! [X33] : hAPP(c_Nat_OSuc,X33) != X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X33] : X33 != hAPP(c_Nat_OSuc,X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_id__apply,axiom,
! [X86,X87] : hAPP(c_Fun_Oid(X87),X86) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__apply) ).
fof(fact_id__def,axiom,
! [X264,X87] : hAPP(c_Fun_Oid(X87),X264) = X264,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__def) ).
fof(fact_Collect__def,axiom,
! [X38,X7] : hAPP(c_Set_OCollect(X7),X38) = X38,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(help_c__COMBI__1,axiom,
! [X79,X87] : hAPP(c_COMBI(X87),X79) = X79,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(fact_is__none__code_I1_J,axiom,
! [X87] : c_Option_Ois__none(X87,c_Option_Ooption_ONone(X87)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__none__code_I1_J) ).
fof(fact_zero__neq__one,axiom,
! [X87] :
( class_Rings_Ozero__neq__one(X87)
=> c_Groups_Ozero__class_Ozero(X87) != c_Groups_Oone__class_Oone(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [X87] :
( class_Rings_Ozero__neq__one(X87)
=> c_Groups_Oone__class_Oone(X87) != c_Groups_Ozero__class_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(fact_com_Osimps_I19_J,axiom,
! [X34] : hAPP(c_Com_Ocom_OBODY,X34) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I19_J) ).
fof(fact_com_Osimps_I18_J,axiom,
! [X34] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I18_J) ).
fof(fact_size__char,axiom,
! [X10] : hAPP(c_Nat_Osize__class_Osize(tc_String_Ochar),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_size__char) ).
fof(fact_size__literal__def,axiom,
! [X9] : hAPP(c_Nat_Osize__class_Osize(tc_String_Oliteral),X9) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_size__literal__def) ).
fof(fact_beyond__zero,axiom,
! [X96] : c_Quickcheck_Obeyond(X96,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_beyond__zero) ).
fof(fact_wf__int__ge__less__than2,axiom,
! [X136] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X136)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__int__ge__less__than2) ).
fof(fact_wf__int__ge__less__than,axiom,
! [X136] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X136)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__int__ge__less__than) ).
fof(fact_number__of__is__id,axiom,
! [X96] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X96) = X96,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(fact_nat__size,axiom,
! [X33] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X33) = X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
! [X337] :
( class_Finite__Set_Ofinite(X337)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X337)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(fact_vname_Osimps_I1_J,axiom,
! [X99,X100] :
( c_Com_Ovname_OGlb(X100) = c_Com_Ovname_OGlb(X99)
<=> X100 = X99 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I1_J) ).
fof(fact_vname_Osimps_I2_J,axiom,
! [X69,X67] :
( c_Com_Ovname_OLoc(X67) = c_Com_Ovname_OLoc(X69)
<=> X67 = X69 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I2_J) ).
fof(fact_vname_Osimps_I3_J,axiom,
! [X101,X93] : c_Com_Ovname_OGlb(X93) != c_Com_Ovname_OLoc(X101),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I3_J) ).
fof(fact_vname_Osimps_I4_J,axiom,
! [X93,X101] : c_Com_Ovname_OLoc(X101) != c_Com_Ovname_OGlb(X93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I4_J) ).
fof(fact_vname_Osize_I1_J,axiom,
! [X93] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X93)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osize_I1_J) ).
fof(fact_vname_Osize_I2_J,axiom,
! [X81] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X81)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osize_I2_J) ).
fof(fact_identity__equivp,axiom,
! [X7] : c_Equiv__Relations_Oequivp(X7,c_fequal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_identity__equivp) ).
fof(help_c__fFalse__1,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
fof(fact_Nitpick_OFrac__def,axiom,
c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_OFrac__def) ).
fof(fact_min__weak__def,axiom,
c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__weak__def) ).
fof(fact_max__weak__def,axiom,
c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__weak__def) ).
fof(fact_max__rpair__set,axiom,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__rpair__set) ).
fof(fact_min__rpair__set,axiom,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__rpair__set) ).
fof(fact_pred__nat__def,axiom,
c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__nat__def) ).
fof(fact_One__int__def,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__int__def) ).
fof(fact_Zero__int__def,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__int__def) ).
fof(fact_UNIV__char,axiom,
c_Orderings_Otop__class_Otop(tc_fun(tc_String_Ochar,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_prod(tc_String_Onibble,tc_String_Onibble),tc_String_Ochar,hAPP(c_Product__Type_Oprod_Oprod__case(tc_String_Onibble,tc_String_Onibble,tc_String_Ochar),c_String_Ochar_OChar)),hAPP(hAPP(c_Product__Type_OSigma(tc_String_Onibble,tc_String_Onibble),c_Orderings_Otop__class_Otop(tc_fun(tc_String_Onibble,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(tc_String_Onibble,tc_HOL_Obool),tc_String_Onibble),c_Orderings_Otop__class_Otop(tc_fun(tc_String_Onibble,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__char) ).
fof(fact_type__definition__Integ,axiom,
c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition__Integ) ).
fof(fact_type__definition__code__numeral,axiom,
c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition__code__numeral) ).
fof(fact_wf__less,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__less) ).
fof(fact_int__of__def,axiom,
c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__of__def) ).
fof(fact_number__of__code__numeral__def,axiom,
c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__code__numeral__def) ).
fof(fact_Integ__def,axiom,
c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Integ__def) ).
fof(fact_transfer__morphism__int__nat,axiom,
c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__morphism__int__nat) ).
fof(fact_inj__int,axiom,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__int) ).
fof(fact_INT__greaterThan__UNIV,axiom,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__greaterThan__UNIV) ).
fof(fact_UN__atLeast__UNIV,axiom,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__atLeast__UNIV) ).
fof(fact_UN__atMost__UNIV,axiom,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__atMost__UNIV) ).
fof(fact_UN__lessThan__UNIV,axiom,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__lessThan__UNIV) ).
fof(fact_transfer__morphism__nat__int,axiom,
c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__morphism__nat__int) ).
fof(fact_pair__less__def,axiom,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__less__def) ).
fof(fact_finite__dom__body,axiom,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__dom__body) ).
fof(fact_equiv__intrel,axiom,
c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__intrel) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J) ).
fof(fact_greaterThan__0,axiom,
hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__0) ).
fof(fact_number__of2,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of2) ).
fof(fact_atMost__0,axiom,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__0) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_int__0__less__1,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(fact_bin__less__0__simps_I2_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I2_J) ).
fof(fact_rel__simps_I19_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).
fof(fact_rel__simps_I23_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I23_J) ).
fof(fact_rel__simps_I24_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I24_J) ).
fof(fact_rel__simps_I6_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I6_J) ).
fof(fact_neg__number__of__Min,axiom,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Min) ).
fof(fact_card__UNIV__unit,axiom,
hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).
fof(fact_code__numeral__zero__minus__one,axiom,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__zero__minus__one) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).
fof(fact_body__def,axiom,
c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_body__def) ).
fof(fact_eq__number__of__Pls__Min,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).
fof(fact_int__Suc0__eq__1,axiom,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).
fof(fact_atLeast__0,axiom,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__0) ).
fof(fact_lessThan__0,axiom,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__0) ).
fof(fact_wf__pair__less,axiom,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pair__less) ).
fof(fact_max__strict__def,axiom,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__strict__def) ).
fof(fact_min__strict__def,axiom,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__strict__def) ).
fof(fact_nat__1,axiom,
hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1) ).
fof(fact_WT_OSkip,axiom,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OSkip) ).
fof(fact_WT_Oequations_I1_J,axiom,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I1_J) ).
fof(fact_zminus__0,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__0) ).
fof(fact_int__1,axiom,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__1) ).
fof(fact_int__0,axiom,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0) ).
fof(fact_code__numeral_Osize_I3_J,axiom,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osize_I3_J) ).
fof(fact_nat_Osize_I3_J,axiom,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
fof(fact_transfer__int__nat__numerals_I2_J,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
fof(fact_transfer__int__nat__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
fof(fact_Int_OMin__def,axiom,
c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int_OMin__def) ).
fof(fact_nat__number__of__Pls,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).
fof(fact_bool_Osize_I4_J,axiom,
hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I4_J) ).
fof(fact_bool_Osize_I3_J,axiom,
hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I3_J) ).
fof(fact_com_Osize_I9_J,axiom,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I9_J) ).
fof(fact_nat__0,axiom,
hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0) ).
fof(fact_zero__code__numeral__code,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__code__numeral__code) ).
fof(fact_zero__is__num__zero,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).
fof(fact_semiring__norm_I113_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).
fof(fact_one__code__numeral__def,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__code__numeral__def) ).
fof(fact_transfer__nat__int__numerals_I2_J,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(fact_zero__code__numeral__def,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__code__numeral__def) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_minus__Pls,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Pls) ).
fof(fact_wf__pred__nat,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
fof(fact_wf__less__than,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__less__than) ).
fof(fact_code__numeral_Osize_I1_J,axiom,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osize_I1_J) ).
fof(fact_nat_Osize_I1_J,axiom,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__list__functions_I2_J) ).
fof(fact_int__0__neq__1,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
fof(fact_of__int__eq__id,axiom,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__eq__id) ).
fof(fact_inf__nat__def,axiom,
c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__nat__def) ).
fof(fact_bot__nat__def,axiom,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__nat__def) ).
fof(fact_sup__nat__def,axiom,
c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__nat__def) ).
fof(fact_bool_Osize_I2_J,axiom,
c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).
fof(fact_bool_Osize_I1_J,axiom,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).
fof(fact_com_Osize_I1_J,axiom,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I1_J) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).
fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
class_Groups_Osemigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osemigroup__add) ).
fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
class_Groups_Osemigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Osemigroup__add) ).
fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
class_Smallcheck_Osmall(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Smallcheck_Osmall) ).
fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
class_Smallcheck_Osmall(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Smallcheck_Osmall) ).
fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
class_Orderings_Owellorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Odistrib__lattice) ).
fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).
fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(arity_Nat__Onat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
fof(arity_String__Onibble__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_String_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_String__Onibble__Finite__Set_Ofinite) ).
fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(arity_String__Ochar__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_String_Ochar),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_String__Ochar__Finite__Set_Ofinite) ).
fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
fof(arity_HOL__Obool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__sup) ).
fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
fof(arity_Int__Oint__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).
fof(arity_HOL__Obool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(arity_Nat__Onat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Odvd) ).
fof(arity_Int__Oint__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(arity_Nat__Onat__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).
fof(arity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_Int__Oint__Groups_Oabs__if,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).
fof(arity_Int__Oint__Int_Onumber,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(arity_Nat__Onat__Int_Onumber,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
fof(arity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).
fof(arity_Int__Oint__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(arity_HOL__Obool__Groups_Ominus,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(arity_Nat__Onat__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(arity_Int__Oint__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(arity_HOL__Obool__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(arity_Int__Oint__Divides_Oring__div,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).
fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
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class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(help_c__fTrue__1,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(fact_Code__Numeral_Oof__nat__code,axiom,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).
fof(fact_subtract__code__numeral__def,axiom,
c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subtract__code__numeral__def) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(fact_rel__simps_I37_J,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).
fof(fact_rel__simps_I40_J,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).
fof(i_0_5163,plain,
! [X94,X7] :
( class_Rings_Oring__1(X7)
=> ( ( X94 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(c_Int_Oring__1__class_Oof__int(X7),X94) = c_Groups_Ozero__class_Ozero(X7) )
& ( X94 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X7),X94) = hAPP(c_Groups_Ouminus__class_Ouminus(X7),hAPP(c_Int_Oring__1__class_Oof__int(X7),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X94))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X7),X94) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X7),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X7,X7)),tc_fun(tc_Int_Oint,X7)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,X7),X7),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X7,X7)),tc_fun(tc_Int_Oint,X7)),tc_Int_Oint),c_COMBB(tc_fun(X7,X7),X7,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X7,tc_fun(tc_fun(X7,X7),X7),tc_Int_Oint),c_HOL_OLet(X7,X7)),c_Int_Oring__1__class_Oof__int(X7)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X7,X7),tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,X7)),tc_fun(tc_fun(X7,X7),tc_fun(X7,X7)),tc_Int_Oint),c_COMBS(X7,X7,X7)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X7,X7),tc_fun(X7,tc_fun(X7,X7))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,X7)),tc_fun(tc_fun(X7,X7),tc_fun(X7,tc_fun(X7,X7))),tc_Int_Oint),c_COMBB(X7,tc_fun(X7,X7),X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),tc_Int_Oint),c_If(X7)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X7,X7,X7),c_Groups_Oplus__class_Oplus(X7)),c_COMBI(X7))))),hAPP(hAPP(c_COMBC(X7,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X7),c_Groups_Oplus__class_Oplus(X7)),hAPP(hAPP(c_COMBS(X7,X7,X7),c_Groups_Oplus__class_Oplus(X7)),c_COMBI(X7)))),c_Groups_Oone__class_Oone(X7))))),c_Divides_Odivmod__int(X94,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_of__int__num]) ).
fof(i_0_5164,plain,
! [X98,X86,X87] :
( class_Rings_Olinordered__idom(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X86),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X98),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X87))) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero]) ).
fof(i_0_5165,plain,
! [X71,X87] :
( class_Rings_Olinordered__idom(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Power_Opower__class_Opower(X87),X71),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X87))) ),
inference(fof_simplification,[status(thm)],[fact_power2__less__0]) ).
fof(i_0_5166,plain,
! [X139,X128] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(fof_simplification,[status(thm)],[fact_zmod__number__of__Bit1]) ).
fof(i_0_5167,plain,
! [X128,X139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139))))
=> c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139))))
=> c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn__number__of]) ).
fof(i_0_5168,plain,
! [X128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn__1__number__of]) ).
fof(i_0_5169,plain,
! [X128,X139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn__number__of]) ).
fof(i_0_5170,plain,
! [X128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn__1__number__of]) ).
fof(i_0_5171,plain,
! [X71,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)))
=> c_Divides_OnegDivAlg(X71,X84) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X71),X84)))
=> c_Divides_OnegDivAlg(X71,X84) = hAPP(c_Divides_Oadjust(X84),c_Divides_OnegDivAlg(X71,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X84))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn]) ).
fof(i_0_5172,plain,
! [X71,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),X84))
=> c_Divides_OposDivAlg(X71,X84) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),X84))
=> c_Divides_OposDivAlg(X71,X84) = hAPP(c_Divides_Oadjust(X84),c_Divides_OposDivAlg(X71,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X84))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn]) ).
fof(i_0_5173,plain,
! [X163,X125,X7] :
( class_Int_Onumber__ring(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = hAPP(hAPP(c_HOL_OLet(X7,X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125))),hAPP(hAPP(c_COMBS(X7,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X7),c_Groups_Otimes__class_Otimes(X7)),hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)))),c_COMBI(X7))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = c_Groups_Oone__class_Oone(X7) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__number__of__odd__number__of]) ).
fof(i_0_5174,plain,
! [X26,X125,X7] :
( class_Int_Onumber__ring(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X7),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = hAPP(hAPP(c_HOL_OLet(X7,X7),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125))),hAPP(hAPP(c_COMBS(X7,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X7),c_Groups_Otimes__class_Otimes(X7)),hAPP(c_Groups_Otimes__class_Otimes(X7),X26))),c_COMBI(X7))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X7),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = c_Groups_Oone__class_Oone(X7) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__number__of__odd]) ).
fof(i_0_5175,plain,
! [X26,X125] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26))),c_COMBI(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_zpower__number__of__odd]) ).
fof(i_0_5176,plain,
! [X6,X172,X7] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X7,X7),X172)),c_Transitive__Closure_Ortrancl(X7,X172)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X6)),c_Transitive__Closure_Otrancl(X7,X172))) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__tranclI]) ).
fof(i_0_5177,plain,
! [X136,X23,X24,X25] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23,X136)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24))
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23),X25))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X136))
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23),X25))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X23)) )
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X136))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X136),X24)) ) ) ) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23),X136)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__psubset__iff]) ).
fof(i_0_5178,plain,
! [X172,X7] :
( c_Wellfounded_Oacyclic(X7,X172)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),c_Transitive__Closure_Otrancl(X7,X172))) ),
inference(fof_simplification,[status(thm)],[fact_acyclic__def]) ).
fof(i_0_5179,plain,
! [X139,X128] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X139))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X139))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) ) ),
inference(fof_simplification,[status(thm)],[fact_zdiv__number__of__Bit1]) ).
fof(i_0_5180,plain,
! [X172,X7] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),c_Transitive__Closure_Otrancl(X7,X172)))
=> c_Wellfounded_Oacyclic(X7,X172) ),
inference(fof_simplification,[status(thm)],[fact_acyclicI]) ).
fof(i_0_5181,plain,
! [X125] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X125)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X125)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X125)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__Bit1]) ).
fof(i_0_5182,plain,
! [X33,X90] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33)))
=> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33)))
=> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_upt__rec__number__of]) ).
fof(i_0_5183,plain,
! [X128,X87] :
( ( class_Int_Onumber__ring(X87)
& class_Int_Oring__char__0(X87) )
=> ~ c_Int_Oiszero(X87,hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit1(X128))) ),
inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit1]) ).
fof(i_0_5184,plain,
! [X87] :
( class_Int_Onumber__ring(X87)
=> ~ c_Int_Oiszero(X87,hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OBit1(c_Int_OPls))) ),
inference(fof_simplification,[status(thm)],[fact_not__iszero__Numeral1]) ).
fof(i_0_5185,plain,
! [X33,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X139))),X33) ) ),
inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of__add]) ).
fof(i_0_5186,plain,
! [X113,X114] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> c_List_Oupt(X114,hAPP(c_Nat_OSuc,X113)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X114,X113)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X113),c_List_Olist_ONil(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X114),X113))
=> c_List_Oupt(X114,hAPP(c_Nat_OSuc,X113)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_upt__Suc]) ).
fof(i_0_5187,plain,
! [X113,X114] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> c_List_Oupt(X114,X113) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X114),c_List_Oupt(hAPP(c_Nat_OSuc,X114),X113)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114),X113))
=> c_List_Oupt(X114,X113) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_upt__rec]) ).
fof(i_0_5188,plain,
! [X94,X44,X38] :
( epred1_3(X38,X44,X94)
<=> ( ( X94 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X38,X44)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
=> ! [X147,X117] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X117))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X117),X94))
& X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X147)),X117) )
=> hBOOL(hAPP(X38,X117)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X147,X117] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X117))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X117),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X147)),X117) )
=> hBOOL(hAPP(X38,X117)) ) ) ) ),
introduced(definition) ).
fof(i_0_5189,plain,
! [X94,X44,X38] :
( epred2_3(X38,X44,X94)
<=> ( ( X94 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
=> ! [X147] :
( ? [X117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X117))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X117),X94))
& X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X147)),X117) )
=> hBOOL(hAPP(X38,X147)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X147] :
( ? [X117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X117))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X117),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X44 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X147)),X117) )
=> hBOOL(hAPP(X38,X147)) ) ) ) ),
introduced(definition) ).
fof(i_0_5190,plain,
! [X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X139)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__diff__1]) ).
fof(i_0_5191,plain,
! [X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X139)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__1]) ).
fof(i_0_5192,plain,
! [X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X139)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__1__add__number__of]) ).
fof(i_0_5193,plain,
! [X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X139)) ) ),
inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of]) ).
fof(i_0_5194,plain,
! [X21919] : c_Divides_Oadjust(X21919) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X21919))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X21919))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[fact_adjust__def]) ).
fof(i_0_5195,plain,
! [X21288] : c_Int_Osucc(c_Int_OBit0(X21288)) = c_Int_OBit1(X21288),
inference(variable_rename,[status(thm)],[fact_succ__Bit0]) ).
fof(i_0_5196,plain,
! [X21248] : c_Int_OBit0(X21248) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21248),X21248),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(i_0_5197,plain,
! [X21065] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21065),c_Int_OMin) = c_Int_Osucc(X21065),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I2_J]) ).
fof(i_0_5198,plain,
! [X191,X1,X2,X190,X119,X23,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),X23),hAPP(c_Set_Oimage(tc_prod(X119,X190),tc_prod(X7,X105),c_Product__Type_Omap__pair(X119,X7,X190,X105,X2,X1)),X191)))
=> ~ ! [X3,X82] :
( X23 = hAPP(hAPP(c_Product__Type_OPair(X7,X105),hAPP(X2,X3)),hAPP(X1,X82))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X119,X190)),hAPP(hAPP(c_Product__Type_OPair(X119,X190),X3),X82)),X191)) ) ),
inference(fof_simplification,[status(thm)],[fact_prod__fun__imageE]) ).
fof(i_0_5199,plain,
! [X22053,X22054] :
( ( X22054 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22054,X22053) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( X22053 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22054,X22053) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22054)
| X22054 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X22053 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22054,X22053) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X22053))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22053)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22054))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22053),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22054),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X22054,X22053)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22053))))),c_Divides_Opdivmod(X22054,X22053))))
| X22054 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__pdivmod])])]) ).
fof(i_0_5200,plain,
! [X29460,X29461,X29462,X29463] : c_Product__Type_Oapsnd(X29463,X29462,X29461,X29460) = c_Product__Type_Omap__pair(X29461,X29461,X29463,X29462,c_Fun_Oid(X29461),X29460),
inference(variable_rename,[status(thm)],[fact_apsnd__def]) ).
fof(i_0_5201,plain,
! [X22124,X22125] :
( ( X22125 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22125,X22124) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( X22124 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22125,X22124) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22125)
| X22125 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X22124 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22125,X22124) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X22124))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X22125)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X22124))),c_Divides_Opdivmod(X22125,X22124)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22124))))),c_Divides_Opdivmod(X22125,X22124))))
| X22125 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__code])])]) ).
fof(i_0_5202,plain,
! [X22855,X22856,X22857] : c_Nitpick_Oplus__frac(X22857,X22856,X22855) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X22857),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X22857),X22856),hAPP(c_Nitpick_Odenom(X22857),X22855))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X22857),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X22857),tc_Int_Oint),c_Nitpick_Ofrac(X22857)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22857),X22856))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X22857),X22856))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22857),X22855))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X22857),X22855)))))),c_COMBI(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Oplus__frac__def]) ).
fof(i_0_5203,plain,
! [X26782] : c_Nitpick_Odenom(X26782) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X26782,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X26782)),
inference(variable_rename,[status(thm)],[fact_Nitpick_Odenom__def]) ).
fof(i_0_5204,plain,
! [X26788] : c_Nitpick_Onum(X26788) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X26788,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X26788)),
inference(variable_rename,[status(thm)],[fact_Nitpick_Onum__def]) ).
fof(i_0_5205,plain,
! [X30169,X30170,X30171,X30172] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30172,tc_fun(X30172,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X30172,tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_fun(X30172,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30172,tc_fun(tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_fun(X30172,tc_HOL_Obool)),X30172),c_COMBC(X30172,tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30172,tc_prod(X30172,X30172)),tc_fun(X30172,tc_fun(tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_HOL_Obool)),X30172),hAPP(c_COMBB(tc_prod(X30172,X30172),tc_fun(tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_HOL_Obool),X30172),c_member(tc_prod(X30172,X30172)))),c_Product__Type_OPair(X30172,X30172)))),X30171)),c_fequal),X30170),X30169))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30172,X30172)),hAPP(hAPP(c_Product__Type_OPair(X30172,X30172),X30170),X30169)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool)),X30171),c_Relation_OId(X30172)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30172,X30172)),hAPP(hAPP(c_Product__Type_OPair(X30172,X30172),X30170),X30169)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool)),X30171),c_Relation_OId(X30172))))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30172,tc_fun(X30172,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X30172,tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_fun(X30172,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30172,tc_fun(tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_fun(X30172,tc_HOL_Obool)),X30172),c_COMBC(X30172,tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30172,tc_prod(X30172,X30172)),tc_fun(X30172,tc_fun(tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_HOL_Obool)),X30172),hAPP(c_COMBB(tc_prod(X30172,X30172),tc_fun(tc_fun(tc_prod(X30172,X30172),tc_HOL_Obool),tc_HOL_Obool),X30172),c_member(tc_prod(X30172,X30172)))),c_Product__Type_OPair(X30172,X30172)))),X30171)),c_fequal),X30170),X30169)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq])]) ).
fof(i_0_5206,plain,
! [X30201] : c_Transitive__Closure_Ortrancl(X30201,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X30201,X30201),tc_HOL_Obool))) = c_Relation_OId(X30201),
inference(variable_rename,[status(thm)],[fact_rtrancl__empty]) ).
fof(i_0_5207,plain,
! [X21868,X21869,X21870] : hAPP(c_Divides_Oadjust(X21870),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21869),X21868)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21868),X21870)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21869)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21869)),X21868))),
inference(variable_rename,[status(thm)],[fact_adjust__eq]) ).
fof(i_0_5208,plain,
! [X30165,X30166,X30167,X30168] : c_Transitive__Closure_Otrancl(X30168,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30168,X30168)),hAPP(hAPP(c_Product__Type_OPair(X30168,X30168),X30167),X30166)),X30165)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30168,X30168),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30168,X30165)),hAPP(c_Set_OCollect(tc_prod(X30168,X30168)),hAPP(c_Product__Type_Oprod_Oprod__case(X30168,X30168,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X30168,tc_fun(X30168,tc_HOL_Obool),tc_fun(X30168,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X30168,tc_HOL_Obool),tc_fun(X30168,tc_HOL_Obool)),X30168),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X30168)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30168),c_fconj),hAPP(hAPP(c_COMBC(X30168,tc_fun(tc_prod(X30168,X30168),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X30168,X30168),tc_fun(tc_fun(tc_prod(X30168,X30168),tc_HOL_Obool),tc_HOL_Obool),X30168),c_member(tc_prod(X30168,X30168))),hAPP(hAPP(c_COMBC(X30168,X30168,tc_prod(X30168,X30168)),c_Product__Type_OPair(X30168,X30168)),X30167))),c_Transitive__Closure_Ortrancl(X30168,X30165))))),hAPP(hAPP(c_COMBC(X30168,tc_fun(tc_prod(X30168,X30168),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X30168,X30168),tc_fun(tc_fun(tc_prod(X30168,X30168),tc_HOL_Obool),tc_HOL_Obool),X30168),c_member(tc_prod(X30168,X30168))),hAPP(c_Product__Type_OPair(X30168,X30168),X30166))),c_Transitive__Closure_Ortrancl(X30168,X30165)))))),
inference(variable_rename,[status(thm)],[fact_trancl__insert]) ).
fof(i_0_5209,plain,
! [X30193,X30194] : c_Transitive__Closure_Otrancl(X30194,X30193) = hAPP(hAPP(c_Relation_Orel__comp(X30194,X30194,X30194),X30193),c_Transitive__Closure_Ortrancl(X30194,X30193)),
inference(variable_rename,[status(thm)],[fact_trancl__unfold__left]) ).
fof(i_0_5210,plain,
! [X21942,X21943] :
( ( X21942 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(X21943),X21942) = c_Groups_Ozero__class_Ozero(X21943)
| ~ class_Rings_Oring__1(X21943) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21942),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Oring__1__class_Oof__int(X21943),X21942) = hAPP(c_Groups_Ouminus__class_Ouminus(X21943),hAPP(c_Int_Oring__1__class_Oof__int(X21943),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21942)))
| X21942 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(X21943) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21942),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Oring__1__class_Oof__int(X21943),X21942) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X21943),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X21943,X21943)),tc_fun(tc_Int_Oint,X21943)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21943,X21943),X21943),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X21943,X21943)),tc_fun(tc_Int_Oint,X21943)),tc_Int_Oint),c_COMBB(tc_fun(X21943,X21943),X21943,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X21943,tc_fun(tc_fun(X21943,X21943),X21943),tc_Int_Oint),c_HOL_OLet(X21943,X21943)),c_Int_Oring__1__class_Oof__int(X21943)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X21943,X21943),tc_fun(X21943,X21943)),hAPP(hAPP(c_COMBB(tc_fun(X21943,tc_fun(X21943,X21943)),tc_fun(tc_fun(X21943,X21943),tc_fun(X21943,X21943)),tc_Int_Oint),c_COMBS(X21943,X21943,X21943)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X21943,X21943),tc_fun(X21943,tc_fun(X21943,X21943))),hAPP(hAPP(c_COMBB(tc_fun(X21943,tc_fun(X21943,X21943)),tc_fun(tc_fun(X21943,X21943),tc_fun(X21943,tc_fun(X21943,X21943))),tc_Int_Oint),c_COMBB(X21943,tc_fun(X21943,X21943),X21943)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21943,tc_fun(X21943,X21943)),tc_Int_Oint),c_If(X21943)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X21943,X21943,X21943),c_Groups_Oplus__class_Oplus(X21943)),c_COMBI(X21943))))),hAPP(hAPP(c_COMBC(X21943,X21943,X21943),hAPP(hAPP(c_COMBB(X21943,tc_fun(X21943,X21943),X21943),c_Groups_Oplus__class_Oplus(X21943)),hAPP(hAPP(c_COMBS(X21943,X21943,X21943),c_Groups_Oplus__class_Oplus(X21943)),c_COMBI(X21943)))),c_Groups_Oone__class_Oone(X21943))))),c_Divides_Odivmod__int(X21942,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| X21942 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(X21943) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5163])])]) ).
fof(i_0_5211,plain,
! [X31678,X31679,X31680,X31681] : c_Map_Omap__add(X31681,X31680,X31679,c_Map_Omap__of(X31681,X31680,X31678)) = c_List_Ofoldr(tc_prod(X31681,X31680),tc_fun(X31681,tc_Option_Ooption(X31680)),hAPP(c_Product__Type_Oprod_Oprod__case(X31681,X31680,tc_fun(tc_fun(X31681,tc_Option_Ooption(X31680)),tc_fun(X31681,tc_Option_Ooption(X31680)))),hAPP(hAPP(c_COMBC(X31681,tc_fun(X31680,tc_Option_Ooption(X31680)),tc_fun(X31680,tc_fun(tc_fun(X31681,tc_Option_Ooption(X31680)),tc_fun(X31681,tc_Option_Ooption(X31680))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X31680),tc_fun(tc_fun(X31681,tc_Option_Ooption(X31680)),tc_fun(X31681,tc_Option_Ooption(X31680)))),tc_fun(tc_fun(X31680,tc_Option_Ooption(X31680)),tc_fun(X31680,tc_fun(tc_fun(X31681,tc_Option_Ooption(X31680)),tc_fun(X31681,tc_Option_Ooption(X31680))))),X31681),c_COMBB(tc_Option_Ooption(X31680),tc_fun(tc_fun(X31681,tc_Option_Ooption(X31680)),tc_fun(X31681,tc_Option_Ooption(X31680))),X31680)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31681,tc_Option_Ooption(X31680)),tc_fun(tc_Option_Ooption(X31680),tc_fun(X31681,tc_Option_Ooption(X31680)))),tc_fun(tc_Option_Ooption(X31680),tc_fun(tc_fun(X31681,tc_Option_Ooption(X31680)),tc_fun(X31681,tc_Option_Ooption(X31680)))),X31681),c_COMBC(tc_fun(X31681,tc_Option_Ooption(X31680)),tc_Option_Ooption(X31680),tc_fun(X31681,tc_Option_Ooption(X31680)))),hAPP(c_COMBC(tc_fun(X31681,tc_Option_Ooption(X31680)),X31681,tc_fun(tc_Option_Ooption(X31680),tc_fun(X31681,tc_Option_Ooption(X31680)))),c_Fun_Ofun__upd(X31681,tc_Option_Ooption(X31680)))))),c_Option_Ooption_OSome(X31680))),X31678,X31679),
inference(variable_rename,[status(thm)],[fact_map__add__map__of__foldr]) ).
fof(i_0_5212,plain,
! [X34297,X34298,X34299,X34300,X34301] : c_List_Ofoldr(X34301,X34300,X34299,X34298,X34297) = hAPP(c_List_Ofoldl(X34300,X34301,hAPP(c_COMBC(X34301,X34300,X34300),X34299),X34297),hAPP(c_List_Orev(X34301),X34298)),
inference(variable_rename,[status(thm)],[fact_foldr__foldl]) ).
fof(i_0_5213,plain,
! [X21375,X21376,X21377] :
( ( X21376 = c_Groups_Ozero__class_Ozero(X21377)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21377),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21377),hAPP(hAPP(c_Power_Opower__class_Opower(X21377),X21376),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21377),X21375),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21377)))
| ~ class_Rings_Olinordered__idom(X21377) )
& ( X21375 = c_Groups_Ozero__class_Ozero(X21377)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21377),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21377),hAPP(hAPP(c_Power_Opower__class_Opower(X21377),X21376),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21377),X21375),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21377)))
| ~ class_Rings_Olinordered__idom(X21377) )
& ( X21376 != c_Groups_Ozero__class_Ozero(X21377)
| X21375 != c_Groups_Ozero__class_Ozero(X21377)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21377),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21377),hAPP(hAPP(c_Power_Opower__class_Opower(X21377),X21376),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21377),X21375),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21377)))
| ~ class_Rings_Olinordered__idom(X21377) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff])])]) ).
fof(i_0_5214,plain,
! [X21381,X21382,X21383] :
( ~ class_Rings_Olinordered__idom(X21383)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21383),hAPP(hAPP(c_Power_Opower__class_Opower(X21383),X21382),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21383),X21381),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21383))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5164])]) ).
fof(i_0_5215,plain,
! [X34358,X34359,X34360,X34361] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X34361)),c_List_Otranspose__rel(X34361)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34361)),hAPP(hAPP(c_List_Olist_OCons(X34361),X34360),X34359)),X34358)))
| c_List_Otranspose(X34361,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34361)),hAPP(hAPP(c_List_Olist_OCons(X34361),X34360),X34359)),X34358)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34361)),hAPP(hAPP(c_List_Olist_OCons(X34361),X34360),c_List_Oconcat(X34361,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34361),tc_List_Olist(X34361)),c_List_Olist_Olist__case(tc_List_Olist(X34361),X34361,c_List_Olist_ONil(X34361),hAPP(hAPP(c_COMBB(tc_List_Olist(X34361),tc_fun(tc_List_Olist(X34361),tc_List_Olist(X34361)),X34361),c_COMBK(tc_List_Olist(X34361),tc_List_Olist(X34361))),hAPP(hAPP(c_COMBC(X34361,tc_List_Olist(X34361),tc_List_Olist(X34361)),c_List_Olist_OCons(X34361)),c_List_Olist_ONil(X34361))))),X34358)))),c_List_Otranspose(X34361,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34361)),X34359),c_List_Oconcat(tc_List_Olist(X34361),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34361),tc_List_Olist(tc_List_Olist(X34361))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X34361)),X34361,c_List_Olist_ONil(tc_List_Olist(X34361)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X34361),tc_List_Olist(tc_List_Olist(X34361))),X34361),hAPP(hAPP(c_COMBC(tc_List_Olist(X34361),tc_List_Olist(tc_List_Olist(X34361)),tc_List_Olist(tc_List_Olist(X34361))),c_List_Olist_OCons(tc_List_Olist(X34361))),c_List_Olist_ONil(tc_List_Olist(X34361)))))),X34358))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I3_J])]) ).
fof(i_0_5216,plain,
! [X34265,X34266] : c_List_Oconcat(X34266,X34265) = hAPP(c_List_Ofoldl(tc_List_Olist(X34266),tc_List_Olist(X34266),c_List_Oappend(X34266),c_List_Olist_ONil(X34266)),X34265),
inference(variable_rename,[status(thm)],[fact_concat__conv__foldl]) ).
fof(i_0_5217,plain,
! [X34328,X34329,X34330,X34331] : c_List_Otranspose(X34331,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34331)),hAPP(hAPP(c_List_Olist_OCons(X34331),X34330),X34329)),X34328)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34331)),hAPP(hAPP(c_List_Olist_OCons(X34331),X34330),c_List_Oconcat(X34331,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34331),tc_List_Olist(X34331)),c_List_Olist_Olist__case(tc_List_Olist(X34331),X34331,c_List_Olist_ONil(X34331),hAPP(hAPP(c_COMBB(tc_List_Olist(X34331),tc_fun(tc_List_Olist(X34331),tc_List_Olist(X34331)),X34331),c_COMBK(tc_List_Olist(X34331),tc_List_Olist(X34331))),hAPP(hAPP(c_COMBC(X34331,tc_List_Olist(X34331),tc_List_Olist(X34331)),c_List_Olist_OCons(X34331)),c_List_Olist_ONil(X34331))))),X34328)))),c_List_Otranspose(X34331,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34331)),X34329),c_List_Oconcat(tc_List_Olist(X34331),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34331),tc_List_Olist(tc_List_Olist(X34331))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X34331)),X34331,c_List_Olist_ONil(tc_List_Olist(X34331)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X34331),tc_List_Olist(tc_List_Olist(X34331))),X34331),hAPP(hAPP(c_COMBC(tc_List_Olist(X34331),tc_List_Olist(tc_List_Olist(X34331)),tc_List_Olist(tc_List_Olist(X34331))),c_List_Olist_OCons(tc_List_Olist(X34331))),c_List_Olist_ONil(tc_List_Olist(X34331)))))),X34328))))),
inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I3_J]) ).
fof(i_0_5218,plain,
! [X21408,X21409,X21410] :
( ~ class_Rings_Olinordered__idom(X21410)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21410),X21409),c_Groups_Ozero__class_Ozero(X21410)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21410),hAPP(hAPP(c_Power_Opower__class_Opower(X21410),X21409),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21408)))),c_Groups_Ozero__class_Ozero(X21410))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero])]) ).
fof(i_0_5219,plain,
! [X45,X172,X119,X287,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),X287),hAPP(hAPP(c_Relation_Orel__comp(X7,X119,X105),X172),X45)))
=> ~ ! [X3,X82,X154] :
( X287 = hAPP(hAPP(c_Product__Type_OPair(X7,X105),X3),X154)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X119)),hAPP(hAPP(c_Product__Type_OPair(X7,X119),X3),X82)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X119,X105)),hAPP(hAPP(c_Product__Type_OPair(X119,X105),X82),X154)),X45)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_rel__compE]) ).
fof(i_0_5220,plain,
! [X21405,X21406,X21407] :
( ~ class_Rings_Olinordered__idom(X21407)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21407),c_Groups_Ozero__class_Ozero(X21407)),hAPP(hAPP(c_Power_Opower__class_Opower(X21407),X21406),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21405)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21407),c_Groups_Ozero__class_Ozero(X21407)),X21406)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le])]) ).
fof(i_0_5221,plain,
! [X58,X44,X45,X25,X38,X39] :
( c_Natural_Oevaln(c_Com_Ocom_OCall(X39,X38,X25),X45,X44,X58)
=> ~ ! [X62] :
( X58 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X62),hAPP(c_Natural_Ogetlocs,X45))),X39),hAPP(hAPP(c_Natural_Ogetlocs,X62),c_Com_ORes))
=> ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X38),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X45),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X25,X45)),X44,X62) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I7_J]) ).
fof(i_0_5222,plain,
! [X21402,X21403,X21404] :
( ~ class_Int_Onumber__ring(X21404)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21404),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21404),X21403),X21402)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21404),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21404),hAPP(hAPP(c_Power_Opower__class_Opower(X21404),X21403),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21404),X21402),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21404),hAPP(c_Int_Onumber__class_Onumber__of(X21404),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21403)),X21402)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__diff])]) ).
fof(i_0_5223,plain,
! [X21384,X21385,X21386] :
( ~ class_Int_Onumber__ring(X21386)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21386),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21386),X21385),X21384)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21386),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21386),hAPP(hAPP(c_Power_Opower__class_Opower(X21386),X21385),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21386),X21384),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21386),hAPP(c_Int_Onumber__class_Onumber__of(X21386),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21385)),X21384)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__sum])]) ).
fof(i_0_5224,plain,
! [X94,X107] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X107),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X94)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),X107))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X107),X94)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThan__iff]) ).
fof(i_0_5225,plain,
! [X94,X107] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X107),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X94)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X107),X94))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),X107)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OlessThan__iff]) ).
fof(i_0_5226,plain,
! [X2,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Nitpick_Osetsum_H(X7,X105,X2,X149) = hAPP(c_List_Omonoid__add__class_Olistsum(X105),hAPP(hAPP(c_List_Omap(X7,X105),X2),c_Hilbert__Choice_OEps(tc_List_Olist(X7),hAPP(hAPP(c_COMBS(tc_List_Olist(X7),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X7)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X7)),c_fequal),c_List_Oset(X7))),X149))),c_List_Odistinct(X7))))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Nitpick_Osetsum_H(X7,X105,X2,X149) = c_Groups_Ozero__class_Ozero(X105) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Nitpick_Osetsum_H__def]) ).
fof(i_0_5227,plain,
! [X21378,X21379,X21380] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21380),c_Groups_Ozero__class_Ozero(X21380)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21380),hAPP(hAPP(c_Power_Opower__class_Opower(X21380),X21379),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21380),X21378),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| X21379 != c_Groups_Ozero__class_Ozero(X21380)
| X21378 != c_Groups_Ozero__class_Ozero(X21380)
| ~ class_Rings_Olinordered__idom(X21380) )
& ( X21379 = c_Groups_Ozero__class_Ozero(X21380)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21380),c_Groups_Ozero__class_Ozero(X21380)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21380),hAPP(hAPP(c_Power_Opower__class_Opower(X21380),X21379),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21380),X21378),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(X21380) )
& ( X21378 = c_Groups_Ozero__class_Ozero(X21380)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21380),c_Groups_Ozero__class_Ozero(X21380)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21380),hAPP(hAPP(c_Power_Opower__class_Opower(X21380),X21379),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21380),X21378),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(X21380) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff])])]) ).
fof(i_0_5228,plain,
! [X33847,X33848,X33849,X33850] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33850)),X33849))),c_List_Ofoldr(tc_List_Olist(X33848),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X33848)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X33848))),X33847,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33850)),X33849)),c_List_Ofoldr(tc_List_Olist(X33848),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X33848)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X33848),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X33848)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X33848)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X33848),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X33848)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X33848),tc_List_Olist(X33848),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X33848)))),X33847),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(variable_rename,[status(thm)],[fact_transpose__aux__max]) ).
fof(i_0_5229,plain,
! [X34198,X34199,X34200,X34201] : hAPP(hAPP(c_List_Omap(tc_prod(X34201,tc_Nat_Onat),X34201),c_Product__Type_Ofst(X34201,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X34201,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X34201,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X34201,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X34201,tc_Nat_Onat))),X34200)),hAPP(hAPP(c_List_Ozip(X34201,tc_Nat_Onat),X34199),c_List_Oupt(X34198,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34198),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34201)),X34199)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X34201,tc_Nat_Onat),X34201),c_Product__Type_Ofst(X34201,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X34201,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X34201,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X34201,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X34201,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X34201,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X34201,tc_Nat_Onat))),X34198))),X34200)),hAPP(hAPP(c_List_Ozip(X34201,tc_Nat_Onat),X34199),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34201)),X34199))))),
inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma]) ).
fof(i_0_5230,plain,
! [X34111,X34112] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34112),X34111)) = c_List_Oupt(X34112,X34111),
inference(variable_rename,[status(thm)],[fact_sorted__list__of__set__range]) ).
fof(i_0_5231,plain,
! [X198,X1,X7,X199] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X199),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(X7,X1,X199,X198) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X7)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X199),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(X7,X1,X199,X198) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X1,X198)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X7,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X199),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X198))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7))))),tc_prod(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X7)),hAPP(hAPP(c_COMBB(X7,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X7)))),tc_prod(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X7)),c_Product__Type_Ofst(X7,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
inference(fof_simplification,[status(thm)],[fact_Random_Osimps]) ).
fof(i_0_5232,plain,
! [X21216,X21217] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21217)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21216)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X21217)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21216)),
inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div__number__of]) ).
fof(i_0_5233,plain,
! [X21153,X21154] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21154)))),X21153) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X21154)),X21153),
inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div]) ).
fof(i_0_5234,plain,
! [X22531,X22532] : hAPP(c_New__DSequence_Opos__not__seq(X22532),X22531) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X22532,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X22531))),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__not__seq__def]) ).
fof(i_0_5235,plain,
! [X161,X23,X119,X105,X26,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X26),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X105,X119,tc_fun(X7,tc_HOL_Obool)),X23),X161)))
=> ~ ! [X3,X82] :
( X161 = hAPP(hAPP(c_Product__Type_OPair(X105,X119),X3),X82)
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X26),hAPP(hAPP(X23,X3),X82))) ) ),
inference(fof_simplification,[status(thm)],[fact_mem__splitE]) ).
fof(i_0_5236,plain,
! [X163,X149,X6,X26,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),X163))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ~ ! [X82] :
( X163 = hAPP(hAPP(X2,X6),X82)
=> ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,X149),X82)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).
fof(i_0_5237,plain,
! [X21418] :
( ( X21418 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Code__Numeral_Oint__of,X21418) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X21418,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Code__Numeral_Oint__of,X21418) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X21418),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| X21418 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X21418,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Code__Numeral_Oint__of,X21418) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X21418),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X21418 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__of__code])])]) ).
fof(i_0_5238,plain,
! [X21372,X21373,X21374] :
( ~ class_Rings_Olinordered__idom(X21374)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21374),c_Groups_Ozero__class_Ozero(X21374)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21374),hAPP(hAPP(c_Power_Opower__class_Opower(X21374),X21373),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21374),X21372),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__ge__zero])]) ).
fof(i_0_5239,plain,
! [X2,X105,X149,X7] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),hAPP(c_Set_Oimage(X7,X105,X2),X149)))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X149))),hAPP(hAPP(c_COMBC(X7,X105,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X105,tc_fun(X105,tc_HOL_Obool),X7),c_fequal),X2)),hAPP(X2,X3)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_pigeonhole__infinite]) ).
fof(i_0_5240,plain,
! [X34339,X34340,X34341] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X34341),tc_List_Olist(X34341))),esk492_3(X34339,X34340,X34341)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X34341),tc_List_Olist(X34341))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X34341),tc_List_Olist(X34341)),X34340),X34339))))
| X34340 = X34339
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34341))),X34340) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34341))),X34339)
| c_List_Oconcat(X34341,X34340) != c_List_Oconcat(X34341,X34339) )
& ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X34341),tc_List_Olist(X34341),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X34341),tc_fun(tc_List_Olist(X34341),tc_Nat_Onat),tc_fun(tc_List_Olist(X34341),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X34341),tc_Nat_Onat),tc_fun(tc_List_Olist(X34341),tc_HOL_Obool)),tc_List_Olist(X34341)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34341))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X34341)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X34341))))),c_Nat_Osize__class_Osize(tc_List_Olist(X34341)))),esk492_3(X34339,X34340,X34341)))
| X34340 = X34339
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34341))),X34340) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34341))),X34339)
| c_List_Oconcat(X34341,X34340) != c_List_Oconcat(X34341,X34339) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_concat__injective])])])]) ).
fof(i_0_5241,plain,
! [X34335,X34336,X34337] :
( ( c_List_Oconcat(X34337,X34336) != c_List_Oconcat(X34337,X34335)
| X34336 = X34335
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34337))),X34336) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34337))),X34335)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X34337),tc_List_Olist(X34337))),esk491_3(X34335,X34336,X34337)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X34337),tc_List_Olist(X34337))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X34337),tc_List_Olist(X34337)),X34336),X34335)))) )
& ( X34336 != X34335
| c_List_Oconcat(X34337,X34336) = c_List_Oconcat(X34337,X34335)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34337))),X34336) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34337))),X34335)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X34337),tc_List_Olist(X34337))),esk491_3(X34335,X34336,X34337)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X34337),tc_List_Olist(X34337))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X34337),tc_List_Olist(X34337)),X34336),X34335)))) )
& ( c_List_Oconcat(X34337,X34336) != c_List_Oconcat(X34337,X34335)
| X34336 = X34335
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34337))),X34336) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34337))),X34335)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X34337),tc_List_Olist(X34337),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X34337),tc_fun(tc_List_Olist(X34337),tc_Nat_Onat),tc_fun(tc_List_Olist(X34337),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X34337),tc_Nat_Onat),tc_fun(tc_List_Olist(X34337),tc_HOL_Obool)),tc_List_Olist(X34337)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34337))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X34337)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X34337))))),c_Nat_Osize__class_Osize(tc_List_Olist(X34337)))),esk491_3(X34335,X34336,X34337))) )
& ( X34336 != X34335
| c_List_Oconcat(X34337,X34336) = c_List_Oconcat(X34337,X34335)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34337))),X34336) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34337))),X34335)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X34337),tc_List_Olist(X34337),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X34337),tc_fun(tc_List_Olist(X34337),tc_Nat_Onat),tc_fun(tc_List_Olist(X34337),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X34337),tc_Nat_Onat),tc_fun(tc_List_Olist(X34337),tc_HOL_Obool)),tc_List_Olist(X34337)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34337))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X34337)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X34337))))),c_Nat_Osize__class_Osize(tc_List_Olist(X34337)))),esk491_3(X34335,X34336,X34337))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_concat__eq__concat__iff])])])]) ).
fof(i_0_5242,plain,
! [X21944,X21945,X21946,X21947,X21948] : hAPP(c_Nat_Onat_Onat__rec(X21948,X21947,X21946),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21945)),X21944)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21948),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21945))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21948,X21948),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21948,tc_fun(X21948,X21948)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21948,tc_fun(X21948,X21948)),tc_Int_Oint),c_If(X21948)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X21948,X21947,X21946),X21944))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21948,X21948),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X21948,X21948),tc_Int_Oint),X21946),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X21944))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21948,tc_Int_Oint),c_Nat_Onat_Onat__rec(X21948,X21947,X21946)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X21944))))),
inference(variable_rename,[status(thm)],[fact_nat__rec__add__eq__if]) ).
fof(i_0_5243,plain,
! [X21122] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21122),c_Int_OMin) = c_Int_Opred(X21122),
inference(variable_rename,[status(thm)],[fact_add__Min__right]) ).
fof(i_0_5244,plain,
! [X21218,X21219] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21219),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21218)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21219)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21218),c_Groups_Oone__class_Oone(tc_Int_Oint)),X21219))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zmod__mult__2])]) ).
fof(i_0_5245,plain,
! [X21222,X21223] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21223),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21222))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21223)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21222),c_Groups_Oone__class_Oone(tc_Int_Oint))),X21223) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2])]) ).
fof(i_0_5246,plain,
! [X21224,X21225] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21225))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21224))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21225)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21224),X21225) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zdiv__mult__2])]) ).
fof(i_0_5247,plain,
! [X21873,X21874] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21874) != hAPP(c_Nat_OSuc,X21873)
| hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21874))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X21873))))) )
& ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21874))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X21873)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21874) = hAPP(c_Nat_OSuc,X21873) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__Suc])]) ).
fof(i_0_5248,plain,
! [X21875,X21876] :
( ( hAPP(c_Nat_OSuc,X21876) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21875)
| hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21875))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X21876))))) )
& ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21875))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X21876)))))
| hAPP(c_Nat_OSuc,X21876) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21875) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__eq__number__of])]) ).
fof(i_0_5249,plain,
! [X149,X7] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Nitpick_Ocard_H(X7,X149) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),c_Hilbert__Choice_OEps(tc_List_Olist(X7),hAPP(hAPP(c_COMBS(tc_List_Olist(X7),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X7)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X7)),c_fequal),c_List_Oset(X7))),X149))),c_List_Odistinct(X7)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> c_Nitpick_Ocard_H(X7,X149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_Nitpick_Ocard_H__def]) ).
fof(i_0_5250,plain,
! [X107,X210] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X210))
=> hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X210))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X107)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X210))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X107))))) ),
inference(fof_simplification,[status(thm)],[fact_card__less__Suc2]) ).
fof(i_0_5251,plain,
! [X21345,X21346,X21347] :
( ~ class_Rings_Olinordered__semidom(X21347)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21347),hAPP(hAPP(c_Power_Opower__class_Opower(X21347),X21346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21347),X21345),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21347),c_Groups_Ozero__class_Ozero(X21347)),X21345))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21347),X21346),X21345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le])]) ).
fof(i_0_5252,plain,
! [X21369,X21370,X21371] :
( ~ class_Rings_Olinordered__semidom(X21371)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21371),hAPP(hAPP(c_Power_Opower__class_Opower(X21371),X21370),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21371),X21369),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21371),c_Groups_Ozero__class_Ozero(X21371)),X21369))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21371),X21370),X21369)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less])]) ).
fof(i_0_5253,plain,
! [X155,X105,X136,X149,X23,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X136),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBC(X105,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X105),c_If(X7)),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X155))),X23)),X136)),X149) = c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X136),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBC(X105,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X105),c_If(X7)),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X155))),X23)),X136)),X149) = X155 ) ) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X136),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBC(X105,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X105),c_If(X7)),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X155))),X23)),X136)),X149) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X105,tc_HOL_Obool)),X155) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X136),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(hAPP(c_COMBC(X105,X7,X7),hAPP(hAPP(c_COMBC(X105,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X105),c_If(X7)),hAPP(hAPP(c_COMBC(X105,tc_fun(X105,tc_HOL_Obool),tc_HOL_Obool),c_member(X105)),X155))),X23)),X136)),X149) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_vimage__if]) ).
fof(i_0_5254,plain,
! [X21226,X21227] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21227))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21226)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21227)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21226,X21227))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2])]) ).
fof(i_0_5255,plain,
! [X21210,X21211] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21211))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21210)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X21211),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21210)),
inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod__number__of]) ).
fof(i_0_5256,plain,
! [X21387,X21388,X21389] :
( ~ class_Rings_Olinordered__idom(X21389)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21389),c_Groups_Ozero__class_Ozero(X21389)),hAPP(hAPP(c_Power_Opower__class_Opower(X21389),X21388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21387)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H])]) ).
fof(i_0_5257,plain,
! [X21212,X21213] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21213))),X21212) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X21213),X21212),
inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod]) ).
fof(i_0_5258,plain,
! [X21214,X21215] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21215,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21214)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21215,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X21214)),
inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__mod__add3]) ).
fof(i_0_5259,plain,
! [X21151,X21152] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21152),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21151)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X21151)),
inference(variable_rename,[status(thm)],[fact_div__Suc__eq__div__add3]) ).
fof(i_0_5260,plain,
! [X30162,X30163,X30164] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30164,X30164),tc_HOL_Obool)),X30163),X30162))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30164,X30164),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X30164,X30164,X30164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X30164,X30164),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30164,X30163)),X30162)),X30163)),X30162))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30164,X30164),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30164,X30163)),X30162)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__Int__subset])]) ).
fof(i_0_5261,plain,
! [X23,X24,X25,X209,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),X23)),X209) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(X24,X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X105),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X209)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),X23)),X209) = hAPP(hAPP(c_Power_Opower__class_Opower(X105),X23),hAPP(c_Finite__Set_Ocard(X7),X209)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__gen__delta]) ).
fof(i_0_5262,plain,
! [X24,X25,X209,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),c_Groups_Oone__class_Oone(X105))),X209) = hAPP(X24,X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),c_Groups_Oone__class_Oone(X105))),X209) = c_Groups_Oone__class_Oone(X105) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__delta]) ).
fof(i_0_5263,plain,
! [X24,X25,X209,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),c_Groups_Ozero__class_Ozero(X105))),X209) = hAPP(X24,X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X24)),c_Groups_Ozero__class_Ozero(X105))),X209) = c_Groups_Ozero__class_Ozero(X105) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__delta]) ).
fof(i_0_5264,plain,
! [X21888,X21889] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21889)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21888)))
| hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21888))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21889)),c_Int_Onat))))) )
& ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21888))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21889)),c_Int_Onat)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21889)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21888))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of])]) ).
fof(i_0_5265,plain,
! [X21884,X21885] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21885)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21884)))
| hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21884))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21885)),c_Int_Onat))))) )
& ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21884))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21885)),c_Int_Onat)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21885)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21884))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of])]) ).
fof(i_0_5266,plain,
! [X22713,X22714,X22715,X22716,X22717,X22718,X22719] : hAPP(c_Product__Type_Oapsnd(X22719,X22718,X22717,X22716),hAPP(c_Product__Type_Oapfst(X22715,X22717,X22719,X22714),X22713)) = hAPP(c_Product__Type_Oapfst(X22715,X22717,X22718,X22714),hAPP(c_Product__Type_Oapsnd(X22719,X22718,X22715,X22716),X22713)),
inference(variable_rename,[status(thm)],[fact_apsnd__apfst__commute]) ).
fof(i_0_5267,plain,
! [X29456,X29457,X29458,X29459] : c_Product__Type_Oapfst(X29459,X29458,X29457,X29456) = c_Product__Type_Omap__pair(X29459,X29458,X29457,X29457,X29456,c_Fun_Oid(X29457)),
inference(variable_rename,[status(thm)],[fact_apfst__def]) ).
fof(i_0_5268,plain,
! [X172,X163,X160,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Oappend(X7),X6),X160)),hAPP(hAPP(c_List_Oappend(X7),X6),X163))),c_List_Olexord(X7,X172)))
=> ( ! [X110] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X110),X110)),X172))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X160),X163)),c_List_Olexord(X7,X172))) ) ),
inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD]) ).
fof(i_0_5269,plain,
! [X21353,X21354] :
( ~ class_Rings_Olinordered__idom(X21354)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21354),hAPP(hAPP(c_Power_Opower__class_Opower(X21354),X21353),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X21354))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5165])]) ).
fof(i_0_5270,plain,
! [X191,X44,X26,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)))
=> ( ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X6 != X26 )
=> ~ ! [X82,X116] :
( X44 = hAPP(c_Nat_OSuc,X116)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X82)),X191))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X116),X191))) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_rel__pow__E2]) ).
fof(i_0_5271,plain,
! [X31729,X31730,X31731,X31732,X31733,X31734,X31735,X31737,X31738,X31739,X31740,X31741,X31742,X31743,X31744] :
( ( hAPP(X31731,X31730) = hAPP(c_Option_Ooption_OSome(X31735),esk434_7(X31729,X31730,X31731,X31732,X31733,X31734,X31735))
| c_Map_Omap__comp(X31735,X31734,X31733,X31732,X31731,X31730) != hAPP(c_Option_Ooption_OSome(X31734),X31729) )
& ( hAPP(X31732,esk434_7(X31729,X31730,X31731,X31732,X31733,X31734,X31735)) = hAPP(c_Option_Ooption_OSome(X31734),X31729)
| c_Map_Omap__comp(X31735,X31734,X31733,X31732,X31731,X31730) != hAPP(c_Option_Ooption_OSome(X31734),X31729) )
& ( hAPP(X31739,X31738) != hAPP(c_Option_Ooption_OSome(X31743),X31744)
| hAPP(X31740,X31744) != hAPP(c_Option_Ooption_OSome(X31742),X31737)
| c_Map_Omap__comp(X31743,X31742,X31741,X31740,X31739,X31738) = hAPP(c_Option_Ooption_OSome(X31742),X31737) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__Some__iff])])])])])]) ).
fof(i_0_5272,plain,
! [X31713,X31714,X31715,X31716,X31717,X31718] : c_Map_Omap__comp(X31718,X31717,X31716,X31715,X31714,X31713) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X31717),X31718,c_Option_Ooption_ONone(X31717),X31715),hAPP(X31714,X31713)),
inference(variable_rename,[status(thm)],[fact_map__comp__def]) ).
fof(i_0_5273,plain,
! [X24,X25] :
( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25,X24) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X25)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff]) ).
fof(i_0_5274,plain,
! [X157,X94] :
( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X94,X157) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),X157))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X157),X94)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff]) ).
fof(i_0_5275,plain,
! [X24,X25] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25,X24)
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X25)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff2]) ).
fof(i_0_5276,plain,
! [X157,X94] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X94,X157)
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X94),X157))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X157),X94)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff2]) ).
fof(i_0_5277,plain,
! [X127,X6,X2,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X7,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X127),X6)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(X2,X6)),hAPP(X2,X127))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ostrict__monoD]) ).
fof(i_0_5278,plain,
! [X21393,X21394,X21395] :
( ~ class_Groups_Omonoid__mult(X21395)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21395),X21394),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21393))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21395),X21394),hAPP(hAPP(c_Power_Opower__class_Opower(X21395),hAPP(hAPP(c_Power_Opower__class_Opower(X21395),X21394),X21393)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__odd__eq])]) ).
fof(i_0_5279,plain,
! [X58,X45,X25,X38,X39] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X39,X38,X25)),X45),X58))
=> ~ ! [X62] :
( X58 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X62),hAPP(c_Natural_Ogetlocs,X45))),X39),hAPP(hAPP(c_Natural_Ogetlocs,X62),c_Com_ORes))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X38)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X45),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X25,X45))),X62)) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc__elim__cases_I7_J]) ).
fof(i_0_5280,plain,
! [X26650,X26651,X26652,X26653,X26654,X26655,X26656] : hAPP(c_Product__Type_Oapsnd(X26656,X26655,X26654,X26653),hAPP(c_Product__Type_Oapsnd(X26652,X26656,X26654,X26651),X26650)) = hAPP(c_Product__Type_Oapsnd(X26652,X26655,X26654,hAPP(c_Fun_Ocomp(X26656,X26655,X26652,X26653),X26651)),X26650),
inference(variable_rename,[status(thm)],[fact_apsnd__compose]) ).
fof(i_0_5281,plain,
! [X26643,X26644,X26645,X26646,X26647,X26648,X26649] : hAPP(c_Product__Type_Oapfst(X26649,X26648,X26647,X26646),hAPP(c_Product__Type_Oapfst(X26645,X26649,X26647,X26644),X26643)) = hAPP(c_Product__Type_Oapfst(X26645,X26648,X26647,hAPP(c_Fun_Ocomp(X26649,X26648,X26645,X26646),X26644)),X26643),
inference(variable_rename,[status(thm)],[fact_apfst__compose]) ).
fof(i_0_5282,plain,
! [X21355,X21356,X21357] :
( ( X21356 = c_Groups_Ozero__class_Ozero(X21357)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21357),hAPP(hAPP(c_Power_Opower__class_Opower(X21357),X21356),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21357),X21355),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X21357)
| ~ class_Rings_Olinordered__idom(X21357) )
& ( X21355 = c_Groups_Ozero__class_Ozero(X21357)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21357),hAPP(hAPP(c_Power_Opower__class_Opower(X21357),X21356),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21357),X21355),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X21357)
| ~ class_Rings_Olinordered__idom(X21357) )
& ( X21356 != c_Groups_Ozero__class_Ozero(X21357)
| X21355 != c_Groups_Ozero__class_Ozero(X21357)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21357),hAPP(hAPP(c_Power_Opower__class_Opower(X21357),X21356),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X21357),X21355),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X21357)
| ~ class_Rings_Olinordered__idom(X21357) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff])])]) ).
fof(i_0_5283,plain,
! [X46,X44,X45,X23,X25,X60] :
( c_Natural_Oevaln(c_Com_Ocom_OLocal(X60,X25,X23),X45,X44,X46)
=> ~ ! [X62] :
( X46 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X62),c_Com_Ovname_OLoc(X60)),hAPP(hAPP(c_Natural_Ogetlocs,X45),X60))
=> ~ c_Natural_Oevaln(X23,hAPP(hAPP(hAPP(c_Natural_Oupdate,X45),c_Com_Ovname_OLoc(X60)),hAPP(X25,X45)),X44,X62) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I3_J]) ).
fof(i_0_5284,plain,
! [X34202,X34203,X34204] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk488_3(X34202,X34203,X34204)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34203))),X34204)))
| c_List_Otranspose(X34203,X34204) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X34203)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34203)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X34203),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34203)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X34203)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X34203),hAPP(hAPP(c_COMBB(tc_List_Olist(X34203),tc_fun(tc_Nat_Onat,X34203),tc_Nat_Onat),c_List_Onth(X34203)),hAPP(c_List_Onth(tc_List_Olist(X34203)),X34204))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34203))),X34204)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34202))
| X34204 = c_List_Olist_ONil(tc_List_Olist(X34203)) )
& ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34203)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34203)),X34204),esk488_3(X34202,X34203,X34204))) != X34202
| c_List_Otranspose(X34203,X34204) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X34203)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34203)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X34203),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34203)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X34203)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X34203),hAPP(hAPP(c_COMBB(tc_List_Olist(X34203),tc_fun(tc_Nat_Onat,X34203),tc_Nat_Onat),c_List_Onth(X34203)),hAPP(c_List_Onth(tc_List_Olist(X34203)),X34204))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34203))),X34204)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34202))
| X34204 = c_List_Olist_ONil(tc_List_Olist(X34203)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk488_3(X34202,X34203,X34204)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34203))),X34204)))
| c_List_Otranspose(X34203,X34204) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X34203)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34203)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X34203),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34203)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X34203)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X34203),hAPP(hAPP(c_COMBB(tc_List_Olist(X34203),tc_fun(tc_Nat_Onat,X34203),tc_Nat_Onat),c_List_Onth(X34203)),hAPP(c_List_Onth(tc_List_Olist(X34203)),X34204))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34203))),X34204)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34202))
| X34202 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34203)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34203)),X34204),esk488_3(X34202,X34203,X34204))) != X34202
| c_List_Otranspose(X34203,X34204) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X34203)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34203)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X34203),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34203)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X34203)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X34203),hAPP(hAPP(c_COMBB(tc_List_Olist(X34203),tc_fun(tc_Nat_Onat,X34203),tc_Nat_Onat),c_List_Onth(X34203)),hAPP(c_List_Onth(tc_List_Olist(X34203)),X34204))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34203))),X34204)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34202))
| X34202 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__rectangle])])])]) ).
fof(i_0_5285,plain,
! [X21220,X21221] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21221)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21220)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21221))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21220),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21221)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21221)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21220)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21221))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21220)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21221)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5166])]) ).
fof(i_0_5286,plain,
! [X22029,X22030,X22031] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk81_3(X22029,X22030,X22031)),esk82_3(X22029,X22030,X22031))))
| hBOOL(hAPP(hAPP(X22029,X22031),X22030))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22031),X22030))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk81_3(X22029,X22030,X22031)),esk82_3(X22029,X22030,X22031))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk82_3(X22029,X22030,X22031)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X22029,esk81_3(X22029,X22030,X22031)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk82_3(X22029,X22030,X22031))))
| hBOOL(hAPP(hAPP(X22029,X22031),X22030))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22031),X22030))) )
& ( ~ hBOOL(hAPP(hAPP(X22029,esk81_3(X22029,X22030,X22031)),esk82_3(X22029,X22030,X22031)))
| hBOOL(hAPP(hAPP(X22029,X22031),X22030))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22031),X22030))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opinduct])])])]) ).
fof(i_0_5287,plain,
! [X24,X25,X209,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(c_fequal,X25))),X24)),c_Groups_Oone__class_Oone(X105))),X209) = hAPP(X24,X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(c_fequal,X25))),X24)),c_Groups_Oone__class_Oone(X105))),X209) = c_Groups_Oone__class_Oone(X105) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__delta_H]) ).
fof(i_0_5288,plain,
! [X24,X25,X209,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X209))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(c_fequal,X25))),X24)),c_Groups_Ozero__class_Ozero(X105))),X209) = hAPP(X24,X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X209))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),hAPP(hAPP(c_COMBC(X7,X105,X105),hAPP(hAPP(c_COMBS(X7,X105,tc_fun(X105,X105)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X105,tc_fun(X105,X105)),X7),c_If(X105)),hAPP(c_fequal,X25))),X24)),c_Groups_Ozero__class_Ozero(X105))),X209) = c_Groups_Ozero__class_Ozero(X105) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__delta_H]) ).
fof(i_0_5289,plain,
! [X22046,X22047,X22048] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk83_3(X22046,X22047,X22048)),esk84_3(X22046,X22047,X22048))))
| hBOOL(hAPP(hAPP(X22046,X22048),X22047))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22048),X22047))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk83_3(X22046,X22047,X22048)),esk84_3(X22046,X22047,X22048)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk84_3(X22046,X22047,X22048)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X22046,esk83_3(X22046,X22047,X22048)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk84_3(X22046,X22047,X22048))))
| hBOOL(hAPP(hAPP(X22046,X22048),X22047))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22048),X22047))) )
& ( ~ hBOOL(hAPP(hAPP(X22046,esk83_3(X22046,X22047,X22048)),esk84_3(X22046,X22047,X22048)))
| hBOOL(hAPP(hAPP(X22046,X22048),X22047))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22048),X22047))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opinduct])])])]) ).
fof(i_0_5290,plain,
! [X172,X293,X127,X292,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X293))),c_List_Olistrel(X7,X172)))
=> ~ ! [X3,X307] :
( X292 = hAPP(hAPP(c_List_Olist_OCons(X7),X3),X307)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X127)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X307),X293)),c_List_Olistrel(X7,X172))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_listrel__Cons2]) ).
fof(i_0_5291,plain,
! [X191,X44,X26,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),hAPP(c_Nat_OSuc,X44)),X191)))
=> ~ ! [X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X82)),X191))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191))) ) ),
inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E2]) ).
fof(i_0_5292,plain,
! [X22877,X22878,X22879] : c_Nitpick_Otimes__frac(X22879,X22878,X22877) = hAPP(hAPP(c_Nitpick_Ofrac(X22879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22879),X22878)),hAPP(c_Nitpick_Onum(X22879),X22877))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X22879),X22878)),hAPP(c_Nitpick_Odenom(X22879),X22877))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Otimes__frac__def]) ).
fof(i_0_5293,plain,
! [X191,X44,X26,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)))
=> ( ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X6 != X26 )
=> ~ ! [X82,X116] :
( X44 = hAPP(c_Nat_OSuc,X116)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X82)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X116),X191)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X26)),X191)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_rel__pow__E]) ).
fof(i_0_5294,plain,
! [X191,X44,X26,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),hAPP(c_Nat_OSuc,X44)),X191)))
=> ~ ! [X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X82)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7,X7),tc_HOL_Obool),X44),X191)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X26)),X191)) ) ),
inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E]) ).
fof(i_0_5295,plain,
! [X21905,X21906] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21905)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21906))))
| c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21906)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21905)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21906))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21905)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21906))))
| c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21906)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21906)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21906))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21906))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5167])])]) ).
fof(i_0_5296,plain,
! [X21959,X21960] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21960),X21959)))
| c_Divides_OnegDivAlg(X21960,X21959) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21960),X21959))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21960),X21959))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21959),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(X21960,X21959) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21960),X21959))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21960),X21959))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21960),X21959)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21959),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(X21960,X21959) = hAPP(c_Divides_Oadjust(X21959),c_Divides_OnegDivAlg(X21960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21959)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21960),X21959))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opsimps])])]) ).
fof(i_0_5297,plain,
! [X21823] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823))))
| c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823))))
| c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5168])])]) ).
fof(i_0_5298,plain,
! [X22023,X22024] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22024),X22023))
| c_Divides_OposDivAlg(X22024,X22023) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22024)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22024),X22023))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22023),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(X22024,X22023) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22024)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22024),X22023))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22024),X22023))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22023),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(X22024,X22023) = hAPP(c_Divides_Oadjust(X22023),c_Divides_OposDivAlg(X22024,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X22023)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22024),X22023))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opsimps])])]) ).
fof(i_0_5299,plain,
! [X21940,X21941] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21940)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21941)))
| c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21940),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21941)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21940))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21941))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21940)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21941)))
| c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21940),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21941)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21941)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21941))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21941))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5169])])]) ).
fof(i_0_5300,plain,
! [X21390,X21391,X21392] :
( ~ class_Rings_Ocomm__semiring__1(X21392)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21392),X21391),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21390))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21392),X21391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21392),hAPP(hAPP(c_Power_Opower__class_Opower(X21392),X21391),X21390)),hAPP(hAPP(c_Power_Opower__class_Opower(X21392),X21391),X21390))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J])]) ).
fof(i_0_5301,plain,
! [X23040,X23041,X23042] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23042)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X23041))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X23040))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23040)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23042),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23042),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23040),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X23041)))),
inference(variable_rename,[status(thm)],[fact_arith__series__int]) ).
fof(i_0_5302,plain,
! [X21886,X21887] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21887)),hAPP(c_Nat_OSuc,X21886)))
| hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21887))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X21886)))) )
& ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21887))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X21886))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21887)),hAPP(c_Nat_OSuc,X21886))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc])]) ).
fof(i_0_5303,plain,
! [X21882,X21883] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21883)),hAPP(c_Nat_OSuc,X21882)))
| hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21883))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X21882)))) )
& ( ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21883))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X21882))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21883)),hAPP(c_Nat_OSuc,X21882))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc])]) ).
fof(i_0_5304,plain,
! [X21916] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21916)))
| c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21916)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21916))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21916)))
| c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21916)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21916)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21916))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21916))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5170])])]) ).
fof(i_0_5305,plain,
! [X21228,X21229] :
( ~ class_Rings_Osemiring__1(X21229)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21228))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21229),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21228))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21229),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21229),hAPP(c_Int_Onat,X21228))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21229),hAPP(c_Int_Onat,X21228))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__double])]) ).
fof(i_0_5306,plain,
! [X21907,X21908] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21907),X21908)))
| c_Divides_OnegDivAlg(X21907,X21908) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21907),X21908))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21908)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21907),X21908)))
| c_Divides_OnegDivAlg(X21907,X21908) = hAPP(c_Divides_Oadjust(X21908),c_Divides_OnegDivAlg(X21907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21908)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21908)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5171])])]) ).
fof(i_0_5307,plain,
! [X21897,X21898] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21898),X21897)))
| c_Divides_OnegDivAlg(X21898,X21897) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21898),X21897)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21897),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(X21898,X21897) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21898),X21897)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21898),X21897)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21897),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(X21898,X21897) = hAPP(c_Divides_Oadjust(X21897),c_Divides_OnegDivAlg(X21898,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21897))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Osimps])])]) ).
fof(i_0_5308,plain,
! [X21938,X21939] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21938),X21939))
| c_Divides_OposDivAlg(X21938,X21939) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21938)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21939)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21938),X21939))
| c_Divides_OposDivAlg(X21938,X21939) = hAPP(c_Divides_Oadjust(X21939),c_Divides_OposDivAlg(X21938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21939)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21939)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5172])])]) ).
fof(i_0_5309,plain,
! [X21917,X21918] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21918),X21917))
| c_Divides_OposDivAlg(X21918,X21917) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21918) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21917),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(X21918,X21917) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21918) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21918),X21917))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21917),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(X21918,X21917) = hAPP(c_Divides_Oadjust(X21917),c_Divides_OposDivAlg(X21918,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21917))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Osimps])])]) ).
fof(i_0_5310,plain,
! [X21411,X21412] :
( ~ class_Rings_Oring__1(X21412)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21412),hAPP(c_Groups_Ouminus__class_Ouminus(X21412),c_Groups_Oone__class_Oone(X21412))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21411))) = hAPP(c_Groups_Ouminus__class_Ouminus(X21412),c_Groups_Oone__class_Oone(X21412)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__odd])]) ).
fof(i_0_5311,plain,
! [X21366,X21367,X21368] :
( ~ class_Rings_Oring__1(X21368)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21368),hAPP(c_Groups_Ouminus__class_Ouminus(X21368),X21367)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21366)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21368),X21367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21366)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus__even])]) ).
fof(i_0_5312,plain,
! [X21415,X21416] :
( ~ class_Int_Onumber__ring(X21416)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21416),hAPP(c_Int_Onumber__class_Onumber__of(X21416),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21415))) = hAPP(c_Int_Onumber__class_Onumber__of(X21416),c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__odd])]) ).
fof(i_0_5313,plain,
! [X21195] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21195))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X21195),
inference(variable_rename,[status(thm)],[fact_Suc3__eq__add__3]) ).
fof(i_0_5314,plain,
! [X149,X172,X105,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(c_Relation_OImage(X105,X7,X172),X149)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X3),X24)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(X105),X3),X149)) ) ),
inference(fof_simplification,[status(thm)],[fact_ImageE]) ).
fof(i_0_5315,plain,
! [X21911,X21912,X21913,X21914,X21915] : c_Nat_Onat_Onat__case(X21915,X21914,X21913,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21912)),X21911)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21915),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21912))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21915,X21915),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21915,tc_fun(X21915,X21915)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21915,tc_fun(X21915,X21915)),tc_Int_Oint),c_If(X21915)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X21915,X21914,X21913,X21911))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21915,tc_Int_Oint),X21913),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X21911)))),
inference(variable_rename,[status(thm)],[fact_nat__case__add__eq__if]) ).
fof(i_0_5316,plain,
! [X21400] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21400,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21400,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21400,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21400,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod2__gr__0])]) ).
fof(i_0_5317,plain,
! [X22162,X22163,X22164,X22165,X22166,X22167] :
( ( hAPP(c_Product__Type_Oapsnd(X22167,X22166,X22165,X22164),X22163) != hAPP(c_Product__Type_Oapsnd(X22167,X22166,X22165,X22162),X22163)
| hAPP(X22164,hAPP(c_Product__Type_Osnd(X22165,X22167),X22163)) = hAPP(X22162,hAPP(c_Product__Type_Osnd(X22165,X22167),X22163)) )
& ( hAPP(X22164,hAPP(c_Product__Type_Osnd(X22165,X22167),X22163)) != hAPP(X22162,hAPP(c_Product__Type_Osnd(X22165,X22167),X22163))
| hAPP(c_Product__Type_Oapsnd(X22167,X22166,X22165,X22164),X22163) = hAPP(c_Product__Type_Oapsnd(X22167,X22166,X22165,X22162),X22163) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv])]) ).
fof(i_0_5318,plain,
! [X22683,X22684,X22685,X22686,X22687,X22688] :
( ( hAPP(c_Product__Type_Oapfst(X22688,X22687,X22686,X22685),X22684) != hAPP(c_Product__Type_Oapfst(X22688,X22687,X22686,X22683),X22684)
| hAPP(X22685,hAPP(c_Product__Type_Ofst(X22688,X22686),X22684)) = hAPP(X22683,hAPP(c_Product__Type_Ofst(X22688,X22686),X22684)) )
& ( hAPP(X22685,hAPP(c_Product__Type_Ofst(X22688,X22686),X22684)) != hAPP(X22683,hAPP(c_Product__Type_Ofst(X22688,X22686),X22684))
| hAPP(c_Product__Type_Oapfst(X22688,X22687,X22686,X22685),X22684) = hAPP(c_Product__Type_Oapfst(X22688,X22687,X22686,X22683),X22684) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv])]) ).
fof(i_0_5319,plain,
! [X30322] : c_Relation_OId(X30322) = hAPP(c_Set_OCollect(tc_prod(X30322,X30322)),hAPP(hAPP(c_COMBB(tc_fun(X30322,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X30322,X30322)),c_HOL_OEx(X30322)),hAPP(hAPP(c_COMBC(tc_prod(X30322,X30322),tc_fun(X30322,tc_prod(X30322,X30322)),tc_fun(X30322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X30322,X30322),tc_HOL_Obool),tc_fun(tc_fun(X30322,tc_prod(X30322,X30322)),tc_fun(X30322,tc_HOL_Obool)),tc_prod(X30322,X30322)),c_COMBB(tc_prod(X30322,X30322),tc_HOL_Obool,X30322)),c_fequal)),hAPP(hAPP(c_COMBS(X30322,X30322,tc_prod(X30322,X30322)),c_Product__Type_OPair(X30322,X30322)),c_COMBI(X30322))))),
inference(variable_rename,[status(thm)],[fact_Id__def]) ).
fof(i_0_5320,plain,
! [X22724,X22725,X22726,X22727,X22728,X22729,X22730] : hAPP(c_Product__Type_Oapsnd(X22730,X22729,X22728,X22727),hAPP(c_Product__Type_Oapfst(X22726,X22728,X22730,X22725),X22724)) = hAPP(hAPP(c_Product__Type_OPair(X22728,X22729),hAPP(X22725,hAPP(c_Product__Type_Ofst(X22726,X22730),X22724))),hAPP(X22727,hAPP(c_Product__Type_Osnd(X22726,X22730),X22724))),
inference(variable_rename,[status(thm)],[fact_apsnd__apfst]) ).
fof(i_0_5321,plain,
! [X22537,X22538,X22539,X22540,X22541,X22542,X22543] : hAPP(c_Product__Type_Oapfst(X22543,X22542,X22541,X22540),hAPP(c_Product__Type_Oapsnd(X22539,X22541,X22543,X22538),X22537)) = hAPP(hAPP(c_Product__Type_OPair(X22542,X22541),hAPP(X22540,hAPP(c_Product__Type_Ofst(X22543,X22539),X22537))),hAPP(X22538,hAPP(c_Product__Type_Osnd(X22543,X22539),X22537))),
inference(variable_rename,[status(thm)],[fact_apfst__apsnd]) ).
fof(i_0_5322,plain,
! [X2,X7] :
( class_Orderings_Oorder(X7)
=> ( ! [X3,X82] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X82))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X82),X3)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(X2,X3)),hAPP(X2,X82))) )
=> c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X7,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ostrict__monoI]) ).
fof(i_0_5323,plain,
! [X21421,X21422] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21422),c_Groups_Ozero__class_Ozero(X21422)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21422),X21421),hAPP(c_Int_Onumber__class_Onumber__of(X21422),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21422),c_Groups_Ozero__class_Ozero(X21422)),X21421))
| ~ class_Fields_Olinordered__field__inverse__zero(X21422)
| ~ class_Int_Onumber__ring(X21422) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21422),c_Groups_Ozero__class_Ozero(X21422)),X21421))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21422),c_Groups_Ozero__class_Ozero(X21422)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21422),X21421),hAPP(c_Int_Onumber__class_Onumber__of(X21422),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21422)
| ~ class_Int_Onumber__ring(X21422) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])]) ).
fof(i_0_5324,plain,
! [X22533,X22534] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22534)),hAPP(c_Nat_OSuc,X22533)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22534))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X22533))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X22533)))),
inference(variable_rename,[status(thm)],[fact_max__Suc__number__of]) ).
fof(i_0_5325,plain,
! [X21351,X21352] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21352),c_Groups_Ozero__class_Ozero(X21352)),hAPP(hAPP(c_Power_Opower__class_Opower(X21352),X21351),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| X21351 != c_Groups_Ozero__class_Ozero(X21352)
| ~ class_Rings_Olinordered__idom(X21352) )
& ( X21351 = c_Groups_Ozero__class_Ozero(X21352)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21352),c_Groups_Ozero__class_Ozero(X21352)),hAPP(hAPP(c_Power_Opower__class_Opower(X21352),X21351),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X21352) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power2])])]) ).
fof(i_0_5326,plain,
! [X22487,X22488] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22488)),hAPP(c_Nat_OSuc,X22487)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22488))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X22487)))),
inference(variable_rename,[status(thm)],[fact_min__Suc__number__of]) ).
fof(i_0_5327,plain,
! [X22019,X22020,X22021,X22022] : hAPP(c_Nat_Onat_Onat__rec(X22022,X22021,X22020),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22019)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X22022),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22019))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X22022,X22022),hAPP(hAPP(c_COMBC(tc_Int_Oint,X22022,tc_fun(X22022,X22022)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X22022,tc_fun(X22022,X22022)),tc_Int_Oint),c_If(X22022)),c_Nat__Numeral_Oneg)),X22021)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X22022,X22022),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X22022,X22022),tc_Int_Oint),X22020),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X22022,tc_Int_Oint),c_Nat_Onat_Onat__rec(X22022,X22021,X22020)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[fact_nat__rec__number__of]) ).
fof(i_0_5328,plain,
! [X34212,X34213] : c_List_Oconcat(X34213,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34213),tc_List_Olist(X34213)),c_List_Olist_Olist__case(tc_List_Olist(X34213),X34213,c_List_Olist_ONil(X34213),hAPP(hAPP(c_COMBB(tc_List_Olist(X34213),tc_fun(tc_List_Olist(X34213),tc_List_Olist(X34213)),X34213),c_COMBK(tc_List_Olist(X34213),tc_List_Olist(X34213))),hAPP(hAPP(c_COMBC(X34213,tc_List_Olist(X34213),tc_List_Olist(X34213)),c_List_Olist_OCons(X34213)),c_List_Olist_ONil(X34213))))),X34212)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X34213),X34213),c_List_Ohd(X34213)),hAPP(c_List_Ofilter(tc_List_Olist(X34213),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X34213)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X34213),tc_List_Olist(X34213),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X34213)))),X34212)),
inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__head]) ).
fof(i_0_5329,plain,
! [X34367,X34368] : c_List_Oconcat(tc_List_Olist(X34368),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34368),tc_List_Olist(tc_List_Olist(X34368))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X34368)),X34368,c_List_Olist_ONil(tc_List_Olist(X34368)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X34368),tc_List_Olist(tc_List_Olist(X34368))),X34368),hAPP(hAPP(c_COMBC(tc_List_Olist(X34368),tc_List_Olist(tc_List_Olist(X34368)),tc_List_Olist(tc_List_Olist(X34368))),c_List_Olist_OCons(tc_List_Olist(X34368))),c_List_Olist_ONil(tc_List_Olist(X34368)))))),X34367)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X34368),tc_List_Olist(X34368)),c_List_Otl(X34368)),hAPP(c_List_Ofilter(tc_List_Olist(X34368),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X34368)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X34368),tc_List_Olist(X34368),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X34368)))),X34367)),
inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__tail]) ).
fof(i_0_5330,plain,
! [X30202,X30203,X30204] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30204,X30204),tc_HOL_Obool)),c_Relation_OId(X30204)),X30203))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30204,X30204),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X30204,X30204,X30204),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X30204,X30204),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30204,X30202)),X30203)),X30202)),X30203))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30204,X30204),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30204,X30202)),X30203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset])]) ).
fof(i_0_5331,plain,
! [X172,X292,X293,X127,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),hAPP(hAPP(c_List_Olist_OCons(X7),X127),X293)),X292)),c_List_Olistrel(X7,X172)))
=> ~ ! [X82,X306] :
( X292 = hAPP(hAPP(c_List_Olist_OCons(X7),X82),X306)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X82)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X293),X306)),c_List_Olistrel(X7,X172))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_listrel__Cons1]) ).
fof(i_0_5332,plain,
! [X21331,X21332,X21333] :
( ~ class_Groups_Omonoid__mult(X21333)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21333),X21332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21331)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21333),hAPP(hAPP(c_Power_Opower__class_Opower(X21333),X21332),X21331)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__even__eq])]) ).
fof(i_0_5333,plain,
! [X34016,X34017,X34018] : c_List_Osublist(X34018,X34017,X34016) = hAPP(hAPP(c_List_Omap(tc_prod(X34018,tc_Nat_Onat),X34018),c_Product__Type_Ofst(X34018,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X34018,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X34018,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X34018,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X34018,tc_Nat_Onat))),X34016)),hAPP(hAPP(c_List_Ozip(X34018,tc_Nat_Onat),X34017),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34018)),X34017))))),
inference(variable_rename,[status(thm)],[fact_sublist__def]) ).
fof(i_0_5334,plain,
! [X41,X43,X42,X2,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,X2,hAPP(hAPP(c_Set_Oinsert(X7),X42),X43)),X41))
<=> ? [X110,X239] :
( hAPP(hAPP(c_Set_Oinsert(X7),X42),X43) = hAPP(hAPP(c_Set_Oinsert(X7),X110),X239)
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,X2,X110,X239),X41))
& ~ hBOOL(hAPP(hAPP(c_member(X7),X110),X239)) ) ),
inference(fof_simplification,[status(thm)],[fact_fold1Set_Oequations]) ).
fof(i_0_5335,plain,
! [X22885,X22886] : c_Nitpick_Ouminus__frac(X22886,X22885) = c_Nitpick_OAbs__Frac(X22886,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22886),X22885))),hAPP(c_Nitpick_Odenom(X22886),X22885))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Ouminus__frac__def]) ).
fof(i_0_5336,plain,
! [X22157,X22158,X22159,X22160,X22161] : hAPP(c_Product__Type_Osnd(X22161,X22160),hAPP(c_Product__Type_Oapsnd(X22159,X22160,X22161,X22158),X22157)) = hAPP(X22158,hAPP(c_Product__Type_Osnd(X22161,X22159),X22157)),
inference(variable_rename,[status(thm)],[fact_snd__apsnd]) ).
fof(i_0_5337,plain,
! [X22678,X22679,X22680,X22681,X22682] : hAPP(c_Product__Type_Ofst(X22682,X22681),hAPP(c_Product__Type_Oapfst(X22680,X22682,X22681,X22679),X22678)) = hAPP(X22679,hAPP(c_Product__Type_Ofst(X22680,X22681),X22678)),
inference(variable_rename,[status(thm)],[fact_fst__apfst]) ).
fof(i_0_5338,plain,
! [X22381,X22382,X22383,X22384,X22385] : hAPP(c_Product__Type_Ofst(X22385,X22384),hAPP(c_Product__Type_Oapsnd(X22383,X22384,X22385,X22382),X22381)) = hAPP(c_Product__Type_Ofst(X22385,X22383),X22381),
inference(variable_rename,[status(thm)],[fact_fst__apsnd]) ).
fof(i_0_5339,plain,
! [X22689,X22690,X22691,X22692,X22693] : hAPP(c_Product__Type_Osnd(X22693,X22692),hAPP(c_Product__Type_Oapfst(X22691,X22693,X22692,X22690),X22689)) = hAPP(c_Product__Type_Osnd(X22691,X22692),X22689),
inference(variable_rename,[status(thm)],[fact_snd__apfst]) ).
fof(i_0_5340,plain,
! [X38,X43,X42,X187] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X187),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X42),X43))))
=> ( ! [X240,X159,X147] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X240),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X159),X147))))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X159),X147))
=> ( hAPP(X240,X147) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
=> hBOOL(hAPP(hAPP(hAPP(X38,X240),X159),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X147),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
=> hBOOL(hAPP(hAPP(hAPP(X38,X240),X159),X147)) ) )
=> hBOOL(hAPP(hAPP(hAPP(X38,X187),X42),X43)) ) ),
inference(fof_simplification,[status(thm)],[fact_small_H_Opinduct]) ).
fof(i_0_5341,plain,
! [X21934,X21935,X21936,X21937] : c_Nat_Onat_Onat__case(X21937,X21936,X21935,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21934)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21937),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21934))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21937,X21937),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21937,tc_fun(X21937,X21937)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21937,tc_fun(X21937,X21937)),tc_Int_Oint),c_If(X21937)),c_Nat__Numeral_Oneg)),X21936)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21937,tc_Int_Oint),X21935),c_Int_Onat))),
inference(variable_rename,[status(thm)],[fact_nat__case__number__of]) ).
fof(i_0_5342,plain,
! [X22535,X22536] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22536)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22535)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22535))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X22536))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22536)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[fact_max__number__of__Suc]) ).
fof(i_0_5343,plain,
! [X22253,X22254] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22254)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22253)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22253))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22254)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[fact_min__number__of__Suc]) ).
fof(i_0_5344,plain,
! [X21417] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21417))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21417),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__n__div__2__gt__zero])]) ).
fof(i_0_5345,plain,
! [X21419,X21420] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21420)
| ~ class_Int_Onumber__ring(X21420)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21420),c_Groups_Ozero__class_Ozero(X21420)),X21419))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21420),c_Groups_Ozero__class_Ozero(X21420)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21420),X21419),hAPP(c_Int_Onumber__class_Onumber__of(X21420),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero])]) ).
fof(i_0_5346,plain,
! [X21363,X21364,X21365] :
( ~ class_Rings_Ocomm__semiring__1(X21365)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21365),X21364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21363)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21365),hAPP(hAPP(c_Power_Opower__class_Opower(X21365),X21364),X21363)),hAPP(hAPP(c_Power_Opower__class_Opower(X21365),X21364),X21363)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])]) ).
fof(i_0_5347,plain,
! [X21401] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21401))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21401),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__2__gt__zero])]) ).
fof(i_0_5348,plain,
! [X21193,X21194] :
( ~ class_Groups_Omonoid__mult(X21194)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21194),X21193),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21194),X21193),X21193)),X21193) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power3__eq__cube])]) ).
fof(i_0_5349,plain,
! [X21343,X21344] :
( ~ class_Rings_Olinordered__idom(X21344)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21344),c_Groups_Ozero__class_Ozero(X21344)),hAPP(hAPP(c_Power_Opower__class_Opower(X21344),X21343),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power2])]) ).
fof(i_0_5350,plain,
! [X21396,X21397] :
( ~ class_Rings_Oring__1(X21397)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21397),hAPP(c_Groups_Ouminus__class_Ouminus(X21397),c_Groups_Oone__class_Oone(X21397))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21396)) = c_Groups_Oone__class_Oone(X21397) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__even])]) ).
fof(i_0_5351,plain,
! [X21413,X21414] :
( ~ class_Int_Onumber__ring(X21414)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21414),hAPP(c_Int_Onumber__class_Onumber__of(X21414),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21413)) = c_Groups_Oone__class_Oone(X21414) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__even])]) ).
fof(i_0_5352,plain,
! [X163,X169] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X169),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X169),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X163),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X169)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
inference(fof_simplification,[status(thm)],[fact_diff__nat__number__of]) ).
fof(i_0_5353,plain,
! [X26,X141] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X141))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X141)) = hAPP(c_Int_Onat,X26) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X141))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X141)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),X141)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
inference(fof_simplification,[status(thm)],[fact_diff__nat__eq__if]) ).
fof(i_0_5354,plain,
! [X25,X6,X149,X24,X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,c_Groups_Otimes__class_Otimes(X7),X24,X149),X6))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X24),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,c_Groups_Otimes__class_Otimes(X7),X25,hAPP(hAPP(c_Set_Oinsert(X7),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),X6)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fold__graph__permute__diff]) ).
fof(i_0_5355,plain,
! [X34347,X34348,X34349,X34350] : c_List_Oconcat(X34350,hAPP(hAPP(c_List_Omap(X34349,tc_List_Olist(X34350)),hAPP(hAPP(c_COMBC(X34349,tc_List_Olist(X34350),tc_List_Olist(X34350)),hAPP(hAPP(c_COMBB(X34350,tc_fun(tc_List_Olist(X34350),tc_List_Olist(X34350)),X34349),c_List_Olist_OCons(X34350)),X34348)),c_List_Olist_ONil(X34350))),X34347)) = hAPP(hAPP(c_List_Omap(X34349,X34350),X34348),X34347),
inference(variable_rename,[status(thm)],[fact_concat__map__singleton]) ).
fof(i_0_5356,plain,
! [X22897,X22898,X22899] :
( ( ~ c_Nitpick_Oless__eq__frac(X22899,X22898,X22897)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22899),c_Nitpick_Oplus__frac(X22899,X22898,c_Nitpick_Ouminus__frac(X22899,X22897)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22899),c_Nitpick_Oplus__frac(X22899,X22898,c_Nitpick_Ouminus__frac(X22899,X22897)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Oless__eq__frac(X22899,X22898,X22897) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def])]) ).
fof(i_0_5357,plain,
! [X22894,X22895,X22896] :
( ( ~ c_Nitpick_Oless__frac(X22896,X22895,X22894)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22896),c_Nitpick_Oplus__frac(X22896,X22895,c_Nitpick_Ouminus__frac(X22896,X22894)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22896),c_Nitpick_Oplus__frac(X22896,X22895,c_Nitpick_Ouminus__frac(X22896,X22894)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Oless__frac(X22896,X22895,X22894) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def])]) ).
fof(i_0_5358,plain,
! [X21348,X21349,X21350] :
( ~ class_Rings_Olinordered__semidom(X21350)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21350),X21349),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X21350),X21348),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21350),c_Groups_Ozero__class_Ozero(X21350)),X21349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21350),c_Groups_Ozero__class_Ozero(X21350)),X21348))
| X21349 = X21348 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq])]) ).
fof(i_0_5359,plain,
! [X21360] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21360),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| X21360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X21360 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__2__cases])]) ).
fof(i_0_5360,plain,
! [X21339] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21339))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21339),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(variable_rename,[status(thm)],[fact_div2__Suc__Suc]) ).
fof(i_0_5361,plain,
! [X21334,X21335] :
( ~ class_Rings_Olinordered__idom(X21335)
| hAPP(c_Groups_Oabs__class_Oabs(X21335),hAPP(hAPP(c_Power_Opower__class_Opower(X21335),X21334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(X21335),X21334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power2])]) ).
fof(i_0_5362,plain,
! [X22880,X22881,X22882] :
( ~ class_Rings_Oinverse(X22882)
| ~ class_Rings_Oring__1(X22882)
| c_Nitpick_Oof__frac(X22881,X22882,X22880) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22882),hAPP(c_Int_Oring__1__class_Oof__int(X22882),hAPP(c_Nitpick_Onum(X22881),X22880))),hAPP(c_Int_Oring__1__class_Oof__int(X22882),hAPP(c_Nitpick_Odenom(X22881),X22880))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def])]) ).
fof(i_0_5363,plain,
! [X172,X279,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),X279),hAPP(c_Relation_Oconverse(X105,X7),X172)))
=> ~ ! [X3,X82] :
( X279 = hAPP(hAPP(c_Product__Type_OPair(X7,X105),X82),X3)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X3),X82)),X172)) ) ),
inference(fof_simplification,[status(thm)],[fact_converseE]) ).
fof(i_0_5364,plain,
! [X2,X44,X95,X7] :
( class_Groups_Oab__group__add(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X7)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(X2,X95)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X7)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44)) = c_Groups_Ozero__class_Ozero(X7) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__natinterval__difff]) ).
fof(i_0_5365,plain,
! [X127,X2,X292,X293,X105,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)),X292))))
=> c_Map_Omap__upds(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X2),X6),hAPP(c_Option_Ooption_OSome(X105),X127)),X292,X293) = c_Map_Omap__upds(X7,X105,X2,X292,X293) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)),X292))))
=> c_Map_Omap__upds(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X2),X6),hAPP(c_Option_Ooption_OSome(X105),X127)),X292,X293) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Omap__upds(X7,X105,X2,X292,X293)),X6),hAPP(c_Option_Ooption_OSome(X105),X127)) ) ),
inference(fof_simplification,[status(thm)],[fact_map__upd__upds__conv__if]) ).
fof(i_0_5366,plain,
! [X26,X127,X149,X24,X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,c_Groups_Otimes__class_Otimes(X7),X24,X149),X127))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X24),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,c_Groups_Otimes__class_Otimes(X7),X26,hAPP(hAPP(c_Set_Oinsert(X7),X24),X149)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X26),X127))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fold__graph__insert__swap]) ).
fof(i_0_5367,plain,
! [X127,X26,X2,X105,X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,X149),X127))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X105,X2,X26,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),hAPP(hAPP(X2,X6),X127))) ) ),
inference(fof_simplification,[status(thm)],[fact_fold__graph_OinsertI]) ).
fof(i_0_5368,plain,
! [X31810,X31811,X31812,X31813,X31814,X31815,X31817,X31818,X31819,X31820,X31821,X31822,X31823] :
( ( hAPP(X31811,X31810) = hAPP(c_Option_Ooption_OSome(X31815),esk435_6(X31810,X31811,X31812,X31813,X31814,X31815))
| hAPP(X31811,X31810) = c_Option_Ooption_ONone(X31815)
| c_Map_Omap__comp(X31815,X31814,X31813,X31812,X31811,X31810) != c_Option_Ooption_ONone(X31814) )
& ( hAPP(X31812,esk435_6(X31810,X31811,X31812,X31813,X31814,X31815)) = c_Option_Ooption_ONone(X31814)
| hAPP(X31811,X31810) = c_Option_Ooption_ONone(X31815)
| c_Map_Omap__comp(X31815,X31814,X31813,X31812,X31811,X31810) != c_Option_Ooption_ONone(X31814) )
& ( hAPP(X31818,X31817) != c_Option_Ooption_ONone(X31822)
| c_Map_Omap__comp(X31822,X31821,X31820,X31819,X31818,X31817) = c_Option_Ooption_ONone(X31821) )
& ( hAPP(X31818,X31817) != hAPP(c_Option_Ooption_OSome(X31822),X31823)
| hAPP(X31819,X31823) != c_Option_Ooption_ONone(X31821)
| c_Map_Omap__comp(X31822,X31821,X31820,X31819,X31818,X31817) = c_Option_Ooption_ONone(X31821) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__None__iff])])])])])]) ).
fof(i_0_5369,plain,
! [X30642,X30643,X30644,X30645] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30645,X30645)),hAPP(hAPP(c_Product__Type_OPair(X30645,X30645),X30644),esk387_4(X30642,X30643,X30644,X30645))),X30642))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30645,X30645)),hAPP(hAPP(c_Product__Type_OPair(X30645,X30645),X30644),X30643)),c_Transitive__Closure_Otrancl(X30645,X30642))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30645,X30645)),hAPP(hAPP(c_Product__Type_OPair(X30645,X30645),esk387_4(X30642,X30643,X30644,X30645)),X30643)),c_Transitive__Closure_Ortrancl(X30645,X30642)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30645,X30645)),hAPP(hAPP(c_Product__Type_OPair(X30645,X30645),X30644),X30643)),c_Transitive__Closure_Otrancl(X30645,X30642))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD])])])]) ).
fof(i_0_5370,plain,
! [X30637,X30638,X30639,X30640] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30640,X30640)),hAPP(hAPP(c_Product__Type_OPair(X30640,X30640),X30639),esk386_4(X30637,X30638,X30639,X30640))),c_Transitive__Closure_Ortrancl(X30640,X30637)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30640,X30640)),hAPP(hAPP(c_Product__Type_OPair(X30640,X30640),X30639),X30638)),c_Transitive__Closure_Otrancl(X30640,X30637))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30640,X30640)),hAPP(hAPP(c_Product__Type_OPair(X30640,X30640),esk386_4(X30637,X30638,X30639,X30640)),X30638)),X30637))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30640,X30640)),hAPP(hAPP(c_Product__Type_OPair(X30640,X30640),X30639),X30638)),c_Transitive__Closure_Otrancl(X30640,X30637))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD2])])])]) ).
fof(i_0_5371,plain,
! [X22672,X22673,X22674,X22675,X22676,X22677] : hAPP(c_Product__Type_Oapfst(X22677,X22676,X22675,X22674),hAPP(hAPP(c_Product__Type_OPair(X22677,X22675),X22673),X22672)) = hAPP(hAPP(c_Product__Type_OPair(X22676,X22675),hAPP(X22674,X22673)),X22672),
inference(variable_rename,[status(thm)],[fact_apfst__conv]) ).
fof(i_0_5372,plain,
! [X22055,X22056,X22057,X22058,X22059,X22060] : hAPP(c_Product__Type_Oapsnd(X22060,X22059,X22058,X22057),hAPP(hAPP(c_Product__Type_OPair(X22058,X22060),X22056),X22055)) = hAPP(hAPP(c_Product__Type_OPair(X22058,X22059),X22056),hAPP(X22057,X22055)),
inference(variable_rename,[status(thm)],[fact_apsnd__conv]) ).
fof(i_0_5373,plain,
! [X46,X149,X192,X136] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),X192))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X149))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X207),X206) ) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X46)))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X192)),X46))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_aset_I10_J]) ).
fof(i_0_5374,plain,
! [X46,X155,X192,X136] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),X192))
=> ! [X3] :
( ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X206),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X192)))
=> ! [X207] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X207),X155))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X207),X206) ) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X46)))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X192)),X46))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_bset_I10_J]) ).
fof(i_0_5375,plain,
! [X321,X24,X95,X105,X322,X25,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_List_Oset(X7),X322)))
=> c_Map_Omap__upds(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X95),X25),hAPP(c_Option_Ooption_OSome(X105),X24)),X322,X321) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Omap__upds(X7,X105,X95,X322,X321)),X25),hAPP(c_Option_Ooption_OSome(X105),X24)) ),
inference(fof_simplification,[status(thm)],[fact_map__upds__twist]) ).
fof(i_0_5376,plain,
! [X46,X45,X23,X25,X60] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X60,X25,X23)),X45),X46))
=> ~ ! [X62] :
( X46 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X62),c_Com_Ovname_OLoc(X60)),hAPP(hAPP(c_Natural_Ogetlocs,X45),X60))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),hAPP(hAPP(hAPP(c_Natural_Oupdate,X45),c_Com_Ovname_OLoc(X60)),hAPP(X25,X45))),X62)) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc__elim__cases_I3_J]) ).
fof(i_0_5377,plain,
! [X33964,X33965] : c_List_Ofoldr(tc_List_Olist(X33965),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X33965)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X33965))),c_List_Otranspose(X33965,X33964),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X33965))),hAPP(c_List_Ofilter(tc_List_Olist(X33965),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X33965)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X33965),tc_List_Olist(X33965),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X33965)))),X33964)),
inference(variable_rename,[status(thm)],[fact_transpose__max__length]) ).
fof(i_0_5378,plain,
! [X21340,X21341] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21341)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21340))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21341),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21340))),
inference(variable_rename,[status(thm)],[fact_zmod__number__of__Bit0]) ).
fof(i_0_5379,plain,
! [X21336,X21337] :
( ~ class_Rings_Olinordered__idom(X21337)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21337),hAPP(c_Groups_Oabs__class_Oabs(X21337),X21336)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X21337),X21336),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__abs])]) ).
fof(i_0_5380,plain,
! [X21327,X21328] :
( ~ class_Rings_Oring__1(X21328)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21328),hAPP(c_Groups_Ouminus__class_Ouminus(X21328),X21327)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X21328),X21327),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__minus])]) ).
fof(i_0_5381,plain,
! [X21338] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21338)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21338,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[fact_mod2__Suc__Suc]) ).
fof(i_0_5382,plain,
! [X38,X149,X215,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X215))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X215),X149))
=> ( hBOOL(hAPP(X38,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> ( ! [X110,X241] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X241))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X110),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X110),X241))
=> ( hBOOL(hAPP(X38,X241))
=> hBOOL(hAPP(X38,hAPP(hAPP(c_Set_Oinsert(X7),X110),X241))) ) ) ) )
=> hBOOL(hAPP(X38,X215)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_finite__subset__induct]) ).
fof(i_0_5383,plain,
! [X21312,X21313] :
( ~ class_Int_Onumber__ring(X21313)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21313),hAPP(c_Int_Onumber__class_Onumber__of(X21313),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21312) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21313),X21312),X21312) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])]) ).
fof(i_0_5384,plain,
! [X21329] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21329) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21329),X21329),
inference(variable_rename,[status(thm)],[fact_nat__mult__2]) ).
fof(i_0_5385,plain,
! [X21325] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21325) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21325)),
inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc]) ).
fof(i_0_5386,plain,
! [X6,X149,X215,X1,X26,X2,X105,X7] :
( c_Finite__Set_Ofolding__image__simple(X7,X105,X2,X26,X1,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X105),X6),X149))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X105),X6),X149)) = hAPP(hAPP(X2,hAPP(X1,X6)),hAPP(X215,X149)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).
fof(i_0_5387,plain,
! [X172,X105,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(c_Relation_ORange(X105,X7),X172)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X105,X7)),hAPP(hAPP(c_Product__Type_OPair(X105,X7),X3),X24)),X172)) ),
inference(fof_simplification,[status(thm)],[fact_RangeE]) ).
fof(i_0_5388,plain,
! [X30133,X30134,X30135,X30136,X30137] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30137,X30137)),hAPP(hAPP(c_Product__Type_OPair(X30137,X30137),X30136),X30135)),c_Transitive__Closure_Otrancl(X30137,X30134)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30137,X30137)),hAPP(hAPP(c_Product__Type_OPair(X30137,X30137),X30135),X30133)),c_Transitive__Closure_Otrancl(X30137,X30134)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30137,X30137)),hAPP(hAPP(c_Product__Type_OPair(X30137,X30137),X30136),X30133)),c_Transitive__Closure_Otrancl(X30137,X30134))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__trans])]) ).
fof(i_0_5389,plain,
! [X30420,X30421,X30422,X30423] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30423,X30423)),hAPP(hAPP(c_Product__Type_OPair(X30423,X30423),X30422),X30421)),hAPP(c_Relation_Oconverse(X30423,X30423),c_Transitive__Closure_Otrancl(X30423,X30420))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30423,X30423)),hAPP(hAPP(c_Product__Type_OPair(X30423,X30423),X30422),X30421)),c_Transitive__Closure_Otrancl(X30423,hAPP(c_Relation_Oconverse(X30423,X30423),X30420)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseI])]) ).
fof(i_0_5390,plain,
! [X30424,X30425,X30426,X30427] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30427,X30427)),hAPP(hAPP(c_Product__Type_OPair(X30427,X30427),X30426),X30425)),c_Transitive__Closure_Otrancl(X30427,hAPP(c_Relation_Oconverse(X30427,X30427),X30424))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30427,X30427)),hAPP(hAPP(c_Product__Type_OPair(X30427,X30427),X30426),X30425)),hAPP(c_Relation_Oconverse(X30427,X30427),c_Transitive__Closure_Otrancl(X30427,X30424)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseD])]) ).
fof(i_0_5391,plain,
! [X127,X95,X105,X192,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X192))
=> c_Map_Orestrict__map(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X95),X6),X127),X192) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Orestrict__map(X7,X105,X95,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X192),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),X6),X127) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X192))
=> c_Map_Orestrict__map(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X95),X6),X127),X192) = c_Map_Orestrict__map(X7,X105,X95,X192) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__fun__upd]) ).
fof(i_0_5392,plain,
! [X6,X149,X25,X2,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X7,X2,X25,X149),X6))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,X2,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)),X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_fold1Set_Ointros]) ).
fof(i_0_5393,plain,
! [X21361,X21362] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X21362),X21361),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(X21362)
| X21361 = c_Groups_Oone__class_Oone(X21362)
| X21361 = hAPP(c_Groups_Ouminus__class_Ouminus(X21362),c_Groups_Oone__class_Oone(X21362))
| ~ class_Rings_Oring__1__no__zero__divisors(X21362) )
& ( X21361 != c_Groups_Oone__class_Oone(X21362)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21362),X21361),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X21362)
| ~ class_Rings_Oring__1__no__zero__divisors(X21362) )
& ( X21361 != hAPP(c_Groups_Ouminus__class_Ouminus(X21362),c_Groups_Oone__class_Oone(X21362))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21362),X21361),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X21362)
| ~ class_Rings_Oring__1__no__zero__divisors(X21362) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff])])]) ).
fof(i_0_5394,plain,
! [X21318,X21319] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X21319),X21318),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X21319)
| X21318 = c_Groups_Ozero__class_Ozero(X21319)
| ~ class_Rings_Oring__1__no__zero__divisors(X21319) )
& ( X21318 != c_Groups_Ozero__class_Ozero(X21319)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21319),X21318),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X21319)
| ~ class_Rings_Oring__1__no__zero__divisors(X21319) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])]) ).
fof(i_0_5395,plain,
! [X26,X127,X6,X302,X292,X105,X293,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X293) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X292)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X302) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X292)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X105),X6),hAPP(c_List_Oset(X105),X292)))
=> ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,tc_Option_Ooption(X7)),c_Map_Omap__of(X105,X7,hAPP(hAPP(c_List_Ozip(X105,X7),X292),X293))),X6),hAPP(c_Option_Ooption_OSome(X7),X127)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X105,tc_Option_Ooption(X7)),c_Map_Omap__of(X105,X7,hAPP(hAPP(c_List_Ozip(X105,X7),X292),X302))),X6),hAPP(c_Option_Ooption_OSome(X7),X26))
=> c_Map_Omap__of(X105,X7,hAPP(hAPP(c_List_Ozip(X105,X7),X292),X293)) = c_Map_Omap__of(X105,X7,hAPP(hAPP(c_List_Ozip(X105,X7),X292),X302)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_map__of__zip__upd]) ).
fof(i_0_5396,plain,
! [X34325,X34326,X34327] : hAPP(c_List_Orotate(X34327,X34326),hAPP(c_List_Orev(X34327),X34325)) = hAPP(c_List_Orev(X34327),hAPP(c_List_Orotate(X34327,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34327)),X34325)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X34326,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34327)),X34325)))),X34325)),
inference(variable_rename,[status(thm)],[fact_rotate__rev]) ).
fof(i_0_5397,plain,
! [X33522,X33523] : c_List_Orotate(X33523,X33522) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X33523),tc_List_Olist(X33523)),X33522),c_List_Orotate1(X33523)),
inference(variable_rename,[status(thm)],[fact_rotate__def]) ).
fof(i_0_5398,plain,
! [X30269,X30270,X30271,X30272,X30273] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30273,X30273)),hAPP(hAPP(c_Product__Type_OPair(X30273,X30273),X30272),X30271)),c_Transitive__Closure_Ortrancl(X30273,X30270)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30273,X30273)),hAPP(hAPP(c_Product__Type_OPair(X30273,X30273),X30271),X30269)),c_Transitive__Closure_Otrancl(X30273,X30270)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30273,X30273)),hAPP(hAPP(c_Product__Type_OPair(X30273,X30273),X30272),X30269)),c_Transitive__Closure_Otrancl(X30273,X30270))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl])]) ).
fof(i_0_5399,plain,
! [X30274,X30275,X30276,X30277,X30278] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30278,X30278)),hAPP(hAPP(c_Product__Type_OPair(X30278,X30278),X30277),X30276)),c_Transitive__Closure_Otrancl(X30278,X30275)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30278,X30278)),hAPP(hAPP(c_Product__Type_OPair(X30278,X30278),X30276),X30274)),c_Transitive__Closure_Ortrancl(X30278,X30275)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30278,X30278)),hAPP(hAPP(c_Product__Type_OPair(X30278,X30278),X30277),X30274)),c_Transitive__Closure_Otrancl(X30278,X30275))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl])]) ).
fof(i_0_5400,plain,
! [X30143,X30144,X30145,X30146,X30147] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30147,X30147)),hAPP(hAPP(c_Product__Type_OPair(X30147,X30147),X30146),X30145)),X30144))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30147,X30147)),hAPP(hAPP(c_Product__Type_OPair(X30147,X30147),X30145),X30143)),c_Transitive__Closure_Otrancl(X30147,X30144)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30147,X30147)),hAPP(hAPP(c_Product__Type_OPair(X30147,X30147),X30146),X30143)),c_Transitive__Closure_Otrancl(X30147,X30144))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2])]) ).
fof(i_0_5401,plain,
! [X30138,X30139,X30140,X30141,X30142] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30142,X30142)),hAPP(hAPP(c_Product__Type_OPair(X30142,X30142),X30141),X30140)),c_Transitive__Closure_Otrancl(X30142,X30139)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30142,X30142)),hAPP(hAPP(c_Product__Type_OPair(X30142,X30142),X30140),X30138)),X30139))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30142,X30142)),hAPP(hAPP(c_Product__Type_OPair(X30142,X30142),X30141),X30138)),c_Transitive__Closure_Otrancl(X30142,X30139))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl])]) ).
fof(i_0_5402,plain,
! [X7,X25,X38] :
( ( hBOOL(hAPP(X38,X25))
=> hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X38)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(X38,X25))
=> hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X25))),X38)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
inference(fof_simplification,[status(thm)],[fact_Collect__conv__if]) ).
fof(i_0_5403,plain,
! [X31793,X31794,X31795,X31796,X31797,X31798,X31799] : c_List_Ofoldr(X31799,X31798,X31797,hAPP(hAPP(c_List_Omap(X31796,X31799),X31795),X31794),X31793) = c_List_Ofoldr(X31796,X31798,hAPP(c_Fun_Ocomp(X31799,tc_fun(X31798,X31798),X31796,X31797),X31795),X31794,X31793),
inference(variable_rename,[status(thm)],[fact_foldr__map]) ).
fof(i_0_5404,plain,
! [X30159,X30160,X30161] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool)),X30160),hAPP(hAPP(c_Product__Type_OSigma(X30161,X30161),X30159),hAPP(c_COMBK(tc_fun(X30161,tc_HOL_Obool),X30161),X30159))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30161,X30160)),hAPP(hAPP(c_Product__Type_OSigma(X30161,X30161),X30159),hAPP(c_COMBK(tc_fun(X30161,tc_HOL_Obool),X30161),X30159)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma])]) ).
fof(i_0_5405,plain,
! [X21899,X21900,X21901] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21900)))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21901),hAPP(c_Int_Onumber__class_Onumber__of(X21901),X21899)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21900))) = hAPP(hAPP(c_HOL_OLet(X21901,X21901),hAPP(hAPP(c_Power_Opower__class_Opower(X21901),hAPP(c_Int_Onumber__class_Onumber__of(X21901),X21899)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21900))),hAPP(hAPP(c_COMBS(X21901,X21901,X21901),hAPP(hAPP(c_COMBB(X21901,tc_fun(X21901,X21901),X21901),c_Groups_Otimes__class_Otimes(X21901)),hAPP(c_Groups_Otimes__class_Otimes(X21901),hAPP(c_Int_Onumber__class_Onumber__of(X21901),X21899)))),c_COMBI(X21901)))
| ~ class_Int_Onumber__ring(X21901) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21900)))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21901),hAPP(c_Int_Onumber__class_Onumber__of(X21901),X21899)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21900))) = c_Groups_Oone__class_Oone(X21901)
| ~ class_Int_Onumber__ring(X21901) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5173])])]) ).
fof(i_0_5406,plain,
! [X24,X25] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X25),X24)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X25,X24) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X25,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( ~ ( X25 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X25,X24) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X25),X24)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_norm__frac_Opsimps]) ).
fof(i_0_5407,plain,
! [X32975,X32976,X32977,X32978,X32979,X32980] : c_List_Ofoldr(X32980,X32979,X32978,hAPP(hAPP(c_List_Oappend(X32980),X32977),X32976),X32975) = c_List_Ofoldr(X32980,X32979,X32978,X32977,c_List_Ofoldr(X32980,X32979,X32978,X32976,X32975)),
inference(variable_rename,[status(thm)],[fact_foldr__append]) ).
fof(i_0_5408,plain,
! [X155,X6,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),X155)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),X155)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X155)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_psubset__insert__iff]) ).
fof(i_0_5409,plain,
! [X127,X172,X7] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X127),X127)),c_List_Olexord(X7,X172))) ),
inference(fof_simplification,[status(thm)],[fact_lexord__irreflexive]) ).
fof(i_0_5410,plain,
! [X21305,X21306] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X21306)),c_Int_OBit1(X21305)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X21306)),X21305)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I8_J]) ).
fof(i_0_5411,plain,
! [X149,X25,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,hAPP(hAPP(c_Set_Oinsert(X7),X25),X149))
<=> ( c_Fun_Oinj__on(X7,X105,X2,X149)
& ~ hBOOL(hAPP(hAPP(c_member(X105),hAPP(X2,X25)),hAPP(c_Set_Oimage(X7,X105,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))) ) ),
inference(fof_simplification,[status(thm)],[fact_inj__on__insert]) ).
fof(i_0_5412,plain,
! [X29441,X29442] : c_Product__Type_Oapfst(X29442,X29442,X29441,c_Fun_Oid(X29442)) = c_Fun_Oid(tc_prod(X29442,X29441)),
inference(variable_rename,[status(thm)],[fact_apfst__id]) ).
fof(i_0_5413,plain,
! [X29443,X29444] : c_Product__Type_Oapsnd(X29444,X29444,X29443,c_Fun_Oid(X29444)) = c_Fun_Oid(tc_prod(X29443,X29444)),
inference(variable_rename,[status(thm)],[fact_apsnd__id]) ).
fof(i_0_5414,plain,
! [X30191,X30192] : c_Transitive__Closure_Otrancl(X30192,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30192,X30192),tc_HOL_Obool)),X30191),c_Relation_OId(X30192))) = c_Transitive__Closure_Ortrancl(X30192,X30191),
inference(variable_rename,[status(thm)],[fact_trancl__reflcl]) ).
fof(i_0_5415,plain,
! [X155,X6,X149,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),X155)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X155)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert__iff]) ).
fof(i_0_5416,plain,
! [X21145,X21146] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X21146),X21145) != c_Groups_Oone__class_Oone(X21146)
| c_Int_Oiszero(X21146,hAPP(c_Int_Onumber__class_Onumber__of(X21146),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21145),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(X21146) )
& ( ~ c_Int_Oiszero(X21146,hAPP(c_Int_Onumber__class_Onumber__of(X21146),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21145),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(X21146),X21145) = c_Groups_Oone__class_Oone(X21146)
| ~ class_Int_Onumber__ring(X21146) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J])])]) ).
fof(i_0_5417,plain,
! [X21143,X21144] :
( ( c_Groups_Oone__class_Oone(X21144) != hAPP(c_Int_Onumber__class_Onumber__of(X21144),X21143)
| c_Int_Oiszero(X21144,hAPP(c_Int_Onumber__class_Onumber__of(X21144),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21143))))
| ~ class_Int_Onumber__ring(X21144) )
& ( ~ c_Int_Oiszero(X21144,hAPP(c_Int_Onumber__class_Onumber__of(X21144),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21143))))
| c_Groups_Oone__class_Oone(X21144) = hAPP(c_Int_Onumber__class_Onumber__of(X21144),X21143)
| ~ class_Int_Onumber__ring(X21144) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J])])]) ).
fof(i_0_5418,plain,
! [X107,X136,X2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X136),X107))))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),X107))
=> c_Smallcheck_Osmall_H(X2,X136,X107) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),X107))
=> c_Smallcheck_Osmall_H(X2,X136,X107) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X2,X136,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X107)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_small_H_Opsimps]) ).
fof(i_0_5419,plain,
! [X25,X24] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X25,X24) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X25,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( ~ ( X25 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X25,X24) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X25),X24)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24))) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_norm__frac_Osimps]) ).
fof(i_0_5420,plain,
! [X30288,X30289,X30290,X30291,X30292] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30292,X30292)),hAPP(hAPP(c_Product__Type_OPair(X30292,X30292),X30291),X30290)),X30289))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30292,X30292)),hAPP(hAPP(c_Product__Type_OPair(X30292,X30292),X30290),X30288)),c_Transitive__Closure_Ortrancl(X30292,X30289)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30292,X30292)),hAPP(hAPP(c_Product__Type_OPair(X30292,X30292),X30291),X30288)),c_Transitive__Closure_Otrancl(X30292,X30289))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2])]) ).
fof(i_0_5421,plain,
! [X30279,X30280,X30281,X30282,X30283] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30283,X30283)),hAPP(hAPP(c_Product__Type_OPair(X30283,X30283),X30282),X30281)),c_Transitive__Closure_Ortrancl(X30283,X30280)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30283,X30283)),hAPP(hAPP(c_Product__Type_OPair(X30283,X30283),X30281),X30279)),X30280))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30283,X30283)),hAPP(hAPP(c_Product__Type_OPair(X30283,X30283),X30282),X30279)),c_Transitive__Closure_Otrancl(X30283,X30280))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1])]) ).
fof(i_0_5422,plain,
! [X21892,X21893,X21894] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21893)))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21894),X21892),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21893))) = hAPP(hAPP(c_HOL_OLet(X21894,X21894),hAPP(hAPP(c_Power_Opower__class_Opower(X21894),X21892),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21893))),hAPP(hAPP(c_COMBS(X21894,X21894,X21894),hAPP(hAPP(c_COMBB(X21894,tc_fun(X21894,X21894),X21894),c_Groups_Otimes__class_Otimes(X21894)),hAPP(c_Groups_Otimes__class_Otimes(X21894),X21892))),c_COMBI(X21894)))
| ~ class_Int_Onumber__ring(X21894) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21893)))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21894),X21892),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21893))) = c_Groups_Oone__class_Oone(X21894)
| ~ class_Int_Onumber__ring(X21894) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5174])])]) ).
fof(i_0_5423,plain,
! [X21358,X21359] :
( ~ class_Groups_Omonoid__mult(X21359)
| ~ class_Int_Onumber(X21359)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21359),hAPP(c_Int_Onumber__class_Onumber__of(X21359),X21358)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21359),hAPP(c_Int_Onumber__class_Onumber__of(X21359),X21358)),hAPP(c_Int_Onumber__class_Onumber__of(X21359),X21358)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of])]) ).
fof(i_0_5424,plain,
! [X30148,X30149,X30150,X30151,X30152] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30152,X30152)),hAPP(hAPP(c_Product__Type_OPair(X30152,X30152),X30151),X30150)),X30149))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30152,X30152)),hAPP(hAPP(c_Product__Type_OPair(X30152,X30152),X30150),X30148)),X30149))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30152,X30152)),hAPP(hAPP(c_Product__Type_OPair(X30152,X30152),X30151),X30148)),c_Transitive__Closure_Otrancl(X30152,X30149))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).
fof(i_0_5425,plain,
! [X172,X105,X25,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Relation_ODomain(X7,X105),X172)))
=> ~ ! [X82] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X82)),X172)) ),
inference(fof_simplification,[status(thm)],[fact_DomainE]) ).
fof(i_0_5426,plain,
! [X21342] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21342),X21342)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X21342,
inference(variable_rename,[status(thm)],[fact_add__self__div__2]) ).
fof(i_0_5427,plain,
! [X136,X23,X24,X25] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23,X136)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24))
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23),X25))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X136)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__subset__iff]) ).
fof(i_0_5428,plain,
! [X21314,X21315] :
( ~ class_Int_Onumber__ring(X21315)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21315),X21314),hAPP(c_Int_Onumber__class_Onumber__of(X21315),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21315),X21314),X21314) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).
fof(i_0_5429,plain,
! [X21322,X21323] :
( ~ class_Groups_Omonoid__mult(X21323)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21323),X21322),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21323),X21322),X21322) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square])]) ).
fof(i_0_5430,plain,
! [X21320,X21321] :
( ~ class_Rings_Ocomm__semiring__1(X21321)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21321),X21320),X21320) = hAPP(hAPP(c_Power_Opower__class_Opower(X21321),X21320),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J])]) ).
fof(i_0_5431,plain,
! [X25,X23,X24,X155,X149,X119,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_fun(X119,tc_HOL_Obool))),X149),X155),X24),X23))
=> ( ~ hBOOL(hAPP(hAPP(hAPP(X155,X25),X24),X23))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149)) ) ),
inference(fof_simplification,[status(thm)],[fact_INF2__E]) ).
fof(i_0_5432,plain,
! [X21330] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21330),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21330),X21330),
inference(variable_rename,[status(thm)],[fact_nat__mult__2__right]) ).
fof(i_0_5433,plain,
! [X21324] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21324),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21324)),
inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H]) ).
fof(i_0_5434,plain,
! [X21326] :
( ~ class_Rings_Osemiring__1(X21326)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21326),c_Groups_Oone__class_Oone(X21326)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X21326) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__power2])]) ).
fof(i_0_5435,plain,
! [X21317] :
( ~ class_Rings_Osemiring__1(X21317)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21317),c_Groups_Ozero__class_Ozero(X21317)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X21317) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__power2])]) ).
fof(i_0_5436,plain,
! [X21895,X21896] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21896)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21895),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21896))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21895),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21896))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21895))),c_COMBI(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21896)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21895),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21896))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5175])]) ).
fof(i_0_5437,plain,
! [X30153,X30154,X30155,X30156] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30156,X30156)),X30155),c_Transitive__Closure_Otrancl(X30156,X30154)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30156,X30156),tc_HOL_Obool)),X30154),X30153))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30156,X30156)),X30155),c_Transitive__Closure_Otrancl(X30156,X30153))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__mono])]) ).
fof(i_0_5438,plain,
! [X98,X86,X87] :
( class_Rings_Olinordered__ring(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X86),X86)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X98),X98))),c_Groups_Ozero__class_Ozero(X87))) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(i_0_5439,plain,
! [X30121,X30122] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30122,X30122),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30122,X30121)),hAPP(hAPP(c_Product__Type_OSigma(X30122,X30122),hAPP(c_Relation_OField(X30122),X30121)),hAPP(c_COMBK(tc_fun(X30122,tc_HOL_Obool),X30122),hAPP(c_Relation_OField(X30122),X30121))))),
inference(variable_rename,[status(thm)],[fact_trancl__subset__Field2]) ).
fof(i_0_5440,plain,
! [X127,X6,X155,X149,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X149),X155),X6),X127))
=> ( ~ hBOOL(hAPP(hAPP(X149,X6),X127))
=> hBOOL(hAPP(hAPP(X155,X6),X127)) ) ),
inference(fof_simplification,[status(thm)],[fact_sup2E]) ).
fof(i_0_5441,plain,
! [X30293,X30294,X30295,X30296] :
( ( X30295 != X30294
| X30295 = X30294
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30296,X30296)),hAPP(hAPP(c_Product__Type_OPair(X30296,X30296),X30295),X30294)),c_Transitive__Closure_Ortrancl(X30296,X30293))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30296,X30296)),hAPP(hAPP(c_Product__Type_OPair(X30296,X30296),X30295),X30294)),c_Transitive__Closure_Otrancl(X30296,X30293)))
| X30295 = X30294
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30296,X30296)),hAPP(hAPP(c_Product__Type_OPair(X30296,X30296),X30295),X30294)),c_Transitive__Closure_Ortrancl(X30296,X30293))) )
& ( X30295 != X30294
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30296,X30296)),hAPP(hAPP(c_Product__Type_OPair(X30296,X30296),X30295),X30294)),c_Transitive__Closure_Ortrancl(X30296,X30293))) )
& ( X30295 = X30294
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30296,X30296)),hAPP(hAPP(c_Product__Type_OPair(X30296,X30296),X30295),X30294)),c_Transitive__Closure_Otrancl(X30296,X30293)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30296,X30296)),hAPP(hAPP(c_Product__Type_OPair(X30296,X30296),X30295),X30294)),c_Transitive__Closure_Ortrancl(X30296,X30293))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl])])]) ).
fof(i_0_5442,plain,
! [X30181,X30182,X30183,X30184] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30184,X30184)),hAPP(hAPP(c_Product__Type_OPair(X30184,X30184),X30183),X30182)),c_Transitive__Closure_Otrancl(X30184,X30181)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30184,X30184)),hAPP(hAPP(c_Product__Type_OPair(X30184,X30184),X30183),X30182)),c_Transitive__Closure_Ortrancl(X30184,X30181))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl])]) ).
fof(i_0_5443,plain,
! [X127,X6,X155,X149,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X149),X155),X6),X127))
=> ~ ( hBOOL(hAPP(hAPP(X149,X6),X127))
=> ~ hBOOL(hAPP(hAPP(X155,X6),X127)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf2E]) ).
fof(i_0_5444,plain,
! [X21159,X21160] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21160)),c_Int_OBit1(X21159)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21160),X21159)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21160),X21159))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21160)),c_Int_OBit1(X21159))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J])]) ).
fof(i_0_5445,plain,
! [X21157,X21158] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21158)),c_Int_OBit1(X21157)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21158),X21157)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21158),X21157))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21158)),c_Int_OBit1(X21157))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])]) ).
fof(i_0_5446,plain,
! [X21163,X21164] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21164)),c_Int_OBit1(X21163)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21164),X21163)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21164),X21163))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21164)),c_Int_OBit1(X21163))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J])]) ).
fof(i_0_5447,plain,
! [X21161,X21162] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21162)),c_Int_OBit1(X21161)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21162),X21161)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21162),X21161))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21162)),c_Int_OBit1(X21161))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])]) ).
fof(i_0_5448,plain,
! [X30332,X30333,X30334] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X30334,X30334),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X30334,X30334),X30333)),c_Transitive__Closure_Ortrancl(X30334,X30333)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X30334,X30334),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30334,X30334)),hAPP(hAPP(c_Product__Type_OPair(X30334,X30334),X30332),X30332)),c_Transitive__Closure_Otrancl(X30334,X30333))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5176])]) ).
fof(i_0_5449,plain,
! [X34004,X34005] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34005))),c_List_Otranspose(X34005,X34004)) = c_List_Ofoldr(tc_List_Olist(X34005),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X34005)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X34005))),X34004,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_length__transpose]) ).
fof(i_0_5450,plain,
! [X30524,X30525,X30526,X30528,X30529,X30530,X30531] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk368_3(X30524,X30525,X30526)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30526,X30526)),X30525),c_Transitive__Closure_Otrancl(X30526,X30524))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30526,X30526)),X30525),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30526,X30526),tc_HOL_Obool),esk368_3(X30524,X30525,X30526)),X30524)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30526,X30526)),X30525),c_Transitive__Closure_Otrancl(X30526,X30524))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30531))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30530,X30530)),X30529),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30530,X30530),tc_HOL_Obool),X30531),X30528)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30530,X30530)),X30529),c_Transitive__Closure_Otrancl(X30530,X30528))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__power])])])])])]) ).
fof(i_0_5451,plain,
! [X34274,X34275,X34276] : c_List_Oconcat(X34276,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X34276)),X34275),X34274)) = hAPP(hAPP(c_List_Oappend(X34276),c_List_Oconcat(X34276,X34275)),c_List_Oconcat(X34276,X34274)),
inference(variable_rename,[status(thm)],[fact_concat__append]) ).
fof(i_0_5452,plain,
! [X107,X25,X292,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),X292))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_List_Oset(X7),X292)),hAPP(hAPP(c_Set_Oinsert(X7),hAPP(hAPP(c_List_Onth(X7),X292),X107)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))
=> hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Olist__update(X7,X292),X107),X25))) ) ),
inference(fof_simplification,[status(thm)],[fact_distinct__list__update]) ).
fof(i_0_5453,plain,
! [X149,X2,X105,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),hAPP(c_Set_Oimage(X105,X7,X2),X149))),hAPP(c_Finite__Set_Ocard(X105),X149)))
=> ~ c_Fun_Oinj__on(X105,X7,X2,X149) ),
inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).
fof(i_0_5454,plain,
! [X30284,X30285,X30286,X30287] :
( ( X30286 != X30285
| X30286 = X30285
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30287,X30287)),hAPP(hAPP(c_Product__Type_OPair(X30287,X30287),X30286),X30285)),c_Transitive__Closure_Ortrancl(X30287,X30284))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30287,X30287)),hAPP(hAPP(c_Product__Type_OPair(X30287,X30287),X30286),X30285)),c_Transitive__Closure_Otrancl(X30287,X30284)))
| X30286 = X30285
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30287,X30287)),hAPP(hAPP(c_Product__Type_OPair(X30287,X30287),X30286),X30285)),c_Transitive__Closure_Ortrancl(X30287,X30284))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtranclD])])]) ).
fof(i_0_5455,plain,
! [X30117,X30118,X30119,X30120] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30120,X30120)),hAPP(hAPP(c_Product__Type_OPair(X30120,X30120),X30119),X30118)),X30117))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30120,X30120)),hAPP(hAPP(c_Product__Type_OPair(X30120,X30120),X30119),X30118)),c_Transitive__Closure_Otrancl(X30120,X30117))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl])]) ).
fof(i_0_5456,plain,
! [X24141,X24142,X24143,X24144] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142),X24144))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144),X24143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144,X24143)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142,X24141))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24143),X24141))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144),X24143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144,X24143)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142,X24141))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24143),X24141))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142),X24144))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144),X24143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144,X24143)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142,X24141))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24141),X24143))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142),X24144))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144),X24143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144,X24143)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142,X24141))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24143),X24141))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144),X24142))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144),X24143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144,X24143)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142,X24141))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24141),X24143))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144),X24142))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144),X24143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144,X24143)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142,X24141))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142),X24141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144,X24143)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142,X24141))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144),X24143))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142),X24141))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144,X24143)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142,X24141))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142),X24144))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144),X24142))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142),X24144))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24143),X24141))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142),X24141))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144,X24143)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142,X24141))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24143),X24141))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24141),X24143))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142),X24144))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24143),X24141))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142),X24141))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24144,X24143)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24142,X24141))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5177])])]) ).
fof(i_0_5457,plain,
! [X125,X23,X24,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of]) ).
fof(i_0_5458,plain,
! [X125,X23,X24,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of]) ).
fof(i_0_5459,plain,
! [X23,X24,X125,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of]) ).
fof(i_0_5460,plain,
! [X23,X24,X125,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of]) ).
fof(i_0_5461,plain,
! [X7,X25,X38] :
( ( hBOOL(hAPP(X38,X25))
=> hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(c_fequal,X25))),X38)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(X38,X25))
=> hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(c_fequal,X25))),X38)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
inference(fof_simplification,[status(thm)],[fact_Collect__conv__if2]) ).
fof(i_0_5462,plain,
! [X33551,X33552,X33553] : hAPP(c_List_Orotate(X33553,X33552),X33551) = hAPP(hAPP(c_List_Oappend(X33553),hAPP(hAPP(c_List_Odrop(X33553),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33552,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33553)),X33551))),X33551)),hAPP(hAPP(c_List_Otake(X33553),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33552,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33553)),X33551))),X33551)),
inference(variable_rename,[status(thm)],[fact_rotate__drop__take]) ).
fof(i_0_5463,plain,
! [X30111,X30112,X30113,X30114,X30115] :
( ( ~ c_Wellfounded_Oacyclic(X30112,X30111)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30112,X30112)),hAPP(hAPP(c_Product__Type_OPair(X30112,X30112),X30113),X30113)),c_Transitive__Closure_Otrancl(X30112,X30111))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30115,X30115)),hAPP(hAPP(c_Product__Type_OPair(X30115,X30115),esk365_2(X30114,X30115)),esk365_2(X30114,X30115))),c_Transitive__Closure_Otrancl(X30115,X30114)))
| c_Wellfounded_Oacyclic(X30115,X30114) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5178])])])])]) ).
fof(i_0_5464,plain,
! [X293,X292,X127,X6,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X6),X127)),hAPP(c_List_Oset(tc_prod(X7,X105)),hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293))))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> ~ hBOOL(hAPP(hAPP(c_member(X105),X127),hAPP(c_List_Oset(X105),X293))) ) ),
inference(fof_simplification,[status(thm)],[fact_in__set__zipE]) ).
fof(i_0_5465,plain,
! [X276,X277,X278,X105,X95,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X95),c_Map_Odom(X7,X105,X278)))
=> c_Map_Omap__add(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X277),X95),hAPP(c_Option_Ooption_OSome(X105),X276)),X278) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Omap__add(X7,X105,X277,X278)),X95),hAPP(c_Option_Ooption_OSome(X105),X276)) ),
inference(fof_simplification,[status(thm)],[fact_map__add__upd__left]) ).
fof(i_0_5466,plain,
! [X172,X6,X127,X7] :
( c_Wellfounded_Oacyclic(X7,hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X6)),X172))
<=> ( c_Wellfounded_Oacyclic(X7,X172)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,X172))) ) ),
inference(fof_simplification,[status(thm)],[fact_acyclic__insert]) ).
fof(i_0_5467,plain,
! [X172,X6,X127,X7] :
( c_Wellfounded_Owf(X7,hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X127),X6)),X172))
<=> ( c_Wellfounded_Owf(X7,X172)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,X172))) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__insert]) ).
fof(i_0_5468,plain,
! [X30157,X30158] : c_Transitive__Closure_Otrancl(X30158,X30157) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30158,X30158),tc_HOL_Obool)),X30157),hAPP(hAPP(c_Relation_Orel__comp(X30158,X30158,X30158),c_Transitive__Closure_Otrancl(X30158,X30157)),X30157)),
inference(variable_rename,[status(thm)],[fact_trancl__unfold]) ).
fof(i_0_5469,plain,
! [X172,X7] :
( c_Wellfounded_Owf(X7,X172)
<=> ! [X274] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X7),X3),X274))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X274))
& ! [X82] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X82),X3)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X82),X274)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__eq__minimal]) ).
fof(i_0_5470,plain,
! [X21293,X21294] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21294)),c_Int_OBit0(X21293)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21294),X21293)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21294),X21293))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21294)),c_Int_OBit0(X21293))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J])]) ).
fof(i_0_5471,plain,
! [X21291,X21292] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21292)),c_Int_OBit0(X21291)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21292),X21291)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21292),X21291))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21292)),c_Int_OBit0(X21291))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])]) ).
fof(i_0_5472,plain,
! [X21267,X21268] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21268)),c_Int_OBit0(X21267)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21268),X21267)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21268),X21267))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21268)),c_Int_OBit0(X21267))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J])]) ).
fof(i_0_5473,plain,
! [X21265,X21266] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21266)),c_Int_OBit0(X21265)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21266),X21265)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21266),X21265))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21266)),c_Int_OBit0(X21265))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])]) ).
fof(i_0_5474,plain,
! [X95,X105,X192,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X192))
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Orestrict__map(X7,X105,X95,X192)),X6),c_Option_Ooption_ONone(X105)) = c_Map_Orestrict__map(X7,X105,X95,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X192),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X192))
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),c_Map_Orestrict__map(X7,X105,X95,X192)),X6),c_Option_Ooption_ONone(X105)) = c_Map_Orestrict__map(X7,X105,X95,X192) ) ),
inference(fof_simplification,[status(thm)],[fact_fun__upd__None__restrict]) ).
fof(i_0_5475,plain,
! [X21016,X21017] : c_Nitpick_Oint__lcm(X21017,X21016) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21017)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21016)))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__lcm__def]) ).
fof(i_0_5476,plain,
! [X21006,X21007] : c_Nitpick_Onat__lcm(X21007,X21006) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21007),X21006)),c_Nitpick_Onat__gcd(X21007,X21006)),
inference(variable_rename,[status(thm)],[fact_Nitpick_Onat__lcm__def]) ).
fof(i_0_5477,plain,
! [X32300,X32301,X32302,X32303,X32304,X32305] : c_List_Ofoldr(X32305,X32304,X32303,hAPP(hAPP(c_List_Olist_OCons(X32305),X32302),X32301),X32300) = hAPP(hAPP(X32303,X32302),c_List_Ofoldr(X32305,X32304,X32303,X32301,X32300)),
inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I2_J]) ).
fof(i_0_5478,plain,
! [X6,X25,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X6)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X25)),X172)) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__not__sym]) ).
fof(i_0_5479,plain,
! [X6,X25,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X6)),X172))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X25)),X172)) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__asym]) ).
fof(i_0_5480,plain,
! [X195,X44,X95] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X95,X44),X195))
<=> ( X95 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X195)),X44)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X195))
& ( X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X195) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X44 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X195)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X195)),X44)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X195)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X195)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__def]) ).
fof(i_0_5481,plain,
! [X25,X125,X24,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X25))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of1]) ).
fof(i_0_5482,plain,
! [X25,X125,X24,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X25))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of1]) ).
fof(i_0_5483,plain,
! [X21178] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X21178)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21178))),
inference(variable_rename,[status(thm)],[fact_minus__Bit1]) ).
fof(i_0_5484,plain,
! [X46,X44,X45,X23,X24] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X45,X44,X46)
=> ( ( X46 = X45
=> hBOOL(hAPP(X24,X45)) )
=> ~ ( hBOOL(hAPP(X24,X45))
=> ! [X62] :
( c_Natural_Oevaln(X23,X45,X44,X62)
=> ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X62,X44,X46) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__WHILE__case]) ).
fof(i_0_5485,plain,
! [X72,X47,X43,X41,X42] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X42,X41),X43,X47,X72)
<=> ( ( X72 = X43
& ~ hBOOL(hAPP(X42,X43)) )
| ( hBOOL(hAPP(X42,X43))
& ? [X62] :
( c_Natural_Oevaln(X41,X43,X47,X62)
& c_Natural_Oevaln(c_Com_Ocom_OWhile(X42,X41),X62,X47,X72) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln_Oequations_I8_J]) ).
fof(i_0_5486,plain,
! [X35,X33,X9,X48,X49] :
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X49,X48),X9,X33,X35)
=> ~ ! [X62] :
( c_Natural_Oevaln(X49,X9,X33,X62)
=> ~ c_Natural_Oevaln(X48,X62,X33,X35) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I4_J]) ).
fof(i_0_5487,plain,
! [X30107,X30108] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X30108),X30107)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30108),X30107)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30108),X30107))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X30108),X30107)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq])]) ).
fof(i_0_5488,plain,
! [X172,X149,X39,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X39),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X149),X172)))
=> ~ ! [X3] :
( X39 = hAPP(c_Relation_OImage(X7,X7,X172),hAPP(hAPP(c_Set_Oinsert(X7),X3),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X3),X149)) ) ),
inference(fof_simplification,[status(thm)],[fact_quotientE]) ).
fof(i_0_5489,plain,
! [X22229,X22230] :
( ( X22230 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Divides_Odivmod__nat(X22229,X22230) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22229) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22229),X22230))
| c_Divides_Odivmod__nat(X22229,X22230) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22229) )
& ( X22230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22229),X22230))
| c_Divides_Odivmod__nat(X22229,X22230) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22229),X22230),X22230)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__if])])]) ).
fof(i_0_5490,plain,
! [X22983,X22984] : c_Divides_Odivmod__nat(X22984,X22983) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X22984,X22983)),
inference(variable_rename,[status(thm)],[fact_divmod__nat__def]) ).
fof(i_0_5491,plain,
! [X21169] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21169)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21169),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21169),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21169)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I4_J])]) ).
fof(i_0_5492,plain,
! [X326,X327,X328,X329,X7] :
( hAPP(hAPP(c_List_Oappend(X7),X329),X328) = hAPP(hAPP(c_List_Oappend(X7),X327),X326)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X329)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X327)))
=> ( X329 = hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X329)),X327)
& X328 = hAPP(hAPP(c_List_Oappend(X7),hAPP(hAPP(c_List_Odrop(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X329)),X327)),X326) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X329)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X327)))
=> ( hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X327)),X329) = X327
& hAPP(hAPP(c_List_Oappend(X7),hAPP(hAPP(c_List_Odrop(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X327)),X329)),X328) = X326 ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_append__eq__append__conv__if]) ).
fof(i_0_5493,plain,
! [X21173] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21173)),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21173),c_Int_OMin)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21173),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21173)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J])]) ).
fof(i_0_5494,plain,
! [X21190] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21190)),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21190),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21190),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21190)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])]) ).
fof(i_0_5495,plain,
! [X21171] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21171)),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21171),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21171),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21171)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])]) ).
fof(i_0_5496,plain,
! [X21175] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21175)),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21175),c_Int_OMin)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21175),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21175)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J])]) ).
fof(i_0_5497,plain,
! [X21177] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21177))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21177))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21177)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21177)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1])]) ).
fof(i_0_5498,plain,
! [X21196,X21197] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21197),c_Groups_Oone__class_Oone(X21197)),hAPP(c_Int_Onumber__class_Onumber__of(X21197),X21196)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21196))
| ~ class_Int_Onumber__ring(X21197)
| ~ class_Rings_Olinordered__idom(X21197) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21196))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21197),c_Groups_Oone__class_Oone(X21197)),hAPP(c_Int_Onumber__class_Onumber__of(X21197),X21196)))
| ~ class_Int_Onumber__ring(X21197)
| ~ class_Rings_Olinordered__idom(X21197) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I2_J])])]) ).
fof(i_0_5499,plain,
! [X21200,X21201] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21201),c_Groups_Oone__class_Oone(X21201)),hAPP(c_Int_Onumber__class_Onumber__of(X21201),X21200)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21200))
| ~ class_Int_Onumber__ring(X21201)
| ~ class_Rings_Olinordered__idom(X21201) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21200))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21201),c_Groups_Oone__class_Oone(X21201)),hAPP(c_Int_Onumber__class_Onumber__of(X21201),X21200)))
| ~ class_Int_Onumber__ring(X21201)
| ~ class_Rings_Olinordered__idom(X21201) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I2_J])])]) ).
fof(i_0_5500,plain,
! [X125,X24,X25,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of1]) ).
fof(i_0_5501,plain,
! [X125,X24,X25,X7] :
( ( class_Fields_Olinordered__field__inverse__zero(X7)
& class_Int_Onumber(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125))),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of1]) ).
fof(i_0_5502,plain,
! [X105,X7,X149,X127,X6,X155] :
( ( ~ hBOOL(hAPP(hAPP(X155,X6),X127))
=> hBOOL(hAPP(hAPP(X149,X6),X127)) )
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X149),X155),X6),X127)) ),
inference(fof_simplification,[status(thm)],[fact_sup2CI]) ).
fof(i_0_5503,plain,
! [X191,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),c_Wellfounded_Oacc(X7,X191)))
=> ~ ! [X154] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X154),X6)),X191))
=> hBOOL(hAPP(hAPP(c_member(X7),X154),c_Wellfounded_Oacc(X7,X191))) ) ),
inference(fof_simplification,[status(thm)],[fact_not__acc__down]) ).
fof(i_0_5504,plain,
! [X24,X149,X7] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(X7,X24,X149) = X24 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(X7,X24,X149) = c_HOL_OThe(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
inference(fof_simplification,[status(thm)],[fact_flat__lub__def]) ).
fof(i_0_5505,plain,
! [X46,X45,X23,X24] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X45),X46))
=> ( ( X46 = X45
=> hBOOL(hAPP(X24,X45)) )
=> ~ ( hBOOL(hAPP(X24,X45))
=> ! [X62] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X45),X62))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X62),X46)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc__WHILE__case]) ).
fof(i_0_5506,plain,
! [X61,X43,X41,X42] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X42,X41)),X43),X61))
<=> ( ( X61 = X43
& ~ hBOOL(hAPP(X42,X43)) )
| ( hBOOL(hAPP(X42,X43))
& ? [X62] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X41),X43),X62))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X42,X41)),X62),X61)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc_Oequations_I8_J]) ).
fof(i_0_5507,plain,
! [X21398,X21399] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21399)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21398))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21399))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21398)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21399)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21399)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21398))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21399))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21398)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21399)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5179])]) ).
fof(i_0_5508,plain,
! [X30559,X30560] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X30560,X30560)),hAPP(hAPP(c_Product__Type_OPair(X30560,X30560),esk375_2(X30559,X30560)),esk375_2(X30559,X30560))),c_Transitive__Closure_Otrancl(X30560,X30559)))
| c_Wellfounded_Oacyclic(X30560,X30559) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5180])])]) ).
fof(i_0_5509,plain,
! [X172,X292,X7] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_ONil(X7)),X292)),c_List_Olistrel1(X7,X172))),
inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1]) ).
fof(i_0_5510,plain,
! [X172,X293,X7] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),c_List_Olist_ONil(X7)),X293)),c_List_Olex(X7,X172))),
inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex]) ).
fof(i_0_5511,plain,
! [X127,X2,X105,X149,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Set_Oimage(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X127)),X149) = hAPP(hAPP(c_Set_Oinsert(X105),X127),hAPP(c_Set_Oimage(X7,X105,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Set_Oimage(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X127)),X149) = hAPP(c_Set_Oimage(X7,X105,X2),X149) ) ),
inference(fof_simplification,[status(thm)],[fact_fun__upd__image]) ).
fof(i_0_5512,plain,
! [X172,X292,X7] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),c_List_Olist_ONil(X7))),c_List_Olistrel1(X7,X172))),
inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil]) ).
fof(i_0_5513,plain,
! [X172,X6,X7] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X6),c_List_Olist_ONil(X7))),c_List_Olexord(X7,X172))),
inference(fof_simplification,[status(thm)],[fact_lexord__Nil__right]) ).
fof(i_0_5514,plain,
! [X172,X292,X7] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7),tc_List_Olist(X7))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X292),c_List_Olist_ONil(X7))),c_List_Olex(X7,X172))),
inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex]) ).
fof(i_0_5515,plain,
! [X33602,X33603,X33604] :
( ~ class_Groups_Omonoid__add(X33604)
| hAPP(c_List_Ofoldl(X33604,X33604,c_Groups_Oplus__class_Oplus(X33604),X33603),X33602) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33604),X33603),c_List_Ofoldr(X33604,X33604,c_Groups_Oplus__class_Oplus(X33604),X33602,c_Groups_Ozero__class_Ozero(X33604))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma])]) ).
fof(i_0_5516,plain,
! [X30266,X30267,X30268] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30268,X30268)),hAPP(hAPP(c_Product__Type_OPair(X30268,X30268),X30267),X30266)),c_Relation_OId(X30268)))
| X30267 = X30266 )
& ( X30267 != X30266
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30268,X30268)),hAPP(hAPP(c_Product__Type_OPair(X30268,X30268),X30267),X30266)),c_Relation_OId(X30268))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv])]) ).
fof(i_0_5517,plain,
! [X6,X288,X7,X105] :
( hAPP(c_Map_Omap__of(X105,X7,X288),X6) = c_Option_Ooption_ONone(X7)
<=> ~ hBOOL(hAPP(hAPP(c_member(X105),X6),hAPP(c_Set_Oimage(tc_prod(X105,X7),X105,c_Product__Type_Ofst(X105,X7)),hAPP(c_List_Oset(tc_prod(X105,X7)),X288)))) ),
inference(fof_simplification,[status(thm)],[fact_map__of__eq__None__iff]) ).
fof(i_0_5518,plain,
! [X21316] :
( ~ class_Int_Onumber__ring(X21316)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21316),c_Groups_Oone__class_Oone(X21316)),c_Groups_Oone__class_Oone(X21316)) = hAPP(c_Int_Onumber__class_Onumber__of(X21316),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__add__one__is__two])]) ).
fof(i_0_5519,plain,
! [X293,X2,X105,X292,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hAPP(c_Map_Omap__upds(X7,X105,X2,X292,X293),X6) = hAPP(X2,X6) ),
inference(fof_simplification,[status(thm)],[fact_map__upds__apply__nontin]) ).
fof(i_0_5520,plain,
! [X1,X2,X105,X149,X25,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(c_Fun_Ooverride__on(X7,X105,X2,X1,X149),X25) = hAPP(X1,X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(c_Fun_Ooverride__on(X7,X105,X2,X1,X149),X25) = hAPP(X2,X25) ) ),
inference(fof_simplification,[status(thm)],[fact_override__on__def]) ).
fof(i_0_5521,plain,
! [X21830,X21831] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21831),X21830))
| c_Divides_Odivmod__nat(X21830,X21831) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21830),X21831)),X21831))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21830),X21831),X21831)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__step])]) ).
fof(i_0_5522,plain,
! [X35,X9,X48,X49] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X49,X48)),X9),X35))
=> ~ ! [X62] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X49),X9),X62))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X48),X62),X35)) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc__elim__cases_I4_J]) ).
fof(i_0_5523,plain,
! [X34292,X34293,X34294,X34295,X34296] : hAPP(c_List_Ofoldl(X34296,X34295,X34294,X34293),X34292) = c_List_Ofoldr(X34295,X34296,hAPP(c_COMBC(X34296,X34295,X34296),X34294),hAPP(c_List_Orev(X34295),X34292),X34293),
inference(variable_rename,[status(thm)],[fact_foldl__foldr]) ).
fof(i_0_5524,plain,
! [X1,X2,X105,X149,X25,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(c_Fun_Ooverride__on(X7,X105,X2,X1,X149),X25) = hAPP(X2,X25) ),
inference(fof_simplification,[status(thm)],[fact_override__on__apply__notin]) ).
fof(i_0_5525,plain,
! [X1,X149,X215,X26,X2,X105,X7] :
( c_Big__Operators_Ocomm__monoid__big(X7,X105,X2,X26,X215)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> hAPP(hAPP(X215,X1),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X105,X2),X1),X26),X149) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> hAPP(hAPP(X215,X1),X149) = X26 ) ) ),
inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).
fof(i_0_5526,plain,
! [X25545,X25546,X25547,X25548] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25548,X25548)),hAPP(hAPP(c_Product__Type_OPair(X25548,X25548),X25547),X25546)),hAPP(c_Wellfounded_Omeasure(X25548),X25545)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X25545,X25547)),hAPP(X25545,X25546))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X25545,X25547)),hAPP(X25545,X25546)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X25548,X25548)),hAPP(hAPP(c_Product__Type_OPair(X25548,X25548),X25547),X25546)),hAPP(c_Wellfounded_Omeasure(X25548),X25545))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).
fof(i_0_5527,plain,
! [X26412] : c_Wellfounded_Omeasure(X26412) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X26412),c_Wellfounded_Oless__than),
inference(variable_rename,[status(thm)],[fact_measure__def]) ).
fof(i_0_5528,plain,
! [X155,X149,X24,X25,X105,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X105)),hAPP(hAPP(c_Product__Type_OPair(X7,X105),X25),X24)),hAPP(hAPP(c_Product__Type_OSigma(X7,X105),X149),X155)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ~ hBOOL(hAPP(hAPP(c_member(X105),X24),hAPP(X155,X25))) ) ),
inference(fof_simplification,[status(thm)],[fact_SigmaE2]) ).
fof(i_0_5529,plain,
! [X34255,X34256,X34257,X34258] : hAPP(hAPP(c_List_Omap(X34258,X34257),X34256),c_List_Oconcat(X34258,X34255)) = c_List_Oconcat(X34257,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34258),tc_List_Olist(X34257)),hAPP(c_List_Omap(X34258,X34257),X34256)),X34255)),
inference(variable_rename,[status(thm)],[fact_map__concat]) ).
fof(i_0_5530,plain,
! [X21274,X21275] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X21275)),c_Int_OBit0(X21274)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21275),X21274)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I9_J]) ).
fof(i_0_5531,plain,
! [X21271,X21272] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X21272)),c_Int_OBit0(X21271)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21272),X21271)),
inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0]) ).
fof(i_0_5532,plain,
! [X292,X105,X6,X2,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X6)),hAPP(c_Set_Oimage(X105,X7,X2),hAPP(c_List_Oset(X105),X292))))
=> c_List_Olinorder__class_Oinsort__insert__key(X105,X7,X2,X6,X292) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),X292) ) ),
inference(fof_simplification,[status(thm)],[fact_insort__insert__insort__key]) ).
fof(i_0_5533,plain,
! [X30444,X30445,X30446] :
( ( ~ c_Relation_Ototal__on(X30446,X30445,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X30446,X30446),tc_HOL_Obool)),X30444),c_Relation_OId(X30446)))
| c_Relation_Ototal__on(X30446,X30445,X30444) )
& ( ~ c_Relation_Ototal__on(X30446,X30445,X30444)
| c_Relation_Ototal__on(X30446,X30445,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X30446,X30446),tc_HOL_Obool)),X30444),c_Relation_OId(X30446))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id])]) ).
fof(i_0_5534,plain,
! [X21208,X21209] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X21209))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21208)),X21209) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21209),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__eq__diff__pred])]) ).
fof(i_0_5535,plain,
! [X21299,X21300] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X21300)),X21299) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21300),X21299))),X21299),
inference(variable_rename,[status(thm)],[fact_mult__Bit1]) ).
fof(i_0_5536,plain,
! [X21311] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21311))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21311))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21311))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21311))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of1])])]) ).
fof(i_0_5537,plain,
! [X21307,X21308] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X21308)),c_Int_OBit1(X21307)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21308),c_Int_Osucc(X21307))),
inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit1]) ).
fof(i_0_5538,plain,
! [X21261,X21262] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21262)),c_Int_OBit1(X21261)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21262),X21261)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21262),X21261))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21262)),c_Int_OBit1(X21261))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])]) ).
fof(i_0_5539,plain,
! [X21259,X21260] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21260)),c_Int_OBit1(X21259)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21260),X21259)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21260),X21259))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21260)),c_Int_OBit1(X21259))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J])]) ).
fof(i_0_5540,plain,
! [X21297,X21298] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21298)),c_Int_OBit1(X21297)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21298),X21297)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21298),X21297))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21298)),c_Int_OBit1(X21297))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])]) ).
fof(i_0_5541,plain,
! [X21295,X21296] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21296)),c_Int_OBit1(X21295)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21296),X21295)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21296),X21295))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21296)),c_Int_OBit1(X21295))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J])]) ).
fof(i_0_5542,plain,
! [X21881] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21881)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21881)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21881)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21881)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21881)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5181])]) ).
fof(i_0_5543,plain,
! [X30131,X30132] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30132,X30132)),c_Transitive__Closure_Otrancl(X30132,X30131)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30132,X30132)),X30131)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30132,X30132)),X30131))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30132,X30132)),c_Transitive__Closure_Otrancl(X30132,X30131))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__trancl])]) ).
fof(i_0_5544,plain,
! [X155,X25,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X155))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__Diff__insert]) ).
fof(i_0_5545,plain,
! [X34263,X34264] : hAPP(c_List_Orev(X34264),c_List_Oconcat(X34264,X34263)) = c_List_Oconcat(X34264,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34264),tc_List_Olist(X34264)),c_List_Orev(X34264)),hAPP(c_List_Orev(tc_List_Olist(X34264)),X34263))),
inference(variable_rename,[status(thm)],[fact_rev__concat]) ).
fof(i_0_5546,plain,
! [X26,X1,X25,X149,X7,X105] :
( class_Groups_Oab__semigroup__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),X26),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(X1,X25)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),X26),X149)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fold__image__insert]) ).
fof(i_0_5547,plain,
! [X34216,X34217,X34218] : hAPP(c_List_Ofilter(X34218,X34217),c_List_Oconcat(X34218,X34216)) = c_List_Oconcat(X34218,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34218),tc_List_Olist(X34218)),c_List_Ofilter(X34218,X34217)),X34216)),
inference(variable_rename,[status(thm)],[fact_filter__concat]) ).
fof(i_0_5548,plain,
! [X25,X23,X24,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),X25))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq]) ).
fof(i_0_5549,plain,
! [X25,X23,X24,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)),X25))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X25)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).
fof(i_0_5550,plain,
! [X33508,X33509,X33510] :
( ( ~ hBOOL(hAPP(c_List_Odistinct(X33510),hAPP(c_List_Orotate(X33510,X33509),X33508)))
| hBOOL(hAPP(c_List_Odistinct(X33510),X33508)) )
& ( ~ hBOOL(hAPP(c_List_Odistinct(X33510),X33508))
| hBOOL(hAPP(c_List_Odistinct(X33510),hAPP(c_List_Orotate(X33510,X33509),X33508))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rotate])]) ).
fof(i_0_5551,plain,
! [X127,X191,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_Relation_ODomain(X7,X7),X191)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X6),X127)),c_Transitive__Closure_Ortrancl(X7,X191)))
<=> X6 = X127 ) ),
inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl]) ).
fof(i_0_5552,plain,
! [X21269,X21270] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X21270)),c_Int_OBit1(X21269)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21270),X21269)),
inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1]) ).
fof(i_0_5553,plain,
! [X1,X149,X215,X26,X2,X105,X7] :
( c_Big__Operators_Ocomm__monoid__big(X7,X105,X2,X26,X215)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X105),X149))
=> hAPP(hAPP(X215,X1),X149) = X26 ) ),
inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).
fof(i_0_5554,plain,
! [X21149,X21150] :
( ~ class_Int_Onumber__ring(X21150)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21150),hAPP(c_Int_Onumber__class_Onumber__of(X21150),X21149)),c_Groups_Oone__class_Oone(X21150)) = hAPP(c_Int_Onumber__class_Onumber__of(X21150),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21149),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I2_J])]) ).
fof(i_0_5555,plain,
! [X292,X6,X2,X7,X105] :
( class_Orderings_Olinorder(X105)
=> ( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X105,X2),X6),X292)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
& hBOOL(hAPP(c_List_Odistinct(X7),X292)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_distinct__insort]) ).
fof(i_0_5556,plain,
! [X21147,X21148] :
( ~ class_Int_Onumber__ring(X21148)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21148),c_Groups_Oone__class_Oone(X21148)),hAPP(c_Int_Onumber__class_Onumber__of(X21148),X21147)) = hAPP(c_Int_Onumber__class_Onumber__of(X21148),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21147))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J])]) ).
fof(i_0_5557,plain,
! [X30123,X30124,X30125] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30125,X30125)),X30124),X30123))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30125,X30125)),X30124),c_Transitive__Closure_Otrancl(X30125,X30123))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])]) ).
fof(i_0_5558,plain,
! [X34228,X34229,X34230] : c_List_Oconcat(X34230,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34230)),X34229),X34228)) = hAPP(hAPP(c_List_Oappend(X34230),X34229),c_List_Oconcat(X34230,X34228)),
inference(variable_rename,[status(thm)],[fact_concat_Osimps_I2_J]) ).
fof(i_0_5559,plain,
! [X21206,X21207] :
( ~ class_Int_Onumber__ring(X21207)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21207),c_Groups_Oone__class_Oone(X21207)),hAPP(c_Int_Onumber__class_Onumber__of(X21207),X21206)) = hAPP(c_Int_Onumber__class_Onumber__of(X21207),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21206)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).
fof(i_0_5560,plain,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X23,X136)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X23),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),X136))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),X25))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),X136)) ) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X23),X136)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).
fof(i_0_5561,plain,
! [X34120,X34121] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34121)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34120)))
| c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34121),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34120)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34121)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34121)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34120))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34121)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34120)))
| c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34121),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34120)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5182])]) ).
fof(i_0_5562,plain,
! [X215,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X6),X215))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),X6),X215)))
=> ! [X206] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X206),hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),X6),X215)))
=> ( X3 != X206
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3),X206) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X6),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X215)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__partition]) ).
fof(i_0_5563,plain,
! [X30189,X30190] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30190,X30190),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30190,X30189)),c_Relation_OId(X30190)) = c_Transitive__Closure_Ortrancl(X30190,X30189),
inference(variable_rename,[status(thm)],[fact_reflcl__trancl]) ).
fof(i_0_5564,plain,
! [X86,X301,X300,X87,X33] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Olist__update(X87,hAPP(hAPP(c_List_Oappend(X87),X300),X301)),X33),X86) = hAPP(hAPP(c_List_Oappend(X87),hAPP(hAPP(c_List_Olist__update(X87,X300),X33),X86)),X301) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Olist__update(X87,hAPP(hAPP(c_List_Oappend(X87),X300),X301)),X33),X86) = hAPP(hAPP(c_List_Oappend(X87),X300),hAPP(hAPP(c_List_Olist__update(X87,X301),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300))),X86)) ) ),
inference(fof_simplification,[status(thm)],[fact_list__update__append]) ).
fof(i_0_5565,plain,
! [X23,X24,X25,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__divide__eq]) ).
fof(i_0_5566,plain,
! [X23,X24,X25,X7] :
( class_Fields_Olinordered__field__inverse__zero(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),X24),X23)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23)),X24)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X23))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X25),X23))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X23),c_Groups_Ozero__class_Ozero(X7)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),c_Groups_Ozero__class_Ozero(X7))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).
fof(i_0_5567,plain,
! [X21183,X21184] :
( ~ class_Int_Onumber__ring(X21184)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21184),hAPP(c_Int_Onumber__class_Onumber__of(X21184),c_Int_OBit1(c_Int_OPls))),X21183) = X21183 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1])]) ).
fof(i_0_5568,plain,
! [X33534,X33535,X33536] : c_List_Orotate(X33536,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33535),X33534)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X33536),tc_List_Olist(X33536),tc_List_Olist(X33536),c_List_Orotate(X33536,X33535)),c_List_Orotate(X33536,X33534)),
inference(variable_rename,[status(thm)],[fact_rotate__add]) ).
fof(i_0_5569,plain,
! [X136,X23,X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X23,X136)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X23),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X24),X136)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__subset__iff]) ).
fof(i_0_5570,plain,
! [X21198,X21199] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21199),hAPP(c_Int_Onumber__class_Onumber__of(X21199),X21198)),c_Groups_Oone__class_Oone(X21199)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21198),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X21199)
| ~ class_Rings_Olinordered__idom(X21199) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21198),c_Int_OBit1(c_Int_OPls)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21199),hAPP(c_Int_Onumber__class_Onumber__of(X21199),X21198)),c_Groups_Oone__class_Oone(X21199)))
| ~ class_Int_Onumber__ring(X21199)
| ~ class_Rings_Olinordered__idom(X21199) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I4_J])])]) ).
fof(i_0_5571,plain,
! [X21202,X21203] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21203),hAPP(c_Int_Onumber__class_Onumber__of(X21203),X21202)),c_Groups_Oone__class_Oone(X21203)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21202),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X21203)
| ~ class_Rings_Olinordered__idom(X21203) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21202),c_Int_OBit1(c_Int_OPls)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21203),hAPP(c_Int_Onumber__class_Onumber__of(X21203),X21202)),c_Groups_Oone__class_Oone(X21203)))
| ~ class_Int_Onumber__ring(X21203)
| ~ class_Rings_Olinordered__idom(X21203) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I4_J])])]) ).
fof(i_0_5572,plain,
! [X30647,X30648] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30648,X30648)),X30647),c_Relation_OId(X30648)))
| X30647 = hAPP(hAPP(c_Product__Type_OPair(X30648,X30648),esk388_2(X30647,X30648)),esk388_2(X30647,X30648)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IdE])])]) ).
fof(i_0_5573,plain,
! [X47,X43,X41,X61,X42] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X42,X61,X41)),X43),X47))
<=> ( ( hBOOL(hAPP(X42,X43))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X61),X43),X47)) )
| ( ~ hBOOL(hAPP(X42,X43))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X41),X43),X47)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc_Oequations_I6_J]) ).
fof(i_0_5574,plain,
! [X47,X43,X61,X41,X42] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X42,X41,X61)),X43),X47))
<=> ( ( hBOOL(hAPP(X42,X43))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X41),X43),X47)) )
| ( ~ hBOOL(hAPP(X42,X43))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X61),X43),X47)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc_Oequations_I5_J]) ).
fof(i_0_5575,plain,
! [X46,X45,X56,X57,X24] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X24,X57,X56)),X45),X46))
=> ( ( hBOOL(hAPP(X24,X45))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X57),X45),X46)) )
=> ~ ( ~ hBOOL(hAPP(X24,X45))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X56),X45),X46)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc__elim__cases_I5_J]) ).
fof(i_0_5576,plain,
! [X21191] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X21191)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X21191)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I4_J]) ).
fof(i_0_5577,plain,
! [X30179,X30180] : hBOOL(hAPP(hAPP(c_member(tc_prod(X30180,X30180)),hAPP(hAPP(c_Product__Type_OPair(X30180,X30180),X30179),X30179)),c_Relation_OId(X30180))),
inference(variable_rename,[status(thm)],[fact_IdI]) ).
fof(i_0_5578,plain,
! [X34269,X34270,X34271] : hAPP(c_List_Ofoldl(tc_List_Olist(X34271),tc_List_Olist(X34271),c_List_Oappend(X34271),X34270),X34269) = hAPP(hAPP(c_List_Oappend(X34271),X34270),c_List_Oconcat(X34271,X34269)),
inference(variable_rename,[status(thm)],[fact_foldl__conv__concat]) ).
fof(i_0_5579,plain,
! [X21276,X21277] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X21277)),c_Int_OBit1(X21276)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21277),X21276)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I10_J]) ).
fof(i_0_5580,plain,
! [X292,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> c_List_Olinorder__class_Oinsort__insert__key(X7,X7,c_COMBI(X7),X6,X292) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7)),X6),X292) ) ),
inference(fof_simplification,[status(thm)],[fact_insort__insert__insort]) ).
fof(i_0_5581,plain,
! [X172,X7] :
( c_Relation_Oirrefl(X7,X172)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),X172)) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).
fof(i_0_5582,plain,
! [X25,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X25)),X172)) ),
inference(fof_simplification,[status(thm)],[fact_wf__not__refl]) ).
fof(i_0_5583,plain,
! [X25,X172,X7] :
( c_Wellfounded_Owf(X7,X172)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X25)),X172)) ),
inference(fof_simplification,[status(thm)],[fact_wf__irrefl]) ).
fof(i_0_5584,plain,
! [X30209,X30210] : c_Transitive__Closure_Ortrancl(X30210,X30209) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30210,X30210),tc_HOL_Obool)),c_Relation_OId(X30210)),hAPP(hAPP(c_Relation_Orel__comp(X30210,X30210,X30210),c_Transitive__Closure_Ortrancl(X30210,X30209)),X30209)),
inference(variable_rename,[status(thm)],[fact_rtrancl__unfold]) ).
fof(i_0_5585,plain,
! [X25,X155,X149,X105,X24,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X105,tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X24),hAPP(X155,X25)))
=> ~ hBOOL(hAPP(hAPP(c_member(X105),X25),X149)) ) ),
inference(fof_simplification,[status(thm)],[fact_INT__E]) ).
fof(i_0_5586,plain,
! [X21170] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X21170)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21170)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21170))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X21170))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])]) ).
fof(i_0_5587,plain,
! [X21189] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X21189)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21189)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21189))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X21189))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])]) ).
fof(i_0_5588,plain,
! [X21174] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X21174)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X21174)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X21174))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X21174))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J])]) ).
fof(i_0_5589,plain,
! [X21176] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X21176)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21176)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21176))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X21176))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J])]) ).
fof(i_0_5590,plain,
! [X21858,X21859,X21860] :
( ~ class_Int_Onumber__ring(X21860)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21860),hAPP(c_Int_Onumber__class_Onumber__of(X21860),X21859)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21858))) = hAPP(hAPP(c_HOL_OLet(X21860,X21860),hAPP(hAPP(c_Power_Opower__class_Opower(X21860),hAPP(c_Int_Onumber__class_Onumber__of(X21860),X21859)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21858))),hAPP(hAPP(c_COMBS(X21860,X21860,X21860),c_Groups_Otimes__class_Otimes(X21860)),c_COMBI(X21860))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of])]) ).
fof(i_0_5591,plain,
! [X6,X127,X149,X2,X105,X7] :
( c_Fun_Oinj__on(X7,X105,X2,X149)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X105),X127),hAPP(c_Set_Oimage(X7,X105,X2),X149)))
=> c_Fun_Oinj__on(X7,X105,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X6),X127),X149) ) ),
inference(fof_simplification,[status(thm)],[fact_inj__on__fun__updI]) ).
fof(i_0_5592,plain,
! [X6,X127,X23] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X127))
=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6),X127)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X23)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X127),X23)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X127))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X127))
=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6),X127)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X127))
=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6),X127)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_image__minus__const__atLeastLessThan__nat]) ).
fof(i_0_5593,plain,
! [X33605,X33606] :
( ~ class_Groups_Omonoid__add(X33606)
| hAPP(c_List_Ofoldl(X33606,X33606,c_Groups_Oplus__class_Oplus(X33606),c_Groups_Ozero__class_Ozero(X33606)),X33605) = c_List_Ofoldr(X33606,X33606,c_Groups_Oplus__class_Oplus(X33606),X33605,c_Groups_Ozero__class_Ozero(X33606)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1])]) ).
fof(i_0_5594,plain,
! [X34172,X34173,X34174,X34175,X34176] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34176),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X34175),X34174)))
| hAPP(hAPP(c_List_Onth(X34173),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X34173),X34172),c_List_Oupt(X34174,X34175))),X34176) = hAPP(X34172,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34174),X34176)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map__upt])]) ).
fof(i_0_5595,plain,
! [X33511,X33512,X33513,X33514] : hAPP(c_List_Orotate(X33514,X33513),hAPP(c_List_Orotate(X33514,X33512),X33511)) = hAPP(c_List_Orotate(X33514,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33513),X33512)),X33511),
inference(variable_rename,[status(thm)],[fact_rotate__rotate]) ).
fof(i_0_5596,plain,
! [X33564,X33565,X33566] :
( ~ class_Groups_Oab__semigroup__add(X33566)
| c_List_Ofoldr(X33566,X33566,c_Groups_Oplus__class_Oplus(X33566),X33565,X33564) = hAPP(c_List_Ofoldl(X33566,X33566,c_Groups_Oplus__class_Oplus(X33566),X33564),X33565) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__conv__foldl])]) ).
fof(i_0_5597,plain,
! [X2,X105,X292,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hAPP(c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Ozip(X7,X105),X292),hAPP(hAPP(c_List_Omap(X7,X105),X2),X292))),X6) = hAPP(c_Option_Ooption_OSome(X105),hAPP(X2,X6)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hAPP(c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Ozip(X7,X105),X292),hAPP(hAPP(c_List_Omap(X7,X105),X2),X292))),X6) = c_Option_Ooption_ONone(X105) ) ),
inference(fof_simplification,[status(thm)],[fact_map__of__zip__map]) ).
fof(i_0_5598,plain,
! [X33485,X33486,X33487] : hAPP(c_List_Orotate(X33487,X33486),X33485) = hAPP(c_List_Orotate(X33487,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33486,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33487)),X33485))),X33485),
inference(variable_rename,[status(thm)],[fact_rotate__conv__mod]) ).
fof(i_0_5599,plain,
! [X21179,X21180] :
( ~ class_Int_Onumber__ring(X21180)
| ~ class_Int_Oring__char__0(X21180)
| ~ c_Int_Oiszero(X21180,hAPP(c_Int_Onumber__class_Onumber__of(X21180),c_Int_OBit1(X21179))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5183])]) ).
fof(i_0_5600,plain,
! [X127,X95,X105,X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Set_Oimage(X7,tc_Option_Ooption(X105),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X105)),X95),X6),hAPP(c_Option_Ooption_OSome(X105),X127))),X149) = hAPP(c_Set_Oimage(X7,tc_Option_Ooption(X105),X95),X149) ),
inference(fof_simplification,[status(thm)],[fact_image__map__upd]) ).
fof(i_0_5601,plain,
! [X21283] : c_Int_Opred(c_Int_OBit0(X21283)) = c_Int_OBit1(c_Int_Opred(X21283)),
inference(variable_rename,[status(thm)],[fact_pred__Bit0]) ).
fof(i_0_5602,plain,
! [X25,X2,X149,X7,X105] :
( class_Fields_Ofield(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( hAPP(X2,X25) != c_Groups_Ozero__class_Ozero(X105)
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149)),hAPP(X2,X25)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__diff1]) ).
fof(i_0_5603,plain,
! [X30320,X30321] : c_Relation_Orefl__on(X30321,c_Orderings_Otop__class_Otop(tc_fun(X30321,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30321,X30321),tc_HOL_Obool)),X30320),c_Relation_OId(X30321))),
inference(variable_rename,[status(thm)],[fact_refl__reflcl]) ).
fof(i_0_5604,plain,
! [X2,X25,X149,X7,X105] :
( class_Groups_Oab__group__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X105),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149)),hAPP(X2,X25)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__diff1]) ).
fof(i_0_5605,plain,
! [X34302,X34303] : hAPP(c_List_Oset(X34303),c_List_Oconcat(X34303,X34302)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X34303),tc_fun(X34303,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X34303)),X34302)),c_List_Oset(X34303)),
inference(variable_rename,[status(thm)],[fact_set__concat]) ).
fof(i_0_5606,plain,
! [X34219,X34220] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34220)),c_List_Oconcat(X34220,X34219)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34220),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34220))),X34219)),
inference(variable_rename,[status(thm)],[fact_length__concat]) ).
fof(i_0_5607,plain,
! [X25,X24,X155,X149,X105,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X105,tc_HOL_Obool)),X149),X155),X24))
=> ( ~ hBOOL(hAPP(hAPP(X155,X25),X24))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149)) ) ),
inference(fof_simplification,[status(thm)],[fact_INF1__E]) ).
fof(i_0_5608,plain,
! [X34355,X34356,X34357] :
( ( X34356 != c_List_Olist_ONil(X34357)
| c_List_Ofoldr(X34357,X34357,c_Orderings_Oord__class_Omax(X34357),X34356,X34355) = X34355
| ~ c_List_Olinorder__class_Osorted(X34357,hAPP(c_List_Orev(X34357),X34356))
| ~ class_Orderings_Olinorder(X34357) )
& ( X34356 = c_List_Olist_ONil(X34357)
| c_List_Ofoldr(X34357,X34357,c_Orderings_Oord__class_Omax(X34357),X34356,X34355) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X34357),hAPP(hAPP(c_List_Onth(X34357),X34356),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X34355)
| ~ c_List_Olinorder__class_Osorted(X34357,hAPP(c_List_Orev(X34357),X34356))
| ~ class_Orderings_Olinorder(X34357) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__max__sorted])])]) ).
fof(i_0_5609,plain,
! [X38,X292,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> ( ~ hBOOL(hAPP(X38,X6))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(c_List_Ofilter(X7,X38),X292))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292))) ) ),
inference(fof_simplification,[status(thm)],[fact_length__filter__less]) ).
fof(i_0_5610,plain,
! [X30227,X30228] : c_Transitive__Closure_Ortrancl(X30228,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30228,X30228),tc_HOL_Obool)),X30227),c_Relation_OId(X30228))) = c_Transitive__Closure_Ortrancl(X30228,X30227),
inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl]) ).
fof(i_0_5611,plain,
! [X30254,X30255] : c_Transitive__Closure_Ortrancl(X30255,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X30255,X30255),tc_HOL_Obool)),X30254),c_Relation_OId(X30255))) = c_Transitive__Closure_Ortrancl(X30255,X30254),
inference(variable_rename,[status(thm)],[fact_rtrancl__r__diff__Id]) ).
fof(i_0_5612,plain,
! [X30323,X30324] : c_Relation_Oirrefl(X30324,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X30324,X30324),tc_HOL_Obool)),X30323),c_Relation_OId(X30324))),
inference(variable_rename,[status(thm)],[fact_irrefl__diff__Id]) ).
fof(i_0_5613,plain,
! [X21192] :
( ~ class_Int_Onumber__ring(X21192)
| ~ c_Int_Oiszero(X21192,hAPP(c_Int_Onumber__class_Onumber__of(X21192),c_Int_OBit1(c_Int_OPls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5184])]) ).
fof(i_0_5614,plain,
! [X138,X144,X84,X71] :
( X71 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X144)),X138)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X138))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X138),X84)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X138))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X138),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X71,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X144),X138))) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__relI]) ).
fof(i_0_5615,plain,
! [X21303] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21303)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X21303)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I5_J]) ).
fof(i_0_5616,plain,
! [X2,X149,X25,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X149)),hAPP(X2,X25)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X2),X149) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__diff1__nat]) ).
fof(i_0_5617,plain,
! [X30410,X30411] :
( ~ c_Wellfounded_Owf(X30411,hAPP(c_Relation_Oconverse(X30411,X30411),X30410))
| c_Wellfounded_Owf(X30411,hAPP(c_Relation_Oconverse(X30411,X30411),c_Transitive__Closure_Otrancl(X30411,X30410))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__converse__trancl])]) ).
fof(i_0_5618,plain,
! [X2,X107,X136] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),X107))
=> c_Smallcheck_Osmall_H(X2,X136,X107) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),X107))
=> c_Smallcheck_Osmall_H(X2,X136,X107) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X2,X136,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X107)) ) ),
inference(fof_simplification,[status(thm)],[fact_small_H_Osimps]) ).
fof(i_0_5619,plain,
! [X34243,X34244,X34245,X34246,X34247] :
( ( c_List_Oconcat(X34244,X34243) != c_List_Olist_ONil(X34244)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X34244)),X34245),hAPP(c_List_Oset(tc_List_Olist(X34244)),X34243)))
| X34245 = c_List_Olist_ONil(X34244) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X34247)),esk490_2(X34246,X34247)),hAPP(c_List_Oset(tc_List_Olist(X34247)),X34246)))
| c_List_Oconcat(X34247,X34246) = c_List_Olist_ONil(X34247) )
& ( esk490_2(X34246,X34247) != c_List_Olist_ONil(X34247)
| c_List_Oconcat(X34247,X34246) = c_List_Olist_ONil(X34247) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_concat__eq__Nil__conv])])])])])]) ).
fof(i_0_5620,plain,
! [X34237,X34238,X34239,X34240,X34241] :
( ( c_List_Olist_ONil(X34238) != c_List_Oconcat(X34238,X34237)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X34238)),X34239),hAPP(c_List_Oset(tc_List_Olist(X34238)),X34237)))
| X34239 = c_List_Olist_ONil(X34238) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X34241)),esk489_2(X34240,X34241)),hAPP(c_List_Oset(tc_List_Olist(X34241)),X34240)))
| c_List_Olist_ONil(X34241) = c_List_Oconcat(X34241,X34240) )
& ( esk489_2(X34240,X34241) != c_List_Olist_ONil(X34241)
| c_List_Olist_ONil(X34241) = c_List_Oconcat(X34241,X34240) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__eq__concat__conv])])])])])]) ).
fof(i_0_5621,plain,
! [X34058,X34059,X34060] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34060),X34059))
| c_List_Oupt(X34060,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34059),X34058)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X34060,X34059)),c_List_Oupt(X34059,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34059),X34058))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__add__eq__append])]) ).
fof(i_0_5622,plain,
! [X2,X95,X44,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X95))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(c_Nat_OSuc,X44))) = c_Groups_Ozero__class_Ozero(X7) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X95))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(c_Nat_OSuc,X44))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X44))),hAPP(X2,hAPP(c_Nat_OSuc,X44))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).
fof(i_0_5623,plain,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ) ),
inference(fof_simplification,[status(thm)],[fact_UnE]) ).
fof(i_0_5624,plain,
! [X6,X149,X215,X2,X105,X7] :
( c_Finite__Set_Ofolding(X7,X105,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(c_Fun_Ocomp(X105,X105,X105,hAPP(X215,X149)),hAPP(X2,X6)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding_Oinsert]) ).
fof(i_0_5625,plain,
! [X21287] : c_Int_Osucc(c_Int_OBit1(X21287)) = c_Int_OBit0(c_Int_Osucc(X21287)),
inference(variable_rename,[status(thm)],[fact_succ__Bit1]) ).
fof(i_0_5626,plain,
! [X51,X33,X9,X79] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X79),X9,X33,X51)
=> ~ ! [X70] :
( X33 = hAPP(c_Nat_OSuc,X70)
=> ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X79)),X9,X70,X51) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I6_J]) ).
fof(i_0_5627,plain,
! [X21853,X21854,X21855] :
( ~ class_Int_Onumber__ring(X21855)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21855),X21854),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21853))) = hAPP(hAPP(c_HOL_OLet(X21855,X21855),hAPP(hAPP(c_Power_Opower__class_Opower(X21855),X21854),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21853))),hAPP(hAPP(c_COMBS(X21855,X21855,X21855),c_Groups_Otimes__class_Otimes(X21855)),c_COMBI(X21855))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even])]) ).
fof(i_0_5628,plain,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
& ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ) ),
inference(fof_simplification,[status(thm)],[fact_Diff__iff]) ).
fof(i_0_5629,plain,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ),
inference(fof_simplification,[status(thm)],[fact_DiffD2]) ).
fof(i_0_5630,plain,
! [X94,X149,X7] :
( hAPP(c_Finite__Set_Ocard(X7),X149) = hAPP(c_Nat_OSuc,X94)
<=> ? [X188,X221] :
( X149 = hAPP(hAPP(c_Set_Oinsert(X7),X188),X221)
& ~ hBOOL(hAPP(hAPP(c_member(X7),X188),X221))
& hAPP(c_Finite__Set_Ocard(X7),X221) = X94
& ( X94 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X221 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__Suc__eq]) ).
fof(i_0_5631,plain,
! [X34043,X34044,X34045] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34045),X34044)),X34043))
| hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X34044),c_List_Oupt(X34045,X34043)) = c_List_Oupt(X34045,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34045),X34044)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__upt])]) ).
fof(i_0_5632,plain,
! [X33498,X33499,X33500,X33501,X33502] : hAPP(c_List_Orotate(X33502,X33501),hAPP(hAPP(c_List_Omap(X33500,X33502),X33499),X33498)) = hAPP(hAPP(c_List_Omap(X33500,X33502),X33499),hAPP(c_List_Orotate(X33500,X33501),X33498)),
inference(variable_rename,[status(thm)],[fact_rotate__map]) ).
fof(i_0_5633,plain,
! [X30408,X30409] : c_Transitive__Closure_Otrancl(X30409,hAPP(c_Relation_Oconverse(X30409,X30409),X30408)) = hAPP(c_Relation_Oconverse(X30409,X30409),c_Transitive__Closure_Otrancl(X30409,X30408)),
inference(variable_rename,[status(thm)],[fact_trancl__converse]) ).
fof(i_0_5634,plain,
! [X293,X105,X127,X6,X2,X7] :
( class_Orderings_Olinorder(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X2,X6)),hAPP(X2,X127)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),hAPP(hAPP(c_List_Olist_OCons(X105),X127),X293)) = hAPP(hAPP(c_List_Olist_OCons(X105),X6),hAPP(hAPP(c_List_Olist_OCons(X105),X127),X293)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X2,X6)),hAPP(X2,X127)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),hAPP(hAPP(c_List_Olist_OCons(X105),X127),X293)) = hAPP(hAPP(c_List_Olist_OCons(X105),X127),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X105,X7,X2),X6),X293)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_insort__key_Osimps_I2_J]) ).
fof(i_0_5635,plain,
! [X33,X90] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33)))
=> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33)))
=> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_upto__rec__number__of]) ).
fof(i_0_5636,plain,
! [X155,X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),X155)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).
fof(i_0_5637,plain,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X155)) ) ),
inference(fof_simplification,[status(thm)],[fact_IntE]) ).
fof(i_0_5638,plain,
! [X158,X107] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X107),X158)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X107),X158))
=> c_List_Oupto(X107,X158) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X107),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint)),X158)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X107),X158))
=> c_List_Oupto(X107,X158) = c_List_Olist_ONil(tc_Int_Oint) ) ) ),
inference(fof_simplification,[status(thm)],[fact_upto_Opsimps]) ).
fof(i_0_5639,plain,
! [X26,X6,X149,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(X2,X6),hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),X149)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).
fof(i_0_5640,plain,
! [X59,X58,X57,X45,X24] :
( ~ hBOOL(hAPP(X24,X45))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X57),X45),X58))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X24,X59,X57)),X45),X58)) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc_OIfFalse]) ).
fof(i_0_5641,plain,
! [X6,X293,X105,X292,X7] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X105)),X293)
=> ( hAPP(c_Map_Omap__of(X7,X105,hAPP(hAPP(c_List_Ozip(X7,X105),X292),X293)),X6) = c_Option_Ooption_ONone(X105)
<=> ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292))) ) ),
inference(fof_simplification,[status(thm)],[fact_map__of__zip__is__None]) ).
fof(i_0_5642,plain,
! [X163,X2,X105,X292,X127,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X127),hAPP(c_List_Oset(X7),X292)))
=> hAPP(hAPP(c_List_Omap(X7,X105),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X105),X2),X127),X163)),X292) = hAPP(hAPP(c_List_Omap(X7,X105),X2),X292) ),
inference(fof_simplification,[status(thm)],[fact_map__fun__upd]) ).
fof(i_0_5643,plain,
! [X211,X292,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),c_List_Osublist(X7,X292,X211)))) ),
inference(fof_simplification,[status(thm)],[fact_notin__set__sublistI]) ).
fof(i_0_5644,plain,
! [X127,X292,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),c_List_Oremove1(X7,X127,X292)))) ),
inference(fof_simplification,[status(thm)],[fact_notin__set__remove1]) ).
fof(i_0_5645,plain,
! [X34160,X34161,X34162] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34162),X34161)),X34160))
| hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X34162,X34160)),X34161) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34162),X34161) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__upt])]) ).
fof(i_0_5646,plain,
! [X21856,X21857] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21857),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21856))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21857),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21856))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_zpower__number__of__even]) ).
fof(i_0_5647,plain,
! [X1,X2,X7,X105] :
( class_Orderings_Oord(X105)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,X105)),X2),X1))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X105)),X2),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X105)),X1),X2)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_5648,plain,
! [X300,X86,X87,X114] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X114),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X87),X86)))
=> hAPP(c_Random_Opick(X87,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X87)),X86),X300)),X114) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X87),X86) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X114),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X87),X86)))
=> hAPP(c_Random_Opick(X87,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X87)),X86),X300)),X114) = hAPP(c_Random_Opick(X87,X300),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X114),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X87),X86))) ) ),
inference(fof_simplification,[status(thm)],[fact_pick_Osimps]) ).
fof(i_0_5649,plain,
! [X193,X149,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X149),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X193)))
=> ~ ! [X273] :
( hBOOL(hAPP(hAPP(c_member(X7),X149),X273))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X273),X193)) ) ),
inference(fof_simplification,[status(thm)],[fact_UnionE]) ).
fof(i_0_5650,plain,
! [X21234,X21235] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21235)),c_Int_OBit0(X21234)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21235),X21234)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21235),X21234))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21235)),c_Int_OBit0(X21234))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J])]) ).
fof(i_0_5651,plain,
! [X21232,X21233] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21233)),c_Int_OBit0(X21232)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21233),X21232)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21233),X21232))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21233)),c_Int_OBit0(X21232))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])]) ).
fof(i_0_5652,plain,
! [X21238,X21239] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21239)),c_Int_OBit0(X21238)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21239),X21238)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21239),X21238))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21239)),c_Int_OBit0(X21238))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J])]) ).
fof(i_0_5653,plain,
! [X21236,X21237] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21237)),c_Int_OBit0(X21236)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21237),X21236)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21237),X21236))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21237)),c_Int_OBit0(X21236))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])]) ).
fof(i_0_5654,plain,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),X149)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X7),X149) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__Diff__singleton__if]) ).
fof(i_0_5655,plain,
! [X21204,X21205] :
( ~ class_Int_Onumber__ring(X21205)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21205),hAPP(c_Int_Onumber__class_Onumber__of(X21205),X21204)),c_Groups_Oone__class_Oone(X21205)) = hAPP(c_Int_Onumber__class_Onumber__of(X21205),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21204),c_Int_OBit1(c_Int_OPls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I3_J])]) ).
fof(i_0_5656,plain,
! [X125,X163,X7] :
( ( class_Int_Onumber(X7)
& class_Orderings_Olinorder(X7) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X125)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X163))) ) ),
inference(fof_simplification,[status(thm)],[fact_le__number__of__eq__not__less]) ).
fof(i_0_5657,plain,
! [X127,X6,X105,X7] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_fun(X105,tc_HOL_Obool))),X6),X127)),
inference(fof_simplification,[status(thm)],[fact_bot2E]) ).
fof(i_0_5658,plain,
! [X61,X47,X43,X41,X72,X42] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X42,X72,X41),X43,X47,X61)
<=> ( ( hBOOL(hAPP(X42,X43))
& c_Natural_Oevaln(X72,X43,X47,X61) )
| ( ~ hBOOL(hAPP(X42,X43))
& c_Natural_Oevaln(X41,X43,X47,X61) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln_Oequations_I6_J]) ).
fof(i_0_5659,plain,
! [X61,X47,X43,X72,X41,X42] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X42,X41,X72),X43,X47,X61)
<=> ( ( hBOOL(hAPP(X42,X43))
& c_Natural_Oevaln(X41,X43,X47,X61) )
| ( ~ hBOOL(hAPP(X42,X43))
& c_Natural_Oevaln(X72,X43,X47,X61) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln_Oequations_I5_J]) ).
fof(i_0_5660,plain,
! [X46,X44,X45,X56,X57,X24] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X24,X57,X56),X45,X44,X46)
=> ( ( hBOOL(hAPP(X24,X45))
=> ~ c_Natural_Oevaln(X57,X45,X44,X46) )
=> ~ ( ~ hBOOL(hAPP(X24,X45))
=> ~ c_Natural_Oevaln(X56,X45,X44,X46) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I5_J]) ).
fof(i_0_5661,plain,
! [X98,X150,X151,X120] :
( X120 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X151),X150)),X98)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X151))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X151)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X151))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X151),X98))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> ( X151 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X120,X151) = X98 ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).
fof(i_0_5662,plain,
! [X32520,X32521,X32522,X32523] : c_List_Ofoldr(X32523,X32522,X32521,c_List_Olist_ONil(X32523),X32520) = X32520,
inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I1_J]) ).
fof(i_0_5663,plain,
! [X152,X98,X151,X120] :
( X120 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X151),X98)),X152)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X151))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X152))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X152),X151)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X151))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X151),X152))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X152),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> ( X151 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X120),X151) = X98 ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__eq]) ).
fof(i_0_5664,plain,
! [X33527,X33528,X33529] : hAPP(c_List_Orotate(X33529,hAPP(c_Nat_OSuc,X33528)),X33527) = hAPP(c_List_Orotate1(X33529),hAPP(c_List_Orotate(X33529,X33528),X33527)),
inference(variable_rename,[status(thm)],[fact_rotate__Suc]) ).
fof(i_0_5665,plain,
! [X26,X6,X149,X2,X105,X7] :
( c_Finite__Set_Ofun__left__comm(X7,X105,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),X26),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X105,X2),hAPP(hAPP(X2,X6),X26)),X149) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).
fof(i_0_5666,plain,
! [X34039,X34040,X34041,X34042] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34042),X34041))
| c_List_Oupt(X34042,X34041) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34040),X34039) )
& ( X34042 = X34040
| c_List_Oupt(X34042,X34041) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34040),X34039) )
& ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34042),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X34041) = X34039
| c_List_Oupt(X34042,X34041) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34040),X34039) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34042),X34041))
| X34042 != X34040
| c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34042),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X34041) != X34039
| c_List_Oupt(X34042,X34041) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34040),X34039) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Cons__conv])])]) ).
fof(i_0_5667,plain,
! [X2,X95,X44,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X95))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X44))) = c_Groups_Ozero__class_Ozero(X7) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X95))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X44))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X44))),hAPP(X2,X44)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__op__ivl__Suc]) ).
fof(i_0_5668,plain,
! [X6,X155,X149,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155),X6))
=> ( ~ hBOOL(hAPP(X149,X6))
=> hBOOL(hAPP(X155,X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_sup1E]) ).
fof(i_0_5669,plain,
! [X21284] : c_Int_Opred(c_Int_OBit1(X21284)) = c_Int_OBit0(X21284),
inference(variable_rename,[status(thm)],[fact_pred__Bit1]) ).
fof(i_0_5670,plain,
! [X96,X165,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),X96) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),X165))),X96) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__left]) ).
fof(i_0_5671,plain,
! [X30126] : c_Transitive__Closure_Otrancl(X30126,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X30126,X30126),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X30126,X30126),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_trancl__empty]) ).
fof(i_0_5672,plain,
! [X34152,X34153,X34154,X34155] :
( ~ class_Groups_Ocomm__monoid__add(X34155)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X34155),X34154),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X34153,X34152))) = hAPP(c_List_Omonoid__add__class_Olistsum(X34155),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X34155),X34154),c_List_Oupt(X34153,X34152))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upt__conv__listsum__nat])]) ).
fof(i_0_5673,plain,
! [X34156,X34157,X34158,X34159] :
( ~ class_Groups_Ocomm__monoid__add(X34159)
| hAPP(c_List_Omonoid__add__class_Olistsum(X34159),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X34159),X34158),c_List_Oupt(X34157,X34156))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X34159),X34158),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X34157,X34156))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__nat])]) ).
fof(i_0_5674,plain,
! [X6,X155,X149,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155),X6))
=> ~ ( hBOOL(hAPP(X149,X6))
=> ~ hBOOL(hAPP(X155,X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf1E]) ).
fof(i_0_5675,plain,
! [X33524,X33525,X33526] : hAPP(c_List_Orotate1(X33526),hAPP(c_List_Orotate(X33526,X33525),X33524)) = hAPP(c_List_Orotate(X33526,X33525),hAPP(c_List_Orotate1(X33526),X33524)),
inference(variable_rename,[status(thm)],[fact_rotate1__rotate__swap]) ).
fof(i_0_5676,plain,
! [X21181,X21182] :
( ~ class_Int_Onumber__ring(X21182)
| hAPP(c_Int_Onumber__class_Onumber__of(X21182),c_Int_OBit1(X21181)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21182),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21182),c_Groups_Oone__class_Oone(X21182)),hAPP(c_Int_Onumber__class_Onumber__of(X21182),X21181))),hAPP(c_Int_Onumber__class_Onumber__of(X21182),X21181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])]) ).
fof(i_0_5677,plain,
! [X155,X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X155))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ) ),
inference(fof_simplification,[status(thm)],[fact_DiffI]) ).
fof(i_0_5678,plain,
! [X21826,X21827,X21828,X21829] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X21829,X21828,X21827,c_Code__Numeral_OSuc__code__numeral(X21826)) = hAPP(hAPP(X21827,X21826),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X21829,X21828,X21827,X21826)),
inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I2_J]) ).
fof(i_0_5679,plain,
! [X22759] : c_Code__Numeral_OSuc__code__numeral(X22759) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X22759))),
inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__def]) ).
fof(i_0_5680,plain,
! [X149,X7] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ocard(X7),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X7),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X149) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ocard(X7),X149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_card__def]) ).
fof(i_0_5681,plain,
! [X30263,X30264,X30265] : hAPP(hAPP(c_Relation_Orel__comp(X30265,X30265,X30264),c_Relation_OId(X30265)),X30263) = X30263,
inference(variable_rename,[status(thm)],[fact_Id__O__R]) ).
fof(i_0_5682,plain,
! [X21712,X21713] :
( ~ class_Fields_Ofield(X21713)
| ~ class_Int_Onumber__ring(X21713)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21713),X21712),hAPP(c_Int_Onumber__class_Onumber__of(X21713),c_Int_OBit1(c_Int_OPls))) = X21712 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__numeral__1])]) ).
fof(i_0_5683,plain,
! [X21710,X21711] :
( ~ class_Fields_Ofield(X21711)
| ~ class_Int_Onumber__ring(X21711)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21711),X21710),hAPP(c_Int_Onumber__class_Onumber__of(X21711),c_Int_OBit1(c_Int_OPls))) = X21710 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral1])]) ).
fof(i_0_5684,plain,
! [X86,X84,X71,X87] :
( class_Lattices_Osemilattice__sup(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X87),X71),X84)),X86))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X86))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X86)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__supE]) ).
fof(i_0_5685,plain,
! [X86,X84,X71,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),hAPP(hAPP(c_Orderings_Oord__class_Omax(X87),X71),X84)),X86))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X71),X86))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X84),X86)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_Ole__supE]) ).
fof(i_0_5686,plain,
! [X21185,X21186] :
( ~ class_Int_Onumber__ring(X21186)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21186),X21185),hAPP(c_Int_Onumber__class_Onumber__of(X21186),c_Int_OBit1(c_Int_OPls))) = X21185 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right])]) ).
fof(i_0_5687,plain,
! [X33470,X33471,X33472] :
( X33472 = c_List_Olist_ONil(X33471)
| hAPP(c_List_Ohd(X33471),hAPP(c_List_Orotate(X33471,X33470),X33472)) = hAPP(hAPP(c_List_Onth(X33471),X33472),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33470,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33471)),X33472))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rotate__conv__nth])]) ).
fof(i_0_5688,plain,
! [X96,X165,X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)),X96)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X139),X165))),X96) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left]) ).
fof(i_0_5689,plain,
! [X33540,X33541,X33542] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33542)),X33541)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| hAPP(c_List_Orotate(X33542,X33540),X33541) = X33541 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__length01])]) ).
fof(i_0_5690,plain,
! [X155,X193,X25,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X193))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)),X193) = hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X193))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)),X193) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193) ) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__left]) ).
fof(i_0_5691,plain,
! [X149,X155,X23,X7] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X155))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),X149)) )
=> hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155))) ),
inference(fof_simplification,[status(thm)],[fact_UnCI]) ).
fof(i_0_5692,plain,
! [X281,X280,X105,X95,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X95),c_Map_Odom(X7,X105,X280)))
=> hAPP(c_Map_Omap__add(X7,X105,X280,X281),X95) = hAPP(X281,X95) ),
inference(fof_simplification,[status(thm)],[fact_map__add__dom__app__simps_I2_J]) ).
fof(i_0_5693,plain,
! [X280,X281,X105,X95,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X95),c_Map_Odom(X7,X105,X281)))
=> hAPP(c_Map_Omap__add(X7,X105,X280,X281),X95) = hAPP(X280,X95) ),
inference(fof_simplification,[status(thm)],[fact_map__add__dom__app__simps_I3_J]) ).
fof(i_0_5694,plain,
! [X71,X87] :
( class_Rings_Olinordered__ring(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X87),X71),X71)),c_Groups_Ozero__class_Ozero(X87))) ),
inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).
fof(i_0_5695,plain,
! [X21256] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21256)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21256),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21256),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21256)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I3_J])]) ).
fof(i_0_5696,plain,
! [X21280,X21281] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21281))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21280))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21281)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21280)),
inference(variable_rename,[status(thm)],[fact_zdiv__number__of__Bit0]) ).
fof(i_0_5697,plain,
! [X33,X96,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X90),X96)),X33))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X33)) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_5698,plain,
! [X21258] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21258)),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21258),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21258),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21258)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])]) ).
fof(i_0_5699,plain,
! [X21278] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21278)),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21278),c_Int_OMin)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21278),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21278)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J])]) ).
fof(i_0_5700,plain,
! [X21301] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21301)),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21301),c_Int_OMin)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21301),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21301)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J])]) ).
fof(i_0_5701,plain,
! [X21264] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21264)),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21264),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21264),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21264)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])]) ).
fof(i_0_5702,plain,
! [X21282] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21282))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21282))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21282)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21282)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0])]) ).
fof(i_0_5703,plain,
! [X30258,X30259] : hAPP(c_Relation_OImage(X30259,X30259,c_Relation_OId(X30259)),X30258) = X30258,
inference(variable_rename,[status(thm)],[fact_Image__Id]) ).
fof(i_0_5704,plain,
! [X149,X155,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),X155) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),X155) = hAPP(hAPP(c_Set_Oinsert(X7),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X149),X155)) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__Diff__if]) ).
fof(i_0_5705,plain,
! [X31800,X31801,X31802,X31803,X31804] : c_Map_Omap__comp(X31804,X31803,X31802,hAPP(c_COMBK(tc_Option_Ooption(X31803),X31804),c_Option_Ooption_ONone(X31803)),X31801,X31800) = c_Option_Ooption_ONone(X31803),
inference(variable_rename,[status(thm)],[fact_map__comp__empty_I2_J]) ).
fof(i_0_5706,plain,
! [X31805,X31806,X31807,X31808,X31809] : c_Map_Omap__comp(X31809,X31808,X31807,X31806,hAPP(c_COMBK(tc_Option_Ooption(X31809),X31807),c_Option_Ooption_ONone(X31809)),X31805) = c_Option_Ooption_ONone(X31808),
inference(variable_rename,[status(thm)],[fact_map__comp__empty_I1_J]) ).
fof(i_0_5707,plain,
! [X21118,X21119] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21119),X21118))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X21119)),X21118)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X21119)),X21118))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21119),X21118)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less])]) ).
fof(i_0_5708,plain,
! [X21304] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X21304)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X21304)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I6_J]) ).
fof(i_0_5709,plain,
! [X21046,X21047] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21047)))
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21047)),X21046)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21046) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21047)))
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21047)),X21046)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X21047))),X21046) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5185])]) ).
fof(i_0_5710,plain,
! [X59,X58,X44,X57,X45,X24] :
( ~ hBOOL(hAPP(X24,X45))
=> ( c_Natural_Oevaln(X57,X45,X44,X58)
=> c_Natural_Oevaln(c_Com_Ocom_OCond(X24,X59,X57),X45,X44,X58) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln_OIfFalse]) ).
fof(i_0_5711,plain,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),X33)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_div__if]) ).
fof(i_0_5712,plain,
! [X90,X33] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X33) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)),X33)) ) ),
inference(fof_simplification,[status(thm)],[fact_div__geq]) ).
fof(i_0_5713,plain,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X33))))),
inference(fof_simplification,[status(thm)],[fact_not__zle__0__negative]) ).
fof(i_0_5714,plain,
! [X30232,X30233] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30233,X30233),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30233,X30232)),c_Relation_OId(X30233)) = c_Transitive__Closure_Ortrancl(X30233,X30232),
inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl__absorb]) ).
fof(i_0_5715,plain,
! [X34063,X34064] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34064),X34063))
| c_List_Oupt(X34064,hAPP(c_Nat_OSuc,X34063)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X34064,X34063)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34063),c_List_Olist_ONil(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__Suc__append])]) ).
fof(i_0_5716,plain,
! [X34061,X34062] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34062),X34061))
| c_List_Oupt(X34062,hAPP(c_Nat_OSuc,X34061)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X34062,X34061)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34061),c_List_Olist_ONil(tc_Nat_Onat))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34062),X34061))
| c_List_Oupt(X34062,hAPP(c_Nat_OSuc,X34061)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5186])]) ).
fof(i_0_5717,plain,
! [X155,X149,X25,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)) = hAPP(hAPP(c_Set_Oinsert(X7),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) ) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__right]) ).
fof(i_0_5718,plain,
! [X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Otimes__class_Otimes(X105)),X1),c_Groups_Oone__class_Oone(X105)),X149) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149) = c_Groups_Oone__class_Oone(X105) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod_OF__eq]) ).
fof(i_0_5719,plain,
! [X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X105,X7,c_Groups_Oplus__class_Oplus(X105)),X1),c_Groups_Ozero__class_Ozero(X105)),X149) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149) = c_Groups_Ozero__class_Ozero(X105) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum_OF__eq]) ).
fof(i_0_5720,plain,
! [X301,X300,X87,X33] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)),X33) = hAPP(hAPP(c_List_Onth(X87),X300),X33) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300)))
=> hAPP(hAPP(c_List_Onth(X87),hAPP(hAPP(c_List_Oappend(X87),X300),X301)),X33) = hAPP(hAPP(c_List_Onth(X87),X301),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X87)),X300))) ) ),
inference(fof_simplification,[status(thm)],[fact_nth__append]) ).
fof(i_0_5721,plain,
! [X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149)) ),
inference(fof_simplification,[status(thm)],[fact_ComplE]) ).
fof(i_0_5722,plain,
! [X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149)) ),
inference(fof_simplification,[status(thm)],[fact_ComplD]) ).
fof(i_0_5723,plain,
! [X149,X23,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149)))
<=> ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149)) ),
inference(fof_simplification,[status(thm)],[fact_Compl__iff]) ).
fof(i_0_5724,plain,
! [X21848] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21848)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21848)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_nat__number__of__Bit0]) ).
fof(i_0_5725,plain,
! [X139,X63,X7] :
( ( class_Int_Onumber(X7)
& class_Orderings_Oord(X7) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X139) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X63) ) ) ),
inference(fof_simplification,[status(thm)],[fact_max__number__of]) ).
fof(i_0_5726,plain,
! [X139,X63,X7] :
( ( class_Int_Onumber(X7)
& class_Orderings_Oord(X7) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X63) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X7),X139) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__number__of]) ).
fof(i_0_5727,plain,
! [X113,X114] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X114),X113)),X114)),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_5728,plain,
! [X114,X113] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X114)),X114)),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_5729,plain,
! [X293,X292,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> c_List_Oremove1(X7,X6,hAPP(hAPP(c_List_Oappend(X7),X292),X293)) = hAPP(hAPP(c_List_Oappend(X7),c_List_Oremove1(X7,X6,X292)),X293) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> c_List_Oremove1(X7,X6,hAPP(hAPP(c_List_Oappend(X7),X292),X293)) = hAPP(hAPP(c_List_Oappend(X7),X292),c_List_Oremove1(X7,X6,X293)) ) ),
inference(fof_simplification,[status(thm)],[fact_remove1__append]) ).
fof(i_0_5730,plain,
! [X21098] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21098))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21098) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21098) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21098)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0])]) ).
fof(i_0_5731,plain,
! [X6,X2,X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,X2,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X6)),
inference(fof_simplification,[status(thm)],[fact_empty__fold1SetE]) ).
fof(i_0_5732,plain,
! [X21155,X21156] :
( ( c_Int_OBit1(X21156) != c_Int_OBit1(X21155)
| X21156 = X21155 )
& ( X21156 != X21155
| c_Int_OBit1(X21156) = c_Int_OBit1(X21155) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])]) ).
fof(i_0_5733,plain,
! [X95,X105,X149,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Map_Orestrict__map(X7,X105,X95,X149),X6) = hAPP(X95,X6) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Map_Orestrict__map(X7,X105,X95,X149),X6) = c_Option_Ooption_ONone(X105) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__map__def]) ).
fof(i_0_5734,plain,
! [X24,X25,X38] :
( hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X24)))
<=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X24))
& ~ hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X159] :
( X25 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X159)
& ~ hBOOL(hAPP(X38,X159)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(i_0_5735,plain,
! [X292,X6,X7] :
( hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
& hBOOL(hAPP(c_List_Odistinct(X7),X292)) ) ),
inference(fof_simplification,[status(thm)],[fact_distinct_Osimps_I2_J]) ).
fof(i_0_5736,plain,
! [X2,X105,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Map_Odom(X7,X105,X2)))
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))
=> ? [X3] : hAPP(X2,X3) = c_Option_Ooption_ONone(X105) ) ),
inference(fof_simplification,[status(thm)],[fact_finite__map__freshness]) ).
fof(i_0_5737,plain,
! [X33488,X33489,X33490] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33490)),hAPP(c_List_Orotate(X33490,X33489),X33488)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33490)),X33488),
inference(variable_rename,[status(thm)],[fact_length__rotate]) ).
fof(i_0_5738,plain,
! [X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)),hAPP(hAPP(c_Set_Oinsert(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X149 ),
inference(fof_simplification,[status(thm)],[fact_Diff__insert__absorb]) ).
fof(i_0_5739,plain,
! [X1,X6,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(X1,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod_Oinsert]) ).
fof(i_0_5740,plain,
! [X2,X25,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),hAPP(X2,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__insert]) ).
fof(i_0_5741,plain,
! [X1,X6,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(X1,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum_Oinsert]) ).
fof(i_0_5742,plain,
! [X2,X25,X215,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X215))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X215))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),hAPP(hAPP(c_Set_Oinsert(X7),X25),X215)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X105),hAPP(X2,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X215)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__insert]) ).
fof(i_0_5743,plain,
! [X34077,X34078,X34079] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X34079),c_List_Oupt(X34078,X34077)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34078),X34079),X34077),
inference(variable_rename,[status(thm)],[fact_drop__upt]) ).
fof(i_0_5744,plain,
! [X292,X38,X7] :
( hAPP(c_List_Ofilter(X7,X38),X292) = c_List_Olist_ONil(X7)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X292)))
=> ~ hBOOL(hAPP(X38,X3)) ) ),
inference(fof_simplification,[status(thm)],[fact_filter__empty__conv]) ).
fof(i_0_5745,plain,
! [X90,X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)))),
inference(fof_simplification,[status(thm)],[fact_not__int__zless__negative]) ).
fof(i_0_5746,plain,
! [X33503,X33504,X33505] : hAPP(c_List_Oset(X33505),hAPP(c_List_Orotate(X33505,X33504),X33503)) = hAPP(c_List_Oset(X33505),X33503),
inference(variable_rename,[status(thm)],[fact_set__rotate]) ).
fof(i_0_5747,plain,
! [X7,X149,X6,X155] :
( ( ~ hBOOL(hAPP(X155,X6))
=> hBOOL(hAPP(X149,X6)) )
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X149),X155),X6)) ),
inference(fof_simplification,[status(thm)],[fact_sup1CI]) ).
fof(i_0_5748,plain,
! [X332,X333,X292,X38,X7] :
( c_List_Opartition(X7,X38,X292) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7),tc_List_Olist(X7)),X333),X332)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X333)))
=> hBOOL(hAPP(X38,X3)) )
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),hAPP(c_List_Oset(X7),X332)))
=> ~ hBOOL(hAPP(X38,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_partition__P]) ).
fof(i_0_5749,plain,
! [X30127,X30128] : hAPP(c_Relation_ODomain(X30128,X30128),c_Transitive__Closure_Otrancl(X30128,X30127)) = hAPP(c_Relation_ODomain(X30128,X30128),X30127),
inference(variable_rename,[status(thm)],[fact_trancl__domain]) ).
fof(i_0_5750,plain,
! [X30129,X30130] : hAPP(c_Relation_ORange(X30130,X30130),c_Transitive__Closure_Otrancl(X30130,X30129)) = hAPP(c_Relation_ORange(X30130,X30130),X30129),
inference(variable_rename,[status(thm)],[fact_trancl__range]) ).
fof(i_0_5751,plain,
! [X169,X163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X163),X169))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X163),c_Int_OPls)) ) ),
inference(fof_simplification,[status(thm)],[fact_le__nat__number__of]) ).
fof(i_0_5752,plain,
! [X97,X98,X86] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X86)) )
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X97))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X98)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X97))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X86)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__trans]) ).
fof(i_0_5753,plain,
! [X21251,X21252] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X21252)),c_Int_OBit0(X21251)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21252),X21251)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I7_J]) ).
fof(i_0_5754,plain,
! [X21246,X21247] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X21247)),c_Int_OBit0(X21246)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21247),X21246)),
inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0]) ).
fof(i_0_5755,plain,
! [X6,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,X2),X6),X149) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).
fof(i_0_5756,plain,
! [X6] :
~ ! [X82] :
( X6 = hAPP(c_Int_OAbs__Integ,X82)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X82),c_Int_OInteg)) ),
inference(fof_simplification,[status(thm)],[fact_Abs__Integ__cases]) ).
fof(i_0_5757,plain,
! [X34090,X34091] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34091),X34090))
| c_List_Oupt(X34091,X34090) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34091),c_List_Oupt(hAPP(c_Nat_OSuc,X34091),X34090)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Cons])]) ).
fof(i_0_5758,plain,
! [X34088,X34089] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34089),X34088))
| c_List_Oupt(X34089,X34088) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34089),c_List_Oupt(hAPP(c_Nat_OSuc,X34089),X34088)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34089),X34088))
| c_List_Oupt(X34089,X34088) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5187])]) ).
fof(i_0_5759,plain,
! [X31722,X31723,X31724,X31725,X31726,X31727,X31728] :
( hAPP(X31728,X31727) != hAPP(c_Option_Ooption_OSome(X31726),X31725)
| c_Map_Omap__comp(X31726,X31724,X31723,X31722,X31728,X31727) = hAPP(X31722,X31725) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__simps_I2_J])]) ).
fof(i_0_5760,plain,
! [X292,X2,X7,X6,X38,X105] :
( class_Orderings_Olinorder(X105)
=> ( ~ hBOOL(hAPP(X38,X6))
=> hAPP(c_List_Ofilter(X7,X38),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X105,X2),X6),X292)) = hAPP(c_List_Ofilter(X7,X38),X292) ) ),
inference(fof_simplification,[status(thm)],[fact_filter__insort__triv]) ).
fof(i_0_5761,plain,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omin(X7)),X6),X149) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).
fof(i_0_5762,plain,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omax(X7)),X6),X149) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).
fof(i_0_5763,plain,
! [X95,X26] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),X95))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
=> X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__dvd__iff]) ).
fof(i_0_5764,plain,
! [X149,X7] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X149),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_not__psubset__empty]) ).
fof(i_0_5765,plain,
! [X95,X105,X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Map_Orestrict__map(X7,X105,X95,X149),X6) = c_Option_Ooption_ONone(X105) ),
inference(fof_simplification,[status(thm)],[fact_restrict__out]) ).
fof(i_0_5766,plain,
! [X25,X149,X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Groups_Otimes__class_Otimes(X7)),X25),X149) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fold1__eq__fold]) ).
fof(i_0_5767,plain,
! [X21289,X21290] :
( ~ class_Int_Onumber__ring(X21290)
| hAPP(c_Int_Onumber__class_Onumber__of(X21290),c_Int_OBit0(X21289)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21290),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21290),c_Groups_Ozero__class_Ozero(X21290)),hAPP(c_Int_Onumber__class_Onumber__of(X21290),X21289))),hAPP(c_Int_Onumber__class_Onumber__of(X21290),X21289)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit0])]) ).
fof(i_0_5768,plain,
! [X34147,X34148] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X34148),hAPP(c_List_Onth(X34148),X34147)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34148)),X34147))) = X34147,
inference(variable_rename,[status(thm)],[fact_map__nth]) ).
fof(i_0_5769,plain,
! [X84,X71,X86,X87] :
( class_Lattices_Osemilattice__inf(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X87),X71),X84)))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X71))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X84)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__infE]) ).
fof(i_0_5770,plain,
! [X84,X71,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),hAPP(hAPP(c_Orderings_Oord__class_Omin(X87),X71),X84)))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X71))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X84)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_Ole__infE]) ).
fof(i_0_5771,plain,
! [X292,X6,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),c_List_Oremove1(X7,X6,X292)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),c_List_Oremove1(X7,X6,X292)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X292) ) ),
inference(fof_simplification,[status(thm)],[fact_length__remove1]) ).
fof(i_0_5772,plain,
! [X155,X193,X25,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X193))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)),X193) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X155),X193) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__left__if0]) ).
fof(i_0_5773,plain,
! [X21794,X21795] :
( ( X21795 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| c_Code__Numeral_Onat__of__aux(X21795,X21794) = X21794 )
& ( X21795 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| c_Code__Numeral_Onat__of__aux(X21795,X21794) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X21795),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X21794)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__aux__code])]) ).
fof(i_0_5774,plain,
! [X22752,X22753] : c_Code__Numeral_Onat__of__aux(X22753,X22752) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22753)),X22752),
inference(variable_rename,[status(thm)],[fact_nat__of__aux__def]) ).
fof(i_0_5775,plain,
! [X30109,X30110] :
( ~ c_Wellfounded_Owf(X30110,X30109)
| c_Wellfounded_Owf(X30110,c_Transitive__Closure_Otrancl(X30110,X30109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__trancl])]) ).
fof(i_0_5776,plain,
! [X30260,X30261,X30262] : hAPP(hAPP(c_Relation_Orel__comp(X30262,X30261,X30261),X30260),c_Relation_OId(X30261)) = X30260,
inference(variable_rename,[status(thm)],[fact_R__O__Id]) ).
fof(i_0_5777,plain,
! [X31745,X31746,X31747,X31748,X31749,X31750] :
( hAPP(X31750,X31749) != c_Option_Ooption_ONone(X31748)
| c_Map_Omap__comp(X31748,X31747,X31746,X31745,X31750,X31749) = c_Option_Ooption_ONone(X31747) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__simps_I1_J])]) ).
fof(i_0_5778,plain,
! [X30195,X30196] : c_Transitive__Closure_Otrancl(X30196,X30195) = hAPP(hAPP(c_Relation_Orel__comp(X30196,X30196,X30196),c_Transitive__Closure_Ortrancl(X30196,X30195)),X30195),
inference(variable_rename,[status(thm)],[fact_trancl__unfold__right]) ).
fof(i_0_5779,plain,
! [X30187,X30188] : c_Transitive__Closure_Ortrancl(X30188,c_Transitive__Closure_Otrancl(X30188,X30187)) = c_Transitive__Closure_Ortrancl(X30188,X30187),
inference(variable_rename,[status(thm)],[fact_trancl__rtrancl__absorb]) ).
fof(i_0_5780,plain,
! [X34253] : c_List_Oconcat(X34253,c_List_Olist_ONil(tc_List_Olist(X34253))) = c_List_Olist_ONil(X34253),
inference(variable_rename,[status(thm)],[fact_concat_Osimps_I1_J]) ).
fof(i_0_5781,plain,
! [X24,X25] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24)) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff]) ).
fof(i_0_5782,plain,
! [X24,X25] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24)
<=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24)) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff2]) ).
fof(i_0_5783,plain,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)),X6),X149) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).
fof(i_0_5784,plain,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omin(X7)),X6),X149) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Min_Oeq__fold_H]) ).
fof(i_0_5785,plain,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Orderings_Oord__class_Omax(X7)),X6),X149) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Max_Oeq__fold_H]) ).
fof(i_0_5786,plain,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Finite__Set_Ofold(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7)),X6),X149) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).
fof(i_0_5787,plain,
! [X169,X163] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X163) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)
<=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X163)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X163)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X163) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
=> X163 = X169 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_eq__nat__number__of]) ).
fof(i_0_5788,plain,
! [X86,X87] :
( ( class_Int_Onumber__ring(X87)
& class_Rings_Olinordered__idom(X87) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X86)),c_Groups_Ozero__class_Ozero(X87)))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X86)) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X86)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X86)),c_Groups_Ozero__class_Ozero(X87)))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),hAPP(c_Int_Onumber__class_Onumber__of(X87),X86)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),X86) ) ) ),
inference(fof_simplification,[status(thm)],[fact_abs__number__of]) ).
fof(i_0_5789,plain,
! [X30343] : hAPP(c_Relation_Oconverse(X30343,X30343),c_Relation_OId(X30343)) = c_Relation_OId(X30343),
inference(variable_rename,[status(thm)],[fact_converse__Id]) ).
fof(i_0_5790,plain,
! [X165,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165))) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_mod__nat__number__of]) ).
fof(i_0_5791,plain,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),X149)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).
fof(i_0_5792,plain,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),X149)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).
fof(i_0_5793,plain,
! [X21249,X21250] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X21250)),X21249) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21250),X21249)),
inference(variable_rename,[status(thm)],[fact_mult__Bit0]) ).
fof(i_0_5794,plain,
! [X97,X98,X86] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X97))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X98)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X97))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X86)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less__trans]) ).
fof(i_0_5795,plain,
! [X97,X98,X86] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X86)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X97))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X97))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X86)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le__trans]) ).
fof(i_0_5796,plain,
! [X128,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128))) ) ),
inference(fof_simplification,[status(thm)],[fact_power__nat__number__of__number__of]) ).
fof(i_0_5797,plain,
! [X165,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165))) ) ),
inference(fof_simplification,[status(thm)],[fact_div__nat__number__of]) ).
fof(i_0_5798,plain,
! [X6,X149,X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),hAPP(c_Finite__Set_Ofold1(X7,c_Groups_Otimes__class_Otimes(X7)),X149)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fold1__insert]) ).
fof(i_0_5799,plain,
! [X25,X24] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X25))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24)) )
=> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25,X24) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__empty]) ).
fof(i_0_5800,plain,
! [X21115,X21116] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21116))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21115)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21116)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21115),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X21116))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of])]) ).
fof(i_0_5801,plain,
! [X44,X38] :
( ~ hBOOL(hAPP(X38,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X38,X44))
=> ? [X118] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X118),X44))
& ! [X147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X147),X118))
=> ~ hBOOL(hAPP(X38,X147)) )
& hBOOL(hAPP(X38,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X118),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).
fof(i_0_5802,plain,
! [X34163,X34164] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X34164,X34163) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X34164),hAPP(c_Nat_OSuc,X34163))),
inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upt]) ).
fof(i_0_5803,plain,
! [X21257] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21257)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21257)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21257))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21257))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])]) ).
fof(i_0_5804,plain,
! [X21263] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21263)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21263)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21263))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21263))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])]) ).
fof(i_0_5805,plain,
! [X21302] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21302)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21302)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21302))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21302))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J])]) ).
fof(i_0_5806,plain,
! [X21279] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21279)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21279)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21279))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21279))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J])]) ).
fof(i_0_5807,plain,
! [X155,X149,X25,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),hAPP(hAPP(c_Set_Oinsert(X7),X25),X155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X149),X155) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__right__if0]) ).
fof(i_0_5808,plain,
! [X33537,X33538,X33539] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33539,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33538)),X33537)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_List_Orotate(X33538,X33539),X33537) = X33537 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__id])]) ).
fof(i_0_5809,plain,
! [X33515,X33516,X33517] :
( ( hAPP(c_List_Orotate(X33517,X33516),X33515) != c_List_Olist_ONil(X33517)
| X33515 = c_List_Olist_ONil(X33517) )
& ( X33515 != c_List_Olist_ONil(X33517)
| hAPP(c_List_Orotate(X33517,X33516),X33515) = c_List_Olist_ONil(X33517) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv])]) ).
fof(i_0_5810,plain,
! [X107,X158] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X158),X107))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X107,X158) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X158),X107))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X107,X158) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X107),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint)),X158)) ) ),
inference(fof_simplification,[status(thm)],[fact_simp__from__to]) ).
fof(i_0_5811,plain,
! [X21309,X21310] :
( ~ class_Int_Onumber__ring(X21310)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21310),c_Groups_Oone__class_Oone(X21310)),c_Groups_Oone__class_Oone(X21310))),hAPP(c_Int_Onumber__class_Onumber__of(X21310),X21309)) = hAPP(c_Int_Onumber__class_Onumber__of(X21310),c_Int_OBit0(X21309)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0])]) ).
fof(i_0_5812,plain,
! [X24,X155,X25,X7] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X155))
=> X25 = X24 )
=> hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(hAPP(c_Set_Oinsert(X7),X24),X155))) ),
inference(fof_simplification,[status(thm)],[fact_insertCI]) ).
fof(i_0_5813,plain,
! [X21172] : c_Int_OBit1(X21172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X21172)),X21172),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(i_0_5814,plain,
! [X22871,X22872,X22873,X22874,X22875,X22876] : hAPP(hAPP(c_Product__Type_Ointernal__split(X22876,X22875,X22874),X22873),hAPP(hAPP(c_Product__Type_OPair(X22876,X22875),X22872),X22871)) = hAPP(hAPP(X22873,X22872),X22871),
inference(variable_rename,[status(thm)],[fact_internal__split__conv]) ).
fof(i_0_5815,plain,
! [X22858,X22859,X22860] : c_Product__Type_Ointernal__split(X22860,X22859,X22858) = c_Product__Type_Oprod_Oprod__case(X22860,X22859,X22858),
inference(variable_rename,[status(thm)],[fact_internal__split__def]) ).
fof(i_0_5816,plain,
! [X149,X23,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hBOOL(hAPP(hAPP(c_member(X7),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X149))) ),
inference(fof_simplification,[status(thm)],[fact_ComplI]) ).
fof(i_0_5817,plain,
! [X105,X149,X23,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(c_COMBK(X7,X105),X23)),X149) = c_Orderings_Otop__class_Otop(tc_fun(X105,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X23),X149))
=> hAPP(c_Set_Ovimage(X105,X7,hAPP(c_COMBK(X7,X105),X23)),X149) = c_Orderings_Obot__class_Obot(tc_fun(X105,tc_HOL_Obool)) ) ),
inference(fof_simplification,[status(thm)],[fact_vimage__const]) ).
fof(i_0_5818,plain,
! [X6,X149,X215,X2,X7] :
( c_Finite__Set_Ofolding__one(X7,X2,X215)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> hAPP(X215,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(X2,X6),hAPP(X215,X149)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert]) ).
fof(i_0_5819,plain,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X33))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X33),X90)) ) ),
inference(fof_simplification,[status(thm)],[fact_zdvd__not__zless]) ).
fof(i_0_5820,plain,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X90)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__dvd__not__less]) ).
fof(i_0_5821,plain,
! [X34132,X34133] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X34133,X34132)) = c_List_Oupt(hAPP(c_Nat_OSuc,X34133),hAPP(c_Nat_OSuc,X34132)),
inference(variable_rename,[status(thm)],[fact_map__Suc__upt]) ).
fof(i_0_5822,plain,
! [X84,X71] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> c_Divides_Odivmod__int(X71,X84) = c_Divides_OposDivAlg(X71,X84) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( ( X71 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X71,X84) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( X71 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X71,X84) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84))) ) ) ) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> c_Divides_Odivmod__int(X71,X84) = c_Divides_OnegDivAlg(X71,X84) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> c_Divides_Odivmod__int(X71,X84) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X71),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84))) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__def]) ).
fof(i_0_5823,plain,
! [X30299] : c_Relation_Orefl__on(X30299,c_Orderings_Otop__class_Otop(tc_fun(X30299,tc_HOL_Obool)),c_Relation_OId(X30299)),
inference(variable_rename,[status(thm)],[fact_refl__Id]) ).
fof(i_0_5824,plain,
! [X21188] :
( ~ class_Int_Onumber__ring(X21188)
| hAPP(c_Int_Onumber__class_Onumber__of(X21188),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X21188) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1])]) ).
fof(i_0_5825,plain,
! [X21187] :
( ~ class_Int_Onumber__ring(X21187)
| c_Groups_Oone__class_Oone(X21187) = hAPP(c_Int_Onumber__class_Onumber__of(X21187),c_Int_OBit1(c_Int_OPls)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])]) ).
fof(i_0_5826,plain,
! [X44,X95] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X95)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_5827,plain,
! [X71,X87] :
( class_Groups_Oordered__ab__group__add__abs(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Groups_Oabs__class_Oabs(X87),X71)),c_Groups_Ozero__class_Ozero(X87))) ),
inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).
fof(i_0_5828,plain,
! [X90,X87] :
( class_Rings_Olinordered__semidom(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),X90)),c_Groups_Ozero__class_Ozero(X87))) ),
inference(fof_simplification,[status(thm)],[fact_of__nat__less__0__iff]) ).
fof(i_0_5829,plain,
! [X21285,X21286] :
( ( ~ c_Int_Oiszero(X21286,hAPP(c_Int_Onumber__class_Onumber__of(X21286),c_Int_OBit0(X21285)))
| c_Int_Oiszero(X21286,hAPP(c_Int_Onumber__class_Onumber__of(X21286),X21285))
| ~ class_Int_Onumber__ring(X21286)
| ~ class_Int_Oring__char__0(X21286) )
& ( ~ c_Int_Oiszero(X21286,hAPP(c_Int_Onumber__class_Onumber__of(X21286),X21285))
| c_Int_Oiszero(X21286,hAPP(c_Int_Onumber__class_Onumber__of(X21286),c_Int_OBit0(X21285)))
| ~ class_Int_Onumber__ring(X21286)
| ~ class_Int_Oring__char__0(X21286) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0])])]) ).
fof(i_0_5830,plain,
! [X165,X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X165),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X165),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),X165)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_add__nat__number__of]) ).
fof(i_0_5831,plain,
! [X33,X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),X33) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),X33) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)),X33)) ) ),
inference(fof_simplification,[status(thm)],[fact_power__nat__number__of]) ).
fof(i_0_5832,plain,
! [X21273] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21273)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X21273)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I3_J]) ).
fof(i_0_5833,plain,
! [X138,X115,X96] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X115))
=> c_Random_Ominus__shift(X138,X96,X115) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X138),X96)),X115) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X115))
=> c_Random_Ominus__shift(X138,X96,X115) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X96),X115) ) ),
inference(fof_simplification,[status(thm)],[fact_minus__shift__def]) ).
fof(i_0_5834,axiom,
! [X94,X44,X38] :
( hBOOL(hAPP(X38,c_Divides_Odiv__class_Omod(tc_Int_Oint,X44,X94)))
<=> epred1_3(X38,X44,X94) ),
inference(apply_def,[status(thm)],[fact_split__zmod,c_0_5188]) ).
fof(i_0_5835,plain,
! [X113,X114] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X114),X113))
=> c_List_Oupto(X114,X113) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X114),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X114),c_Groups_Oone__class_Oone(tc_Int_Oint)),X113)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X114),X113))
=> c_List_Oupto(X114,X113) = c_List_Olist_ONil(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_upto_Osimps]) ).
fof(i_0_5836,plain,
! [X21242,X21243] : c_Int_OBit0(X21243) != c_Int_OBit1(X21242),
inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J]) ).
fof(i_0_5837,plain,
! [X21244,X21245] : c_Int_OBit1(X21245) != c_Int_OBit0(X21244),
inference(variable_rename,[status(thm)],[fact_rel__simps_I50_J]) ).
fof(i_0_5838,plain,
! [X21851,X21852] : c_Divides_Odivmod__nat(X21852,X21851) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21852),X21851)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21852,X21851)),
inference(variable_rename,[status(thm)],[fact_divmod__nat__div__mod]) ).
fof(i_0_5839,plain,
! [X21818,X21819,X21820,X21821] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X21821,X21820,X21819,c_Code__Numeral_OSuc__code__numeral(X21818)) = hAPP(X21819,X21818),
inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I5_J]) ).
fof(i_0_5840,plain,
! [X34170,X34171] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X34171,X34170) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X34171),X34170)),
inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upt]) ).
fof(i_0_5841,plain,
! [X96,X87] :
( class_Rings_Oring__1(X87)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),X96) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X87),X96) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onat,X96)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_of__int__of__nat]) ).
fof(i_0_5842,plain,
! [X56,X57,X24] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X24,X57,X56)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X57))
=> ~ hBOOL(hAPP(c_Com_OWT,X56)) ) ),
inference(fof_simplification,[status(thm)],[fact_WTs__elim__cases_I5_J]) ).
fof(i_0_5843,plain,
! [X30297] : hAPP(c_Relation_ODomain(X30297,X30297),c_Relation_OId(X30297)) = c_Orderings_Otop__class_Otop(tc_fun(X30297,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Domain__Id]) ).
fof(i_0_5844,plain,
! [X30298] : hAPP(c_Relation_ORange(X30298,X30298),c_Relation_OId(X30298)) = c_Orderings_Otop__class_Otop(tc_fun(X30298,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Range__Id]) ).
fof(i_0_5845,plain,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X6),c_Big__Operators_Olattice__class_OInf__fin(X7,X149)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oinsert]) ).
fof(i_0_5846,plain,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),X6),c_Big__Operators_Olinorder__class_OMin(X7,X149)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Min_Oinsert]) ).
fof(i_0_5847,plain,
! [X6,X149,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),X6),c_Big__Operators_Olinorder__class_OMax(X7,X149)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Max_Oinsert]) ).
fof(i_0_5848,plain,
! [X6,X149,X7] :
( class_Lattices_Olattice(X7)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( X149 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6),c_Big__Operators_Olattice__class_OSup__fin(X7,X149)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert]) ).
fof(i_0_5849,plain,
! [X30185,X30186] : c_Transitive__Closure_Otrancl(X30186,c_Transitive__Closure_Ortrancl(X30186,X30185)) = c_Transitive__Closure_Ortrancl(X30186,X30185),
inference(variable_rename,[status(thm)],[fact_rtrancl__trancl__absorb]) ).
fof(i_0_5850,plain,
! [X6,X7,X149] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X149))
=> c_List_Osublist(X7,hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7)),X149) = hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X149))
=> c_List_Osublist(X7,hAPP(hAPP(c_List_Olist_OCons(X7),X6),c_List_Olist_ONil(X7)),X149) = c_List_Olist_ONil(X7) ) ),
inference(fof_simplification,[status(thm)],[fact_sublist__singleton]) ).
fof(i_0_5851,plain,
! [X165] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X165))) ) ),
inference(fof_simplification,[status(thm)],[fact_one__mod__nat__number__of]) ).
fof(i_0_5852,plain,
! [X30585] : c_Relation_Osingle__valued(X30585,X30585,c_Relation_OId(X30585)),
inference(variable_rename,[status(thm)],[fact_single__valued__Id]) ).
fof(i_0_5853,plain,
! [X127,X6,X7] :
( class_Orderings_Opreorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X6)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_5854,plain,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X7),X149)) ) ),
inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).
fof(i_0_5855,axiom,
! [X94,X44,X38] :
( hBOOL(hAPP(X38,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X44),X94)))
<=> epred2_3(X38,X44,X94) ),
inference(apply_def,[status(thm)],[fact_split__zdiv,c_0_5189]) ).
fof(i_0_5856,plain,
! [X155,X149,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X155))
=> ( hAPP(hAPP(c_Set_Oinsert(X7),X6),X149) = hAPP(hAPP(c_Set_Oinsert(X7),X6),X155)
<=> X149 = X155 ) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).
fof(i_0_5857,plain,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(c_Finite__Set_Ocard(X7),X149) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X7),X149)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).
fof(i_0_5858,plain,
! [X34139,X34140] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34140),X34139))
| c_List_Olast(tc_Nat_Onat,c_List_Oupt(X34140,X34139)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X34139),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__upt])]) ).
fof(i_0_5859,plain,
! [X21822] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X21822)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X21822,
inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__minus__one]) ).
fof(i_0_5860,plain,
! [X44,X95] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X44))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X95))) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_5861,plain,
! [X34102,X34103] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X34103,X34102))),
inference(variable_rename,[status(thm)],[fact_distinct__upt]) ).
fof(i_0_5862,plain,
! [X30450,X30451] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30451,X30451),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30450) = c_Relation_OId(X30451),
inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I1_J]) ).
fof(i_0_5863,plain,
! [X96] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X96)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(fof_simplification,[status(thm)],[fact_int__less__0__conv]) ).
fof(i_0_5864,plain,
! [X21168] :
( ( c_Int_OMin != c_Int_OBit1(X21168)
| c_Int_OMin = X21168 )
& ( c_Int_OMin != X21168
| c_Int_OMin = c_Int_OBit1(X21168) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J])]) ).
fof(i_0_5865,plain,
! [X21167] :
( ( c_Int_OBit1(X21167) != c_Int_OMin
| X21167 = c_Int_OMin )
& ( X21167 != c_Int_OMin
| c_Int_OBit1(X21167) = c_Int_OMin ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J])]) ).
fof(i_0_5866,plain,
! [X21165] : c_Int_OBit1(X21165) != c_Int_OPls,
inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J]) ).
fof(i_0_5867,plain,
! [X21166] : c_Int_OPls != c_Int_OBit1(X21166),
inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(i_0_5868,plain,
! [X139,X87] :
( class_Int_Onumber__ring(X87)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),X139) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = c_Groups_Ozero__class_Ozero(X87) ) ) ),
inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__lemma]) ).
fof(i_0_5869,plain,
! [X6,X149,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X149))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X6),X149)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X7),X149)) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).
fof(i_0_5870,plain,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
<=> X6 = X127 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_5871,plain,
! [X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X7)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X7),tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__listI]) ).
fof(i_0_5872,plain,
! [X23,X45,X24] :
( ~ hBOOL(hAPP(X24,X45))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X45),X45)) ),
inference(fof_simplification,[status(thm)],[fact_evalc_OWhileFalse]) ).
fof(i_0_5873,plain,
! [X84,X71,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X71)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_5874,plain,
! [X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_5875,plain,
! [X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_5876,plain,
! [X98,X86,X87] :
( class_Orderings_Opreorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_5877,plain,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X127),X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_5878,plain,
! [X86,X98,X87] :
( class_Orderings_Olinorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98)) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_5879,plain,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X127),X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_5880,plain,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X127),X6))
| X6 = X127 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_5881,plain,
! [X71,X84,X87] :
( class_Orderings_Oorder(X87)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X84),X71))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),X84)) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_5882,plain,
! [X165,X139] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X165)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X139),X165)) ) ),
inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of]) ).
fof(i_0_5883,plain,
! [X34083,X34084] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34084),X34083))
| hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X34084,X34083)) = X34084 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__upt])]) ).
fof(i_0_5884,plain,
! [X23,X7] : ~ hBOOL(hAPP(hAPP(c_member(X7),X23),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_empty__iff]) ).
fof(i_0_5885,plain,
! [X25,X7] : ~ hBOOL(hAPP(hAPP(c_member(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_emptyE]) ).
fof(i_0_5886,plain,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,X33)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X33))
=> X90 = hAPP(c_Nat_OSuc,X33) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_5887,plain,
! [X34149,X34150] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34150,X34149) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X34150,hAPP(c_Nat_OSuc,X34149))),
inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upt]) ).
fof(i_0_5888,plain,
! [X44,X95] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X44)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X44),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X44)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X44))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X44)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastLessThanSuc]) ).
fof(i_0_5889,plain,
! [X292,X7,X6,X38] :
( ( hBOOL(hAPP(X38,X6))
=> hAPP(c_List_Ofilter(X7,X38),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)) = hAPP(hAPP(c_List_Olist_OCons(X7),X6),hAPP(c_List_Ofilter(X7,X38),X292)) )
& ( ~ hBOOL(hAPP(X38,X6))
=> hAPP(c_List_Ofilter(X7,X38),hAPP(hAPP(c_List_Olist_OCons(X7),X6),X292)) = hAPP(c_List_Ofilter(X7,X38),X292) ) ),
inference(fof_simplification,[status(thm)],[fact_filter_Osimps_I2_J]) ).
fof(i_0_5890,plain,
! [X95,X44] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X95)))
<=> X44 = X95 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_5891,plain,
! [X90,X33] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X90))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_OSuc,X90)))
=> X90 = X33 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_5892,plain,
! [X33,X90] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),hAPP(c_Nat_OSuc,X33)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> X90 = X33 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_5893,plain,
! [X21995,X21996] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21996,X21995),c_Divides_Odivmod__nat(X21996,X21995))),
inference(variable_rename,[status(thm)],[fact_divmod__nat__rel__divmod__nat]) ).
fof(i_0_5894,plain,
! [X21810] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X21810)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X21810)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_code__numeral_Osize_I4_J]) ).
fof(i_0_5895,plain,
! [X34179] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X34179) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X34179))),
inference(variable_rename,[status(thm)],[fact_atMost__upto]) ).
fof(i_0_5896,plain,
! [X21123] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21123),c_Int_OPls))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21123)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21123),c_Int_OPls))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21123)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X21123)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5190])]) ).
fof(i_0_5897,plain,
! [X21092] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21092),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21092)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21092),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21092)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X21092)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5191])]) ).
fof(i_0_5898,plain,
! [X21141,X21142] :
( ~ class_Int_Onumber__ring(X21142)
| hAPP(c_Int_Onumber__class_Onumber__of(X21142),c_Int_Opred(X21141)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21142),hAPP(c_Groups_Ouminus__class_Ouminus(X21142),c_Groups_Oone__class_Oone(X21142))),hAPP(c_Int_Onumber__class_Onumber__of(X21142),X21141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__pred])]) ).
fof(i_0_5899,plain,
! [X44,X23,X45,X24] :
( ~ hBOOL(hAPP(X24,X45))
=> c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X45,X44,X45) ),
inference(fof_simplification,[status(thm)],[fact_evaln_OWhileFalse]) ).
fof(i_0_5900,plain,
! [X157,X94,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X94,X157)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X94),X157)) ) ),
inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).
fof(i_0_5901,plain,
! [X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).
fof(i_0_5902,plain,
! [X157,X94,X7] :
( class_Orderings_Oorder(X7)
=> ( c_SetInterval_Oord__class_OgreaterThanAtMost(X7,X94,X157) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X94),X157)) ) ),
inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).
fof(i_0_5903,plain,
! [X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(X7,X25,X24) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X25),X24)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff]) ).
fof(i_0_5904,plain,
! [X127,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
<=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X127),X6)) )
| X6 = X127 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less]) ).
fof(i_0_5905,plain,
! [X127,X6] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X127),X6)) )
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X127))
& X6 != X127 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le]) ).
fof(i_0_5906,plain,
! [X84,X71] :
( X71 != X84
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X71),X84))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X71),X84))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X71)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oneq__le__trans]) ).
fof(i_0_5907,plain,
! [X98,X86] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X86),X98))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X98),X86)) )
| X86 = X98 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).
fof(i_0_5908,plain,
! [X84,X71] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X71),X84))
=> ( X71 != X84
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X71),X84))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X71)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__neq__trans]) ).
fof(i_0_5909,plain,
! [X21845,X21846] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21846),X21845))
| c_Divides_Odivmod__nat(X21846,X21845) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21846) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__base])]) ).
fof(i_0_5910,plain,
! [X7,X155,X149] :
( X149 = X155
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X149),X155))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X155),X149)) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_5911,plain,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)),X33)),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_5912,plain,
! [X96,X115] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115))
=> c_SMT_Oz3div(X96,X115) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),X115) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115))
=> c_SMT_Oz3div(X96,X115) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X115))) ) ),
inference(fof_simplification,[status(thm)],[fact_z3div__def]) ).
fof(i_0_5913,plain,
! [X33,X90] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33) = X90 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33),X33) ) ),
inference(fof_simplification,[status(thm)],[fact_mod__if]) ).
fof(i_0_5914,plain,
! [X33,X90] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X33) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33),X33) ),
inference(fof_simplification,[status(thm)],[fact_mod__geq]) ).
fof(i_0_5915,plain,
! [X127,X6,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X6),X127))
<=> X6 = X127 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_5916,plain,
! [X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X25),X24) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).
fof(i_0_5917,plain,
! [X24,X25,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X25),X24)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X25),X24)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).
fof(i_0_5918,plain,
! [X21093] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21093),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21093)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21093),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21093)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X21093)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5192])]) ).
fof(i_0_5919,negated_conjecture,
~ ! [X231,X232] :
( v_P(X231,X232)
=> ! [X233] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),X232,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X233)
=> v_Q(X231,X233) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(i_0_5920,plain,
! [X21814,X21815] :
( ( c_Code__Numeral_OSuc__code__numeral(X21815) != c_Code__Numeral_OSuc__code__numeral(X21814)
| X21815 = X21814 )
& ( X21815 != X21814
| c_Code__Numeral_OSuc__code__numeral(X21815) = c_Code__Numeral_OSuc__code__numeral(X21814) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject])]) ).
fof(i_0_5921,plain,
! [X21811] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X21811)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X21811)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_code__numeral_Osize_I2_J]) ).
fof(i_0_5922,plain,
! [X21253] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X21253)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21253)),
inference(variable_rename,[status(thm)],[fact_minus__Bit0]) ).
fof(i_0_5923,plain,
! [X21048] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21048)))
| hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21048)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21048)))
| hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21048)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X21048)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5193])]) ).
fof(i_0_5924,plain,
! [X149,X7] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X7),X3),X149))
<=> X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).
fof(i_0_5925,plain,
! [X292,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),hAPP(c_List_Oset(X7),X292)))
=> c_List_Oremove1(X7,X6,X292) = X292 ),
inference(fof_simplification,[status(thm)],[fact_remove1__idem]) ).
fof(i_0_5926,plain,
! [X34035,X34036] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X34036,X34035)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X34035),X34036),
inference(variable_rename,[status(thm)],[fact_length__upt]) ).
fof(i_0_5927,plain,
! [X86,X87] :
( class_Groups_Osgn__if(X87)
=> ( ( X86 = c_Groups_Ozero__class_Ozero(X87)
=> c_Groups_Osgn__class_Osgn(X87,X86) = c_Groups_Ozero__class_Ozero(X87) )
& ( X86 != c_Groups_Ozero__class_Ozero(X87)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> c_Groups_Osgn__class_Osgn(X87,X86) = c_Groups_Oone__class_Oone(X87) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Ozero__class_Ozero(X87)),X86))
=> c_Groups_Osgn__class_Osgn(X87,X86) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),c_Groups_Oone__class_Oone(X87)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_sgn__if]) ).
fof(i_0_5928,plain,
! [X34048,X34049] :
( ( c_List_Oupt(X34049,X34048) != c_List_Olist_ONil(tc_Nat_Onat)
| X34048 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34048),X34049)) )
& ( X34048 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_List_Oupt(X34049,X34048) = c_List_Olist_ONil(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34048),X34049))
| c_List_Oupt(X34049,X34048) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Nil__conv])])]) ).
fof(i_0_5929,plain,
! [X34046,X34047] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34047),X34046))
| c_List_Oupt(X34046,X34047) = c_List_Olist_ONil(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Nil])]) ).
fof(i_0_5930,plain,
! [X96,X115] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115))
=> c_SMT_Oz3mod(X96,X115) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X115) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115))
=> c_SMT_Oz3mod(X96,X115) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X115)) ) ),
inference(fof_simplification,[status(thm)],[fact_z3mod__def]) ).
fof(i_0_5931,plain,
! [X71,X87] :
( class_Groups_Oabs__if(X87)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),X71) = hAPP(c_Groups_Ouminus__class_Ouminus(X87),X71) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X71),c_Groups_Ozero__class_Ozero(X87)))
=> hAPP(c_Groups_Oabs__class_Oabs(X87),X71) = X71 ) ) ),
inference(fof_simplification,[status(thm)],[fact_abs__if]) ).
fof(i_0_5932,plain,
! [X87] :
( class_Rings_Olinordered__semidom(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),c_Groups_Oone__class_Oone(X87)),c_Groups_Ozero__class_Ozero(X87))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_5933,plain,
! [X87] :
( class_Rings_Olinordered__semidom(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),c_Groups_Oone__class_Oone(X87)),c_Groups_Ozero__class_Ozero(X87))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_5934,plain,
! [X33,X90] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X33))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X33)) = X90 ),
inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).
fof(i_0_5935,plain,
! [X34151] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X34151) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34151)),
inference(variable_rename,[status(thm)],[fact_atLeast__upt]) ).
fof(i_0_5936,plain,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( X86 != X98
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_5937,plain,
! [X6,X127,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X127),X6))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X6),X127))
<=> X6 = X127 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_5938,plain,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> ( X86 != X98
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_5939,plain,
! [X98,X86,X87] :
( class_Rings_Olinordered__idom(X87)
=> ( X86 != X98
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X98),X86)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_5940,plain,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_5941,plain,
! [X98,X86,X87] :
( class_Orderings_Olinorder(X87)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86)) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_5942,plain,
! [X86,X98,X87] :
( class_Orderings_Olinorder(X87)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X87),X98),X86))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X98)) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_5943,plain,
! [X34092,X34093] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X34093,X34092)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34093),X34092),
inference(variable_rename,[status(thm)],[fact_set__upt]) ).
fof(i_0_5944,plain,
! [X34094,X34095] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34095),X34094) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X34095,X34094)),
inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upt]) ).
fof(i_0_5945,plain,
! [X21108] : c_Int_Osucc(c_Int_Opred(X21108)) = X21108,
inference(variable_rename,[status(thm)],[fact_succ__pred]) ).
fof(i_0_5946,plain,
! [X21090,X21091] :
( ~ class_Int_Onumber__ring(X21091)
| hAPP(c_Int_Onumber__class_Onumber__of(X21091),c_Int_Osucc(X21090)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21091),c_Groups_Oone__class_Oone(X21091)),hAPP(c_Int_Onumber__class_Onumber__of(X21091),X21090)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__succ])]) ).
fof(i_0_5947,plain,
! [X25,X7,X149] :
( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X25),X149)) ),
inference(fof_simplification,[status(thm)],[fact_equals0D]) ).
fof(i_0_5948,plain,
! [X6] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X6))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ),
inference(fof_simplification,[status(thm)],[fact_not__neg__eq__ge__0]) ).
fof(i_0_5949,plain,
! [X95,X125] :
( hAPP(c_Int_Onat,X125) = X95
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X125))
=> X125 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X125))
=> X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__eq__iff]) ).
fof(i_0_5950,plain,
! [X125,X95] :
( X95 = hAPP(c_Int_Onat,X125)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X125))
=> X125 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X125))
=> X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__eq__iff2]) ).
fof(i_0_5951,plain,
! [X97] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X97)) = X97 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X97)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_int__nat__eq]) ).
fof(i_0_5952,plain,
! [X86,X98] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X86))
=> c_Nat__Transfer_Otsub(X86,X98) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X86),X98) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X86))
=> c_Nat__Transfer_Otsub(X86,X98) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_tsub__def]) ).
fof(i_0_5953,plain,
! [X139,X87] :
( class_Int_Onumber__ring(X87)
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = c_Groups_Ozero__class_Ozero(X87) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X87),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(X87),X139) ) ) ),
inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__eq]) ).
fof(i_0_5954,plain,
! [X22405,X22406] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22406,X22405) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X22406,X22405)),
inference(variable_rename,[status(thm)],[fact_mod__nat__def]) ).
fof(i_0_5955,plain,
! [X292,X7,X6,X38] :
( ~ hBOOL(hAPP(X38,X6))
=> c_List_Oremove1(X7,X6,hAPP(c_List_Ofilter(X7,X38),X292)) = hAPP(c_List_Ofilter(X7,X38),X292) ),
inference(fof_simplification,[status(thm)],[fact_remove1__filter__not]) ).
fof(i_0_5956,plain,
! [X22524,X22525] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22525),X22524) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X22525,X22524)),
inference(variable_rename,[status(thm)],[fact_div__nat__def]) ).
fof(i_0_5957,plain,
! [X139] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X139)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X139) ) ),
inference(fof_simplification,[status(thm)],[fact_int__nat__number__of]) ).
fof(i_0_5958,plain,
! [X114] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X114),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X114) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X114) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X114),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X114) = X114 ) ),
inference(fof_simplification,[status(thm)],[fact_zabs__def]) ).
fof(i_0_5959,plain,
! [X98,X86] :
( X86 != X98
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X86)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_5960,plain,
! [X21997,X21998,X21999] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21999,X21998),X21997))
| c_Divides_Odivmod__nat(X21999,X21998) = X21997 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__eq])]) ).
fof(i_0_5961,plain,
! [X114] :
( ( X114 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X114 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X114))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X114))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_zsgn__def]) ).
fof(i_0_5962,plain,
! [X34107,X34108] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X34108,X34107)),
inference(variable_rename,[status(thm)],[fact_sorted__upt]) ).
fof(i_0_5963,plain,
! [X29592,X29593] : c_Wellfounded_Owf(X29593,hAPP(c_Wellfounded_Omeasure(X29593),X29592)),
inference(variable_rename,[status(thm)],[fact_wf__measure]) ).
fof(i_0_5964,plain,
! [X86,X87] :
( class_Orderings_Opreorder(X87)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X87),X86),X86)) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_5965,plain,
! [X115,X96] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X115))
=> c_Quickcheck_Obeyond(X96,X115) = X115 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X115))
=> c_Quickcheck_Obeyond(X96,X115) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(fof_simplification,[status(thm)],[fact_beyond__def]) ).
fof(i_0_5966,plain,
! [X33533] : c_List_Orotate(X33533,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X33533)),
inference(variable_rename,[status(thm)],[fact_rotate0]) ).
fof(i_0_5967,plain,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_5968,plain,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_5969,plain,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_5970,plain,
! [X48,X49] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X49,X48)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X49))
=> ~ hBOOL(hAPP(c_Com_OWT,X48)) ) ),
inference(fof_simplification,[status(thm)],[fact_WTs__elim__cases_I4_J]) ).
fof(i_0_5971,plain,
! [X21833] : c_Divides_Odivmod__nat(X21833,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21833),
inference(variable_rename,[status(thm)],[fact_divmod__nat__zero]) ).
fof(i_0_5972,plain,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X33)),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_5973,plain,
! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X33)),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_5974,plain,
! [X21230,X21231] :
( ( c_Int_OBit0(X21231) != c_Int_OBit0(X21230)
| X21231 = X21230 )
& ( X21231 != X21230
| c_Int_OBit0(X21231) = c_Int_OBit0(X21230) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])]) ).
fof(i_0_5975,plain,
! [X2,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X2),X149) = c_Groups_Oone__class_Oone(X105) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__infinite]) ).
fof(i_0_5976,plain,
! [X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__mult(X105)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X105),X1),X149) = c_Groups_Oone__class_Oone(X105) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod_Oinfinite]) ).
fof(i_0_5977,plain,
! [X2,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X2),X149) = c_Groups_Ozero__class_Ozero(X105) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__infinite]) ).
fof(i_0_5978,plain,
! [X1,X149,X7,X105] :
( class_Groups_Ocomm__monoid__add(X105)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X105),X1),X149) = c_Groups_Ozero__class_Ozero(X105) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum_Oinfinite]) ).
fof(i_0_5979,plain,
! [X33] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33))),
inference(fof_simplification,[status(thm)],[fact_not__neg__int]) ).
fof(i_0_5980,plain,
! [X21817] : c_Code__Numeral_OSuc__code__numeral(X21817) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I3_J]) ).
fof(i_0_5981,plain,
! [X21816] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X21816),
inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I2_J]) ).
fof(i_0_5982,plain,
! [X194,X38] :
( ~ hBOOL(hAPP(hAPP(c_fimplies,X38),X194))
| ~ hBOOL(X38)
| hBOOL(X194) ),
inference(fof_simplification,[status(thm)],[help_c__fimplies__3]) ).
fof(i_0_5983,plain,
! [X149,X7] :
( hAPP(c_Finite__Set_Ocard(X7),X149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X149 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149)) ) ),
inference(fof_simplification,[status(thm)],[fact_card__eq__0__iff]) ).
fof(i_0_5984,plain,
! [X194,X38] :
( ~ hBOOL(hAPP(hAPP(c_fdisj,X38),X194))
| hBOOL(X38)
| hBOOL(X194) ),
inference(fof_simplification,[status(thm)],[help_c__fdisj__3]) ).
fof(i_0_5985,plain,
! [X194,X38] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X38),X194))
| hBOOL(X38) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(i_0_5986,plain,
! [X194,X38] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X38),X194))
| hBOOL(X194) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).
fof(i_0_5987,plain,
! [X38,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7),X38)
<=> ! [X3] : ~ hBOOL(hAPP(X38,X3)) ),
inference(fof_simplification,[status(thm)],[fact_empty__Collect__eq]) ).
fof(i_0_5988,plain,
! [X38,X7] :
( hAPP(c_Set_OCollect(X7),X38) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X38,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(i_0_5989,plain,
! [X127,X6] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X6),X127))
| X6 = X127 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_5990,plain,
! [X22751] : hAPP(c_Code__Numeral_Onat__of,X22751) = c_Code__Numeral_Onat__of__aux(X22751,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_nat__of__code]) ).
fof(i_0_5991,plain,
! [X21086] : c_Int_Osucc(X21086) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21086),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_succ__def]) ).
fof(i_0_5992,plain,
! [X21120] : c_Int_Opred(X21120) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21120),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_pred__def]) ).
fof(i_0_5993,plain,
! [X34113] : c_List_Oupt(X34113,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_upt__0]) ).
fof(i_0_5994,plain,
! [X194,X38] :
( ~ hBOOL(X38)
| ~ hBOOL(X194)
| hBOOL(hAPP(hAPP(c_fconj,X38),X194)) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).
fof(i_0_5995,plain,
! [X21121] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X21121) = c_Int_Opred(X21121),
inference(variable_rename,[status(thm)],[fact_add__Min]) ).
fof(i_0_5996,plain,
! [X87] :
( class_Int_Onumber__ring(X87)
=> ~ c_Int_Oiszero(X87,hAPP(c_Int_Onumber__class_Onumber__of(X87),c_Int_OMin)) ),
inference(fof_simplification,[status(thm)],[fact_nonzero__number__of__Min]) ).
fof(i_0_5997,plain,
! [X194,X38] :
( ~ hBOOL(X38)
| hBOOL(hAPP(hAPP(c_fdisj,X38),X194)) ),
inference(fof_simplification,[status(thm)],[help_c__fdisj__1]) ).
fof(i_0_5998,plain,
! [X38,X194] :
( ~ hBOOL(X194)
| hBOOL(hAPP(hAPP(c_fdisj,X38),X194)) ),
inference(fof_simplification,[status(thm)],[help_c__fdisj__2]) ).
fof(i_0_5999,plain,
! [X38,X194] :
( ~ hBOOL(X194)
| hBOOL(hAPP(hAPP(c_fimplies,X38),X194)) ),
inference(fof_simplification,[status(thm)],[help_c__fimplies__2]) ).
fof(i_0_6000,plain,
! [X86,X7] : ~ c_Option_Ois__none(X7,hAPP(c_Option_Ooption_OSome(X7),X86)),
inference(fof_simplification,[status(thm)],[fact_is__none__code_I2_J]) ).
fof(i_0_6001,plain,
! [X21240] :
( ( c_Int_OPls != c_Int_OBit0(X21240)
| c_Int_OPls = X21240 )
& ( c_Int_OPls != X21240
| c_Int_OPls = c_Int_OBit0(X21240) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])]) ).
fof(i_0_6002,plain,
! [X21241] :
( ( c_Int_OBit0(X21241) != c_Int_OPls
| X21241 = c_Int_OPls )
& ( X21241 != c_Int_OPls
| c_Int_OBit0(X21241) = c_Int_OPls ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])]) ).
fof(i_0_6003,plain,
! [X21255] : c_Int_OBit0(X21255) != c_Int_OMin,
inference(variable_rename,[status(thm)],[fact_rel__simps_I45_J]) ).
fof(i_0_6004,plain,
! [X21254] : c_Int_OMin != c_Int_OBit0(X21254),
inference(variable_rename,[status(thm)],[fact_rel__simps_I42_J]) ).
fof(i_0_6005,plain,
! [X97] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X97))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X97)) = X97 ),
inference(fof_simplification,[status(thm)],[fact_not__neg__nat]) ).
fof(i_0_6006,plain,
! [X149,X7] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X149))
=> hAPP(c_Finite__Set_Ocard(X7),X149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
fof(i_0_6007,plain,
! [X38] :
( ~ hBOOL(hAPP(c_fNot,X38))
| ~ hBOOL(X38) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(i_0_6008,plain,
! [X87] :
( class_Rings_Osemiring__1(X87)
=> ~ c_Int_Oiszero(X87,c_Groups_Oone__class_Oone(X87)) ),
inference(fof_simplification,[status(thm)],[fact_not__iszero__1]) ).
fof(i_0_6009,plain,
! [X38] :
( hBOOL(X38)
| hBOOL(hAPP(c_fNot,X38)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).
fof(i_0_6010,plain,
! [X27676,X27677,X27678,X27679,X27680,X27681,X27682,X27683,X27684,X27685,X27686] :
( ( hBOOL(hAPP(hAPP(c_member(X27686),esk247_11(X27676,X27677,X27678,X27679,X27680,X27681,X27682,X27683,X27684,X27685,X27686)),X27685))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X27680,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27686,tc_fun(X27680,tc_HOL_Obool)),X27678),hAPP(hAPP(c_COMBB(tc_fun(X27683,tc_fun(X27680,tc_HOL_Obool)),tc_fun(X27680,tc_HOL_Obool),X27686),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27683,tc_fun(X27680,tc_HOL_Obool)),X27677)),X27679))),X27676))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27683,tc_HOL_Obool)),X27677),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27683),X27682),X27681)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27686,tc_HOL_Obool)),X27678),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27686),X27685),X27684)))
| ~ c_Equiv__Relations_Ocongruent2(X27686,X27683,tc_fun(X27680,tc_HOL_Obool),X27684,X27681,X27679)
| ~ c_Equiv__Relations_Oequiv(X27683,X27682,X27681)
| ~ c_Equiv__Relations_Oequiv(X27686,X27685,X27684) )
& ( hBOOL(hAPP(hAPP(c_member(X27683),esk248_11(X27676,X27677,X27678,X27679,X27680,X27681,X27682,X27683,X27684,X27685,X27686)),X27682))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X27680,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27686,tc_fun(X27680,tc_HOL_Obool)),X27678),hAPP(hAPP(c_COMBB(tc_fun(X27683,tc_fun(X27680,tc_HOL_Obool)),tc_fun(X27680,tc_HOL_Obool),X27686),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27683,tc_fun(X27680,tc_HOL_Obool)),X27677)),X27679))),X27676))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27683,tc_HOL_Obool)),X27677),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27683),X27682),X27681)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27686,tc_HOL_Obool)),X27678),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27686),X27685),X27684)))
| ~ c_Equiv__Relations_Ocongruent2(X27686,X27683,tc_fun(X27680,tc_HOL_Obool),X27684,X27681,X27679)
| ~ c_Equiv__Relations_Oequiv(X27683,X27682,X27681)
| ~ c_Equiv__Relations_Oequiv(X27686,X27685,X27684) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27680,tc_HOL_Obool)),hAPP(hAPP(X27679,esk247_11(X27676,X27677,X27678,X27679,X27680,X27681,X27682,X27683,X27684,X27685,X27686)),esk248_11(X27676,X27677,X27678,X27679,X27680,X27681,X27682,X27683,X27684,X27685,X27686))),X27676))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X27680,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27686,tc_fun(X27680,tc_HOL_Obool)),X27678),hAPP(hAPP(c_COMBB(tc_fun(X27683,tc_fun(X27680,tc_HOL_Obool)),tc_fun(X27680,tc_HOL_Obool),X27686),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27683,tc_fun(X27680,tc_HOL_Obool)),X27677)),X27679))),X27676))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27683,tc_HOL_Obool)),X27677),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27683),X27682),X27681)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27686,tc_HOL_Obool)),X27678),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27686),X27685),X27684)))
| ~ c_Equiv__Relations_Ocongruent2(X27686,X27683,tc_fun(X27680,tc_HOL_Obool),X27684,X27681,X27679)
| ~ c_Equiv__Relations_Oequiv(X27683,X27682,X27681)
| ~ c_Equiv__Relations_Oequiv(X27686,X27685,X27684) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type2])])])]) ).
fof(i_0_6011,plain,
! [X17628,X17629,X17630,X17631,X17632,X17633,X17634,X17635,X17636,X17637,X17638,X17639] : c_Com_Ocom_Ocom__rec(X17639,X17638,X17637,X17636,X17635,X17634,X17633,X17632,X17631,c_Com_Ocom_OCond(X17630,X17629,X17628)) = hAPP(hAPP(hAPP(hAPP(hAPP(X17634,X17630),X17629),X17628),c_Com_Ocom_Ocom__rec(X17639,X17638,X17637,X17636,X17635,X17634,X17633,X17632,X17631,X17629)),c_Com_Ocom_Ocom__rec(X17639,X17638,X17637,X17636,X17635,X17634,X17633,X17632,X17631,X17628)),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I5_J]) ).
fof(i_0_6012,plain,
! [X17640,X17641,X17642,X17643,X17644,X17645,X17646,X17647,X17648,X17649,X17650] : c_Com_Ocom_Ocom__rec(X17650,X17649,X17648,X17647,X17646,X17645,X17644,X17643,X17642,c_Com_Ocom_OSemi(X17641,X17640)) = hAPP(hAPP(hAPP(hAPP(X17646,X17641),X17640),c_Com_Ocom_Ocom__rec(X17650,X17649,X17648,X17647,X17646,X17645,X17644,X17643,X17642,X17641)),c_Com_Ocom_Ocom__rec(X17650,X17649,X17648,X17647,X17646,X17645,X17644,X17643,X17642,X17640)),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I4_J]) ).
cnf(i_0_6013,plain,
c_Divides_Oadjust(X1) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(split_conjunct,[status(thm)],[i_0_5194]) ).
cnf(i_0_6014,plain,
c_Int_Osucc(c_Int_OBit0(X1)) = c_Int_OBit1(X1),
inference(split_conjunct,[status(thm)],[i_0_5195]) ).
cnf(i_0_6015,plain,
c_Int_OBit0(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
inference(split_conjunct,[status(thm)],[i_0_5196]) ).
cnf(i_0_6016,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin) = c_Int_Osucc(X1),
inference(split_conjunct,[status(thm)],[i_0_5197]) ).
fof(i_0_6017,plain,
! [X29406,X29407,X29408,X29409,X29410,X29411,X29412] :
( ~ class_Rings_Osemiring__0(X29412)
| ~ c_Fun_Oinj__on(tc_prod(X29411,X29410),X29412,hAPP(c_Product__Type_Oprod_Oprod__case(X29411,X29410,X29412),hAPP(hAPP(c_COMBC(X29411,tc_fun(X29410,X29412),tc_fun(X29410,X29412)),hAPP(hAPP(c_COMBB(tc_fun(X29412,X29412),tc_fun(tc_fun(X29410,X29412),tc_fun(X29410,X29412)),X29411),c_COMBB(X29412,X29412,X29410)),hAPP(hAPP(c_COMBB(X29412,tc_fun(X29412,X29412),X29411),c_Groups_Otimes__class_Otimes(X29412)),X29409))),X29408)),hAPP(hAPP(c_Product__Type_OSigma(X29411,X29410),X29407),hAPP(c_COMBK(tc_fun(X29410,tc_HOL_Obool),X29411),X29406)))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29412),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29411,X29412),X29409),X29407)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29410,X29412),X29408),X29406)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29412,X29412),c_Fun_Oid(X29412)),hAPP(c_Set_OCollect(X29412),hAPP(hAPP(c_COMBB(tc_fun(X29411,tc_HOL_Obool),tc_HOL_Obool,X29412),c_HOL_OEx(X29411)),hAPP(hAPP(c_COMBB(tc_fun(X29411,tc_fun(X29410,tc_HOL_Obool)),tc_fun(X29411,tc_HOL_Obool),X29412),hAPP(c_COMBB(tc_fun(X29410,tc_HOL_Obool),tc_HOL_Obool,X29411),c_HOL_OEx(X29410))),hAPP(hAPP(c_COMBC(X29412,tc_fun(X29411,tc_fun(X29410,tc_HOL_Obool)),tc_fun(X29411,tc_fun(X29410,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29411,tc_fun(tc_fun(X29410,tc_HOL_Obool),tc_fun(X29410,tc_HOL_Obool))),tc_fun(tc_fun(X29411,tc_fun(X29410,tc_HOL_Obool)),tc_fun(X29411,tc_fun(X29410,tc_HOL_Obool))),X29412),c_COMBS(X29411,tc_fun(X29410,tc_HOL_Obool),tc_fun(X29410,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29411,tc_fun(X29410,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29411,tc_fun(tc_fun(X29410,tc_HOL_Obool),tc_fun(X29410,tc_HOL_Obool))),X29412),hAPP(c_COMBB(tc_fun(X29410,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29410,tc_HOL_Obool),tc_fun(X29410,tc_HOL_Obool)),X29411),c_COMBS(X29410,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29411,tc_fun(X29410,tc_HOL_Obool)),tc_fun(X29411,tc_fun(X29410,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X29412),hAPP(c_COMBB(tc_fun(X29410,tc_HOL_Obool),tc_fun(X29410,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29411),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29410),c_fconj))),hAPP(hAPP(c_COMBC(X29412,tc_fun(X29411,tc_fun(X29410,X29412)),tc_fun(X29411,tc_fun(X29410,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29410,X29412),tc_fun(X29410,tc_HOL_Obool)),tc_fun(tc_fun(X29411,tc_fun(X29410,X29412)),tc_fun(X29411,tc_fun(X29410,tc_HOL_Obool))),X29412),c_COMBB(tc_fun(X29410,X29412),tc_fun(X29410,tc_HOL_Obool),X29411)),hAPP(hAPP(c_COMBB(tc_fun(X29412,tc_HOL_Obool),tc_fun(tc_fun(X29410,X29412),tc_fun(X29410,tc_HOL_Obool)),X29412),c_COMBB(X29412,tc_HOL_Obool,X29410)),c_fequal))),hAPP(hAPP(c_COMBC(X29411,tc_fun(X29410,X29412),tc_fun(X29410,X29412)),hAPP(hAPP(c_COMBB(tc_fun(X29412,X29412),tc_fun(tc_fun(X29410,X29412),tc_fun(X29410,X29412)),X29411),c_COMBB(X29412,X29412,X29410)),hAPP(hAPP(c_COMBB(X29412,tc_fun(X29412,X29412),X29411),c_Groups_Otimes__class_Otimes(X29412)),X29409))),X29408)))))),hAPP(hAPP(c_COMBC(X29411,tc_fun(X29410,tc_HOL_Obool),tc_fun(X29410,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29410,tc_HOL_Obool),tc_fun(X29410,tc_HOL_Obool)),X29411),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29410)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29411),c_fconj),hAPP(hAPP(c_COMBC(X29411,tc_fun(X29411,tc_HOL_Obool),tc_HOL_Obool),c_member(X29411)),X29407)))),hAPP(hAPP(c_COMBC(X29410,tc_fun(X29410,tc_HOL_Obool),tc_HOL_Obool),c_member(X29410)),X29406))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mult__setsum__if__inj])]) ).
fof(i_0_6018,plain,
! [X29482,X29483,X29484,X29485,X29486] : hAPP(hAPP(c_Relation_Orel__comp(X29486,X29485,X29484),X29483),X29482) = hAPP(c_Set_OCollect(tc_prod(X29486,X29484)),hAPP(c_Product__Type_Oprod_Oprod__case(X29486,X29484,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29484,tc_fun(X29485,tc_HOL_Obool)),tc_fun(X29484,tc_HOL_Obool),X29486),hAPP(c_COMBB(tc_fun(X29485,tc_HOL_Obool),tc_HOL_Obool,X29484),c_HOL_OEx(X29485))),hAPP(hAPP(c_COMBC(X29486,tc_fun(X29484,tc_fun(X29485,tc_HOL_Obool)),tc_fun(X29484,tc_fun(X29485,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29485,tc_HOL_Obool),tc_fun(X29485,tc_HOL_Obool)),tc_fun(tc_fun(X29484,tc_fun(X29485,tc_HOL_Obool)),tc_fun(X29484,tc_fun(X29485,tc_HOL_Obool))),X29486),c_COMBB(tc_fun(X29485,tc_HOL_Obool),tc_fun(X29485,tc_HOL_Obool),X29484)),hAPP(hAPP(c_COMBB(tc_fun(X29485,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29485,tc_HOL_Obool),tc_fun(X29485,tc_HOL_Obool)),X29486),c_COMBS(X29485,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29485,tc_HOL_Obool),tc_fun(X29485,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29486),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29485),c_fconj)),hAPP(hAPP(c_COMBC(X29486,tc_fun(tc_prod(X29486,X29485),tc_HOL_Obool),tc_fun(X29485,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29485,tc_fun(tc_fun(tc_prod(X29486,X29485),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29486,X29485),tc_HOL_Obool),tc_fun(X29485,tc_HOL_Obool)),X29486),c_COMBC(X29485,tc_fun(tc_prod(X29486,X29485),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29485,tc_prod(X29486,X29485)),tc_fun(X29485,tc_fun(tc_fun(tc_prod(X29486,X29485),tc_HOL_Obool),tc_HOL_Obool)),X29486),hAPP(c_COMBB(tc_prod(X29486,X29485),tc_fun(tc_fun(tc_prod(X29486,X29485),tc_HOL_Obool),tc_HOL_Obool),X29485),c_member(tc_prod(X29486,X29485)))),c_Product__Type_OPair(X29486,X29485)))),X29483))))),hAPP(hAPP(c_COMBC(X29484,tc_fun(tc_prod(X29485,X29484),tc_HOL_Obool),tc_fun(X29485,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29485,tc_fun(tc_fun(tc_prod(X29485,X29484),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29485,X29484),tc_HOL_Obool),tc_fun(X29485,tc_HOL_Obool)),X29484),c_COMBC(X29485,tc_fun(tc_prod(X29485,X29484),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29485,tc_prod(X29485,X29484)),tc_fun(X29485,tc_fun(tc_fun(tc_prod(X29485,X29484),tc_HOL_Obool),tc_HOL_Obool)),X29484),hAPP(c_COMBB(tc_prod(X29485,X29484),tc_fun(tc_fun(tc_prod(X29485,X29484),tc_HOL_Obool),tc_HOL_Obool),X29485),c_member(tc_prod(X29485,X29484)))),hAPP(c_COMBC(X29485,X29484,tc_prod(X29485,X29484)),c_Product__Type_OPair(X29485,X29484))))),X29482))))),
inference(variable_rename,[status(thm)],[fact_rel__comp__def]) ).
fof(i_0_6019,plain,
! [X29364,X29365,X29366] :
( ~ class_Orderings_Olinorder(X29366)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29366),X29365))
| X29365 = c_Orderings_Obot__class_Obot(tc_fun(X29366,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29366),X29364))
| X29364 = c_Orderings_Obot__class_Obot(tc_fun(X29366,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X29366),c_Big__Operators_Olattice_OInf__fin(X29366,c_Orderings_Oord__class_Omin(X29366),X29365)),c_Big__Operators_Olattice_OInf__fin(X29366,c_Orderings_Oord__class_Omin(X29366),X29364)) = c_Big__Operators_Olattice_OInf__fin(X29366,c_Orderings_Oord__class_Omin(X29366),hAPP(c_Set_OCollect(X29366),hAPP(hAPP(c_COMBB(tc_fun(X29366,tc_HOL_Obool),tc_HOL_Obool,X29366),c_HOL_OEx(X29366)),hAPP(hAPP(c_COMBB(tc_fun(X29366,tc_fun(X29366,tc_HOL_Obool)),tc_fun(X29366,tc_HOL_Obool),X29366),hAPP(c_COMBB(tc_fun(X29366,tc_HOL_Obool),tc_HOL_Obool,X29366),c_HOL_OEx(X29366))),hAPP(hAPP(c_COMBC(X29366,tc_fun(X29366,tc_fun(X29366,tc_HOL_Obool)),tc_fun(X29366,tc_fun(X29366,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29366,tc_fun(tc_fun(X29366,tc_HOL_Obool),tc_fun(X29366,tc_HOL_Obool))),tc_fun(tc_fun(X29366,tc_fun(X29366,tc_HOL_Obool)),tc_fun(X29366,tc_fun(X29366,tc_HOL_Obool))),X29366),c_COMBS(X29366,tc_fun(X29366,tc_HOL_Obool),tc_fun(X29366,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29366,tc_fun(X29366,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29366,tc_fun(tc_fun(X29366,tc_HOL_Obool),tc_fun(X29366,tc_HOL_Obool))),X29366),hAPP(c_COMBB(tc_fun(X29366,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29366,tc_HOL_Obool),tc_fun(X29366,tc_HOL_Obool)),X29366),c_COMBS(X29366,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29366,tc_fun(X29366,tc_HOL_Obool)),tc_fun(X29366,tc_fun(X29366,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X29366),hAPP(c_COMBB(tc_fun(X29366,tc_HOL_Obool),tc_fun(X29366,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29366),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29366),c_fconj))),hAPP(hAPP(c_COMBC(X29366,tc_fun(X29366,tc_fun(X29366,X29366)),tc_fun(X29366,tc_fun(X29366,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29366,X29366),tc_fun(X29366,tc_HOL_Obool)),tc_fun(tc_fun(X29366,tc_fun(X29366,X29366)),tc_fun(X29366,tc_fun(X29366,tc_HOL_Obool))),X29366),c_COMBB(tc_fun(X29366,X29366),tc_fun(X29366,tc_HOL_Obool),X29366)),hAPP(hAPP(c_COMBB(tc_fun(X29366,tc_HOL_Obool),tc_fun(tc_fun(X29366,X29366),tc_fun(X29366,tc_HOL_Obool)),X29366),c_COMBB(X29366,tc_HOL_Obool,X29366)),c_fequal))),c_Orderings_Oord__class_Omax(X29366)))))),hAPP(hAPP(c_COMBC(X29366,tc_fun(X29366,tc_HOL_Obool),tc_fun(X29366,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29366,tc_HOL_Obool),tc_fun(X29366,tc_HOL_Obool)),X29366),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29366)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29366),c_fconj),hAPP(hAPP(c_COMBC(X29366,tc_fun(X29366,tc_HOL_Obool),tc_HOL_Obool),c_member(X29366)),X29365)))),hAPP(hAPP(c_COMBC(X29366,tc_fun(X29366,tc_HOL_Obool),tc_HOL_Obool),c_member(X29366)),X29364))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib])]) ).
fof(i_0_6020,plain,
! [X29361,X29362,X29363] :
( ~ class_Orderings_Olinorder(X29363)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29363),X29362))
| X29362 = c_Orderings_Obot__class_Obot(tc_fun(X29363,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29363),X29361))
| X29361 = c_Orderings_Obot__class_Obot(tc_fun(X29363,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X29363),c_Big__Operators_Olattice_OSup__fin(X29363,c_Orderings_Oord__class_Omax(X29363),X29362)),c_Big__Operators_Olattice_OSup__fin(X29363,c_Orderings_Oord__class_Omax(X29363),X29361)) = c_Big__Operators_Olattice_OSup__fin(X29363,c_Orderings_Oord__class_Omax(X29363),hAPP(c_Set_OCollect(X29363),hAPP(hAPP(c_COMBB(tc_fun(X29363,tc_HOL_Obool),tc_HOL_Obool,X29363),c_HOL_OEx(X29363)),hAPP(hAPP(c_COMBB(tc_fun(X29363,tc_fun(X29363,tc_HOL_Obool)),tc_fun(X29363,tc_HOL_Obool),X29363),hAPP(c_COMBB(tc_fun(X29363,tc_HOL_Obool),tc_HOL_Obool,X29363),c_HOL_OEx(X29363))),hAPP(hAPP(c_COMBC(X29363,tc_fun(X29363,tc_fun(X29363,tc_HOL_Obool)),tc_fun(X29363,tc_fun(X29363,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29363,tc_fun(tc_fun(X29363,tc_HOL_Obool),tc_fun(X29363,tc_HOL_Obool))),tc_fun(tc_fun(X29363,tc_fun(X29363,tc_HOL_Obool)),tc_fun(X29363,tc_fun(X29363,tc_HOL_Obool))),X29363),c_COMBS(X29363,tc_fun(X29363,tc_HOL_Obool),tc_fun(X29363,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29363,tc_fun(X29363,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29363,tc_fun(tc_fun(X29363,tc_HOL_Obool),tc_fun(X29363,tc_HOL_Obool))),X29363),hAPP(c_COMBB(tc_fun(X29363,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29363,tc_HOL_Obool),tc_fun(X29363,tc_HOL_Obool)),X29363),c_COMBS(X29363,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29363,tc_fun(X29363,tc_HOL_Obool)),tc_fun(X29363,tc_fun(X29363,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X29363),hAPP(c_COMBB(tc_fun(X29363,tc_HOL_Obool),tc_fun(X29363,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29363),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29363),c_fconj))),hAPP(hAPP(c_COMBC(X29363,tc_fun(X29363,tc_fun(X29363,X29363)),tc_fun(X29363,tc_fun(X29363,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29363,X29363),tc_fun(X29363,tc_HOL_Obool)),tc_fun(tc_fun(X29363,tc_fun(X29363,X29363)),tc_fun(X29363,tc_fun(X29363,tc_HOL_Obool))),X29363),c_COMBB(tc_fun(X29363,X29363),tc_fun(X29363,tc_HOL_Obool),X29363)),hAPP(hAPP(c_COMBB(tc_fun(X29363,tc_HOL_Obool),tc_fun(tc_fun(X29363,X29363),tc_fun(X29363,tc_HOL_Obool)),X29363),c_COMBB(X29363,tc_HOL_Obool,X29363)),c_fequal))),c_Orderings_Oord__class_Omin(X29363)))))),hAPP(hAPP(c_COMBC(X29363,tc_fun(X29363,tc_HOL_Obool),tc_fun(X29363,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29363,tc_HOL_Obool),tc_fun(X29363,tc_HOL_Obool)),X29363),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29363)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29363),c_fconj),hAPP(hAPP(c_COMBC(X29363,tc_fun(X29363,tc_HOL_Obool),tc_HOL_Obool),c_member(X29363)),X29362)))),hAPP(hAPP(c_COMBC(X29363,tc_fun(X29363,tc_HOL_Obool),tc_HOL_Obool),c_member(X29363)),X29361))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib])]) ).
fof(i_0_6021,plain,
! [X29394,X29395,X29396] :
( ~ class_Lattices_Odistrib__lattice(X29396)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29396),X29395))
| X29395 = c_Orderings_Obot__class_Obot(tc_fun(X29396,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29396),X29394))
| X29394 = c_Orderings_Obot__class_Obot(tc_fun(X29396,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29396),c_Big__Operators_Olattice__class_OSup__fin(X29396,X29395)),c_Big__Operators_Olattice__class_OSup__fin(X29396,X29394)) = c_Big__Operators_Olattice__class_OSup__fin(X29396,hAPP(c_Set_OCollect(X29396),hAPP(hAPP(c_COMBB(tc_fun(X29396,tc_HOL_Obool),tc_HOL_Obool,X29396),c_HOL_OEx(X29396)),hAPP(hAPP(c_COMBB(tc_fun(X29396,tc_fun(X29396,tc_HOL_Obool)),tc_fun(X29396,tc_HOL_Obool),X29396),hAPP(c_COMBB(tc_fun(X29396,tc_HOL_Obool),tc_HOL_Obool,X29396),c_HOL_OEx(X29396))),hAPP(hAPP(c_COMBC(X29396,tc_fun(X29396,tc_fun(X29396,tc_HOL_Obool)),tc_fun(X29396,tc_fun(X29396,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29396,tc_fun(tc_fun(X29396,tc_HOL_Obool),tc_fun(X29396,tc_HOL_Obool))),tc_fun(tc_fun(X29396,tc_fun(X29396,tc_HOL_Obool)),tc_fun(X29396,tc_fun(X29396,tc_HOL_Obool))),X29396),c_COMBS(X29396,tc_fun(X29396,tc_HOL_Obool),tc_fun(X29396,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29396,tc_fun(X29396,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29396,tc_fun(tc_fun(X29396,tc_HOL_Obool),tc_fun(X29396,tc_HOL_Obool))),X29396),hAPP(c_COMBB(tc_fun(X29396,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29396,tc_HOL_Obool),tc_fun(X29396,tc_HOL_Obool)),X29396),c_COMBS(X29396,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29396,tc_fun(X29396,tc_HOL_Obool)),tc_fun(X29396,tc_fun(X29396,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X29396),hAPP(c_COMBB(tc_fun(X29396,tc_HOL_Obool),tc_fun(X29396,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29396),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29396),c_fconj))),hAPP(hAPP(c_COMBC(X29396,tc_fun(X29396,tc_fun(X29396,X29396)),tc_fun(X29396,tc_fun(X29396,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29396,X29396),tc_fun(X29396,tc_HOL_Obool)),tc_fun(tc_fun(X29396,tc_fun(X29396,X29396)),tc_fun(X29396,tc_fun(X29396,tc_HOL_Obool))),X29396),c_COMBB(tc_fun(X29396,X29396),tc_fun(X29396,tc_HOL_Obool),X29396)),hAPP(hAPP(c_COMBB(tc_fun(X29396,tc_HOL_Obool),tc_fun(tc_fun(X29396,X29396),tc_fun(X29396,tc_HOL_Obool)),X29396),c_COMBB(X29396,tc_HOL_Obool,X29396)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X29396)))))),hAPP(hAPP(c_COMBC(X29396,tc_fun(X29396,tc_HOL_Obool),tc_fun(X29396,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29396,tc_HOL_Obool),tc_fun(X29396,tc_HOL_Obool)),X29396),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29396)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29396),c_fconj),hAPP(hAPP(c_COMBC(X29396,tc_fun(X29396,tc_HOL_Obool),tc_HOL_Obool),c_member(X29396)),X29395)))),hAPP(hAPP(c_COMBC(X29396,tc_fun(X29396,tc_HOL_Obool),tc_HOL_Obool),c_member(X29396)),X29394))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib])]) ).
fof(i_0_6022,plain,
! [X29391,X29392,X29393] :
( ~ class_Lattices_Odistrib__lattice(X29393)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29393),X29392))
| X29392 = c_Orderings_Obot__class_Obot(tc_fun(X29393,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29393),X29391))
| X29391 = c_Orderings_Obot__class_Obot(tc_fun(X29393,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29393),c_Big__Operators_Olattice__class_OInf__fin(X29393,X29392)),c_Big__Operators_Olattice__class_OInf__fin(X29393,X29391)) = c_Big__Operators_Olattice__class_OInf__fin(X29393,hAPP(c_Set_OCollect(X29393),hAPP(hAPP(c_COMBB(tc_fun(X29393,tc_HOL_Obool),tc_HOL_Obool,X29393),c_HOL_OEx(X29393)),hAPP(hAPP(c_COMBB(tc_fun(X29393,tc_fun(X29393,tc_HOL_Obool)),tc_fun(X29393,tc_HOL_Obool),X29393),hAPP(c_COMBB(tc_fun(X29393,tc_HOL_Obool),tc_HOL_Obool,X29393),c_HOL_OEx(X29393))),hAPP(hAPP(c_COMBC(X29393,tc_fun(X29393,tc_fun(X29393,tc_HOL_Obool)),tc_fun(X29393,tc_fun(X29393,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29393,tc_fun(tc_fun(X29393,tc_HOL_Obool),tc_fun(X29393,tc_HOL_Obool))),tc_fun(tc_fun(X29393,tc_fun(X29393,tc_HOL_Obool)),tc_fun(X29393,tc_fun(X29393,tc_HOL_Obool))),X29393),c_COMBS(X29393,tc_fun(X29393,tc_HOL_Obool),tc_fun(X29393,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29393,tc_fun(X29393,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29393,tc_fun(tc_fun(X29393,tc_HOL_Obool),tc_fun(X29393,tc_HOL_Obool))),X29393),hAPP(c_COMBB(tc_fun(X29393,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29393,tc_HOL_Obool),tc_fun(X29393,tc_HOL_Obool)),X29393),c_COMBS(X29393,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29393,tc_fun(X29393,tc_HOL_Obool)),tc_fun(X29393,tc_fun(X29393,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X29393),hAPP(c_COMBB(tc_fun(X29393,tc_HOL_Obool),tc_fun(X29393,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29393),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29393),c_fconj))),hAPP(hAPP(c_COMBC(X29393,tc_fun(X29393,tc_fun(X29393,X29393)),tc_fun(X29393,tc_fun(X29393,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29393,X29393),tc_fun(X29393,tc_HOL_Obool)),tc_fun(tc_fun(X29393,tc_fun(X29393,X29393)),tc_fun(X29393,tc_fun(X29393,tc_HOL_Obool))),X29393),c_COMBB(tc_fun(X29393,X29393),tc_fun(X29393,tc_HOL_Obool),X29393)),hAPP(hAPP(c_COMBB(tc_fun(X29393,tc_HOL_Obool),tc_fun(tc_fun(X29393,X29393),tc_fun(X29393,tc_HOL_Obool)),X29393),c_COMBB(X29393,tc_HOL_Obool,X29393)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X29393)))))),hAPP(hAPP(c_COMBC(X29393,tc_fun(X29393,tc_HOL_Obool),tc_fun(X29393,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29393,tc_HOL_Obool),tc_fun(X29393,tc_HOL_Obool)),X29393),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29393)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29393),c_fconj),hAPP(hAPP(c_COMBC(X29393,tc_fun(X29393,tc_HOL_Obool),tc_HOL_Obool),c_member(X29393)),X29392)))),hAPP(hAPP(c_COMBC(X29393,tc_fun(X29393,tc_HOL_Obool),tc_HOL_Obool),c_member(X29393)),X29391))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib])]) ).
fof(i_0_6023,plain,
! [X17616,X17617,X17618,X17619,X17620,X17621,X17622,X17623,X17624,X17625,X17626,X17627] : c_Com_Ocom_Ocom__rec(X17627,X17626,X17625,X17624,X17623,X17622,X17621,X17620,X17619,c_Com_Ocom_OLocal(X17618,X17617,X17616)) = hAPP(hAPP(hAPP(hAPP(X17624,X17618),X17617),X17616),c_Com_Ocom_Ocom__rec(X17627,X17626,X17625,X17624,X17623,X17622,X17621,X17620,X17619,X17616)),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I3_J]) ).
fof(i_0_6024,plain,
! [X17847,X17848,X17849,X17850,X17851,X17852,X17853,X17854,X17855,X17856,X17857] : c_Com_Ocom_Ocom__rec(X17857,X17856,X17855,X17854,X17853,X17852,X17851,X17850,X17849,c_Com_Ocom_OWhile(X17848,X17847)) = hAPP(hAPP(hAPP(X17851,X17848),X17847),c_Com_Ocom_Ocom__rec(X17857,X17856,X17855,X17854,X17853,X17852,X17851,X17850,X17849,X17847)),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I6_J]) ).
fof(i_0_6025,plain,
! [X32376,X32377,X32378] : c_List_Oset__Cons(X32378,X32377,X32376) = hAPP(c_Set_OCollect(tc_List_Olist(X32378)),hAPP(hAPP(c_COMBB(tc_fun(X32378,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X32378)),c_HOL_OEx(X32378)),hAPP(hAPP(c_COMBB(tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_HOL_Obool)),tc_fun(X32378,tc_HOL_Obool),tc_List_Olist(X32378)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X32378),tc_HOL_Obool),tc_HOL_Obool,X32378),c_HOL_OEx(tc_List_Olist(X32378)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32378),tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_HOL_Obool)),tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X32378,tc_fun(tc_fun(tc_List_Olist(X32378),tc_HOL_Obool),tc_fun(tc_List_Olist(X32378),tc_HOL_Obool))),tc_fun(tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_HOL_Obool)),tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_HOL_Obool))),tc_List_Olist(X32378)),c_COMBS(X32378,tc_fun(tc_List_Olist(X32378),tc_HOL_Obool),tc_fun(tc_List_Olist(X32378),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X32378,tc_fun(tc_fun(tc_List_Olist(X32378),tc_HOL_Obool),tc_fun(tc_List_Olist(X32378),tc_HOL_Obool))),tc_List_Olist(X32378)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X32378),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X32378),tc_HOL_Obool),tc_fun(tc_List_Olist(X32378),tc_HOL_Obool)),X32378),c_COMBS(tc_List_Olist(X32378),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_HOL_Obool)),tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X32378)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X32378),tc_HOL_Obool),tc_fun(tc_List_Olist(X32378),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X32378),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32378)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32378),tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_List_Olist(X32378))),tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X32378),tc_List_Olist(X32378)),tc_fun(tc_List_Olist(X32378),tc_HOL_Obool)),tc_fun(tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_List_Olist(X32378))),tc_fun(X32378,tc_fun(tc_List_Olist(X32378),tc_HOL_Obool))),tc_List_Olist(X32378)),c_COMBB(tc_fun(tc_List_Olist(X32378),tc_List_Olist(X32378)),tc_fun(tc_List_Olist(X32378),tc_HOL_Obool),X32378)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32378),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32378),tc_List_Olist(X32378)),tc_fun(tc_List_Olist(X32378),tc_HOL_Obool)),tc_List_Olist(X32378)),c_COMBB(tc_List_Olist(X32378),tc_HOL_Obool,tc_List_Olist(X32378))),c_fequal))),c_List_Olist_OCons(X32378)))))),hAPP(hAPP(c_COMBC(X32378,tc_fun(tc_List_Olist(X32378),tc_HOL_Obool),tc_fun(tc_List_Olist(X32378),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32378),tc_HOL_Obool),tc_fun(tc_List_Olist(X32378),tc_HOL_Obool)),X32378),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X32378))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32378),c_fconj),hAPP(hAPP(c_COMBC(X32378,tc_fun(X32378,tc_HOL_Obool),tc_HOL_Obool),c_member(X32378)),X32377)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32378),tc_fun(tc_List_Olist(X32378),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X32378))),X32376)))))),
inference(variable_rename,[status(thm)],[fact_set__Cons__def]) ).
fof(i_0_6026,plain,
! [X28964,X28965,X28966,X28967,X28968,X28969,X28970,X28971] :
( ( X28969 = hAPP(hAPP(c_Product__Type_OPair(X28971,X28970),hAPP(X28966,esk291_8(X28964,X28965,X28966,X28967,X28968,X28969,X28970,X28971))),hAPP(X28965,esk292_8(X28964,X28965,X28966,X28967,X28968,X28969,X28970,X28971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28971,X28970)),X28969),hAPP(c_Set_Oimage(tc_prod(X28968,X28967),tc_prod(X28971,X28970),c_Product__Type_Omap__pair(X28968,X28971,X28967,X28970,X28966,X28965)),X28964))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28968,X28967)),hAPP(hAPP(c_Product__Type_OPair(X28968,X28967),esk291_8(X28964,X28965,X28966,X28967,X28968,X28969,X28970,X28971)),esk292_8(X28964,X28965,X28966,X28967,X28968,X28969,X28970,X28971))),X28964))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28971,X28970)),X28969),hAPP(c_Set_Oimage(tc_prod(X28968,X28967),tc_prod(X28971,X28970),c_Product__Type_Omap__pair(X28968,X28971,X28967,X28970,X28966,X28965)),X28964))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5198])])])]) ).
fof(i_0_6027,plain,
! [X25666,X25667,X25668,X25669,X25670,X25671,X25672,X25673] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X25673,X25672,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25673)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25673),X25671),hAPP(c_Com_Ocom_OBODY,X25670)),hAPP(hAPP(c_COMBC(X25673,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X25673),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X25669)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,X25668)))),X25667)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25673),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(X25673,X25672,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25673)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25673),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),X25673),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,X25668)))),hAPP(hAPP(c_COMBC(X25673,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X25673),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X25671)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),X25666)))),c_Com_Ocom_OCall(X25667,X25670,X25666)),X25669)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25673),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OCall])]) ).
cnf(i_0_6028,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X2,X1) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_5199]) ).
cnf(i_0_6029,plain,
c_Product__Type_Oapsnd(X1,X2,X3,X4) = c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),
inference(split_conjunct,[status(thm)],[i_0_5200]) ).
cnf(i_0_6030,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X2,X1) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_5201]) ).
fof(i_0_6031,plain,
! [X31436,X31437,X31438,X31439,X31440,X31441,X31442,X31443] :
( ( hBOOL(hAPP(hAPP(c_member(X31439),esk403_8(X31436,X31437,X31438,X31439,X31440,X31441,X31442,X31443)),X31438))
| ~ hBOOL(hAPP(hAPP(c_member(X31439),X31436),X31438))
| hAPP(c_Set_Oimage(X31443,X31442,X31441),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31439,tc_fun(X31443,tc_HOL_Obool)),X31438),X31437)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31439,tc_fun(X31442,tc_HOL_Obool)),X31438),hAPP(hAPP(c_COMBB(tc_fun(X31443,tc_HOL_Obool),tc_fun(X31442,tc_HOL_Obool),X31439),c_Set_Oimage(X31443,X31442,X31441)),X31437))
| ~ c_Fun_Oinj__on(X31443,X31442,X31441,X31440) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31443,tc_HOL_Obool)),hAPP(X31437,esk403_8(X31436,X31437,X31438,X31439,X31440,X31441,X31442,X31443))),X31440))
| ~ hBOOL(hAPP(hAPP(c_member(X31439),X31436),X31438))
| hAPP(c_Set_Oimage(X31443,X31442,X31441),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31439,tc_fun(X31443,tc_HOL_Obool)),X31438),X31437)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31439,tc_fun(X31442,tc_HOL_Obool)),X31438),hAPP(hAPP(c_COMBB(tc_fun(X31443,tc_HOL_Obool),tc_fun(X31442,tc_HOL_Obool),X31439),c_Set_Oimage(X31443,X31442,X31441)),X31437))
| ~ c_Fun_Oinj__on(X31443,X31442,X31441,X31440) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__INT])])])]) ).
fof(i_0_6032,plain,
! [X17262,X17263,X17264,X17265,X17266,X17267,X17268,X17269,X17270,X17271,X17272,X17273] : c_Com_Ocom_Ocom__rec(X17273,X17272,X17271,X17270,X17269,X17268,X17267,X17266,X17265,c_Com_Ocom_OCall(X17264,X17263,X17262)) = hAPP(hAPP(hAPP(X17265,X17264),X17263),X17262),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I8_J]) ).
fof(i_0_6033,plain,
! [X17651,X17652,X17653,X17654,X17655,X17656,X17657,X17658,X17659,X17660,X17661,X17662] : c_Com_Ocom_Ocom__case(X17662,X17661,X17660,X17659,X17658,X17657,X17656,X17655,X17654,c_Com_Ocom_OLocal(X17653,X17652,X17651)) = hAPP(hAPP(hAPP(X17659,X17653),X17652),X17651),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I66_J]) ).
fof(i_0_6034,plain,
! [X17356,X17357,X17358,X17359,X17360,X17361,X17362,X17363,X17364,X17365,X17366,X17367] : c_Com_Ocom_Ocom__case(X17367,X17366,X17365,X17364,X17363,X17362,X17361,X17360,X17359,c_Com_Ocom_OCond(X17358,X17357,X17356)) = hAPP(hAPP(hAPP(X17362,X17358),X17357),X17356),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I68_J]) ).
fof(i_0_6035,plain,
! [X17189,X17190,X17191,X17192,X17193,X17194,X17195,X17196,X17197,X17198,X17199,X17200] : c_Com_Ocom_Ocom__case(X17200,X17199,X17198,X17197,X17196,X17195,X17194,X17193,X17192,c_Com_Ocom_OCall(X17191,X17190,X17189)) = hAPP(hAPP(hAPP(X17192,X17191),X17190),X17189),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I71_J]) ).
fof(i_0_6036,plain,
! [X17292,X17293,X17294,X17295,X17296,X17297,X17298,X17299,X17300,X17301,X17302] : c_Com_Ocom_Ocom__rec(X17302,X17301,X17300,X17299,X17298,X17297,X17296,X17295,X17294,c_Com_Ocom_OAss(X17293,X17292)) = hAPP(hAPP(X17300,X17293),X17292),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I2_J]) ).
fof(i_0_6037,plain,
! [X17861,X17862,X17863,X17864,X17865,X17866,X17867,X17868,X17869,X17870,X17871] : c_Com_Ocom_Ocom__case(X17871,X17870,X17869,X17868,X17867,X17866,X17865,X17864,X17863,c_Com_Ocom_OWhile(X17862,X17861)) = hAPP(hAPP(X17865,X17862),X17861),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I69_J]) ).
fof(i_0_6038,plain,
! [X17321,X17322,X17323,X17324,X17325,X17326,X17327,X17328,X17329,X17330,X17331] : c_Com_Ocom_Ocom__case(X17331,X17330,X17329,X17328,X17327,X17326,X17325,X17324,X17323,c_Com_Ocom_OSemi(X17322,X17321)) = hAPP(hAPP(X17327,X17322),X17321),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I67_J]) ).
fof(i_0_6039,plain,
! [X17178,X17179,X17180,X17181,X17182,X17183,X17184,X17185,X17186,X17187,X17188] : c_Com_Ocom_Ocom__case(X17188,X17187,X17186,X17185,X17184,X17183,X17182,X17181,X17180,c_Com_Ocom_OAss(X17179,X17178)) = hAPP(hAPP(X17186,X17179),X17178),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I65_J]) ).
fof(i_0_6040,plain,
! [X17282,X17283,X17284,X17285,X17286,X17287,X17288,X17289,X17290,X17291] : c_Com_Ocom_Ocom__rec(X17291,X17290,X17289,X17288,X17287,X17286,X17285,X17284,X17283,hAPP(c_Com_Ocom_OBODY,X17282)) = hAPP(X17284,X17282),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I7_J]) ).
fof(i_0_6041,plain,
! [X17116,X17117,X17118,X17119,X17120,X17121,X17122,X17123,X17124,X17125] : c_Com_Ocom_Ocom__case(X17125,X17124,X17123,X17122,X17121,X17120,X17119,X17118,X17117,hAPP(c_Com_Ocom_OBODY,X17116)) = hAPP(X17118,X17116),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I70_J]) ).
fof(i_0_6042,plain,
! [X17253,X17254,X17255,X17256,X17257,X17258,X17259,X17260,X17261] : c_Com_Ocom_Ocom__rec(X17261,X17260,X17259,X17258,X17257,X17256,X17255,X17254,X17253,c_Com_Ocom_OSKIP) = X17260,
inference(variable_rename,[status(thm)],[fact_com_Orecs_I1_J]) ).
fof(i_0_6043,plain,
! [X17169,X17170,X17171,X17172,X17173,X17174,X17175,X17176,X17177] : c_Com_Ocom_Ocom__case(X17177,X17176,X17175,X17174,X17173,X17172,X17171,X17170,X17169,c_Com_Ocom_OSKIP) = X17176,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I64_J]) ).
fof(i_0_6044,plain,
! [X27697,X27698,X27699,X27700,X27701,X27702] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27702,tc_fun(X27701,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X27702,tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_fun(X27701,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27701,tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_fun(X27701,tc_HOL_Obool)),X27702),c_COMBC(X27701,tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27701,tc_prod(X27702,X27701)),tc_fun(X27701,tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),X27702),hAPP(c_COMBB(tc_prod(X27702,X27701),tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool),X27701),c_member(tc_prod(X27702,X27701)))),c_Product__Type_OPair(X27702,X27701)))),X27700)),hAPP(hAPP(c_COMBC(X27702,tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_fun(X27701,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27701,tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_fun(X27701,tc_HOL_Obool)),X27702),c_COMBC(X27701,tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27701,tc_prod(X27702,X27701)),tc_fun(X27701,tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),X27702),hAPP(c_COMBB(tc_prod(X27702,X27701),tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool),X27701),c_member(tc_prod(X27702,X27701)))),c_Product__Type_OPair(X27702,X27701)))),X27699)),X27698),X27697))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X27702,X27701)),hAPP(hAPP(c_Product__Type_OPair(X27702,X27701),X27698),X27697)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool)),X27700),X27699))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27702,X27701)),hAPP(hAPP(c_Product__Type_OPair(X27702,X27701),X27698),X27697)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool)),X27700),X27699)))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27702,tc_fun(X27701,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X27702,tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_fun(X27701,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27701,tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_fun(X27701,tc_HOL_Obool)),X27702),c_COMBC(X27701,tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27701,tc_prod(X27702,X27701)),tc_fun(X27701,tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),X27702),hAPP(c_COMBB(tc_prod(X27702,X27701),tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool),X27701),c_member(tc_prod(X27702,X27701)))),c_Product__Type_OPair(X27702,X27701)))),X27700)),hAPP(hAPP(c_COMBC(X27702,tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_fun(X27701,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27701,tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_fun(X27701,tc_HOL_Obool)),X27702),c_COMBC(X27701,tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27701,tc_prod(X27702,X27701)),tc_fun(X27701,tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool)),X27702),hAPP(c_COMBB(tc_prod(X27702,X27701),tc_fun(tc_fun(tc_prod(X27702,X27701),tc_HOL_Obool),tc_HOL_Obool),X27701),c_member(tc_prod(X27702,X27701)))),c_Product__Type_OPair(X27702,X27701)))),X27699)),X27698),X27697)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])]) ).
fof(i_0_6045,plain,
! [X25099,X25100,X25101,X25102,X25103,X25104] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25104,tc_fun(X25103,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X25104,tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_fun(X25103,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25103,tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_fun(X25103,tc_HOL_Obool)),X25104),c_COMBC(X25103,tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25103,tc_prod(X25104,X25103)),tc_fun(X25103,tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),X25104),hAPP(c_COMBB(tc_prod(X25104,X25103),tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool),X25103),c_member(tc_prod(X25104,X25103)))),c_Product__Type_OPair(X25104,X25103)))),X25102)),hAPP(hAPP(c_COMBC(X25104,tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_fun(X25103,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25103,tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_fun(X25103,tc_HOL_Obool)),X25104),c_COMBC(X25103,tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25103,tc_prod(X25104,X25103)),tc_fun(X25103,tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),X25104),hAPP(c_COMBB(tc_prod(X25104,X25103),tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool),X25103),c_member(tc_prod(X25104,X25103)))),c_Product__Type_OPair(X25104,X25103)))),X25101)),X25100),X25099))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X25104,X25103)),hAPP(hAPP(c_Product__Type_OPair(X25104,X25103),X25100),X25099)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool)),X25102),X25101))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25104,X25103)),hAPP(hAPP(c_Product__Type_OPair(X25104,X25103),X25100),X25099)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool)),X25102),X25101)))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25104,tc_fun(X25103,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X25104,tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_fun(X25103,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25103,tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_fun(X25103,tc_HOL_Obool)),X25104),c_COMBC(X25103,tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25103,tc_prod(X25104,X25103)),tc_fun(X25103,tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),X25104),hAPP(c_COMBB(tc_prod(X25104,X25103),tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool),X25103),c_member(tc_prod(X25104,X25103)))),c_Product__Type_OPair(X25104,X25103)))),X25102)),hAPP(hAPP(c_COMBC(X25104,tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_fun(X25103,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25103,tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_fun(X25103,tc_HOL_Obool)),X25104),c_COMBC(X25103,tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25103,tc_prod(X25104,X25103)),tc_fun(X25103,tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool)),X25104),hAPP(c_COMBB(tc_prod(X25104,X25103),tc_fun(tc_fun(tc_prod(X25104,X25103),tc_HOL_Obool),tc_HOL_Obool),X25103),c_member(tc_prod(X25104,X25103)))),c_Product__Type_OPair(X25104,X25103)))),X25101)),X25100),X25099)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2])]) ).
fof(i_0_6046,plain,
! [X32209,X32210] : c_List_Olenlex(X32210,X32209) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X32210),tc_List_Olist(X32210))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X32210),tc_List_Olist(X32210),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X32210),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32210),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X32210),tc_HOL_Obool),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool)),tc_List_Olist(X32210)),c_COMBS(tc_List_Olist(X32210),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32210),tc_HOL_Obool),tc_fun(tc_List_Olist(X32210),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X32210)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32210)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X32210),tc_fun(tc_List_Olist(X32210),tc_Nat_Onat),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32210),tc_Nat_Onat),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool)),tc_List_Olist(X32210)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32210))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32210)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X32210))))),c_Nat_Osize__class_Osize(tc_List_Olist(X32210)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X32210),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32210),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X32210),tc_HOL_Obool),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool)),tc_List_Olist(X32210)),c_COMBS(tc_List_Olist(X32210),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32210),tc_HOL_Obool),tc_fun(tc_List_Olist(X32210),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X32210)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32210)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X32210),tc_fun(tc_List_Olist(X32210),tc_Nat_Onat),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32210),tc_Nat_Onat),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool)),tc_List_Olist(X32210)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32210))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32210)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X32210))))),c_Nat_Osize__class_Osize(tc_List_Olist(X32210)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32210),tc_fun(tc_prod(tc_List_Olist(X32210),tc_List_Olist(X32210)),tc_HOL_Obool),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32210),tc_fun(tc_fun(tc_prod(tc_List_Olist(X32210),tc_List_Olist(X32210)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X32210),tc_List_Olist(X32210)),tc_HOL_Obool),tc_fun(tc_List_Olist(X32210),tc_HOL_Obool)),tc_List_Olist(X32210)),c_COMBC(tc_List_Olist(X32210),tc_fun(tc_prod(tc_List_Olist(X32210),tc_List_Olist(X32210)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32210),tc_prod(tc_List_Olist(X32210),tc_List_Olist(X32210))),tc_fun(tc_List_Olist(X32210),tc_fun(tc_fun(tc_prod(tc_List_Olist(X32210),tc_List_Olist(X32210)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X32210)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X32210),tc_List_Olist(X32210)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X32210),tc_List_Olist(X32210)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X32210)),c_member(tc_prod(tc_List_Olist(X32210),tc_List_Olist(X32210))))),c_Product__Type_OPair(tc_List_Olist(X32210),tc_List_Olist(X32210))))),c_List_Olex(X32210,X32209)))))),
inference(variable_rename,[status(thm)],[fact_lenlex__conv]) ).
cnf(i_0_6047,plain,
c_Nitpick_Oplus__frac(X1,X2,X3) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X1),X2),hAPP(c_Nitpick_Odenom(X1),X3))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X1),tc_Int_Oint),c_Nitpick_Ofrac(X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X1),X2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X3))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X1),X3)))))),c_COMBI(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_5202]) ).
cnf(i_0_6048,plain,
c_Nitpick_Odenom(X1) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),
inference(split_conjunct,[status(thm)],[i_0_5203]) ).
cnf(i_0_6049,plain,
c_Nitpick_Onum(X1) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),
inference(split_conjunct,[status(thm)],[i_0_5204]) ).
fof(i_0_6050,plain,
! [X31070,X31071,X31072,X31073,X31074,X31075] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31075,tc_fun(X31074,tc_fun(X31073,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X31075,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_fun(X31074,tc_fun(X31073,tc_HOL_Obool)),X31075),hAPP(c_COMBC(X31074,tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_fun(X31073,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31073,tc_fun(tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_fun(X31073,tc_HOL_Obool)),X31074),c_COMBC(X31073,tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31073,tc_prod(X31074,X31073)),tc_fun(X31073,tc_fun(tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_HOL_Obool)),X31074),hAPP(c_COMBB(tc_prod(X31074,X31073),tc_fun(tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_HOL_Obool),X31073),c_member(tc_prod(X31074,X31073)))),c_Product__Type_OPair(X31074,X31073))))),X31072)),X31071),X31070))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X31074,X31073)),hAPP(hAPP(c_Product__Type_OPair(X31074,X31073),X31071),X31070)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31075,tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X31075,tc_HOL_Obool))),X31072))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31074,X31073)),hAPP(hAPP(c_Product__Type_OPair(X31074,X31073),X31071),X31070)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31075,tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X31075,tc_HOL_Obool))),X31072)))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31075,tc_fun(X31074,tc_fun(X31073,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X31075,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_fun(X31074,tc_fun(X31073,tc_HOL_Obool)),X31075),hAPP(c_COMBC(X31074,tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_fun(X31073,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31073,tc_fun(tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_fun(X31073,tc_HOL_Obool)),X31074),c_COMBC(X31073,tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31073,tc_prod(X31074,X31073)),tc_fun(X31073,tc_fun(tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_HOL_Obool)),X31074),hAPP(c_COMBB(tc_prod(X31074,X31073),tc_fun(tc_fun(tc_prod(X31074,X31073),tc_HOL_Obool),tc_HOL_Obool),X31073),c_member(tc_prod(X31074,X31073)))),c_Product__Type_OPair(X31074,X31073))))),X31072)),X31071),X31070)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2])]) ).
fof(i_0_6051,plain,
! [X25288,X25289,X25290,X25291,X25292,X25293] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25293,tc_fun(X25292,tc_fun(X25291,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X25293,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_fun(X25292,tc_fun(X25291,tc_HOL_Obool)),X25293),hAPP(c_COMBC(X25292,tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_fun(X25291,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25291,tc_fun(tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_fun(X25291,tc_HOL_Obool)),X25292),c_COMBC(X25291,tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25291,tc_prod(X25292,X25291)),tc_fun(X25291,tc_fun(tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_HOL_Obool)),X25292),hAPP(c_COMBB(tc_prod(X25292,X25291),tc_fun(tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_HOL_Obool),X25291),c_member(tc_prod(X25292,X25291)))),c_Product__Type_OPair(X25292,X25291))))),X25290)),X25289),X25288))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X25292,X25291)),hAPP(hAPP(c_Product__Type_OPair(X25292,X25291),X25289),X25288)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25293,tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X25293,tc_HOL_Obool))),X25290))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25292,X25291)),hAPP(hAPP(c_Product__Type_OPair(X25292,X25291),X25289),X25288)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25293,tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X25293,tc_HOL_Obool))),X25290)))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25293,tc_fun(X25292,tc_fun(X25291,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X25293,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_fun(X25292,tc_fun(X25291,tc_HOL_Obool)),X25293),hAPP(c_COMBC(X25292,tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_fun(X25291,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25291,tc_fun(tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_fun(X25291,tc_HOL_Obool)),X25292),c_COMBC(X25291,tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25291,tc_prod(X25292,X25291)),tc_fun(X25291,tc_fun(tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_HOL_Obool)),X25292),hAPP(c_COMBB(tc_prod(X25292,X25291),tc_fun(tc_fun(tc_prod(X25292,X25291),tc_HOL_Obool),tc_HOL_Obool),X25291),c_member(tc_prod(X25292,X25291)))),c_Product__Type_OPair(X25292,X25291))))),X25290)),X25289),X25288)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2])]) ).
cnf(i_0_6052,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),c_fequal),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_5205]) ).
cnf(i_0_6053,plain,
c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))) = c_Relation_OId(X1),
inference(split_conjunct,[status(thm)],[i_0_5206]) ).
fof(i_0_6054,plain,
! [X27667,X27668,X27669,X27670,X27671,X27672,X27673] :
( ( hBOOL(hAPP(hAPP(c_member(X27673),esk245_7(X27667,X27668,X27669,X27670,X27671,X27672,X27673)),X27672))
| X27668 = X27667
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27673,tc_HOL_Obool)),X27667),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27673),X27672),X27671)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27673,tc_HOL_Obool)),X27668),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27673),X27672),X27671)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27673,tc_fun(X27670,tc_HOL_Obool)),X27668),X27669) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27673,tc_fun(X27670,tc_HOL_Obool)),X27667),X27669)
| ~ c_Equiv__Relations_Ocongruent(X27673,tc_fun(X27670,tc_HOL_Obool),X27671,X27669)
| ~ c_Equiv__Relations_Oequiv(X27673,X27672,X27671) )
& ( hBOOL(hAPP(hAPP(c_member(X27673),esk246_7(X27667,X27668,X27669,X27670,X27671,X27672,X27673)),X27672))
| X27668 = X27667
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27673,tc_HOL_Obool)),X27667),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27673),X27672),X27671)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27673,tc_HOL_Obool)),X27668),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27673),X27672),X27671)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27673,tc_fun(X27670,tc_HOL_Obool)),X27668),X27669) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27673,tc_fun(X27670,tc_HOL_Obool)),X27667),X27669)
| ~ c_Equiv__Relations_Ocongruent(X27673,tc_fun(X27670,tc_HOL_Obool),X27671,X27669)
| ~ c_Equiv__Relations_Oequiv(X27673,X27672,X27671) )
& ( hAPP(X27669,esk245_7(X27667,X27668,X27669,X27670,X27671,X27672,X27673)) = hAPP(X27669,esk246_7(X27667,X27668,X27669,X27670,X27671,X27672,X27673))
| X27668 = X27667
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27673,tc_HOL_Obool)),X27667),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27673),X27672),X27671)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27673,tc_HOL_Obool)),X27668),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27673),X27672),X27671)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27673,tc_fun(X27670,tc_HOL_Obool)),X27668),X27669) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27673,tc_fun(X27670,tc_HOL_Obool)),X27667),X27669)
| ~ c_Equiv__Relations_Ocongruent(X27673,tc_fun(X27670,tc_HOL_Obool),X27671,X27669)
| ~ c_Equiv__Relations_Oequiv(X27673,X27672,X27671) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27673,X27673)),hAPP(hAPP(c_Product__Type_OPair(X27673,X27673),esk245_7(X27667,X27668,X27669,X27670,X27671,X27672,X27673)),esk246_7(X27667,X27668,X27669,X27670,X27671,X27672,X27673))),X27671))
| X27668 = X27667
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27673,tc_HOL_Obool)),X27667),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27673),X27672),X27671)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27673,tc_HOL_Obool)),X27668),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27673),X27672),X27671)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27673,tc_fun(X27670,tc_HOL_Obool)),X27668),X27669) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27673,tc_fun(X27670,tc_HOL_Obool)),X27667),X27669)
| ~ c_Equiv__Relations_Ocongruent(X27673,tc_fun(X27670,tc_HOL_Obool),X27671,X27669)
| ~ c_Equiv__Relations_Oequiv(X27673,X27672,X27671) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__inject])])])]) ).
fof(i_0_6055,plain,
! [X25730,X25731,X25732,X25733,X25734] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X25734,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X25734),tc_HOL_Obool)),X25733),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X25734),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X25734)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X25734))),hAPP(hAPP(c_COMBB(tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X25734))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X25734)),X25732)),c_Com_Ocom_OBODY)),X25731)),X25730)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X25734),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X25734)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X25734))),hAPP(hAPP(c_COMBB(tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X25734))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X25734)),X25732)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X25731)),X25730))
| c_Hoare__Mirabelle_Ohoare__derivs(X25734,X25733,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X25734),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X25734)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X25734))),hAPP(hAPP(c_COMBB(tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X25734,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X25734))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X25734)),X25732)),c_Com_Ocom_OBODY)),X25731)),X25730)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OBody])]) ).
cnf(i_0_6056,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4)),c_fequal),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),c_Relation_OId(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_5205]) ).
cnf(i_0_6057,plain,
hAPP(c_Divides_Oadjust(X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),X3))),
inference(split_conjunct,[status(thm)],[i_0_5207]) ).
fof(i_0_6058,plain,
! [X29373,X29374,X29375,X29376] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29376),hAPP(c_Set_OCollect(X29376),X29375)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29374),hAPP(c_Set_OCollect(X29374),hAPP(hAPP(c_COMBB(tc_fun(X29376,tc_HOL_Obool),tc_HOL_Obool,X29374),c_HOL_OEx(X29376)),hAPP(hAPP(c_COMBC(X29374,tc_fun(X29376,tc_HOL_Obool),tc_fun(X29376,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29376,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29376,tc_HOL_Obool),tc_fun(X29376,tc_HOL_Obool)),X29374),c_COMBS(X29376,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29376,tc_HOL_Obool),tc_fun(X29376,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29374),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29376),c_fconj)),hAPP(hAPP(c_COMBC(X29374,tc_fun(X29376,X29374),tc_fun(X29376,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29374,tc_HOL_Obool),tc_fun(tc_fun(X29376,X29374),tc_fun(X29376,tc_HOL_Obool)),X29374),c_COMBB(X29374,tc_HOL_Obool,X29376)),c_fequal)),X29373)))),X29375))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__image__set])]) ).
fof(i_0_6059,plain,
! [X30098,X30099,X30100,X30101,X30102,X30103,X30104,X30105] :
( ( hBOOL(hAPP(hAPP(c_member(X30104),esk364_8(X30098,X30099,X30100,X30101,X30102,X30103,X30104,X30105)),X30101))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30103,X30105),X30098),X30100) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30104,X30105),X30099),X30101)
| X30100 != hAPP(c_Set_Oimage(X30104,X30103,X30102),X30101)
| ~ c_Fun_Oinj__on(X30104,X30103,X30102,X30101)
| ~ class_Groups_Ocomm__monoid__add(X30105) )
& ( hAPP(X30099,esk364_8(X30098,X30099,X30100,X30101,X30102,X30103,X30104,X30105)) != hAPP(X30098,hAPP(X30102,esk364_8(X30098,X30099,X30100,X30101,X30102,X30103,X30104,X30105)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30103,X30105),X30098),X30100) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30104,X30105),X30099),X30101)
| X30100 != hAPP(c_Set_Oimage(X30104,X30103,X30102),X30101)
| ~ c_Fun_Oinj__on(X30104,X30103,X30102,X30101)
| ~ class_Groups_Ocomm__monoid__add(X30105) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex__cong])])])]) ).
fof(i_0_6060,plain,
! [X25750,X25751,X25752,X25753,X25754,X25755,X25756,X25757] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X25757,X25756,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25757)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25757),X25755),X25754),hAPP(hAPP(c_COMBC(X25757,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X25757),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X25753)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(X25752))),hAPP(hAPP(c_Natural_Ogetlocs,X25751),X25752))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25757),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(X25757,X25756,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25757)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25757),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),X25757),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,X25751)))),hAPP(hAPP(c_COMBC(X25757,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X25757),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X25755)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(X25752))),X25750)))),c_Com_Ocom_OLocal(X25752,X25750,X25754)),X25753)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25757),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OLocal])]) ).
cnf(i_0_6061,plain,
c_Transitive__Closure_Otrancl(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X4)),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(hAPP(c_COMBC(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),X2))),c_Transitive__Closure_Ortrancl(X1,X4))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(c_Product__Type_OPair(X1,X1),X3))),c_Transitive__Closure_Ortrancl(X1,X4)))))),
inference(split_conjunct,[status(thm)],[i_0_5208]) ).
cnf(i_0_6062,plain,
c_Transitive__Closure_Otrancl(X1,X2) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_5209]) ).
cnf(i_0_6063,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X2),X2),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),tc_Int_Oint),c_COMBB(tc_fun(X2,X2),X2,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,X2),X2),tc_Int_Oint),c_HOL_OLet(X2,X2)),c_Int_Oring__1__class_Oof__int(X2)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,X2)),tc_Int_Oint),c_COMBS(X2,X2,X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),tc_Int_Oint),c_COMBB(X2,tc_fun(X2,X2),X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),tc_Int_Oint),c_If(X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2))))),hAPP(hAPP(c_COMBC(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Oplus__class_Oplus(X2)),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2)))),c_Groups_Oone__class_Oone(X2))))),c_Divides_Odivmod__int(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5210]) ).
fof(i_0_6064,plain,
! [X28440,X28441,X28442,X28443,X28444,X28445,X28446,X28447] :
( ( hBOOL(hAPP(hAPP(c_member(X28446),esk272_8(X28440,X28441,X28442,X28443,X28444,X28445,X28446,X28447)),X28443))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28445,X28447),X28440),X28442) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28446,X28447),X28441),X28443)
| X28442 != hAPP(c_Set_Oimage(X28446,X28445,X28444),X28443)
| ~ c_Fun_Oinj__on(X28446,X28445,X28444,X28443)
| ~ class_Groups_Ocomm__monoid__mult(X28447) )
& ( hAPP(X28441,esk272_8(X28440,X28441,X28442,X28443,X28444,X28445,X28446,X28447)) != hAPP(hAPP(c_Fun_Ocomp(X28445,X28447,X28446,X28440),X28444),esk272_8(X28440,X28441,X28442,X28443,X28444,X28445,X28446,X28447))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28445,X28447),X28440),X28442) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28446,X28447),X28441),X28443)
| X28442 != hAPP(c_Set_Oimage(X28446,X28445,X28444),X28443)
| ~ c_Fun_Oinj__on(X28446,X28445,X28444,X28443)
| ~ class_Groups_Ocomm__monoid__mult(X28447) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strong__setprod__reindex__cong])])])]) ).
fof(i_0_6065,plain,
! [X23737,X23738,X23739,X23740,X23741,X23742,X23743,X23744] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23743),X23741),esk129_8(X23737,X23738,X23739,X23740,X23741,X23742,X23743,X23744)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23743,X23744),X23738),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23743,X23742),X23740)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23743,X23744),X23737),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23743,X23741),X23739))
| X23740 != X23739
| X23742 != X23741
| ~ class_Groups_Ocomm__monoid__add(X23744)
| ~ class_Orderings_Oord(X23743) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23743),esk129_8(X23737,X23738,X23739,X23740,X23741,X23742,X23743,X23744)),X23739))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23743,X23744),X23738),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23743,X23742),X23740)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23743,X23744),X23737),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23743,X23741),X23739))
| X23740 != X23739
| X23742 != X23741
| ~ class_Groups_Ocomm__monoid__add(X23744)
| ~ class_Orderings_Oord(X23743) )
& ( hAPP(X23738,esk129_8(X23737,X23738,X23739,X23740,X23741,X23742,X23743,X23744)) != hAPP(X23737,esk129_8(X23737,X23738,X23739,X23740,X23741,X23742,X23743,X23744))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23743,X23744),X23738),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23743,X23742),X23740)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23743,X23744),X23737),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23743,X23741),X23739))
| X23740 != X23739
| X23742 != X23741
| ~ class_Groups_Ocomm__monoid__add(X23744)
| ~ class_Orderings_Oord(X23743) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__ivl__cong])])])]) ).
fof(i_0_6066,plain,
! [X26761] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26761) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X26761)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
inference(variable_rename,[status(thm)],[fact_minus__int__def]) ).
fof(i_0_6067,plain,
! [X22964,X22965,X22966,X22967,X22968,X22969,X22970] :
( ( hBOOL(hAPP(hAPP(X22970,esk93_7(X22964,X22965,X22966,X22967,X22968,X22969,X22970)),esk92_7(X22964,X22965,X22966,X22967,X22968,X22969,X22970)))
| hBOOL(hAPP(X22966,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22969,X22968,X22964),X22965),X22967)))
| ~ hBOOL(hAPP(hAPP(X22970,hAPP(c_Product__Type_Osnd(X22969,X22968),X22967)),hAPP(c_Product__Type_Ofst(X22969,X22968),X22967))) )
& ( ~ hBOOL(hAPP(X22966,hAPP(hAPP(X22965,esk92_7(X22964,X22965,X22966,X22967,X22968,X22969,X22970)),esk93_7(X22964,X22965,X22966,X22967,X22968,X22969,X22970))))
| hBOOL(hAPP(X22966,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22969,X22968,X22964),X22965),X22967)))
| ~ hBOOL(hAPP(hAPP(X22970,hAPP(c_Product__Type_Osnd(X22969,X22968),X22967)),hAPP(c_Product__Type_Ofst(X22969,X22968),X22967))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exE__realizer])])])]) ).
fof(i_0_6068,plain,
! [X26394,X26395] : c_FunDef_Orp__inv__image(X26395,X26394) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X26395,X26395),tc_HOL_Obool),tc_fun(tc_prod(X26395,X26395),tc_HOL_Obool),tc_fun(tc_fun(X26394,X26395),tc_prod(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X26395,X26395),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X26395,X26395),tc_HOL_Obool),tc_fun(tc_fun(X26394,X26395),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X26395,X26395),tc_HOL_Obool),tc_fun(tc_fun(X26394,X26395),tc_prod(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X26394,X26395),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool)),tc_fun(tc_fun(X26394,X26395),tc_prod(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X26395,X26395),tc_HOL_Obool),tc_fun(tc_fun(X26394,X26395),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X26395,X26395),tc_HOL_Obool),tc_fun(tc_fun(X26394,X26395),tc_prod(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool))))),tc_fun(tc_prod(X26395,X26395),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X26394,X26395),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool)),tc_fun(tc_fun(X26394,X26395),tc_prod(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool))),tc_fun(tc_prod(X26395,X26395),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X26394,X26395),tc_fun(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X26394,X26395),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool)),tc_fun(tc_fun(X26394,X26395),tc_prod(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool)))),tc_fun(tc_prod(X26395,X26395),tc_HOL_Obool)),c_COMBS(tc_fun(X26394,X26395),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X26394,X26395),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool)),tc_fun(tc_fun(X26394,X26395),tc_fun(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool)))),tc_fun(tc_prod(X26395,X26395),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool))),tc_fun(X26394,X26395)),c_Product__Type_OPair(tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool),tc_fun(tc_prod(X26394,X26394),tc_HOL_Obool)))),c_Relation_Oinv__image(X26395,X26394))))),c_Relation_Oinv__image(X26395,X26394))),
inference(variable_rename,[status(thm)],[fact_rp__inv__image__def]) ).
cnf(i_0_6069,plain,
c_Map_Omap__add(X1,X2,X3,c_Map_Omap__of(X1,X2,X4)) = c_List_Ofoldr(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)))))),c_Option_Ooption_OSome(X2))),X4,X3),
inference(split_conjunct,[status(thm)],[i_0_5211]) ).
cnf(i_0_6070,plain,
c_List_Ofoldr(X1,X2,X3,X4,X5) = hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X5),hAPP(c_List_Orev(X1),X4)),
inference(split_conjunct,[status(thm)],[i_0_5212]) ).
fof(i_0_6071,plain,
! [X29344,X29345,X29346,X29347] : hAPP(hAPP(c_Relation_Oinv__image(X29347,X29346),X29345),X29344) = hAPP(c_Set_OCollect(tc_prod(X29346,X29346)),hAPP(c_Product__Type_Oprod_Oprod__case(X29346,X29346,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29346,tc_fun(tc_prod(X29347,X29347),tc_HOL_Obool),tc_fun(X29346,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29346,tc_fun(tc_fun(tc_prod(X29347,X29347),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29347,X29347),tc_HOL_Obool),tc_fun(X29346,tc_HOL_Obool)),X29346),c_COMBC(X29346,tc_fun(tc_prod(X29347,X29347),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29346,tc_prod(X29347,X29347)),tc_fun(X29346,tc_fun(tc_fun(tc_prod(X29347,X29347),tc_HOL_Obool),tc_HOL_Obool)),X29346),hAPP(c_COMBB(tc_prod(X29347,X29347),tc_fun(tc_fun(tc_prod(X29347,X29347),tc_HOL_Obool),tc_HOL_Obool),X29346),c_member(tc_prod(X29347,X29347)))),hAPP(hAPP(c_COMBC(X29346,tc_fun(X29346,X29347),tc_fun(X29346,tc_prod(X29347,X29347))),hAPP(hAPP(c_COMBB(tc_fun(X29347,tc_prod(X29347,X29347)),tc_fun(tc_fun(X29346,X29347),tc_fun(X29346,tc_prod(X29347,X29347))),X29346),c_COMBB(X29347,tc_prod(X29347,X29347),X29346)),hAPP(hAPP(c_COMBB(X29347,tc_fun(X29347,tc_prod(X29347,X29347)),X29346),c_Product__Type_OPair(X29347,X29347)),X29344))),X29344)))),X29345))),
inference(variable_rename,[status(thm)],[fact_inv__image__def]) ).
fof(i_0_6072,plain,
! [X32710,X32711,X32712,X32713] : hAPP(c_List_Oset(tc_prod(X32713,X32712)),hAPP(hAPP(c_List_Ozip(X32713,X32712),X32711),X32710)) = hAPP(c_Set_OCollect(tc_prod(X32713,X32712)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X32713,X32712)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X32713,X32712),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X32713,X32712)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X32713,X32712)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X32713,X32712),tc_fun(tc_Nat_Onat,tc_prod(X32713,X32712)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X32713,X32712),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X32713,X32712)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X32713,X32712)),c_COMBB(tc_prod(X32713,X32712),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X32712,tc_prod(X32713,X32712)),hAPP(hAPP(c_COMBB(X32713,tc_fun(X32712,tc_prod(X32713,X32712)),tc_Nat_Onat),c_Product__Type_OPair(X32713,X32712)),hAPP(c_List_Onth(X32713),X32711))),hAPP(c_List_Onth(X32712),X32710)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32713)),X32711)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32712)),X32710)))))),
inference(variable_rename,[status(thm)],[fact_set__zip]) ).
fof(i_0_6073,plain,
! [X25325,X25326,X25327,X25328] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25328,tc_fun(X25327,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X25328,tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_fun(X25327,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25327,tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_fun(X25327,tc_HOL_Obool)),X25328),c_COMBC(X25327,tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25327,tc_prod(X25328,X25327)),tc_fun(X25327,tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),X25328),hAPP(c_COMBB(tc_prod(X25328,X25327),tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool),X25327),c_member(tc_prod(X25328,X25327)))),c_Product__Type_OPair(X25328,X25327)))),X25326)),hAPP(hAPP(c_COMBC(X25328,tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_fun(X25327,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25327,tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_fun(X25327,tc_HOL_Obool)),X25328),c_COMBC(X25327,tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25327,tc_prod(X25328,X25327)),tc_fun(X25327,tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),X25328),hAPP(c_COMBB(tc_prod(X25328,X25327),tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool),X25327),c_member(tc_prod(X25328,X25327)))),c_Product__Type_OPair(X25328,X25327)))),X25325)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool)),X25326),X25325)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool)),X25326),X25325))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25328,tc_fun(X25327,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X25328,tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_fun(X25327,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25327,tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_fun(X25327,tc_HOL_Obool)),X25328),c_COMBC(X25327,tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25327,tc_prod(X25328,X25327)),tc_fun(X25327,tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),X25328),hAPP(c_COMBB(tc_prod(X25328,X25327),tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool),X25327),c_member(tc_prod(X25328,X25327)))),c_Product__Type_OPair(X25328,X25327)))),X25326)),hAPP(hAPP(c_COMBC(X25328,tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_fun(X25327,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25327,tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_fun(X25327,tc_HOL_Obool)),X25328),c_COMBC(X25327,tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25327,tc_prod(X25328,X25327)),tc_fun(X25327,tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool)),X25328),hAPP(c_COMBB(tc_prod(X25328,X25327),tc_fun(tc_fun(tc_prod(X25328,X25327),tc_HOL_Obool),tc_HOL_Obool),X25327),c_member(tc_prod(X25328,X25327)))),c_Product__Type_OPair(X25328,X25327)))),X25325))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_6074,plain,
! [X29380,X29381] : hAPP(c_Set_OPow(X29381),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29381,tc_HOL_Obool)),X29380)) = hAPP(c_Set_OCollect(tc_fun(X29381,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X29381,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X29381,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X29381,tc_HOL_Obool),tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X29381,tc_HOL_Obool)),c_COMBS(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X29381,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X29381,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X29381,tc_HOL_Obool),tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_fun(X29381,tc_HOL_Obool)),tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_fun(X29381,tc_HOL_Obool)),tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X29381,tc_HOL_Obool)),c_COMBB(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X29381,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X29381,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29381,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X29381,tc_HOL_Obool)),hAPP(c_member(tc_fun(X29381,tc_HOL_Obool)),X29380)),c_Set_OPow(X29381))))),
inference(variable_rename,[status(thm)],[fact_Pow__Compl]) ).
fof(i_0_6075,plain,
! [X33660,X33661,X33662,X33663,X33664] : c_Map_Omap__upds(X33664,X33663,X33662,X33661,X33660) = hAPP(c_List_Ofoldl(tc_fun(X33664,tc_Option_Ooption(X33663)),tc_prod(X33664,X33663),hAPP(hAPP(c_COMBB(tc_fun(X33664,tc_fun(X33663,tc_fun(X33664,tc_Option_Ooption(X33663)))),tc_fun(tc_prod(X33664,X33663),tc_fun(X33664,tc_Option_Ooption(X33663))),tc_fun(X33664,tc_Option_Ooption(X33663))),c_Product__Type_Oprod_Oprod__case(X33664,X33663,tc_fun(X33664,tc_Option_Ooption(X33663)))),hAPP(hAPP(c_COMBC(tc_fun(X33664,tc_Option_Ooption(X33663)),tc_fun(X33663,tc_Option_Ooption(X33663)),tc_fun(X33664,tc_fun(X33663,tc_fun(X33664,tc_Option_Ooption(X33663))))),hAPP(hAPP(c_COMBB(tc_fun(X33664,tc_fun(tc_fun(X33663,tc_Option_Ooption(X33663)),tc_fun(X33663,tc_fun(X33664,tc_Option_Ooption(X33663))))),tc_fun(tc_fun(X33663,tc_Option_Ooption(X33663)),tc_fun(X33664,tc_fun(X33663,tc_fun(X33664,tc_Option_Ooption(X33663))))),tc_fun(X33664,tc_Option_Ooption(X33663))),c_COMBC(X33664,tc_fun(X33663,tc_Option_Ooption(X33663)),tc_fun(X33663,tc_fun(X33664,tc_Option_Ooption(X33663))))),hAPP(hAPP(c_COMBB(tc_fun(X33664,tc_fun(tc_Option_Ooption(X33663),tc_fun(X33664,tc_Option_Ooption(X33663)))),tc_fun(X33664,tc_fun(tc_fun(X33663,tc_Option_Ooption(X33663)),tc_fun(X33663,tc_fun(X33664,tc_Option_Ooption(X33663))))),tc_fun(X33664,tc_Option_Ooption(X33663))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X33663),tc_fun(X33664,tc_Option_Ooption(X33663))),tc_fun(tc_fun(X33663,tc_Option_Ooption(X33663)),tc_fun(X33663,tc_fun(X33664,tc_Option_Ooption(X33663)))),X33664),c_COMBB(tc_Option_Ooption(X33663),tc_fun(X33664,tc_Option_Ooption(X33663)),X33663))),c_Fun_Ofun__upd(X33664,tc_Option_Ooption(X33663))))),c_Option_Ooption_OSome(X33663))),X33662),hAPP(hAPP(c_List_Ozip(X33664,X33663),X33661),X33660)),
inference(variable_rename,[status(thm)],[fact_map__upds__fold__map__upd]) ).
fof(i_0_6076,plain,
! [X27689,X27690,X27691,X27692,X27693,X27694,X27695] :
( ( hBOOL(hAPP(hAPP(c_member(X27695),esk249_7(X27689,X27690,X27691,X27692,X27693,X27694,X27695)),X27694))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X27692,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27695,tc_fun(X27692,tc_HOL_Obool)),X27690),X27691)),X27689))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27695,tc_HOL_Obool)),X27690),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27695),X27694),X27693)))
| ~ c_Equiv__Relations_Ocongruent(X27695,tc_fun(X27692,tc_HOL_Obool),X27693,X27691)
| ~ c_Equiv__Relations_Oequiv(X27695,X27694,X27693) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27692,tc_HOL_Obool)),hAPP(X27691,esk249_7(X27689,X27690,X27691,X27692,X27693,X27694,X27695))),X27689))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X27692,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27695,tc_fun(X27692,tc_HOL_Obool)),X27690),X27691)),X27689))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27695,tc_HOL_Obool)),X27690),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27695),X27694),X27693)))
| ~ c_Equiv__Relations_Ocongruent(X27695,tc_fun(X27692,tc_HOL_Obool),X27693,X27691)
| ~ c_Equiv__Relations_Oequiv(X27695,X27694,X27693) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type])])])]) ).
fof(i_0_6077,plain,
! [X31246,X31247,X31248,X31249,X31250,X31251,X31252,X31253,X31254,X31255,X31256,X31257,X31258,X31259,X31260] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31252,tc_fun(X31251,tc_fun(X31250,tc_HOL_Obool))),X31249),X31248),X31247),X31246))
| ~ hBOOL(hAPP(hAPP(c_member(X31252),X31253),X31249))
| hBOOL(hAPP(hAPP(hAPP(X31248,X31253),X31247),X31246)) )
& ( hBOOL(hAPP(hAPP(c_member(X31260),esk397_7(X31254,X31255,X31256,X31257,X31258,X31259,X31260)),X31257))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31260,tc_fun(X31259,tc_fun(X31258,tc_HOL_Obool))),X31257),X31256),X31255),X31254)) )
& ( ~ hBOOL(hAPP(hAPP(hAPP(X31256,esk397_7(X31254,X31255,X31256,X31257,X31258,X31259,X31260)),X31255),X31254))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31260,tc_fun(X31259,tc_fun(X31258,tc_HOL_Obool))),X31257),X31256),X31255),X31254)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__iff])])])])])]) ).
fof(i_0_6078,plain,
! [X29400,X29401,X29402] :
( ~ class_Orderings_Olinorder(X29402)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29402),X29401))
| X29401 = c_Orderings_Obot__class_Obot(tc_fun(X29402,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X29402),X29400),c_Big__Operators_Olattice_OInf__fin(X29402,c_Orderings_Oord__class_Omin(X29402),X29401)) = c_Big__Operators_Olattice_OInf__fin(X29402,c_Orderings_Oord__class_Omin(X29402),hAPP(c_Set_OCollect(X29402),hAPP(hAPP(c_COMBB(tc_fun(X29402,tc_HOL_Obool),tc_HOL_Obool,X29402),c_HOL_OEx(X29402)),hAPP(hAPP(c_COMBC(X29402,tc_fun(X29402,tc_HOL_Obool),tc_fun(X29402,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29402,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29402,tc_HOL_Obool),tc_fun(X29402,tc_HOL_Obool)),X29402),c_COMBS(X29402,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29402,tc_HOL_Obool),tc_fun(X29402,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29402),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29402),c_fconj)),hAPP(hAPP(c_COMBC(X29402,tc_fun(X29402,X29402),tc_fun(X29402,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29402,tc_HOL_Obool),tc_fun(tc_fun(X29402,X29402),tc_fun(X29402,tc_HOL_Obool)),X29402),c_COMBB(X29402,tc_HOL_Obool,X29402)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X29402),X29400))))),hAPP(hAPP(c_COMBC(X29402,tc_fun(X29402,tc_HOL_Obool),tc_HOL_Obool),c_member(X29402)),X29401))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib])]) ).
fof(i_0_6079,plain,
! [X29403,X29404,X29405] :
( ~ class_Orderings_Olinorder(X29405)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29405),X29404))
| X29404 = c_Orderings_Obot__class_Obot(tc_fun(X29405,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X29405),X29403),c_Big__Operators_Olattice_OSup__fin(X29405,c_Orderings_Oord__class_Omax(X29405),X29404)) = c_Big__Operators_Olattice_OSup__fin(X29405,c_Orderings_Oord__class_Omax(X29405),hAPP(c_Set_OCollect(X29405),hAPP(hAPP(c_COMBB(tc_fun(X29405,tc_HOL_Obool),tc_HOL_Obool,X29405),c_HOL_OEx(X29405)),hAPP(hAPP(c_COMBC(X29405,tc_fun(X29405,tc_HOL_Obool),tc_fun(X29405,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29405,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29405,tc_HOL_Obool),tc_fun(X29405,tc_HOL_Obool)),X29405),c_COMBS(X29405,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29405,tc_HOL_Obool),tc_fun(X29405,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29405),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29405),c_fconj)),hAPP(hAPP(c_COMBC(X29405,tc_fun(X29405,X29405),tc_fun(X29405,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29405,tc_HOL_Obool),tc_fun(tc_fun(X29405,X29405),tc_fun(X29405,tc_HOL_Obool)),X29405),c_COMBB(X29405,tc_HOL_Obool,X29405)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X29405),X29403))))),hAPP(hAPP(c_COMBC(X29405,tc_fun(X29405,tc_HOL_Obool),tc_HOL_Obool),c_member(X29405)),X29404))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib])]) ).
fof(i_0_6080,plain,
! [X29397,X29398,X29399] :
( ~ class_Lattices_Odistrib__lattice(X29399)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29399),X29398))
| X29398 = c_Orderings_Obot__class_Obot(tc_fun(X29399,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29399),X29397),c_Big__Operators_Olattice__class_OSup__fin(X29399,X29398)) = c_Big__Operators_Olattice__class_OSup__fin(X29399,hAPP(c_Set_OCollect(X29399),hAPP(hAPP(c_COMBB(tc_fun(X29399,tc_HOL_Obool),tc_HOL_Obool,X29399),c_HOL_OEx(X29399)),hAPP(hAPP(c_COMBC(X29399,tc_fun(X29399,tc_HOL_Obool),tc_fun(X29399,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29399,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29399,tc_HOL_Obool),tc_fun(X29399,tc_HOL_Obool)),X29399),c_COMBS(X29399,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29399,tc_HOL_Obool),tc_fun(X29399,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29399),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29399),c_fconj)),hAPP(hAPP(c_COMBC(X29399,tc_fun(X29399,X29399),tc_fun(X29399,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29399,tc_HOL_Obool),tc_fun(tc_fun(X29399,X29399),tc_fun(X29399,tc_HOL_Obool)),X29399),c_COMBB(X29399,tc_HOL_Obool,X29399)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29399),X29397))))),hAPP(hAPP(c_COMBC(X29399,tc_fun(X29399,tc_HOL_Obool),tc_HOL_Obool),c_member(X29399)),X29398))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib])]) ).
fof(i_0_6081,plain,
! [X29388,X29389,X29390] :
( ~ class_Lattices_Odistrib__lattice(X29390)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29390),X29389))
| X29389 = c_Orderings_Obot__class_Obot(tc_fun(X29390,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29390),X29388),c_Big__Operators_Olattice__class_OInf__fin(X29390,X29389)) = c_Big__Operators_Olattice__class_OInf__fin(X29390,hAPP(c_Set_OCollect(X29390),hAPP(hAPP(c_COMBB(tc_fun(X29390,tc_HOL_Obool),tc_HOL_Obool,X29390),c_HOL_OEx(X29390)),hAPP(hAPP(c_COMBC(X29390,tc_fun(X29390,tc_HOL_Obool),tc_fun(X29390,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29390,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29390,tc_HOL_Obool),tc_fun(X29390,tc_HOL_Obool)),X29390),c_COMBS(X29390,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29390,tc_HOL_Obool),tc_fun(X29390,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29390),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29390),c_fconj)),hAPP(hAPP(c_COMBC(X29390,tc_fun(X29390,X29390),tc_fun(X29390,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29390,tc_HOL_Obool),tc_fun(tc_fun(X29390,X29390),tc_fun(X29390,tc_HOL_Obool)),X29390),c_COMBB(X29390,tc_HOL_Obool,X29390)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29390),X29388))))),hAPP(hAPP(c_COMBC(X29390,tc_fun(X29390,tc_HOL_Obool),tc_HOL_Obool),c_member(X29390)),X29389))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib])]) ).
fof(i_0_6082,plain,
! [X29382,X29383,X29384] :
( ~ class_Groups_Olinordered__ab__semigroup__add(X29384)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29384),X29383))
| X29383 = c_Orderings_Obot__class_Obot(tc_fun(X29384,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29384),X29382),c_Big__Operators_Olinorder__class_OMin(X29384,X29383)) = c_Big__Operators_Olinorder__class_OMin(X29384,hAPP(c_Set_OCollect(X29384),hAPP(hAPP(c_COMBB(tc_fun(X29384,tc_HOL_Obool),tc_HOL_Obool,X29384),c_HOL_OEx(X29384)),hAPP(hAPP(c_COMBC(X29384,tc_fun(X29384,tc_HOL_Obool),tc_fun(X29384,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29384,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29384,tc_HOL_Obool),tc_fun(X29384,tc_HOL_Obool)),X29384),c_COMBS(X29384,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29384,tc_HOL_Obool),tc_fun(X29384,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29384),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29384),c_fconj)),hAPP(hAPP(c_COMBC(X29384,tc_fun(X29384,X29384),tc_fun(X29384,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29384,tc_HOL_Obool),tc_fun(tc_fun(X29384,X29384),tc_fun(X29384,tc_HOL_Obool)),X29384),c_COMBB(X29384,tc_HOL_Obool,X29384)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X29384),X29382))))),hAPP(hAPP(c_COMBC(X29384,tc_fun(X29384,tc_HOL_Obool),tc_HOL_Obool),c_member(X29384)),X29383))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Min__commute])]) ).
fof(i_0_6083,plain,
! [X29385,X29386,X29387] :
( ~ class_Groups_Olinordered__ab__semigroup__add(X29387)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29387),X29386))
| X29386 = c_Orderings_Obot__class_Obot(tc_fun(X29387,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29387),X29385),c_Big__Operators_Olinorder__class_OMax(X29387,X29386)) = c_Big__Operators_Olinorder__class_OMax(X29387,hAPP(c_Set_OCollect(X29387),hAPP(hAPP(c_COMBB(tc_fun(X29387,tc_HOL_Obool),tc_HOL_Obool,X29387),c_HOL_OEx(X29387)),hAPP(hAPP(c_COMBC(X29387,tc_fun(X29387,tc_HOL_Obool),tc_fun(X29387,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29387,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29387,tc_HOL_Obool),tc_fun(X29387,tc_HOL_Obool)),X29387),c_COMBS(X29387,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29387,tc_HOL_Obool),tc_fun(X29387,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29387),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29387),c_fconj)),hAPP(hAPP(c_COMBC(X29387,tc_fun(X29387,X29387),tc_fun(X29387,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29387,tc_HOL_Obool),tc_fun(tc_fun(X29387,X29387),tc_fun(X29387,tc_HOL_Obool)),X29387),c_COMBB(X29387,tc_HOL_Obool,X29387)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X29387),X29385))))),hAPP(hAPP(c_COMBC(X29387,tc_fun(X29387,tc_HOL_Obool),tc_HOL_Obool),c_member(X29387)),X29386))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Max__commute])]) ).
fof(i_0_6084,plain,
! [X32587,X32588,X32589,X32590,X32591] :
( ( X32591 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Lazy__Sequence_Oanamorph(X32590,X32589,X32588,X32591),X32587) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32589),X32590),c_List_Olist_ONil(X32589)),X32587) )
& ( X32591 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Lazy__Sequence_Oanamorph(X32590,X32589,X32588,X32591),X32587) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X32589),X32590),tc_prod(X32589,X32590),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32589),X32590),c_List_Olist_ONil(X32589)),X32587),hAPP(c_Product__Type_Oprod_Oprod__case(X32589,X32590,tc_prod(tc_List_Olist(X32589),X32590)),hAPP(hAPP(c_COMBC(X32589,tc_fun(X32590,tc_prod(tc_List_Olist(X32589),X32590)),tc_fun(X32590,tc_prod(tc_List_Olist(X32589),X32590))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X32589),X32590),tc_prod(tc_List_Olist(X32589),X32590)),tc_fun(tc_fun(X32590,tc_prod(tc_List_Olist(X32589),X32590)),tc_fun(X32590,tc_prod(tc_List_Olist(X32589),X32590))),X32589),c_COMBB(tc_prod(tc_List_Olist(X32589),X32590),tc_prod(tc_List_Olist(X32589),X32590),X32590)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32589),tc_fun(X32590,tc_prod(tc_List_Olist(X32589),X32590))),tc_fun(tc_prod(tc_List_Olist(X32589),X32590),tc_prod(tc_List_Olist(X32589),X32590)),X32589),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X32589),X32590,tc_prod(tc_List_Olist(X32589),X32590))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32589),tc_List_Olist(X32589)),tc_fun(tc_List_Olist(X32589),tc_fun(X32590,tc_prod(tc_List_Olist(X32589),X32590))),X32589),hAPP(c_COMBB(tc_List_Olist(X32589),tc_fun(X32590,tc_prod(tc_List_Olist(X32589),X32590)),tc_List_Olist(X32589)),c_Product__Type_OPair(tc_List_Olist(X32589),X32590))),c_List_Olist_OCons(X32589))))),c_Lazy__Sequence_Oanamorph(X32590,X32589,X32588,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X32591),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X32588,X32587)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_anamorph_Osimps])]) ).
fof(i_0_6085,plain,
! [X32248,X32249,X32250,X32251,X32252,X32253,X32254,X32255,X32256] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32251)),X32250) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32251)),X32249)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32251),tc_List_Olist(X32251))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32251),tc_List_Olist(X32251)),X32250),X32249)),c_List_Olistrel(X32251,X32248))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32251,X32251)),X32252),hAPP(c_List_Oset(tc_prod(X32251,X32251)),hAPP(hAPP(c_List_Ozip(X32251,X32251),X32250),X32249))))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32251,X32251,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X32251,tc_fun(tc_prod(X32251,X32251),tc_HOL_Obool),tc_fun(X32251,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32251,tc_fun(tc_fun(tc_prod(X32251,X32251),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32251,X32251),tc_HOL_Obool),tc_fun(X32251,tc_HOL_Obool)),X32251),c_COMBC(X32251,tc_fun(tc_prod(X32251,X32251),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32251,tc_prod(X32251,X32251)),tc_fun(X32251,tc_fun(tc_fun(tc_prod(X32251,X32251),tc_HOL_Obool),tc_HOL_Obool)),X32251),hAPP(c_COMBB(tc_prod(X32251,X32251),tc_fun(tc_fun(tc_prod(X32251,X32251),tc_HOL_Obool),tc_HOL_Obool),X32251),c_member(tc_prod(X32251,X32251)))),c_Product__Type_OPair(X32251,X32251)))),X32248)),X32252))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32251),tc_List_Olist(X32251))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32251),tc_List_Olist(X32251)),X32250),X32249)),c_List_Olistrel(X32251,X32248))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32256,X32256)),esk442_4(X32253,X32254,X32255,X32256)),hAPP(c_List_Oset(tc_prod(X32256,X32256)),hAPP(hAPP(c_List_Ozip(X32256,X32256),X32255),X32254))))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32256)),X32255) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32256)),X32254)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32256),tc_List_Olist(X32256))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32256),tc_List_Olist(X32256)),X32255),X32254)),c_List_Olistrel(X32256,X32253))) )
& ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32256,X32256,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X32256,tc_fun(tc_prod(X32256,X32256),tc_HOL_Obool),tc_fun(X32256,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32256,tc_fun(tc_fun(tc_prod(X32256,X32256),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32256,X32256),tc_HOL_Obool),tc_fun(X32256,tc_HOL_Obool)),X32256),c_COMBC(X32256,tc_fun(tc_prod(X32256,X32256),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32256,tc_prod(X32256,X32256)),tc_fun(X32256,tc_fun(tc_fun(tc_prod(X32256,X32256),tc_HOL_Obool),tc_HOL_Obool)),X32256),hAPP(c_COMBB(tc_prod(X32256,X32256),tc_fun(tc_fun(tc_prod(X32256,X32256),tc_HOL_Obool),tc_HOL_Obool),X32256),c_member(tc_prod(X32256,X32256)))),c_Product__Type_OPair(X32256,X32256)))),X32253)),esk442_4(X32253,X32254,X32255,X32256)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32256)),X32255) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32256)),X32254)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32256),tc_List_Olist(X32256))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32256),tc_List_Olist(X32256)),X32255),X32254)),c_List_Olistrel(X32256,X32253))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__iff__zip])])])])])]) ).
fof(i_0_6086,plain,
! [X29853,X29854,X29855,X29856] :
( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X29856,X29855,hAPP(hAPP(c_COMBC(X29856,tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_fun(X29855,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29855,tc_fun(tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_fun(X29855,tc_HOL_Obool)),X29856),c_COMBC(X29855,tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29855,tc_prod(X29856,X29855)),tc_fun(X29855,tc_fun(tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_HOL_Obool)),X29856),hAPP(c_COMBB(tc_prod(X29856,X29855),tc_fun(tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_HOL_Obool),X29855),c_member(tc_prod(X29856,X29855)))),c_Product__Type_OPair(X29856,X29855)))),X29854)),X29853))
| hBOOL(hAPP(hAPP(c_member(X29856),X29853),hAPP(c_Relation_ODomain(X29856,X29855),X29854))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29856),X29853),hAPP(c_Relation_ODomain(X29856,X29855),X29854)))
| hBOOL(hAPP(c_Predicate_ODomainP(X29856,X29855,hAPP(hAPP(c_COMBC(X29856,tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_fun(X29855,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29855,tc_fun(tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_fun(X29855,tc_HOL_Obool)),X29856),c_COMBC(X29855,tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29855,tc_prod(X29856,X29855)),tc_fun(X29855,tc_fun(tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_HOL_Obool)),X29856),hAPP(c_COMBB(tc_prod(X29856,X29855),tc_fun(tc_fun(tc_prod(X29856,X29855),tc_HOL_Obool),tc_HOL_Obool),X29855),c_member(tc_prod(X29856,X29855)))),c_Product__Type_OPair(X29856,X29855)))),X29854)),X29853)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])]) ).
fof(i_0_6087,plain,
! [X29753,X29754,X29755,X29756] :
( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X29756,X29755,hAPP(hAPP(c_COMBC(X29756,tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_fun(X29755,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29755,tc_fun(tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_fun(X29755,tc_HOL_Obool)),X29756),c_COMBC(X29755,tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29755,tc_prod(X29756,X29755)),tc_fun(X29755,tc_fun(tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_HOL_Obool)),X29756),hAPP(c_COMBB(tc_prod(X29756,X29755),tc_fun(tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_HOL_Obool),X29755),c_member(tc_prod(X29756,X29755)))),c_Product__Type_OPair(X29756,X29755)))),X29754)),X29753))
| hBOOL(hAPP(hAPP(c_member(X29755),X29753),hAPP(c_Relation_ORange(X29756,X29755),X29754))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29755),X29753),hAPP(c_Relation_ORange(X29756,X29755),X29754)))
| hBOOL(hAPP(c_Predicate_ORangeP(X29756,X29755,hAPP(hAPP(c_COMBC(X29756,tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_fun(X29755,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29755,tc_fun(tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_fun(X29755,tc_HOL_Obool)),X29756),c_COMBC(X29755,tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29755,tc_prod(X29756,X29755)),tc_fun(X29755,tc_fun(tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_HOL_Obool)),X29756),hAPP(c_COMBB(tc_prod(X29756,X29755),tc_fun(tc_fun(tc_prod(X29756,X29755),tc_HOL_Obool),tc_HOL_Obool),X29755),c_member(tc_prod(X29756,X29755)))),c_Product__Type_OPair(X29756,X29755)))),X29754)),X29753)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])]) ).
fof(i_0_6088,plain,
! [X28506,X28507,X28508] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X28508,hAPP(hAPP(c_COMBC(X28508,tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_fun(X28508,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28508,tc_fun(tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_fun(X28508,tc_HOL_Obool)),X28508),c_COMBC(X28508,tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28508,tc_prod(X28508,X28508)),tc_fun(X28508,tc_fun(tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_HOL_Obool)),X28508),hAPP(c_COMBB(tc_prod(X28508,X28508),tc_fun(tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_HOL_Obool),X28508),c_member(tc_prod(X28508,X28508)))),c_Product__Type_OPair(X28508,X28508)))),X28507)),X28506))
| hBOOL(hAPP(hAPP(c_member(X28508),X28506),c_Wellfounded_Oacc(X28508,X28507))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28508),X28506),c_Wellfounded_Oacc(X28508,X28507)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X28508,hAPP(hAPP(c_COMBC(X28508,tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_fun(X28508,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28508,tc_fun(tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_fun(X28508,tc_HOL_Obool)),X28508),c_COMBC(X28508,tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28508,tc_prod(X28508,X28508)),tc_fun(X28508,tc_fun(tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_HOL_Obool)),X28508),hAPP(c_COMBB(tc_prod(X28508,X28508),tc_fun(tc_fun(tc_prod(X28508,X28508),tc_HOL_Obool),tc_HOL_Obool),X28508),c_member(tc_prod(X28508,X28508)))),c_Product__Type_OPair(X28508,X28508)))),X28507)),X28506)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])]) ).
fof(i_0_6089,plain,
! [X25889,X25890,X25891,X25892,X25893,X25894,X25895,X25898,X25899,X25900,X25901,X25902,X25903,X25904,X25905,X25906] :
( ( hAPP(hAPP(X25893,X25890),X25889) = hAPP(hAPP(X25893,esk198_7(X25889,X25890,X25891,X25892,X25893,X25894,X25895)),esk199_7(X25889,X25890,X25891,X25892,X25893,X25894,X25895))
| X25891 = c_Orderings_Obot__class_Obot(tc_fun(X25895,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X25895,X25894,X25893,X25892,X25891,hAPP(hAPP(X25893,X25890),X25889)) )
& ( hBOOL(hAPP(hAPP(c_member(X25895),esk198_7(X25889,X25890,X25891,X25892,X25893,X25894,X25895)),X25891))
| X25891 = c_Orderings_Obot__class_Obot(tc_fun(X25895,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X25895,X25894,X25893,X25892,X25891,hAPP(hAPP(X25893,X25890),X25889)) )
& ( c_Nitpick_Ofold__graph_H(X25895,X25894,X25893,X25892,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25895,tc_HOL_Obool)),X25891),hAPP(hAPP(c_Set_Oinsert(X25895),esk198_7(X25889,X25890,X25891,X25892,X25893,X25894,X25895)),c_Orderings_Obot__class_Obot(tc_fun(X25895,tc_HOL_Obool)))),esk199_7(X25889,X25890,X25891,X25892,X25893,X25894,X25895))
| X25891 = c_Orderings_Obot__class_Obot(tc_fun(X25895,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X25895,X25894,X25893,X25892,X25891,hAPP(hAPP(X25893,X25890),X25889)) )
& ( hAPP(hAPP(X25893,X25890),X25889) = hAPP(hAPP(X25893,esk198_7(X25889,X25890,X25891,X25892,X25893,X25894,X25895)),esk199_7(X25889,X25890,X25891,X25892,X25893,X25894,X25895))
| hAPP(hAPP(X25893,X25890),X25889) = X25892
| ~ c_Nitpick_Ofold__graph_H(X25895,X25894,X25893,X25892,X25891,hAPP(hAPP(X25893,X25890),X25889)) )
& ( hBOOL(hAPP(hAPP(c_member(X25895),esk198_7(X25889,X25890,X25891,X25892,X25893,X25894,X25895)),X25891))
| hAPP(hAPP(X25893,X25890),X25889) = X25892
| ~ c_Nitpick_Ofold__graph_H(X25895,X25894,X25893,X25892,X25891,hAPP(hAPP(X25893,X25890),X25889)) )
& ( c_Nitpick_Ofold__graph_H(X25895,X25894,X25893,X25892,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25895,tc_HOL_Obool)),X25891),hAPP(hAPP(c_Set_Oinsert(X25895),esk198_7(X25889,X25890,X25891,X25892,X25893,X25894,X25895)),c_Orderings_Obot__class_Obot(tc_fun(X25895,tc_HOL_Obool)))),esk199_7(X25889,X25890,X25891,X25892,X25893,X25894,X25895))
| hAPP(hAPP(X25893,X25890),X25889) = X25892
| ~ c_Nitpick_Ofold__graph_H(X25895,X25894,X25893,X25892,X25891,hAPP(hAPP(X25893,X25890),X25889)) )
& ( X25900 != c_Orderings_Obot__class_Obot(tc_fun(X25904,tc_HOL_Obool))
| hAPP(hAPP(X25902,X25899),X25898) != X25901
| c_Nitpick_Ofold__graph_H(X25904,X25903,X25902,X25901,X25900,hAPP(hAPP(X25902,X25899),X25898)) )
& ( hAPP(hAPP(X25902,X25899),X25898) != hAPP(hAPP(X25902,X25905),X25906)
| ~ hBOOL(hAPP(hAPP(c_member(X25904),X25905),X25900))
| ~ c_Nitpick_Ofold__graph_H(X25904,X25903,X25902,X25901,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25904,tc_HOL_Obool)),X25900),hAPP(hAPP(c_Set_Oinsert(X25904),X25905),c_Orderings_Obot__class_Obot(tc_fun(X25904,tc_HOL_Obool)))),X25906)
| c_Nitpick_Ofold__graph_H(X25904,X25903,X25902,X25901,X25900,hAPP(hAPP(X25902,X25899),X25898)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I2_J])])])])])]) ).
fof(i_0_6090,plain,
! [X25465,X25466,X25467,X25468,X25469,X25470,X25471,X25473,X25474,X25475,X25476,X25477,X25478,X25479,X25480] :
( ( hBOOL(hAPP(hAPP(c_member(X25471),esk174_7(X25465,X25466,X25467,X25468,X25469,X25470,X25471)),X25468))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25471,tc_fun(X25470,tc_fun(X25469,tc_HOL_Obool))),X25468),X25467),X25466),X25465)) )
& ( hBOOL(hAPP(hAPP(hAPP(X25467,esk174_7(X25465,X25466,X25467,X25468,X25469,X25470,X25471)),X25466),X25465))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25471,tc_fun(X25470,tc_fun(X25469,tc_HOL_Obool))),X25468),X25467),X25466),X25465)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25479),X25480),X25476))
| ~ hBOOL(hAPP(hAPP(hAPP(X25475,X25480),X25474),X25473))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25479,tc_fun(X25478,tc_fun(X25477,tc_HOL_Obool))),X25476),X25475),X25474),X25473)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP2__iff])])])])])]) ).
fof(i_0_6091,plain,
! [X33953,X33954,X33955,X33956] : c_List_Opartition(X33956,X33955,hAPP(hAPP(c_List_Olist_OCons(X33956),X33954),X33953)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X33956),tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956))),hAPP(hAPP(c_COMBS(tc_List_Olist(X33956),tc_fun(tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956))),tc_fun(tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X33956),tc_fun(tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)))),tc_fun(tc_fun(tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956))),tc_fun(tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)))),tc_List_Olist(X33956)),c_COMBS(tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956))),tc_fun(tc_List_Olist(X33956),tc_fun(tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)))),tc_List_Olist(X33956)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)),tc_fun(tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956))),tc_List_Olist(X33956)),hAPP(c_If(tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956))),hAPP(X33955,X33954)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X33956),tc_fun(tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956))),tc_List_Olist(X33956)),c_Product__Type_OPair(tc_List_Olist(X33956),tc_List_Olist(X33956))),hAPP(c_List_Olist_OCons(X33956),X33954))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X33956),tc_fun(tc_List_Olist(X33956),tc_List_Olist(X33956)),tc_fun(tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956))),tc_fun(tc_fun(tc_List_Olist(X33956),tc_List_Olist(X33956)),tc_fun(tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)))),tc_List_Olist(X33956)),c_COMBB(tc_List_Olist(X33956),tc_prod(tc_List_Olist(X33956),tc_List_Olist(X33956)),tc_List_Olist(X33956))),c_Product__Type_OPair(tc_List_Olist(X33956),tc_List_Olist(X33956)))),hAPP(c_List_Olist_OCons(X33956),X33954)))),c_List_Opartition(X33956,X33955,X33953)),
inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J]) ).
fof(i_0_6092,plain,
! [X25712,X25713,X25714,X25715,X25716] : c_Hoare__Mirabelle_Ohoare__derivs(X25716,X25715,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25716)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25716),hAPP(hAPP(c_COMBC(X25716,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X25716),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X25714)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X25713)),X25712))),c_Com_Ocom_OAss(X25713,X25712)),X25714)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25716),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_Ass]) ).
fof(i_0_6093,plain,
! [X25707,X25708,X25709,X25710,X25711] : c_Hoare__Mirabelle_Ohoare__derivs(X25711,X25710,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25711)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25711),hAPP(hAPP(c_COMBC(X25711,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X25711),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X25709)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X25708)),X25707))),c_Com_Ocom_OAss(X25708,X25707)),X25709)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25711),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I8_J]) ).
fof(i_0_6094,plain,
! [X32277,X32278,X32279] : hAPP(c_List_Olexn(X32279,X32278),hAPP(c_Nat_OSuc,X32277)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X32279),tc_List_Olist(X32279)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X32279,tc_List_Olist(X32279)),tc_prod(X32279,tc_List_Olist(X32279))),tc_prod(tc_List_Olist(X32279),tc_List_Olist(X32279)),c_Product__Type_Omap__pair(tc_prod(X32279,tc_List_Olist(X32279)),tc_List_Olist(X32279),tc_prod(X32279,tc_List_Olist(X32279)),tc_List_Olist(X32279),hAPP(c_Product__Type_Oprod_Oprod__case(X32279,tc_List_Olist(X32279),tc_List_Olist(X32279)),c_List_Olist_OCons(X32279)),hAPP(c_Product__Type_Oprod_Oprod__case(X32279,tc_List_Olist(X32279),tc_List_Olist(X32279)),c_List_Olist_OCons(X32279)))),c_Wellfounded_Olex__prod(X32279,tc_List_Olist(X32279),X32278,hAPP(c_List_Olexn(X32279,X32278),X32277)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X32279),tc_List_Olist(X32279))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X32279),tc_List_Olist(X32279),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X32279),tc_fun(tc_List_Olist(X32279),tc_HOL_Obool),tc_fun(tc_List_Olist(X32279),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32279),tc_HOL_Obool),tc_fun(tc_List_Olist(X32279),tc_HOL_Obool)),tc_List_Olist(X32279)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X32279))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32279)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X32279),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32279)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X32279)))),hAPP(c_Nat_OSuc,X32277))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32279),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32279)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X32279)))),hAPP(c_Nat_OSuc,X32277)))))),
inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I2_J]) ).
cnf(i_0_6095,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X2)))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5213]) ).
cnf(i_0_6096,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X2)))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5213]) ).
cnf(i_0_6097,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5214]) ).
fof(i_0_6098,plain,
! [X32697,X32698,X32699] : hAPP(c_List_Oset(X32699),c_List_Osublist(X32699,X32698,X32697)) = hAPP(c_Set_OCollect(X32699),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X32699),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X32699,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X32699),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X32699),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X32699,tc_fun(tc_Nat_Onat,X32699),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32699,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X32699),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X32699),c_COMBB(X32699,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X32699),X32698))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32699)),X32698)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X32697))))),
inference(variable_rename,[status(thm)],[fact_set__sublist]) ).
cnf(i_0_6099,plain,
( c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X4)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X3),c_List_Oconcat(tc_List_Olist(X1),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X4)))))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X1)),c_List_Otranspose__rel(X1)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5215]) ).
cnf(i_0_6100,plain,
c_List_Oconcat(X1,X2) = hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_5216]) ).
cnf(i_0_6101,plain,
c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X4)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X3),c_List_Oconcat(tc_List_Olist(X1),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X4))))),
inference(split_conjunct,[status(thm)],[i_0_5217]) ).
fof(i_0_6102,plain,
! [X29565,X29566,X29567,X29568,X29569,X29570,X29571] :
( ( ~ c_Predicate_Opred__comp(X29571,X29570,X29569,hAPP(hAPP(c_COMBC(X29571,tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_fun(X29570,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29570,tc_fun(tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_fun(X29570,tc_HOL_Obool)),X29571),c_COMBC(X29570,tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29570,tc_prod(X29571,X29570)),tc_fun(X29570,tc_fun(tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_HOL_Obool)),X29571),hAPP(c_COMBB(tc_prod(X29571,X29570),tc_fun(tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_HOL_Obool),X29570),c_member(tc_prod(X29571,X29570)))),c_Product__Type_OPair(X29571,X29570)))),X29568),hAPP(hAPP(c_COMBC(X29570,tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_fun(X29569,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29569,tc_fun(tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_fun(X29569,tc_HOL_Obool)),X29570),c_COMBC(X29569,tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29569,tc_prod(X29570,X29569)),tc_fun(X29569,tc_fun(tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_HOL_Obool)),X29570),hAPP(c_COMBB(tc_prod(X29570,X29569),tc_fun(tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_HOL_Obool),X29569),c_member(tc_prod(X29570,X29569)))),c_Product__Type_OPair(X29570,X29569)))),X29567),X29566,X29565)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29571,X29569)),hAPP(hAPP(c_Product__Type_OPair(X29571,X29569),X29566),X29565)),hAPP(hAPP(c_Relation_Orel__comp(X29571,X29570,X29569),X29568),X29567))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29571,X29569)),hAPP(hAPP(c_Product__Type_OPair(X29571,X29569),X29566),X29565)),hAPP(hAPP(c_Relation_Orel__comp(X29571,X29570,X29569),X29568),X29567)))
| c_Predicate_Opred__comp(X29571,X29570,X29569,hAPP(hAPP(c_COMBC(X29571,tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_fun(X29570,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29570,tc_fun(tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_fun(X29570,tc_HOL_Obool)),X29571),c_COMBC(X29570,tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29570,tc_prod(X29571,X29570)),tc_fun(X29570,tc_fun(tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_HOL_Obool)),X29571),hAPP(c_COMBB(tc_prod(X29571,X29570),tc_fun(tc_fun(tc_prod(X29571,X29570),tc_HOL_Obool),tc_HOL_Obool),X29570),c_member(tc_prod(X29571,X29570)))),c_Product__Type_OPair(X29571,X29570)))),X29568),hAPP(hAPP(c_COMBC(X29570,tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_fun(X29569,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29569,tc_fun(tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_fun(X29569,tc_HOL_Obool)),X29570),c_COMBC(X29569,tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29569,tc_prod(X29570,X29569)),tc_fun(X29569,tc_fun(tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_HOL_Obool)),X29570),hAPP(c_COMBB(tc_prod(X29570,X29569),tc_fun(tc_fun(tc_prod(X29570,X29569),tc_HOL_Obool),tc_HOL_Obool),X29569),c_member(tc_prod(X29570,X29569)))),c_Product__Type_OPair(X29570,X29569)))),X29567),X29566,X29565) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq])]) ).
fof(i_0_6103,plain,
! [X29413,X29414,X29415,X29416,X29417,X29418] :
( ( hBOOL(hAPP(hAPP(c_member(X29416),esk314_6(X29413,X29414,X29415,X29416,X29417,X29418)),X29415))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29418,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X29416,tc_HOL_Obool),tc_Nat_Onat,X29418),c_Finite__Set_Ocard(X29416)),hAPP(hAPP(c_COMBB(tc_fun(X29416,tc_HOL_Obool),tc_fun(X29416,tc_HOL_Obool),X29418),c_Set_OCollect(X29416)),hAPP(hAPP(c_COMBB(tc_fun(X29416,tc_HOL_Obool),tc_fun(X29416,tc_HOL_Obool),X29418),hAPP(c_COMBS(X29416,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29416),c_fconj),hAPP(hAPP(c_COMBC(X29416,tc_fun(X29416,tc_HOL_Obool),tc_HOL_Obool),c_member(X29416)),X29415)))),X29414)))),X29417) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29416,tc_Nat_Onat),X29413),X29415)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29416),X29415))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29418),X29417)) )
& ( hAPP(c_Finite__Set_Ocard(X29418),hAPP(c_Set_OCollect(X29418),hAPP(hAPP(c_COMBS(X29418,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29418),c_fconj),hAPP(hAPP(c_COMBC(X29418,tc_fun(X29418,tc_HOL_Obool),tc_HOL_Obool),c_member(X29418)),X29417))),hAPP(hAPP(c_COMBC(X29418,X29416,tc_HOL_Obool),X29414),esk314_6(X29413,X29414,X29415,X29416,X29417,X29418))))) != hAPP(X29413,esk314_6(X29413,X29414,X29415,X29416,X29417,X29418))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29418,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X29416,tc_HOL_Obool),tc_Nat_Onat,X29418),c_Finite__Set_Ocard(X29416)),hAPP(hAPP(c_COMBB(tc_fun(X29416,tc_HOL_Obool),tc_fun(X29416,tc_HOL_Obool),X29418),c_Set_OCollect(X29416)),hAPP(hAPP(c_COMBB(tc_fun(X29416,tc_HOL_Obool),tc_fun(X29416,tc_HOL_Obool),X29418),hAPP(c_COMBS(X29416,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29416),c_fconj),hAPP(hAPP(c_COMBC(X29416,tc_fun(X29416,tc_HOL_Obool),tc_HOL_Obool),c_member(X29416)),X29415)))),X29414)))),X29417) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29416,tc_Nat_Onat),X29413),X29415)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29416),X29415))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29418),X29417)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__multicount__gen])])])]) ).
fof(i_0_6104,plain,
! [X32689,X32690] : hAPP(c_List_Oset(X32690),X32689) = hAPP(c_Set_OCollect(X32690),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X32690),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X32690,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X32690),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X32690),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X32690,tc_fun(tc_Nat_Onat,X32690),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32690,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X32690),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X32690),c_COMBB(X32690,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X32690),X32689))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32690)),X32689))))),
inference(variable_rename,[status(thm)],[fact_set__conv__nth]) ).
fof(i_0_6105,plain,
! [X28801,X28802,X28803,X28804] : hAPP(hAPP(c_Product__Type_OSigma(X28804,X28803),X28802),X28801) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28804,tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool)),X28802),hAPP(hAPP(c_COMBS(X28804,tc_fun(X28803,tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool)),tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28803,tc_HOL_Obool),tc_fun(tc_fun(X28803,tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool)),tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool)),X28804),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28803,tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool))),X28801)),hAPP(hAPP(c_COMBC(X28804,tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool),tc_fun(X28803,tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28803,tc_fun(tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool),tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool),tc_fun(X28803,tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool))),X28804),c_COMBC(X28803,tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool),tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28803,tc_prod(X28804,X28803)),tc_fun(X28803,tc_fun(tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool),tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool))),X28804),hAPP(c_COMBB(tc_prod(X28804,X28803),tc_fun(tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool),tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool)),X28803),c_Set_Oinsert(tc_prod(X28804,X28803)))),c_Product__Type_OPair(X28804,X28803)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28804,X28803),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_Sigma__def]) ).
cnf(i_0_6106,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)))),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5218]) ).
fof(i_0_6107,plain,
! [X29307,X29308,X29309,X29310,X29311,X29312] :
( ( hBOOL(hAPP(hAPP(c_member(X29310),esk312_6(X29307,X29308,X29309,X29310,X29311,X29312)),X29309))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29312,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X29310,tc_HOL_Obool),tc_Nat_Onat,X29312),c_Finite__Set_Ocard(X29310)),hAPP(hAPP(c_COMBB(tc_fun(X29310,tc_HOL_Obool),tc_fun(X29310,tc_HOL_Obool),X29312),c_Set_OCollect(X29310)),hAPP(hAPP(c_COMBB(tc_fun(X29310,tc_HOL_Obool),tc_fun(X29310,tc_HOL_Obool),X29312),hAPP(c_COMBS(X29310,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29310),c_fconj),hAPP(hAPP(c_COMBC(X29310,tc_fun(X29310,tc_HOL_Obool),tc_HOL_Obool),c_member(X29310)),X29309)))),X29308)))),X29311) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29307),hAPP(c_Finite__Set_Ocard(X29310),X29309))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29310),X29309))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29312),X29311)) )
& ( hAPP(c_Finite__Set_Ocard(X29312),hAPP(c_Set_OCollect(X29312),hAPP(hAPP(c_COMBS(X29312,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29312),c_fconj),hAPP(hAPP(c_COMBC(X29312,tc_fun(X29312,tc_HOL_Obool),tc_HOL_Obool),c_member(X29312)),X29311))),hAPP(hAPP(c_COMBC(X29312,X29310,tc_HOL_Obool),X29308),esk312_6(X29307,X29308,X29309,X29310,X29311,X29312))))) != X29307
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29312,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X29310,tc_HOL_Obool),tc_Nat_Onat,X29312),c_Finite__Set_Ocard(X29310)),hAPP(hAPP(c_COMBB(tc_fun(X29310,tc_HOL_Obool),tc_fun(X29310,tc_HOL_Obool),X29312),c_Set_OCollect(X29310)),hAPP(hAPP(c_COMBB(tc_fun(X29310,tc_HOL_Obool),tc_fun(X29310,tc_HOL_Obool),X29312),hAPP(c_COMBS(X29310,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29310),c_fconj),hAPP(hAPP(c_COMBC(X29310,tc_fun(X29310,tc_HOL_Obool),tc_HOL_Obool),c_member(X29310)),X29309)))),X29308)))),X29311) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29307),hAPP(c_Finite__Set_Ocard(X29310),X29309))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29310),X29309))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29312),X29311)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__multicount])])])]) ).
fof(i_0_6108,plain,
! [X29255,X29256,X29257,X29258,X29259,X29260,X29261] :
( ~ class_Groups_Ocomm__monoid__add(X29261)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29260),X29259))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29258),X29257))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29260,X29261),hAPP(hAPP(c_COMBS(X29260,tc_fun(X29258,tc_HOL_Obool),X29261),hAPP(hAPP(c_COMBB(tc_fun(X29258,X29261),tc_fun(tc_fun(X29258,tc_HOL_Obool),X29261),X29260),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29258,X29261)),X29256)),hAPP(hAPP(c_COMBB(tc_fun(X29258,tc_HOL_Obool),tc_fun(X29258,tc_HOL_Obool),X29260),c_Set_OCollect(X29258)),hAPP(hAPP(c_COMBB(tc_fun(X29258,tc_HOL_Obool),tc_fun(X29258,tc_HOL_Obool),X29260),hAPP(c_COMBS(X29258,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29258),c_fconj),hAPP(hAPP(c_COMBC(X29258,tc_fun(X29258,tc_HOL_Obool),tc_HOL_Obool),c_member(X29258)),X29257)))),X29255)))),X29259) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29258,X29261),hAPP(hAPP(c_COMBS(X29258,tc_fun(X29260,tc_HOL_Obool),X29261),hAPP(hAPP(c_COMBB(tc_fun(X29260,X29261),tc_fun(tc_fun(X29260,tc_HOL_Obool),X29261),X29258),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29260,X29261)),hAPP(c_COMBC(X29260,X29258,X29261),X29256))),hAPP(hAPP(c_COMBB(tc_fun(X29260,tc_HOL_Obool),tc_fun(X29260,tc_HOL_Obool),X29258),c_Set_OCollect(X29260)),hAPP(hAPP(c_COMBB(tc_fun(X29260,tc_HOL_Obool),tc_fun(X29260,tc_HOL_Obool),X29258),hAPP(c_COMBS(X29260,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29260),c_fconj),hAPP(hAPP(c_COMBC(X29260,tc_fun(X29260,tc_HOL_Obool),tc_HOL_Obool),c_member(X29260)),X29259)))),hAPP(c_COMBC(X29260,X29258,tc_HOL_Obool),X29255))))),X29257) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict])]) ).
fof(i_0_6109,plain,
! [X30335,X30336,X30337,X30338,X30339] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30339,X30339)),hAPP(hAPP(c_Product__Type_OPair(X30339,X30339),hAPP(X30338,hAPP(c_Nat_OSuc,esk366_5(X30335,X30336,X30337,X30338,X30339)))),hAPP(X30338,esk366_5(X30335,X30336,X30337,X30338,X30339)))),c_Transitive__Closure_Ortrancl(X30339,X30337)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30339,X30339)),hAPP(hAPP(c_Product__Type_OPair(X30339,X30339),hAPP(X30338,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30336),X30335))),hAPP(X30338,X30336))),c_Transitive__Closure_Ortrancl(X30339,X30337))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sequence__trans])])]) ).
fof(i_0_6110,plain,
! [X31663,X31664,X31665,X31666,X31667,X31668] :
( ( X31666 = hAPP(hAPP(c_Product__Type_OPair(X31668,X31667),esk428_6(X31663,X31664,X31665,X31666,X31667,X31668)),esk430_6(X31663,X31664,X31665,X31666,X31667,X31668))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31668,X31667)),X31666),hAPP(hAPP(c_Relation_Orel__comp(X31668,X31665,X31667),X31664),X31663))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31668,X31665)),hAPP(hAPP(c_Product__Type_OPair(X31668,X31665),esk428_6(X31663,X31664,X31665,X31666,X31667,X31668)),esk429_6(X31663,X31664,X31665,X31666,X31667,X31668))),X31664))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31668,X31667)),X31666),hAPP(hAPP(c_Relation_Orel__comp(X31668,X31665,X31667),X31664),X31663))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31665,X31667)),hAPP(hAPP(c_Product__Type_OPair(X31665,X31667),esk429_6(X31663,X31664,X31665,X31666,X31667,X31668)),esk430_6(X31663,X31664,X31665,X31666,X31667,X31668))),X31663))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31668,X31667)),X31666),hAPP(hAPP(c_Relation_Orel__comp(X31668,X31665,X31667),X31664),X31663))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5219])])])]) ).
fof(i_0_6111,plain,
! [X22134,X22135] : c_Divides_Odivmod__int__rel(X22135,X22134) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X22135))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22134)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22134))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X22134))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22134)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22134))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
inference(variable_rename,[status(thm)],[fact_divmod__int__rel__def]) ).
fof(i_0_6112,plain,
! [X23256,X23257,X23258,X23259,X23260,X23261,X23262] :
( ~ class_Rings_Osemiring__0(X23262)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23262),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23261,X23262),X23260),X23259)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23258,X23262),X23257),X23256)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23261,X23262),hAPP(hAPP(c_COMBC(X23261,tc_fun(X23258,tc_HOL_Obool),X23262),hAPP(hAPP(c_COMBB(tc_fun(X23258,X23262),tc_fun(tc_fun(X23258,tc_HOL_Obool),X23262),X23261),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23258,X23262)),hAPP(hAPP(c_COMBC(X23261,tc_fun(X23258,X23262),tc_fun(X23258,X23262)),hAPP(hAPP(c_COMBB(tc_fun(X23262,X23262),tc_fun(tc_fun(X23258,X23262),tc_fun(X23258,X23262)),X23261),c_COMBB(X23262,X23262,X23258)),hAPP(hAPP(c_COMBB(X23262,tc_fun(X23262,X23262),X23261),c_Groups_Otimes__class_Otimes(X23262)),X23260))),X23257))),X23256)),X23259) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__product])]) ).
fof(i_0_6113,plain,
! [X28819,X28820,X28821,X28822,X28823,X28824] :
( ( hBOOL(hAPP(hAPP(c_member(X28823),esk284_6(X28819,X28820,X28821,X28822,X28823,X28824)),X28822))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28824,X28823,c_Groups_Otimes__class_Otimes(X28824)),hAPP(hAPP(c_COMBS(X28823,tc_fun(X28821,tc_HOL_Obool),X28824),hAPP(hAPP(c_COMBC(X28823,X28824,tc_fun(tc_fun(X28821,tc_HOL_Obool),X28824)),hAPP(hAPP(c_COMBB(tc_fun(X28821,X28824),tc_fun(X28824,tc_fun(tc_fun(X28821,tc_HOL_Obool),X28824)),X28823),c_Finite__Set_Ofold__image(X28824,X28821,c_Groups_Otimes__class_Otimes(X28824))),X28819)),c_Groups_Oone__class_Oone(X28824))),X28820)),c_Groups_Oone__class_Oone(X28824)),X28822) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28824,tc_prod(X28823,X28821),c_Groups_Otimes__class_Otimes(X28824)),hAPP(c_Product__Type_Oprod_Oprod__case(X28823,X28821,X28824),X28819)),c_Groups_Oone__class_Oone(X28824)),hAPP(hAPP(c_Product__Type_OSigma(X28823,X28821),X28822),X28820))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28823),X28822))
| ~ class_Groups_Ocomm__monoid__mult(X28824) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28821),hAPP(X28820,esk284_6(X28819,X28820,X28821,X28822,X28823,X28824))))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28824,X28823,c_Groups_Otimes__class_Otimes(X28824)),hAPP(hAPP(c_COMBS(X28823,tc_fun(X28821,tc_HOL_Obool),X28824),hAPP(hAPP(c_COMBC(X28823,X28824,tc_fun(tc_fun(X28821,tc_HOL_Obool),X28824)),hAPP(hAPP(c_COMBB(tc_fun(X28821,X28824),tc_fun(X28824,tc_fun(tc_fun(X28821,tc_HOL_Obool),X28824)),X28823),c_Finite__Set_Ofold__image(X28824,X28821,c_Groups_Otimes__class_Otimes(X28824))),X28819)),c_Groups_Oone__class_Oone(X28824))),X28820)),c_Groups_Oone__class_Oone(X28824)),X28822) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28824,tc_prod(X28823,X28821),c_Groups_Otimes__class_Otimes(X28824)),hAPP(c_Product__Type_Oprod_Oprod__case(X28823,X28821,X28824),X28819)),c_Groups_Oone__class_Oone(X28824)),hAPP(hAPP(c_Product__Type_OSigma(X28823,X28821),X28822),X28820))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28823),X28822))
| ~ class_Groups_Ocomm__monoid__mult(X28824) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__Sigma])])])]) ).
cnf(i_0_6114,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))))) ),
inference(split_conjunct,[status(thm)],[i_0_5220]) ).
fof(i_0_6115,plain,
! [X32243,X32244,X32245] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32245),X32244))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X32245)),hAPP(c_Set_OCollect(tc_List_Olist(X32245)),hAPP(hAPP(c_COMBS(tc_List_Olist(X32245),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32245)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X32245),tc_fun(X32245,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X32245,tc_HOL_Obool),tc_fun(tc_fun(X32245,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X32245)),c_Orderings_Oord__class_Oless__eq(tc_fun(X32245,tc_HOL_Obool))),c_List_Oset(X32245))),X32244))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32245),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32245)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X32245)))),X32243))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le])]) ).
fof(i_0_6116,plain,
! [X32213,X32214,X32215] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32215),X32214))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X32215)),hAPP(c_Set_OCollect(tc_List_Olist(X32215)),hAPP(hAPP(c_COMBS(tc_List_Olist(X32215),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32215)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X32215),tc_fun(X32215,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X32215,tc_HOL_Obool),tc_fun(tc_fun(X32215,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X32215)),c_Orderings_Oord__class_Oless__eq(tc_fun(X32215,tc_HOL_Obool))),c_List_Oset(X32215))),X32214))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32215),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32215)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X32215)))),X32213))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__eq])]) ).
cnf(i_0_6117,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X2)))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5213]) ).
fof(i_0_6118,plain,
! [X29135,X29136,X29137,X29138,X29139,X29140,X29141,X29142] :
( ( hBOOL(hAPP(hAPP(c_member(X29141),esk309_7(X29135,X29136,X29137,X29138,X29139,X29140,X29141)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29141,tc_HOL_Obool)),X29136),X29135)))
| hAPP(X29137,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29141,tc_HOL_Obool)),X29136),X29135)) = hAPP(hAPP(X29140,hAPP(X29137,X29136)),hAPP(X29137,X29135))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29141),X29135))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29141),X29136))
| ~ c_Finite__Set_Ofolding__image__simple(X29142,X29141,X29140,X29139,X29138,X29137) )
& ( hAPP(X29138,esk309_7(X29135,X29136,X29137,X29138,X29139,X29140,X29141)) != X29139
| hAPP(X29137,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29141,tc_HOL_Obool)),X29136),X29135)) = hAPP(hAPP(X29140,hAPP(X29137,X29136)),hAPP(X29137,X29135))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29141),X29135))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29141),X29136))
| ~ c_Finite__Set_Ofolding__image__simple(X29142,X29141,X29140,X29139,X29138,X29137) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter__neutral])])])])])]) ).
fof(i_0_6119,plain,
! [X24914] : hAPP(c_Int_Onat,X24914) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X24914)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
inference(variable_rename,[status(thm)],[fact_nat__def]) ).
fof(i_0_6120,plain,
! [X17923,X17924,X17925,X17926,X17927,X17928,X17930,X17931,X17932,X17933,X17934,X17935,X17936] :
( ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17923),hAPP(c_Natural_Ogetlocs,X17925))),X17928),hAPP(hAPP(c_Natural_Ogetlocs,X17923),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk17_6(X17923,X17924,X17925,X17926,X17927,X17928)),hAPP(c_Natural_Ogetlocs,X17925))),X17928),hAPP(hAPP(c_Natural_Ogetlocs,esk17_6(X17923,X17924,X17925,X17926,X17927,X17928)),c_Com_ORes))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X17928,X17927,X17926),X17925,X17924,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17923),hAPP(c_Natural_Ogetlocs,X17925))),X17928),hAPP(hAPP(c_Natural_Ogetlocs,X17923),c_Com_ORes))) )
& ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17927),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17925),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17926,X17925)),X17924,esk17_6(X17923,X17924,X17925,X17926,X17927,X17928))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X17928,X17927,X17926),X17925,X17924,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17923),hAPP(c_Natural_Ogetlocs,X17925))),X17928),hAPP(hAPP(c_Natural_Ogetlocs,X17923),c_Com_ORes))) )
& ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17930),hAPP(c_Natural_Ogetlocs,X17932))),X17935),hAPP(hAPP(c_Natural_Ogetlocs,X17930),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17936),hAPP(c_Natural_Ogetlocs,X17932))),X17935),hAPP(hAPP(c_Natural_Ogetlocs,X17936),c_Com_ORes))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17934),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17932),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17933,X17932)),X17931,X17936)
| c_Natural_Oevaln(c_Com_Ocom_OCall(X17935,X17934,X17933),X17932,X17931,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17930),hAPP(c_Natural_Ogetlocs,X17932))),X17935),hAPP(hAPP(c_Natural_Ogetlocs,X17930),c_Com_ORes))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I10_J])])])])])]) ).
fof(i_0_6121,plain,
! [X17955,X17956,X17957,X17958,X17959,X17960] :
( ( X17955 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk20_6(X17955,X17956,X17957,X17958,X17959,X17960)),hAPP(c_Natural_Ogetlocs,X17957))),X17960),hAPP(hAPP(c_Natural_Ogetlocs,esk20_6(X17955,X17956,X17957,X17958,X17959,X17960)),c_Com_ORes))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X17960,X17959,X17958),X17957,X17956,X17955) )
& ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17959),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17957),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17958,X17957)),X17956,esk20_6(X17955,X17956,X17957,X17958,X17959,X17960))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X17960,X17959,X17958),X17957,X17956,X17955) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5221])])])]) ).
fof(i_0_6122,plain,
! [X21423,X21424,X21425,X21426] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21426),esk77_4(X21423,X21424,X21425,X21426)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21423),hAPP(X21424,X21425)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21424,X21426)),X21423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21426),X21425))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21426),esk76_4(X21423,X21424,X21425,X21426))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_4(X21423,X21424,X21425,X21426)),X21425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21423),hAPP(X21424,X21425)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21424,X21426)),X21423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21426),X21425))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21426),esk76_4(X21423,X21424,X21425,X21426))) )
& ( hAPP(X21424,esk77_4(X21423,X21424,X21425,X21426)) = X21423
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21423),hAPP(X21424,X21425)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21424,X21426)),X21423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21426),X21425))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21426),esk76_4(X21423,X21424,X21425,X21426))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21426),esk77_4(X21423,X21424,X21425,X21426)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21423),hAPP(X21424,X21425)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21424,X21426)),X21423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21426),X21425))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_4(X21423,X21424,X21425,X21426)),X21425)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_4(X21423,X21424,X21425,X21426)),X21425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21423),hAPP(X21424,X21425)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21424,X21426)),X21423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21426),X21425))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_4(X21423,X21424,X21425,X21426)),X21425)) )
& ( hAPP(X21424,esk77_4(X21423,X21424,X21425,X21426)) = X21423
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21423),hAPP(X21424,X21425)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21424,X21426)),X21423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21426),X21425))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_4(X21423,X21424,X21425,X21426)),X21425)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21426),esk77_4(X21423,X21424,X21425,X21426)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21423),hAPP(X21424,X21425)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21424,X21426)),X21423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21426),X21425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X21424,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk76_4(X21423,X21424,X21425,X21426)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21424,esk76_4(X21423,X21424,X21425,X21426))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_4(X21423,X21424,X21425,X21426)),X21425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21423),hAPP(X21424,X21425)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21424,X21426)),X21423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21426),X21425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X21424,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk76_4(X21423,X21424,X21425,X21426)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21424,esk76_4(X21423,X21424,X21425,X21426))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( hAPP(X21424,esk77_4(X21423,X21424,X21425,X21426)) = X21423
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21423),hAPP(X21424,X21425)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21424,X21426)),X21423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21426),X21425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X21424,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk76_4(X21423,X21424,X21425,X21426)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21424,esk76_4(X21423,X21424,X21425,X21426))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__intermed__int__val])])])]) ).
fof(i_0_6123,plain,
! [X30037,X30038,X30039,X30040,X30041,X30042] :
( ( hBOOL(hAPP(hAPP(c_member(X30042),esk352_6(X30037,X30038,X30039,X30040,X30041,X30042)),X30041))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30042,X30039),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X30042,X30039),X30041),X30038)),hAPP(hAPP(c_Product__Type_OSigma(X30042,X30039),X30040),X30037)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30042,tc_HOL_Obool)),X30041),X30040)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30039,tc_HOL_Obool)),hAPP(X30038,esk352_6(X30037,X30038,X30039,X30040,X30041,X30042))),hAPP(X30037,esk352_6(X30037,X30038,X30039,X30040,X30041,X30042))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30042,X30039),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X30042,X30039),X30041),X30038)),hAPP(hAPP(c_Product__Type_OSigma(X30042,X30039),X30040),X30037)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30042,tc_HOL_Obool)),X30041),X30040)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sigma__mono])])])]) ).
fof(i_0_6124,plain,
! [X30079,X30080,X30081,X30082,X30083,X30084] :
( ( hBOOL(hAPP(hAPP(c_member(X30083),esk360_6(X30079,X30080,X30081,X30082,X30083,X30084)),X30081))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X30084),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X30083,X30084),X30080),X30081)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X30083,X30084),X30079),X30082)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30083,tc_HOL_Obool)),X30081),X30082))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30083),X30082))
| ~ class_Rings_Ocomm__semiring__1(X30084) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X30084),hAPP(X30080,esk360_6(X30079,X30080,X30081,X30082,X30083,X30084))),hAPP(X30079,esk360_6(X30079,X30080,X30081,X30082,X30083,X30084))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X30084),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X30083,X30084),X30080),X30081)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X30083,X30084),X30079),X30082)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30083,tc_HOL_Obool)),X30081),X30082))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30083),X30082))
| ~ class_Rings_Ocomm__semiring__1(X30084) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__dvd__setprod__subset2])])])]) ).
fof(i_0_6125,plain,
! [X29985,X29986,X29987,X29988,X29989,X29990] :
( ( X29990 = hAPP(hAPP(c_Product__Type_OPair(X29989,X29988),esk346_6(X29985,X29986,X29987,X29988,X29989,X29990)),esk347_6(X29985,X29986,X29987,X29988,X29989,X29990))
| hBOOL(hAPP(hAPP(c_member(X29987),X29986),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29989,X29988,tc_fun(X29987,tc_HOL_Obool)),X29985),X29990))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29987),X29986),hAPP(hAPP(X29985,esk346_6(X29985,X29986,X29987,X29988,X29989,X29990)),esk347_6(X29985,X29986,X29987,X29988,X29989,X29990))))
| hBOOL(hAPP(hAPP(c_member(X29987),X29986),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29989,X29988,tc_fun(X29987,tc_HOL_Obool)),X29985),X29990))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI2])])])]) ).
cnf(i_0_6126,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5222]) ).
cnf(i_0_6127,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5223]) ).
fof(i_0_6128,plain,
! [X25501,X25502] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25501),X25502))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25502),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25501))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25502),X25501))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25502),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25501))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25501),X25502))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25502),X25501))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25502),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25501))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5224])])]) ).
fof(i_0_6129,plain,
! [X25499,X25500] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25500),X25499))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25500),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25499))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25499),X25500))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25500),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25499))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25500),X25499))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25499),X25500))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25500),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25499))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5225])])]) ).
fof(i_0_6130,plain,
! [X30441,X30442,X30443] : hAPP(c_Relation_Oconverse(X30443,X30442),X30441) = hAPP(c_Set_OCollect(tc_prod(X30442,X30443)),hAPP(c_Product__Type_Oprod_Oprod__case(X30442,X30443,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X30442,tc_fun(tc_prod(X30443,X30442),tc_HOL_Obool),tc_fun(X30443,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30443,tc_fun(tc_fun(tc_prod(X30443,X30442),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30443,X30442),tc_HOL_Obool),tc_fun(X30443,tc_HOL_Obool)),X30442),c_COMBC(X30443,tc_fun(tc_prod(X30443,X30442),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30443,tc_prod(X30443,X30442)),tc_fun(X30443,tc_fun(tc_fun(tc_prod(X30443,X30442),tc_HOL_Obool),tc_HOL_Obool)),X30442),hAPP(c_COMBB(tc_prod(X30443,X30442),tc_fun(tc_fun(tc_prod(X30443,X30442),tc_HOL_Obool),tc_HOL_Obool),X30443),c_member(tc_prod(X30443,X30442)))),hAPP(c_COMBC(X30443,X30442,tc_prod(X30443,X30442)),c_Product__Type_OPair(X30443,X30442))))),X30441))),
inference(variable_rename,[status(thm)],[fact_converse__def]) ).
fof(i_0_6131,plain,
! [X32480,X32481,X32482,X32483] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32482),X32481))
| c_Nitpick_Osetsum_H(X32482,X32483,X32480,X32481) = hAPP(c_List_Omonoid__add__class_Olistsum(X32483),hAPP(hAPP(c_List_Omap(X32482,X32483),X32480),c_Hilbert__Choice_OEps(tc_List_Olist(X32482),hAPP(hAPP(c_COMBS(tc_List_Olist(X32482),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32482)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X32482),tc_fun(X32482,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X32482,tc_HOL_Obool),tc_fun(tc_fun(X32482,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X32482)),c_fequal),c_List_Oset(X32482))),X32481))),c_List_Odistinct(X32482)))))
| ~ class_Groups_Ocomm__monoid__add(X32483) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X32482),X32481))
| c_Nitpick_Osetsum_H(X32482,X32483,X32480,X32481) = c_Groups_Ozero__class_Ozero(X32483)
| ~ class_Groups_Ocomm__monoid__add(X32483) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5226])])]) ).
cnf(i_0_6132,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5227]) ).
cnf(i_0_6133,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),c_List_Ofoldr(tc_List_Olist(X3),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3))),X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_List_Ofoldr(tc_List_Olist(X3),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_List_Olist(X3),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X3)))),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(split_conjunct,[status(thm)],[i_0_5228]) ).
cnf(i_0_6134,plain,
hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Oupt(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X1,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X4))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))),
inference(split_conjunct,[status(thm)],[i_0_5229]) ).
cnf(i_0_6135,plain,
c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = c_List_Oupt(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_5230]) ).
fof(i_0_6136,plain,
! [X29298,X29299] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29299))
| hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X29299))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X29298))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X29299))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X29298))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less__Suc])]) ).
fof(i_0_6137,plain,
! [X29282,X29283,X29284,X29285,X29286,X29287] :
( ~ class_Groups_Ocomm__monoid__add(X29287)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29286),X29285))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29286,X29287),X29284),X29285) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29283,X29287),hAPP(hAPP(c_COMBB(tc_fun(X29286,tc_HOL_Obool),X29287,X29283),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29286,X29287),X29284)),hAPP(hAPP(c_COMBB(tc_fun(X29286,tc_HOL_Obool),tc_fun(X29286,tc_HOL_Obool),X29283),c_Set_OCollect(X29286)),hAPP(hAPP(c_COMBB(tc_fun(X29286,tc_HOL_Obool),tc_fun(X29286,tc_HOL_Obool),X29283),hAPP(c_COMBS(X29286,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29286),c_fconj),hAPP(hAPP(c_COMBC(X29286,tc_fun(X29286,tc_HOL_Obool),tc_HOL_Obool),c_member(X29286)),X29285)))),hAPP(c_COMBC(X29286,X29283,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X29283,tc_fun(X29283,tc_HOL_Obool),X29286),c_fequal),X29282)))))),hAPP(c_Set_Oimage(X29286,X29283,X29282),X29285)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__image__gen])]) ).
fof(i_0_6138,plain,
! [X29919,X29920,X29921,X29922,X29923,X29924,X29925,X29926] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29921,X29921)),X29922),X29919))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29921,X29921,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29921,tc_fun(X29921,tc_HOL_Obool),tc_fun(X29921,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29921,tc_HOL_Obool),tc_fun(X29921,tc_HOL_Obool)),X29921),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29921)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29921),c_fconj),hAPP(hAPP(c_COMBC(X29921,tc_fun(X29921,tc_HOL_Obool),tc_HOL_Obool),c_member(X29921)),X29920)))),hAPP(hAPP(c_COMBC(X29921,tc_fun(X29921,tc_HOL_Obool),tc_HOL_Obool),c_member(X29921)),X29920))),X29922))
| ~ c_Relation_Orefl__on(X29921,X29920,X29919) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29921),X29923),X29920))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29921,X29921)),hAPP(hAPP(c_Product__Type_OPair(X29921,X29921),X29923),X29923)),X29919))
| ~ c_Relation_Orefl__on(X29921,X29920,X29919) )
& ( hBOOL(hAPP(hAPP(c_member(X29926),esk332_3(X29924,X29925,X29926)),X29925))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29926,X29926)),esk331_3(X29924,X29925,X29926)),X29924))
| c_Relation_Orefl__on(X29926,X29925,X29924) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29926,X29926)),hAPP(hAPP(c_Product__Type_OPair(X29926,X29926),esk332_3(X29924,X29925,X29926)),esk332_3(X29924,X29925,X29926))),X29924))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29926,X29926)),esk331_3(X29924,X29925,X29926)),X29924))
| c_Relation_Orefl__on(X29926,X29925,X29924) )
& ( hBOOL(hAPP(hAPP(c_member(X29926),esk332_3(X29924,X29925,X29926)),X29925))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29926,X29926,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29926,tc_fun(X29926,tc_HOL_Obool),tc_fun(X29926,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29926,tc_HOL_Obool),tc_fun(X29926,tc_HOL_Obool)),X29926),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29926)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29926),c_fconj),hAPP(hAPP(c_COMBC(X29926,tc_fun(X29926,tc_HOL_Obool),tc_HOL_Obool),c_member(X29926)),X29925)))),hAPP(hAPP(c_COMBC(X29926,tc_fun(X29926,tc_HOL_Obool),tc_HOL_Obool),c_member(X29926)),X29925))),esk331_3(X29924,X29925,X29926)))
| c_Relation_Orefl__on(X29926,X29925,X29924) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29926,X29926)),hAPP(hAPP(c_Product__Type_OPair(X29926,X29926),esk332_3(X29924,X29925,X29926)),esk332_3(X29924,X29925,X29926))),X29924))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29926,X29926,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29926,tc_fun(X29926,tc_HOL_Obool),tc_fun(X29926,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29926,tc_HOL_Obool),tc_fun(X29926,tc_HOL_Obool)),X29926),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29926)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29926),c_fconj),hAPP(hAPP(c_COMBC(X29926,tc_fun(X29926,tc_HOL_Obool),tc_HOL_Obool),c_member(X29926)),X29925)))),hAPP(hAPP(c_COMBC(X29926,tc_fun(X29926,tc_HOL_Obool),tc_HOL_Obool),c_member(X29926)),X29925))),esk331_3(X29924,X29925,X29926)))
| c_Relation_Orefl__on(X29926,X29925,X29924) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__def_H])])])])])]) ).
fof(i_0_6139,plain,
! [X22960,X22961,X22962,X22963] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X22963),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
| c_Random__Sequence_ORandom(X22962,X22961,X22963,X22960) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X22962)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X22963),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
| c_Random__Sequence_ORandom(X22962,X22961,X22963,X22960) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X22962,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X22961,X22960)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X22962,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X22962,X22961,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X22963),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X22960))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X22962,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962))))),tc_prod(X22962,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X22962)),hAPP(hAPP(c_COMBB(X22962,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22962)))),tc_prod(X22962,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X22962)),c_Product__Type_Ofst(X22962,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5231])]) ).
cnf(i_0_6140,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),
inference(split_conjunct,[status(thm)],[i_0_5232]) ).
cnf(i_0_6141,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_5233]) ).
cnf(i_0_6142,plain,
hAPP(c_New__DSequence_Opos__not__seq(X1),X2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X2))),
inference(split_conjunct,[status(thm)],[i_0_5234]) ).
fof(i_0_6143,plain,
! [X32601,X32602,X32603,X32604,X32605] : hAPP(hAPP(c_List_Ozip(X32605,X32604),X32603),hAPP(hAPP(c_List_Olist_OCons(X32604),X32602),X32601)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X32605,X32604)),X32605,c_List_Olist_ONil(tc_prod(X32605,X32604)),hAPP(hAPP(c_COMBC(X32605,tc_fun(tc_List_Olist(X32605),tc_List_Olist(tc_prod(X32605,X32604))),tc_fun(tc_List_Olist(X32605),tc_List_Olist(tc_prod(X32605,X32604)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X32605,X32604)),tc_List_Olist(tc_prod(X32605,X32604))),tc_fun(tc_fun(tc_List_Olist(X32605),tc_List_Olist(tc_prod(X32605,X32604))),tc_fun(tc_List_Olist(X32605),tc_List_Olist(tc_prod(X32605,X32604)))),X32605),c_COMBB(tc_List_Olist(tc_prod(X32605,X32604)),tc_List_Olist(tc_prod(X32605,X32604)),tc_List_Olist(X32605))),hAPP(hAPP(c_COMBB(tc_prod(X32605,X32604),tc_fun(tc_List_Olist(tc_prod(X32605,X32604)),tc_List_Olist(tc_prod(X32605,X32604))),X32605),c_List_Olist_OCons(tc_prod(X32605,X32604))),hAPP(hAPP(c_COMBC(X32605,X32604,tc_prod(X32605,X32604)),c_Product__Type_OPair(X32605,X32604)),X32602)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32605),tc_List_Olist(X32604),tc_List_Olist(tc_prod(X32605,X32604))),c_List_Ozip(X32605,X32604)),X32601))),X32603),
inference(variable_rename,[status(thm)],[fact_zip__Cons]) ).
fof(i_0_6144,plain,
! [X26372,X26373,X26374,X26375] :
( ( ~ c_Wellfounded_Omax__extp(X26375,hAPP(hAPP(c_COMBC(X26375,tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_fun(X26375,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26375,tc_fun(tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_fun(X26375,tc_HOL_Obool)),X26375),c_COMBC(X26375,tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26375,tc_prod(X26375,X26375)),tc_fun(X26375,tc_fun(tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_HOL_Obool)),X26375),hAPP(c_COMBB(tc_prod(X26375,X26375),tc_fun(tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_HOL_Obool),X26375),c_member(tc_prod(X26375,X26375)))),c_Product__Type_OPair(X26375,X26375)))),X26374),X26373,X26372)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X26375,tc_HOL_Obool),tc_fun(X26375,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X26375,tc_HOL_Obool),tc_fun(X26375,tc_HOL_Obool)),X26373),X26372)),c_Wellfounded_Omax__ext(X26375,X26374))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X26375,tc_HOL_Obool),tc_fun(X26375,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X26375,tc_HOL_Obool),tc_fun(X26375,tc_HOL_Obool)),X26373),X26372)),c_Wellfounded_Omax__ext(X26375,X26374)))
| c_Wellfounded_Omax__extp(X26375,hAPP(hAPP(c_COMBC(X26375,tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_fun(X26375,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26375,tc_fun(tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_fun(X26375,tc_HOL_Obool)),X26375),c_COMBC(X26375,tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26375,tc_prod(X26375,X26375)),tc_fun(X26375,tc_fun(tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_HOL_Obool)),X26375),hAPP(c_COMBB(tc_prod(X26375,X26375),tc_fun(tc_fun(tc_prod(X26375,X26375),tc_HOL_Obool),tc_HOL_Obool),X26375),c_member(tc_prod(X26375,X26375)))),c_Product__Type_OPair(X26375,X26375)))),X26374),X26373,X26372) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq])]) ).
fof(i_0_6145,plain,
! [X32273,X32274,X32275,X32276] :
( ( ~ c_List_Olistrelp(X32276,hAPP(hAPP(c_COMBC(X32276,tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_fun(X32276,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32276,tc_fun(tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_fun(X32276,tc_HOL_Obool)),X32276),c_COMBC(X32276,tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32276,tc_prod(X32276,X32276)),tc_fun(X32276,tc_fun(tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_HOL_Obool)),X32276),hAPP(c_COMBB(tc_prod(X32276,X32276),tc_fun(tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_HOL_Obool),X32276),c_member(tc_prod(X32276,X32276)))),c_Product__Type_OPair(X32276,X32276)))),X32275),X32274,X32273)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32276),tc_List_Olist(X32276))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32276),tc_List_Olist(X32276)),X32274),X32273)),c_List_Olistrel(X32276,X32275))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32276),tc_List_Olist(X32276))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32276),tc_List_Olist(X32276)),X32274),X32273)),c_List_Olistrel(X32276,X32275)))
| c_List_Olistrelp(X32276,hAPP(hAPP(c_COMBC(X32276,tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_fun(X32276,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32276,tc_fun(tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_fun(X32276,tc_HOL_Obool)),X32276),c_COMBC(X32276,tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32276,tc_prod(X32276,X32276)),tc_fun(X32276,tc_fun(tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_HOL_Obool)),X32276),hAPP(c_COMBB(tc_prod(X32276,X32276),tc_fun(tc_fun(tc_prod(X32276,X32276),tc_HOL_Obool),tc_HOL_Obool),X32276),c_member(tc_prod(X32276,X32276)))),c_Product__Type_OPair(X32276,X32276)))),X32275),X32274,X32273) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])]) ).
fof(i_0_6146,plain,
! [X28793,X28794,X28795,X28796,X28797,X28798,X28799,X28800] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X28800,X28799),tc_fun(tc_prod(X28798,X28797),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28800,X28799),X28796),hAPP(c_COMBK(tc_fun(X28799,tc_HOL_Obool),X28800),X28795))),hAPP(c_Product__Type_Oprod_Oprod__case(X28800,X28799,tc_fun(tc_prod(X28798,X28797),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X28800,tc_fun(X28799,tc_fun(X28798,tc_fun(X28797,tc_HOL_Obool))),tc_fun(X28799,tc_fun(tc_prod(X28798,X28797),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X28798,tc_fun(X28797,tc_HOL_Obool)),tc_fun(tc_prod(X28798,X28797),tc_HOL_Obool)),tc_fun(tc_fun(X28799,tc_fun(X28798,tc_fun(X28797,tc_HOL_Obool))),tc_fun(X28799,tc_fun(tc_prod(X28798,X28797),tc_HOL_Obool))),X28800),c_COMBB(tc_fun(X28798,tc_fun(X28797,tc_HOL_Obool)),tc_fun(tc_prod(X28798,X28797),tc_HOL_Obool),X28799)),hAPP(hAPP(c_COMBB(tc_fun(X28798,tc_HOL_Obool),tc_fun(tc_fun(X28798,tc_fun(X28797,tc_HOL_Obool)),tc_fun(tc_prod(X28798,X28797),tc_HOL_Obool)),X28800),c_Product__Type_OSigma(X28798,X28797)),X28794))),hAPP(hAPP(c_COMBB(tc_fun(X28797,tc_HOL_Obool),tc_fun(X28798,tc_fun(X28797,tc_HOL_Obool)),X28799),c_COMBK(tc_fun(X28797,tc_HOL_Obool),X28798)),X28793)))) = hAPP(hAPP(c_Product__Type_OSigma(X28798,X28797),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28800,tc_fun(X28798,tc_HOL_Obool)),X28796),X28794)),hAPP(c_COMBK(tc_fun(X28797,tc_HOL_Obool),X28798),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28799,tc_fun(X28797,tc_HOL_Obool)),X28795),X28793))),
inference(variable_rename,[status(thm)],[fact_UN__Times__distrib]) ).
fof(i_0_6147,plain,
! [X27811,X27812] :
( ( ~ c_Equiv__Relations_Oequiv(X27812,c_Orderings_Otop__class_Otop(tc_fun(X27812,tc_HOL_Obool)),X27811)
| c_Equiv__Relations_Oequivp(X27812,hAPP(hAPP(c_COMBC(X27812,tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_fun(X27812,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27812,tc_fun(tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_fun(X27812,tc_HOL_Obool)),X27812),c_COMBC(X27812,tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27812,tc_prod(X27812,X27812)),tc_fun(X27812,tc_fun(tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_HOL_Obool)),X27812),hAPP(c_COMBB(tc_prod(X27812,X27812),tc_fun(tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_HOL_Obool),X27812),c_member(tc_prod(X27812,X27812)))),c_Product__Type_OPair(X27812,X27812)))),X27811)) )
& ( ~ c_Equiv__Relations_Oequivp(X27812,hAPP(hAPP(c_COMBC(X27812,tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_fun(X27812,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27812,tc_fun(tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_fun(X27812,tc_HOL_Obool)),X27812),c_COMBC(X27812,tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27812,tc_prod(X27812,X27812)),tc_fun(X27812,tc_fun(tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_HOL_Obool)),X27812),hAPP(c_COMBB(tc_prod(X27812,X27812),tc_fun(tc_fun(tc_prod(X27812,X27812),tc_HOL_Obool),tc_HOL_Obool),X27812),c_member(tc_prod(X27812,X27812)))),c_Product__Type_OPair(X27812,X27812)))),X27811))
| c_Equiv__Relations_Oequiv(X27812,c_Orderings_Otop__class_Otop(tc_fun(X27812,tc_HOL_Obool)),X27811) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__equiv])]) ).
fof(i_0_6148,plain,
! [X29848,X29849] :
( ( ~ c_Wellfounded_OwfP(X29849,hAPP(hAPP(c_COMBC(X29849,tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_fun(X29849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29849,tc_fun(tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_fun(X29849,tc_HOL_Obool)),X29849),c_COMBC(X29849,tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29849,tc_prod(X29849,X29849)),tc_fun(X29849,tc_fun(tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_HOL_Obool)),X29849),hAPP(c_COMBB(tc_prod(X29849,X29849),tc_fun(tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_HOL_Obool),X29849),c_member(tc_prod(X29849,X29849)))),c_Product__Type_OPair(X29849,X29849)))),X29848))
| c_Wellfounded_Owf(X29849,X29848) )
& ( ~ c_Wellfounded_Owf(X29849,X29848)
| c_Wellfounded_OwfP(X29849,hAPP(hAPP(c_COMBC(X29849,tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_fun(X29849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29849,tc_fun(tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_fun(X29849,tc_HOL_Obool)),X29849),c_COMBC(X29849,tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29849,tc_prod(X29849,X29849)),tc_fun(X29849,tc_fun(tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_HOL_Obool)),X29849),hAPP(c_COMBB(tc_prod(X29849,X29849),tc_fun(tc_fun(tc_prod(X29849,X29849),tc_HOL_Obool),tc_HOL_Obool),X29849),c_member(tc_prod(X29849,X29849)))),c_Product__Type_OPair(X29849,X29849)))),X29848)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq])]) ).
fof(i_0_6149,plain,
! [X25095,X25096,X25097,X25098] :
( ( hAPP(hAPP(c_COMBC(X25098,tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_fun(X25097,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25097,tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_fun(X25097,tc_HOL_Obool)),X25098),c_COMBC(X25097,tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25097,tc_prod(X25098,X25097)),tc_fun(X25097,tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),X25098),hAPP(c_COMBB(tc_prod(X25098,X25097),tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool),X25097),c_member(tc_prod(X25098,X25097)))),c_Product__Type_OPair(X25098,X25097)))),X25096) != hAPP(hAPP(c_COMBC(X25098,tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_fun(X25097,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25097,tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_fun(X25097,tc_HOL_Obool)),X25098),c_COMBC(X25097,tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25097,tc_prod(X25098,X25097)),tc_fun(X25097,tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),X25098),hAPP(c_COMBB(tc_prod(X25098,X25097),tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool),X25097),c_member(tc_prod(X25098,X25097)))),c_Product__Type_OPair(X25098,X25097)))),X25095)
| X25096 = X25095 )
& ( X25096 != X25095
| hAPP(hAPP(c_COMBC(X25098,tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_fun(X25097,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25097,tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_fun(X25097,tc_HOL_Obool)),X25098),c_COMBC(X25097,tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25097,tc_prod(X25098,X25097)),tc_fun(X25097,tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),X25098),hAPP(c_COMBB(tc_prod(X25098,X25097),tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool),X25097),c_member(tc_prod(X25098,X25097)))),c_Product__Type_OPair(X25098,X25097)))),X25096) = hAPP(hAPP(c_COMBC(X25098,tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_fun(X25097,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25097,tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_fun(X25097,tc_HOL_Obool)),X25098),c_COMBC(X25097,tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25097,tc_prod(X25098,X25097)),tc_fun(X25097,tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool)),X25098),hAPP(c_COMBB(tc_prod(X25098,X25097),tc_fun(tc_fun(tc_prod(X25098,X25097),tc_HOL_Obool),tc_HOL_Obool),X25097),c_member(tc_prod(X25098,X25097)))),c_Product__Type_OPair(X25098,X25097)))),X25095) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_6150,plain,
! [X29993,X29994,X29995,X29996,X29997,X29998] :
( ( X29993 = hAPP(hAPP(c_Product__Type_OPair(X29996,X29995),esk348_6(X29993,X29994,X29995,X29996,X29997,X29998)),esk349_6(X29993,X29994,X29995,X29996,X29997,X29998))
| ~ hBOOL(hAPP(hAPP(c_member(X29998),X29997),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29996,X29995,tc_fun(X29998,tc_HOL_Obool)),X29994),X29993))) )
& ( hBOOL(hAPP(hAPP(c_member(X29998),X29997),hAPP(hAPP(X29994,esk348_6(X29993,X29994,X29995,X29996,X29997,X29998)),esk349_6(X29993,X29994,X29995,X29996,X29997,X29998))))
| ~ hBOOL(hAPP(hAPP(c_member(X29998),X29997),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29996,X29995,tc_fun(X29998,tc_HOL_Obool)),X29994),X29993))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5235])])])]) ).
fof(i_0_6151,plain,
! [X32061,X32062,X32063,X32064,X32065,X32066,X32067,X32068] : hAPP(hAPP(c_List_Omap(tc_prod(X32068,X32067),X32066),X32065),hAPP(hAPP(c_List_Ozip(X32068,X32067),X32064),hAPP(hAPP(c_List_Omap(X32063,X32067),X32062),X32061))) = hAPP(hAPP(c_List_Omap(tc_prod(X32068,X32063),X32066),hAPP(c_Product__Type_Oprod_Oprod__case(X32068,X32063,X32066),hAPP(hAPP(c_COMBB(tc_fun(X32063,tc_prod(X32068,X32067)),tc_fun(X32063,X32066),X32068),hAPP(c_COMBB(tc_prod(X32068,X32067),X32066,X32063),X32065)),hAPP(hAPP(c_COMBC(X32068,tc_fun(X32063,X32067),tc_fun(X32063,tc_prod(X32068,X32067))),hAPP(hAPP(c_COMBB(tc_fun(X32067,tc_prod(X32068,X32067)),tc_fun(tc_fun(X32063,X32067),tc_fun(X32063,tc_prod(X32068,X32067))),X32068),c_COMBB(X32067,tc_prod(X32068,X32067),X32063)),c_Product__Type_OPair(X32068,X32067))),X32062)))),hAPP(hAPP(c_List_Ozip(X32068,X32063),X32064),X32061)),
inference(variable_rename,[status(thm)],[fact_map__zip__map2]) ).
fof(i_0_6152,plain,
! [X30845,X30846,X30847,X30848,X30849,X30850,X30851] :
( ( X30846 = hAPP(hAPP(X30849,X30845),esk389_7(X30845,X30846,X30847,X30848,X30849,X30850,X30851))
| ~ hBOOL(hAPP(hAPP(c_member(X30851),X30845),X30847))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30851,X30850,X30849,X30848,X30847),X30846))
| ~ c_Finite__Set_Ofun__left__comm(X30851,X30850,X30849) )
& ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30851,X30850,X30849,X30848,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30851,tc_HOL_Obool)),X30847),hAPP(hAPP(c_Set_Oinsert(X30851),X30845),c_Orderings_Obot__class_Obot(tc_fun(X30851,tc_HOL_Obool))))),esk389_7(X30845,X30846,X30847,X30848,X30849,X30850,X30851)))
| ~ hBOOL(hAPP(hAPP(c_member(X30851),X30845),X30847))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30851,X30850,X30849,X30848,X30847),X30846))
| ~ c_Finite__Set_Ofun__left__comm(X30851,X30850,X30849) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE__aux])])])]) ).
fof(i_0_6153,plain,
! [X31479,X31480,X31481,X31482,X31483,X31484,X31485] :
( ( X31479 = hAPP(hAPP(X31483,X31481),esk413_7(X31479,X31480,X31481,X31482,X31483,X31484,X31485))
| hBOOL(hAPP(hAPP(c_member(X31485),X31481),X31480))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X31485,X31484,X31483,X31482,hAPP(hAPP(c_Set_Oinsert(X31485),X31481),X31480)),X31479))
| ~ c_Finite__Set_Ofun__left__comm(X31485,X31484,X31483) )
& ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X31485,X31484,X31483,X31482,X31480),esk413_7(X31479,X31480,X31481,X31482,X31483,X31484,X31485)))
| hBOOL(hAPP(hAPP(c_member(X31485),X31481),X31480))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X31485,X31484,X31483,X31482,hAPP(hAPP(c_Set_Oinsert(X31485),X31481),X31480)),X31479))
| ~ c_Finite__Set_Ofun__left__comm(X31485,X31484,X31483) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5236])])])]) ).
fof(i_0_6154,plain,
! [X31824,X31825,X31826,X31827,X31828] : c_Map_Omap__of(X31828,X31827,hAPP(hAPP(c_List_Omap(tc_prod(X31828,X31826),tc_prod(X31828,X31827)),hAPP(c_Product__Type_Oprod_Oprod__case(X31828,X31826,tc_prod(X31828,X31827)),hAPP(hAPP(c_COMBC(X31828,tc_fun(X31826,X31827),tc_fun(X31826,tc_prod(X31828,X31827))),hAPP(hAPP(c_COMBB(tc_fun(X31827,tc_prod(X31828,X31827)),tc_fun(tc_fun(X31826,X31827),tc_fun(X31826,tc_prod(X31828,X31827))),X31828),c_COMBB(X31827,tc_prod(X31828,X31827),X31826)),c_Product__Type_OPair(X31828,X31827))),X31825))),X31824)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31826),tc_Option_Ooption(X31827),X31828,hAPP(c_Option_Omap(X31826,X31827),X31825)),c_Map_Omap__of(X31828,X31826,X31824)),
inference(variable_rename,[status(thm)],[fact_map__of__map]) ).
fof(i_0_6155,plain,
! [X32596,X32597,X32598,X32599,X32600] : hAPP(hAPP(c_List_Ozip(X32600,X32599),hAPP(hAPP(c_List_Olist_OCons(X32600),X32598),X32597)),X32596) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X32600,X32599)),X32599,c_List_Olist_ONil(tc_prod(X32600,X32599)),hAPP(hAPP(c_COMBC(X32599,tc_fun(tc_List_Olist(X32599),tc_List_Olist(tc_prod(X32600,X32599))),tc_fun(tc_List_Olist(X32599),tc_List_Olist(tc_prod(X32600,X32599)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X32600,X32599)),tc_List_Olist(tc_prod(X32600,X32599))),tc_fun(tc_fun(tc_List_Olist(X32599),tc_List_Olist(tc_prod(X32600,X32599))),tc_fun(tc_List_Olist(X32599),tc_List_Olist(tc_prod(X32600,X32599)))),X32599),c_COMBB(tc_List_Olist(tc_prod(X32600,X32599)),tc_List_Olist(tc_prod(X32600,X32599)),tc_List_Olist(X32599))),hAPP(hAPP(c_COMBB(tc_prod(X32600,X32599),tc_fun(tc_List_Olist(tc_prod(X32600,X32599)),tc_List_Olist(tc_prod(X32600,X32599))),X32599),c_List_Olist_OCons(tc_prod(X32600,X32599))),hAPP(c_Product__Type_OPair(X32600,X32599),X32598)))),hAPP(c_List_Ozip(X32600,X32599),X32597))),X32596),
inference(variable_rename,[status(thm)],[fact_zip__Cons1]) ).
cnf(i_0_6156,plain,
( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Code__Numeral_Oint__of,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(split_conjunct,[status(thm)],[i_0_5237]) ).
cnf(i_0_6157,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5227]) ).
cnf(i_0_6158,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5227]) ).
cnf(i_0_6159,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5238]) ).
fof(i_0_6160,plain,
! [X29911,X29912,X29913,X29914] :
( ( hBOOL(hAPP(hAPP(c_member(X29914),esk330_4(X29911,X29912,X29913,X29914)),X29913))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29912),hAPP(c_Set_Oimage(X29914,X29912,X29911),X29913)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29914),X29913)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29914),hAPP(c_Set_OCollect(X29914),hAPP(hAPP(c_COMBS(X29914,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29914),c_fconj),hAPP(hAPP(c_COMBC(X29914,tc_fun(X29914,tc_HOL_Obool),tc_HOL_Obool),c_member(X29914)),X29913))),hAPP(hAPP(c_COMBC(X29914,X29912,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X29912,tc_fun(X29912,tc_HOL_Obool),X29914),c_fequal),X29911)),hAPP(X29911,esk330_4(X29911,X29912,X29913,X29914)))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29912),hAPP(c_Set_Oimage(X29914,X29912,X29911),X29913)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29914),X29913)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5239])])])]) ).
fof(i_0_6161,plain,
! [X29686,X29687,X29688,X29689] :
( ( hBOOL(hAPP(X29689,esk321_4(X29686,X29687,X29688,X29689)))
| c_Wellfounded_Owf(X29686,hAPP(c_Set_OCollect(tc_prod(X29686,X29686)),hAPP(c_Product__Type_Oprod_Oprod__case(X29686,X29686,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29686,tc_HOL_Obool),tc_fun(X29686,tc_HOL_Obool),X29686),hAPP(c_COMBS(X29686,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29686),c_fconj),X29689))),hAPP(hAPP(c_COMBC(X29686,tc_fun(X29686,X29686),tc_fun(X29686,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29686,tc_HOL_Obool),tc_fun(tc_fun(X29686,X29686),tc_fun(X29686,tc_HOL_Obool)),X29686),c_COMBB(X29686,tc_HOL_Obool,X29686)),c_fequal)),X29687))))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X29688,hAPP(X29687,esk321_4(X29686,X29687,X29688,X29689)))),hAPP(X29688,esk321_4(X29686,X29687,X29688,X29689))))
| c_Wellfounded_Owf(X29686,hAPP(c_Set_OCollect(tc_prod(X29686,X29686)),hAPP(c_Product__Type_Oprod_Oprod__case(X29686,X29686,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29686,tc_HOL_Obool),tc_fun(X29686,tc_HOL_Obool),X29686),hAPP(c_COMBS(X29686,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29686),c_fconj),X29689))),hAPP(hAPP(c_COMBC(X29686,tc_fun(X29686,X29686),tc_fun(X29686,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29686,tc_HOL_Obool),tc_fun(tc_fun(X29686,X29686),tc_fun(X29686,tc_HOL_Obool)),X29686),c_COMBB(X29686,tc_HOL_Obool,X29686)),c_fequal)),X29687))))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__if__measure])])])]) ).
fof(i_0_6162,plain,
! [X29559,X29560,X29561] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29561,X29561),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29561,X29561,X29561),X29560),X29559)),X29560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X29561,tc_HOL_Obool),tc_fun(X29561,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X29561,tc_HOL_Obool),tc_fun(X29561,tc_HOL_Obool),tc_fun(X29561,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X29561,X29560)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X29561,tc_HOL_Obool),tc_fun(X29561,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X29561,X29559)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X29561,tc_HOL_Obool),tc_fun(X29561,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X29561,tc_HOL_Obool),tc_fun(X29561,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X29561,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X29561,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X29561,tc_HOL_Obool),tc_fun(X29561,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X29561,X29560))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__compat])]) ).
fof(i_0_6163,plain,
! [X29562,X29563,X29564] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29564,X29564),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29564,X29564,X29564),X29563),X29562)),X29563))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X29564,tc_HOL_Obool),tc_fun(X29564,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X29564,tc_HOL_Obool),tc_fun(X29564,tc_HOL_Obool),tc_fun(X29564,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X29564,X29563)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X29564,tc_HOL_Obool),tc_fun(X29564,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X29564,X29562)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X29564,tc_HOL_Obool),tc_fun(X29564,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X29564,tc_HOL_Obool),tc_fun(X29564,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X29564,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X29564,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X29564,tc_HOL_Obool),tc_fun(X29564,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X29564,X29563))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__compat])]) ).
fof(i_0_6164,plain,
! [X26770,X26771,X26772,X26773,X26774,X26775,X26776] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X26776,X26775,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X26776)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X26776),c_Hoare__Mirabelle_Opeek__and(X26776,X26774,X26773)),X26772),X26771)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X26776),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X26776,X26775,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X26776)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X26776),c_Hoare__Mirabelle_Opeek__and(X26776,X26774,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X26773))),X26770),X26771)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X26776),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(X26776,X26775,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X26776)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X26776),X26774),c_Com_Ocom_OCond(X26773,X26772,X26770)),X26771)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X26776),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OIf])]) ).
cnf(i_0_6165,plain,
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk492_3(X2,X3,X1)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)
| c_List_Oconcat(X1,X3) != c_List_Oconcat(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_5240]) ).
cnf(i_0_6166,plain,
( X2 = X3
| c_List_Oconcat(X1,X2) != c_List_Oconcat(X1,X3)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk491_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5241]) ).
fof(i_0_6167,plain,
! [X29277,X29278,X29279,X29280,X29281] :
( ~ class_Groups_Ocomm__monoid__add(X29281)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29280),X29279))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29280,X29281),X29278),hAPP(c_Set_OCollect(X29280),hAPP(hAPP(c_COMBS(X29280,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29280),c_fconj),hAPP(hAPP(c_COMBC(X29280,tc_fun(X29280,tc_HOL_Obool),tc_HOL_Obool),c_member(X29280)),X29279))),hAPP(hAPP(c_COMBC(X29280,tc_fun(X29280,tc_HOL_Obool),tc_HOL_Obool),c_member(X29280)),X29277)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29280,X29281),hAPP(hAPP(c_COMBC(X29280,X29281,X29281),hAPP(hAPP(c_COMBS(X29280,X29281,tc_fun(X29281,X29281)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X29281,tc_fun(X29281,X29281)),X29280),c_If(X29281)),hAPP(hAPP(c_COMBC(X29280,tc_fun(X29280,tc_HOL_Obool),tc_HOL_Obool),c_member(X29280)),X29277))),X29278)),c_Groups_Ozero__class_Ozero(X29281))),X29279) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set_H])]) ).
cnf(i_0_6168,plain,
hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)),X5)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X2,X3)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))))),
inference(split_conjunct,[status(thm)],[i_0_5242]) ).
cnf(i_0_6169,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin) = c_Int_Opred(X1),
inference(split_conjunct,[status(thm)],[i_0_5243]) ).
cnf(i_0_6170,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_5244]) ).
fof(i_0_6171,plain,
! [X32111,X32112,X32113,X32114,X32115,X32116,X32117,X32118] : hAPP(hAPP(c_List_Ozip(X32118,X32117),hAPP(hAPP(c_List_Omap(X32116,X32118),X32115),X32114)),hAPP(hAPP(c_List_Omap(X32113,X32117),X32112),X32111)) = hAPP(hAPP(c_List_Omap(tc_prod(X32116,X32113),tc_prod(X32118,X32117)),hAPP(c_Product__Type_Oprod_Oprod__case(X32116,X32113,tc_prod(X32118,X32117)),hAPP(hAPP(c_COMBC(X32116,tc_fun(X32113,X32117),tc_fun(X32113,tc_prod(X32118,X32117))),hAPP(hAPP(c_COMBB(tc_fun(X32117,tc_prod(X32118,X32117)),tc_fun(tc_fun(X32113,X32117),tc_fun(X32113,tc_prod(X32118,X32117))),X32116),c_COMBB(X32117,tc_prod(X32118,X32117),X32113)),hAPP(hAPP(c_COMBB(X32118,tc_fun(X32117,tc_prod(X32118,X32117)),X32116),c_Product__Type_OPair(X32118,X32117)),X32115))),X32112))),hAPP(hAPP(c_List_Ozip(X32116,X32113),X32114),X32111)),
inference(variable_rename,[status(thm)],[fact_zip__map__map]) ).
cnf(i_0_6172,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_5245]) ).
cnf(i_0_6173,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5246]) ).
fof(i_0_6174,plain,
! [X29343] : c_Wellfounded_Ofinite__psubset(X29343) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X29343,tc_HOL_Obool),tc_fun(X29343,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X29343,tc_HOL_Obool),tc_fun(X29343,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X29343,tc_HOL_Obool),tc_fun(tc_fun(X29343,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29343,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29343,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X29343,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29343,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X29343,tc_HOL_Obool)),c_COMBS(tc_fun(X29343,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29343,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29343,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X29343,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X29343,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X29343,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X29343)))),
inference(variable_rename,[status(thm)],[fact_finite__psubset__def]) ).
cnf(i_0_6175,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Nat_OSuc,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2))))) ),
inference(split_conjunct,[status(thm)],[i_0_5247]) ).
cnf(i_0_6176,plain,
( hAPP(c_Nat_OSuc,X2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2))))) ),
inference(split_conjunct,[status(thm)],[i_0_5248]) ).
fof(i_0_6177,plain,
! [X32246,X32247] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32247),X32246))
| c_Nitpick_Ocard_H(X32247,X32246) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32247)),c_Hilbert__Choice_OEps(tc_List_Olist(X32247),hAPP(hAPP(c_COMBS(tc_List_Olist(X32247),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32247)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X32247),tc_fun(X32247,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X32247,tc_HOL_Obool),tc_fun(tc_fun(X32247,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X32247)),c_fequal),c_List_Oset(X32247))),X32246))),c_List_Odistinct(X32247)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X32247),X32246))
| c_Nitpick_Ocard_H(X32247,X32246) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5249])]) ).
fof(i_0_6178,plain,
! [X29144,X29145] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29145))
| hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X29145))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X29144)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X29145))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X29144))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5250])]) ).
fof(i_0_6179,plain,
! [X28871,X28872,X28873,X28874,X28875,X28876,X28877,X28878,X28879] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28879,X28878)),hAPP(hAPP(c_Product__Type_OPair(X28879,X28878),X28877),X28876)),X28875))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X28874,X28873)),hAPP(hAPP(c_Product__Type_OPair(X28874,X28873),hAPP(X28872,X28877)),hAPP(X28871,X28876))),hAPP(c_Set_Oimage(tc_prod(X28879,X28878),tc_prod(X28874,X28873),c_Product__Type_Omap__pair(X28879,X28874,X28878,X28873,X28872,X28871)),X28875))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__imageI])]) ).
cnf(i_0_6180,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_5251]) ).
cnf(i_0_6181,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_5252]) ).
fof(i_0_6182,plain,
! [X22887,X22888,X22889,X22890,X22891,X22892,X22893] : c_New__Random__Sequence_Oneg__decr__bind(X22893,X22892,X22891,X22890,X22889,X22888,X22887) = c_New__DSequence_Oneg__decr__bind(X22893,X22892,hAPP(hAPP(hAPP(X22891,X22889),X22888),X22887),hAPP(hAPP(c_COMBC(X22893,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X22892)))),hAPP(hAPP(c_COMBC(X22893,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X22892))))),hAPP(hAPP(c_COMBC(X22893,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X22892)))))),X22890),X22889)),X22888)),X22887)),
inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def]) ).
fof(i_0_6183,plain,
! [X31149,X31150,X31151,X31152] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31152,tc_fun(X31151,tc_HOL_Obool)),X31150),X31149) = hAPP(c_Set_OCollect(X31151),hAPP(hAPP(c_COMBB(tc_fun(X31152,tc_HOL_Obool),tc_HOL_Obool,X31151),c_HOL_OAll(X31152)),hAPP(hAPP(c_COMBB(tc_fun(X31152,tc_HOL_Obool),tc_fun(X31152,tc_HOL_Obool),X31151),hAPP(c_COMBS(X31152,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31152),c_fimplies),hAPP(hAPP(c_COMBC(X31152,tc_fun(X31152,tc_HOL_Obool),tc_HOL_Obool),c_member(X31152)),X31150)))),hAPP(hAPP(c_COMBC(X31151,tc_fun(X31152,tc_fun(X31151,tc_HOL_Obool)),tc_fun(X31152,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31151,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X31152,tc_fun(X31151,tc_HOL_Obool)),tc_fun(X31152,tc_HOL_Obool)),X31151),c_COMBB(tc_fun(X31151,tc_HOL_Obool),tc_HOL_Obool,X31152)),c_member(X31151))),X31149)))),
inference(variable_rename,[status(thm)],[fact_INTER__def]) ).
fof(i_0_6184,plain,
! [X29940,X29941,X29942,X29943,X29944,X29945,X29946,X29947,X29948] :
( ( ~ c_Equiv__Relations_Ocongruent(X29943,X29942,X29941,X29940)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29943,X29943)),X29944),X29941))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29943,X29943,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29943,tc_fun(X29943,X29942),tc_fun(X29943,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29942,tc_HOL_Obool),tc_fun(tc_fun(X29943,X29942),tc_fun(X29943,tc_HOL_Obool)),X29943),c_COMBB(X29942,tc_HOL_Obool,X29943)),hAPP(hAPP(c_COMBB(X29942,tc_fun(X29942,tc_HOL_Obool),X29943),c_fequal),X29940))),X29940)),X29944)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29948,X29948)),esk334_4(X29945,X29946,X29947,X29948)),X29946))
| c_Equiv__Relations_Ocongruent(X29948,X29947,X29946,X29945) )
& ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29948,X29948,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29948,tc_fun(X29948,X29947),tc_fun(X29948,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29947,tc_HOL_Obool),tc_fun(tc_fun(X29948,X29947),tc_fun(X29948,tc_HOL_Obool)),X29948),c_COMBB(X29947,tc_HOL_Obool,X29948)),hAPP(hAPP(c_COMBB(X29947,tc_fun(X29947,tc_HOL_Obool),X29948),c_fequal),X29945))),X29945)),esk334_4(X29945,X29946,X29947,X29948)))
| c_Equiv__Relations_Ocongruent(X29948,X29947,X29946,X29945) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent__def])])])])])]) ).
fof(i_0_6185,plain,
! [X29367,X29368,X29369,X29370,X29371] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29368),hAPP(c_Set_OCollect(X29368),hAPP(hAPP(c_COMBB(tc_fun(X29370,tc_HOL_Obool),tc_HOL_Obool,X29368),c_HOL_OEx(X29370)),hAPP(hAPP(c_COMBB(tc_fun(X29370,tc_HOL_Obool),tc_fun(X29370,tc_HOL_Obool),X29368),hAPP(c_COMBS(X29370,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29370),c_fconj),X29369))),X29367)))))
| ~ hBOOL(hAPP(X29369,X29371))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29368),hAPP(c_Set_OCollect(X29368),hAPP(hAPP(c_COMBC(X29368,X29370,tc_HOL_Obool),X29367),X29371))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29370),hAPP(c_Set_OCollect(X29370),X29369))) )
& ( hBOOL(hAPP(X29369,esk313_4(X29367,X29368,X29369,X29370)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29368),hAPP(c_Set_OCollect(X29368),hAPP(hAPP(c_COMBB(tc_fun(X29370,tc_HOL_Obool),tc_HOL_Obool,X29368),c_HOL_OEx(X29370)),hAPP(hAPP(c_COMBB(tc_fun(X29370,tc_HOL_Obool),tc_fun(X29370,tc_HOL_Obool),X29368),hAPP(c_COMBS(X29370,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29370),c_fconj),X29369))),X29367)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29370),hAPP(c_Set_OCollect(X29370),X29369))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29368),hAPP(c_Set_OCollect(X29368),hAPP(hAPP(c_COMBC(X29368,X29370,tc_HOL_Obool),X29367),esk313_4(X29367,X29368,X29369,X29370)))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29368),hAPP(c_Set_OCollect(X29368),hAPP(hAPP(c_COMBB(tc_fun(X29370,tc_HOL_Obool),tc_HOL_Obool,X29368),c_HOL_OEx(X29370)),hAPP(hAPP(c_COMBB(tc_fun(X29370,tc_HOL_Obool),tc_fun(X29370,tc_HOL_Obool),X29368),hAPP(c_COMBS(X29370,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29370),c_fconj),X29369))),X29367)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29370),hAPP(c_Set_OCollect(X29370),X29369))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__bounded__ex])])])])]) ).
fof(i_0_6186,plain,
! [X28831,X28832,X28833,X28834,X28835,X28836] :
( ( hBOOL(hAPP(hAPP(c_member(X28835),esk286_6(X28831,X28832,X28833,X28834,X28835,X28836)),X28834))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28835,X28836),hAPP(hAPP(c_COMBS(X28835,tc_fun(X28833,tc_HOL_Obool),X28836),hAPP(hAPP(c_COMBB(tc_fun(X28833,X28836),tc_fun(tc_fun(X28833,tc_HOL_Obool),X28836),X28835),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28833,X28836)),X28831)),X28832)),X28834) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X28835,X28833),X28836),hAPP(c_Product__Type_Oprod_Oprod__case(X28835,X28833,X28836),X28831)),hAPP(hAPP(c_Product__Type_OSigma(X28835,X28833),X28834),X28832))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28835),X28834))
| ~ class_Groups_Ocomm__monoid__mult(X28836) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28833),hAPP(X28832,esk286_6(X28831,X28832,X28833,X28834,X28835,X28836))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28835,X28836),hAPP(hAPP(c_COMBS(X28835,tc_fun(X28833,tc_HOL_Obool),X28836),hAPP(hAPP(c_COMBB(tc_fun(X28833,X28836),tc_fun(tc_fun(X28833,tc_HOL_Obool),X28836),X28835),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28833,X28836)),X28831)),X28832)),X28834) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X28835,X28833),X28836),hAPP(c_Product__Type_Oprod_Oprod__case(X28835,X28833,X28836),X28831)),hAPP(hAPP(c_Product__Type_OSigma(X28835,X28833),X28834),X28832))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28835),X28834))
| ~ class_Groups_Ocomm__monoid__mult(X28836) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Sigma])])])]) ).
fof(i_0_6187,plain,
! [X28838,X28839,X28840,X28841,X28842,X28843] :
( ( hBOOL(hAPP(hAPP(c_member(X28842),esk287_6(X28838,X28839,X28840,X28841,X28842,X28843)),X28841))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28842,X28843),hAPP(hAPP(c_COMBS(X28842,tc_fun(X28840,tc_HOL_Obool),X28843),hAPP(hAPP(c_COMBB(tc_fun(X28840,X28843),tc_fun(tc_fun(X28840,tc_HOL_Obool),X28843),X28842),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28840,X28843)),X28838)),X28839)),X28841) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X28842,X28840),X28843),hAPP(c_Product__Type_Oprod_Oprod__case(X28842,X28840,X28843),X28838)),hAPP(hAPP(c_Product__Type_OSigma(X28842,X28840),X28841),X28839))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28842),X28841))
| ~ class_Groups_Ocomm__monoid__add(X28843) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28840),hAPP(X28839,esk287_6(X28838,X28839,X28840,X28841,X28842,X28843))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28842,X28843),hAPP(hAPP(c_COMBS(X28842,tc_fun(X28840,tc_HOL_Obool),X28843),hAPP(hAPP(c_COMBB(tc_fun(X28840,X28843),tc_fun(tc_fun(X28840,tc_HOL_Obool),X28843),X28842),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28840,X28843)),X28838)),X28839)),X28841) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X28842,X28840),X28843),hAPP(c_Product__Type_Oprod_Oprod__case(X28842,X28840,X28843),X28838)),hAPP(hAPP(c_Product__Type_OSigma(X28842,X28840),X28841),X28839))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28842),X28841))
| ~ class_Groups_Ocomm__monoid__add(X28843) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Sigma])])])]) ).
fof(i_0_6188,plain,
! [X27543,X27544,X27545,X27546,X27547] :
( ~ class_Groups_Ocomm__monoid__add(X27547)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27546),X27545))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27546,X27547),X27544),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27546,tc_HOL_Obool)),X27545),X27543)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27546,X27547),hAPP(hAPP(c_COMBC(X27546,X27547,X27547),hAPP(hAPP(c_COMBS(X27546,X27547,tc_fun(X27547,X27547)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27547,tc_fun(X27547,X27547)),X27546),c_If(X27547)),hAPP(hAPP(c_COMBC(X27546,tc_fun(X27546,tc_HOL_Obool),tc_HOL_Obool),c_member(X27546)),X27543))),X27544)),c_Groups_Ozero__class_Ozero(X27547))),X27545) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set])]) ).
fof(i_0_6189,plain,
! [X28423,X28424,X28425,X28426,X28427,X28428] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28428),X28425),X28426))
| hAPP(c_Set_Ovimage(X28424,X28428,hAPP(hAPP(c_COMBC(X28424,X28428,X28428),hAPP(hAPP(c_COMBC(X28424,X28428,tc_fun(X28428,X28428)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X28428,tc_fun(X28428,X28428)),X28424),c_If(X28428)),hAPP(hAPP(c_COMBC(X28424,tc_fun(X28424,tc_HOL_Obool),tc_HOL_Obool),c_member(X28424)),X28423))),X28427)),X28425)),X28426) = c_Orderings_Otop__class_Otop(tc_fun(X28424,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X28428),X28427),X28426)) )
& ( hBOOL(hAPP(hAPP(c_member(X28428),X28425),X28426))
| hAPP(c_Set_Ovimage(X28424,X28428,hAPP(hAPP(c_COMBC(X28424,X28428,X28428),hAPP(hAPP(c_COMBC(X28424,X28428,tc_fun(X28428,X28428)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X28428,tc_fun(X28428,X28428)),X28424),c_If(X28428)),hAPP(hAPP(c_COMBC(X28424,tc_fun(X28424,tc_HOL_Obool),tc_HOL_Obool),c_member(X28424)),X28423))),X28427)),X28425)),X28426) = X28423
| ~ hBOOL(hAPP(hAPP(c_member(X28428),X28427),X28426)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28428),X28425),X28426))
| hAPP(c_Set_Ovimage(X28424,X28428,hAPP(hAPP(c_COMBC(X28424,X28428,X28428),hAPP(hAPP(c_COMBC(X28424,X28428,tc_fun(X28428,X28428)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X28428,tc_fun(X28428,X28428)),X28424),c_If(X28428)),hAPP(hAPP(c_COMBC(X28424,tc_fun(X28424,tc_HOL_Obool),tc_HOL_Obool),c_member(X28424)),X28423))),X28427)),X28425)),X28426) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28424,tc_HOL_Obool)),X28423)
| hBOOL(hAPP(hAPP(c_member(X28428),X28427),X28426)) )
& ( hBOOL(hAPP(hAPP(c_member(X28428),X28425),X28426))
| hAPP(c_Set_Ovimage(X28424,X28428,hAPP(hAPP(c_COMBC(X28424,X28428,X28428),hAPP(hAPP(c_COMBC(X28424,X28428,tc_fun(X28428,X28428)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X28428,tc_fun(X28428,X28428)),X28424),c_If(X28428)),hAPP(hAPP(c_COMBC(X28424,tc_fun(X28424,tc_HOL_Obool),tc_HOL_Obool),c_member(X28424)),X28423))),X28427)),X28425)),X28426) = c_Orderings_Obot__class_Obot(tc_fun(X28424,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X28428),X28427),X28426)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5253])])]) ).
fof(i_0_6190,plain,
! [X24347,X24348,X24349,X24350] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24350,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24350,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk149_4(X24347,X24348,X24349,X24350))),X24349)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24350,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk149_4(X24347,X24348,X24349,X24350)),X24348))),X24347)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24350,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24350,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X24349)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24350,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X24347))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__subset])])]) ).
cnf(i_0_6191,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5254]) ).
fof(i_0_6192,plain,
! [X22900,X22901,X22902,X22903,X22904,X22905,X22906] : c_New__Random__Sequence_Opos__decr__bind(X22906,X22905,X22904,X22903,X22902,X22901,X22900) = c_New__DSequence_Opos__decr__bind(X22906,X22905,hAPP(hAPP(hAPP(X22904,X22902),X22901),X22900),hAPP(hAPP(c_COMBC(X22906,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X22905))),hAPP(hAPP(c_COMBC(X22906,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X22905)))),hAPP(hAPP(c_COMBC(X22906,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X22905))))),X22903),X22902)),X22901)),X22900)),
inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Opos__decr__bind__def]) ).
cnf(i_0_6193,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),
inference(split_conjunct,[status(thm)],[i_0_5255]) ).
cnf(i_0_6194,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5256]) ).
cnf(i_0_6195,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_5257]) ).
cnf(i_0_6196,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X2)),
inference(split_conjunct,[status(thm)],[i_0_5258]) ).
cnf(i_0_6197,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X2)),
inference(split_conjunct,[status(thm)],[i_0_5259]) ).
fof(i_0_6198,plain,
! [X28617,X28618,X28619,X28620,X28621,X28622] : hAPP(c_Set_Oimage(X28622,tc_prod(X28621,X28620),hAPP(hAPP(c_COMBS(X28622,X28620,tc_prod(X28621,X28620)),hAPP(hAPP(c_COMBB(X28621,tc_fun(X28620,tc_prod(X28621,X28620)),X28622),c_Product__Type_OPair(X28621,X28620)),X28619)),X28618)),X28617) = hAPP(hAPP(c_Product__Type_OSigma(X28621,X28620),hAPP(c_Set_Oimage(X28622,X28621,X28619),X28617)),hAPP(hAPP(c_COMBB(tc_fun(X28622,tc_HOL_Obool),tc_fun(X28620,tc_HOL_Obool),X28621),c_Set_Oimage(X28622,X28620,X28618)),hAPP(hAPP(c_COMBC(X28621,tc_fun(X28622,tc_HOL_Obool),tc_fun(X28622,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28622,tc_HOL_Obool),tc_fun(tc_fun(X28622,tc_HOL_Obool),tc_fun(X28622,tc_HOL_Obool)),X28621),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28622,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28621,tc_HOL_Obool),tc_fun(X28622,tc_HOL_Obool),X28621),c_Set_Ovimage(X28622,X28621,X28619)),hAPP(hAPP(c_COMBC(X28621,tc_fun(X28621,tc_HOL_Obool),tc_fun(X28621,tc_HOL_Obool)),c_Set_Oinsert(X28621)),c_Orderings_Obot__class_Obot(tc_fun(X28621,tc_HOL_Obool)))))),X28617))),
inference(variable_rename,[status(thm)],[fact_image__split__eq__Sigma]) ).
cnf(i_0_6199,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),X3)),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_5260]) ).
fof(i_0_6200,plain,
! [X31318,X31319] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31319)
| c_Complete__Lattice_OSup__class_OSup(X31319,X31318) = c_Complete__Lattice_OInf__class_OInf(X31319,hAPP(c_Set_OCollect(X31319),hAPP(hAPP(c_COMBB(tc_fun(X31319,tc_HOL_Obool),tc_HOL_Obool,X31319),c_HOL_OAll(X31319)),hAPP(hAPP(c_COMBB(tc_fun(X31319,tc_HOL_Obool),tc_fun(X31319,tc_HOL_Obool),X31319),hAPP(c_COMBS(X31319,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31319),c_fimplies),hAPP(hAPP(c_COMBC(X31319,tc_fun(X31319,tc_HOL_Obool),tc_HOL_Obool),c_member(X31319)),X31318)))),hAPP(c_COMBC(X31319,X31319,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X31319)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__Inf])]) ).
fof(i_0_6201,plain,
! [X26021,X26022,X26023,X26024,X26025,X26026] :
( ( hBOOL(hAPP(hAPP(c_member(X26025),esk209_6(X26021,X26022,X26023,X26024,X26025,X26026)),X26024))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26025,X26026),X26023),X26024) != X26022
| ~ hBOOL(hAPP(hAPP(c_member(X26025),X26021),X26024))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26026),hAPP(X26023,X26021)),X26022))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26025),X26024))
| ~ class_Groups_Oordered__ab__group__add(X26026) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26026),c_Groups_Ozero__class_Ozero(X26026)),hAPP(X26023,esk209_6(X26021,X26022,X26023,X26024,X26025,X26026))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26025,X26026),X26023),X26024) != X26022
| ~ hBOOL(hAPP(hAPP(c_member(X26025),X26021),X26024))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26026),hAPP(X26023,X26021)),X26022))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26025),X26024))
| ~ class_Groups_Oordered__ab__group__add(X26026) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__leq__bound])])])]) ).
fof(i_0_6202,plain,
! [X26015,X26016,X26017,X26018,X26019,X26020] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X26019),X26017),X26018))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26019,X26020),hAPP(hAPP(c_COMBC(X26019,X26020,X26020),hAPP(hAPP(c_COMBS(X26019,X26020,tc_fun(X26020,X26020)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26020,tc_fun(X26020,X26020)),X26019),c_If(X26020)),hAPP(hAPP(c_COMBC(X26019,X26019,tc_HOL_Obool),c_fequal),X26017))),X26016)),X26015)),X26018) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26020),hAPP(X26016,X26017)),hAPP(hAPP(c_Power_Opower__class_Opower(X26020),X26015),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X26019),X26018)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26019),X26018))
| ~ class_Groups_Ocomm__monoid__mult(X26020) )
& ( hBOOL(hAPP(hAPP(c_member(X26019),X26017),X26018))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26019,X26020),hAPP(hAPP(c_COMBC(X26019,X26020,X26020),hAPP(hAPP(c_COMBS(X26019,X26020,tc_fun(X26020,X26020)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26020,tc_fun(X26020,X26020)),X26019),c_If(X26020)),hAPP(hAPP(c_COMBC(X26019,X26019,tc_HOL_Obool),c_fequal),X26017))),X26016)),X26015)),X26018) = hAPP(hAPP(c_Power_Opower__class_Opower(X26020),X26015),hAPP(c_Finite__Set_Ocard(X26019),X26018))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26019),X26018))
| ~ class_Groups_Ocomm__monoid__mult(X26020) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5261])])]) ).
fof(i_0_6203,plain,
! [X26170,X26171,X26172,X26173,X26174] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X26173),X26171),X26172))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26173,X26174),hAPP(hAPP(c_COMBC(X26173,X26174,X26174),hAPP(hAPP(c_COMBS(X26173,X26174,tc_fun(X26174,X26174)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26174,tc_fun(X26174,X26174)),X26173),c_If(X26174)),hAPP(hAPP(c_COMBC(X26173,X26173,tc_HOL_Obool),c_fequal),X26171))),X26170)),c_Groups_Oone__class_Oone(X26174))),X26172) = hAPP(X26170,X26171)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26173),X26172))
| ~ class_Groups_Ocomm__monoid__mult(X26174) )
& ( hBOOL(hAPP(hAPP(c_member(X26173),X26171),X26172))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26173,X26174),hAPP(hAPP(c_COMBC(X26173,X26174,X26174),hAPP(hAPP(c_COMBS(X26173,X26174,tc_fun(X26174,X26174)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26174,tc_fun(X26174,X26174)),X26173),c_If(X26174)),hAPP(hAPP(c_COMBC(X26173,X26173,tc_HOL_Obool),c_fequal),X26171))),X26170)),c_Groups_Oone__class_Oone(X26174))),X26172) = c_Groups_Oone__class_Oone(X26174)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26173),X26172))
| ~ class_Groups_Ocomm__monoid__mult(X26174) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5262])])]) ).
fof(i_0_6204,plain,
! [X25342,X25343,X25344,X25345,X25346] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25345),X25343),X25344))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25345,X25346),hAPP(hAPP(c_COMBC(X25345,X25346,X25346),hAPP(hAPP(c_COMBS(X25345,X25346,tc_fun(X25346,X25346)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25346,tc_fun(X25346,X25346)),X25345),c_If(X25346)),hAPP(hAPP(c_COMBC(X25345,X25345,tc_HOL_Obool),c_fequal),X25343))),X25342)),c_Groups_Ozero__class_Ozero(X25346))),X25344) = hAPP(X25342,X25343)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25345),X25344))
| ~ class_Groups_Ocomm__monoid__add(X25346) )
& ( hBOOL(hAPP(hAPP(c_member(X25345),X25343),X25344))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25345,X25346),hAPP(hAPP(c_COMBC(X25345,X25346,X25346),hAPP(hAPP(c_COMBS(X25345,X25346,tc_fun(X25346,X25346)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25346,tc_fun(X25346,X25346)),X25345),c_If(X25346)),hAPP(hAPP(c_COMBC(X25345,X25345,tc_HOL_Obool),c_fequal),X25343))),X25342)),c_Groups_Ozero__class_Ozero(X25346))),X25344) = c_Groups_Ozero__class_Ozero(X25346)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25345),X25344))
| ~ class_Groups_Ocomm__monoid__add(X25346) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5263])])]) ).
fof(i_0_6205,plain,
! [X31320,X31321] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31321)
| c_Complete__Lattice_OInf__class_OInf(X31321,X31320) = c_Complete__Lattice_OSup__class_OSup(X31321,hAPP(c_Set_OCollect(X31321),hAPP(hAPP(c_COMBB(tc_fun(X31321,tc_HOL_Obool),tc_HOL_Obool,X31321),c_HOL_OAll(X31321)),hAPP(hAPP(c_COMBB(tc_fun(X31321,tc_HOL_Obool),tc_fun(X31321,tc_HOL_Obool),X31321),hAPP(c_COMBS(X31321,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31321),c_fimplies),hAPP(hAPP(c_COMBC(X31321,tc_fun(X31321,tc_HOL_Obool),tc_HOL_Obool),c_member(X31321)),X31320)))),c_Orderings_Oord__class_Oless__eq(X31321))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__Sup])]) ).
fof(i_0_6206,plain,
! [X27296,X27297,X27298,X27299,X27300,X27301,X27302] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27302,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27301,tc_fun(X27302,tc_HOL_Obool)),X27300),X27299)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27298,tc_fun(X27302,tc_HOL_Obool)),X27297),X27296)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27301,tc_fun(X27302,tc_HOL_Obool)),X27300),hAPP(hAPP(c_COMBB(tc_fun(X27298,tc_fun(X27302,tc_HOL_Obool)),tc_fun(X27302,tc_HOL_Obool),X27301),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27298,tc_fun(X27302,tc_HOL_Obool)),X27297)),hAPP(hAPP(c_COMBC(X27301,tc_fun(X27298,tc_fun(X27302,tc_HOL_Obool)),tc_fun(X27298,tc_fun(X27302,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27302,tc_HOL_Obool),tc_fun(X27302,tc_HOL_Obool)),tc_fun(tc_fun(X27298,tc_fun(X27302,tc_HOL_Obool)),tc_fun(X27298,tc_fun(X27302,tc_HOL_Obool))),X27301),c_COMBB(tc_fun(X27302,tc_HOL_Obool),tc_fun(X27302,tc_HOL_Obool),X27298)),hAPP(hAPP(c_COMBB(tc_fun(X27302,tc_HOL_Obool),tc_fun(tc_fun(X27302,tc_HOL_Obool),tc_fun(X27302,tc_HOL_Obool)),X27301),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27302,tc_HOL_Obool))),X27299))),X27296))),
inference(variable_rename,[status(thm)],[fact_Int__UN__distrib2]) ).
fof(i_0_6207,plain,
! [X31107,X31108,X31109,X31110,X31111,X31112,X31113] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31113,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31112,tc_fun(X31113,tc_HOL_Obool)),X31111),X31110)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31109,tc_fun(X31113,tc_HOL_Obool)),X31108),X31107)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31112,tc_fun(X31113,tc_HOL_Obool)),X31111),hAPP(hAPP(c_COMBB(tc_fun(X31109,tc_fun(X31113,tc_HOL_Obool)),tc_fun(X31113,tc_HOL_Obool),X31112),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31109,tc_fun(X31113,tc_HOL_Obool)),X31108)),hAPP(hAPP(c_COMBC(X31112,tc_fun(X31109,tc_fun(X31113,tc_HOL_Obool)),tc_fun(X31109,tc_fun(X31113,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31113,tc_HOL_Obool),tc_fun(X31113,tc_HOL_Obool)),tc_fun(tc_fun(X31109,tc_fun(X31113,tc_HOL_Obool)),tc_fun(X31109,tc_fun(X31113,tc_HOL_Obool))),X31112),c_COMBB(tc_fun(X31113,tc_HOL_Obool),tc_fun(X31113,tc_HOL_Obool),X31109)),hAPP(hAPP(c_COMBB(tc_fun(X31113,tc_HOL_Obool),tc_fun(tc_fun(X31113,tc_HOL_Obool),tc_fun(X31113,tc_HOL_Obool)),X31112),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31113,tc_HOL_Obool))),X31110))),X31107))),
inference(variable_rename,[status(thm)],[fact_Un__INT__distrib2]) ).
cnf(i_0_6208,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2)),c_Int_Onat))))) ),
inference(split_conjunct,[status(thm)],[i_0_5264]) ).
cnf(i_0_6209,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Int_Onat))))) ),
inference(split_conjunct,[status(thm)],[i_0_5265]) ).
cnf(i_0_6210,plain,
hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(c_Product__Type_Oapfst(X5,X3,X1,X6),X7)) = hAPP(c_Product__Type_Oapfst(X5,X3,X2,X6),hAPP(c_Product__Type_Oapsnd(X1,X2,X5,X4),X7)),
inference(split_conjunct,[status(thm)],[i_0_5266]) ).
cnf(i_0_6211,plain,
c_Product__Type_Oapfst(X1,X2,X3,X4) = c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),
inference(split_conjunct,[status(thm)],[i_0_5267]) ).
fof(i_0_6212,plain,
! [X22918,X22919,X22920,X22921,X22922,X22923,X22924] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X22924,X22923,X22922,X22921),X22920),X22919),X22918) = c_New__DSequence_Oneg__bind(X22924,X22923,hAPP(hAPP(hAPP(X22922,X22920),X22919),X22918),hAPP(hAPP(c_COMBC(X22924,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X22923)))),hAPP(hAPP(c_COMBC(X22924,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X22923))))),hAPP(hAPP(c_COMBC(X22924,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X22923)))))),X22921),X22920)),X22919)),X22918)),
inference(variable_rename,[status(thm)],[fact_neg__bind__def]) ).
fof(i_0_6213,plain,
! [X33201,X33202,X33203,X33204,X33205] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33205),tc_List_Olist(X33205))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33205),tc_List_Olist(X33205)),hAPP(hAPP(c_List_Oappend(X33205),X33204),X33203)),hAPP(hAPP(c_List_Oappend(X33205),X33204),X33202))),c_List_Olexord(X33205,X33201)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X33205,X33205)),hAPP(hAPP(c_Product__Type_OPair(X33205,X33205),esk460_5(X33201,X33202,X33203,X33204,X33205)),esk460_5(X33201,X33202,X33203,X33204,X33205))),X33201))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33205),tc_List_Olist(X33205))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33205),tc_List_Olist(X33205)),X33203),X33202)),c_List_Olexord(X33205,X33201))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5268])])]) ).
fof(i_0_6214,plain,
! [X31266,X31267] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31267,tc_HOL_Obool),X31266) = hAPP(c_Set_OCollect(X31267),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31267,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X31267),c_HOL_OAll(tc_fun(X31267,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31267,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X31267,tc_HOL_Obool),tc_HOL_Obool),X31267),hAPP(c_COMBS(tc_fun(X31267,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X31267,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X31267,tc_HOL_Obool),tc_fun(tc_fun(X31267,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X31267,tc_HOL_Obool))),X31266)))),c_member(X31267)))),
inference(variable_rename,[status(thm)],[fact_Inter__eq]) ).
fof(i_0_6215,plain,
! [X30612,X30613,X30614,X30615,X30616] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30616,X30616)),hAPP(hAPP(c_Product__Type_OPair(X30616,X30616),X30615),esk381_5(X30612,X30613,X30614,X30615,X30616))),c_Transitive__Closure_Ortrancl(X30616,X30613)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30616,X30616)),hAPP(hAPP(c_Product__Type_OPair(X30616,X30616),X30615),X30614)),c_Transitive__Closure_Ortrancl(X30616,X30613)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30616,X30616)),hAPP(hAPP(c_Product__Type_OPair(X30616,X30616),X30615),X30614)),c_Transitive__Closure_Ortrancl(X30616,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30616,X30616),tc_HOL_Obool)),X30613),X30612)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30616,X30616)),hAPP(hAPP(c_Product__Type_OPair(X30616,X30616),esk381_5(X30612,X30613,X30614,X30615,X30616)),esk382_5(X30612,X30613,X30614,X30615,X30616))),X30612))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30616,X30616)),hAPP(hAPP(c_Product__Type_OPair(X30616,X30616),X30615),X30614)),c_Transitive__Closure_Ortrancl(X30616,X30613)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30616,X30616)),hAPP(hAPP(c_Product__Type_OPair(X30616,X30616),X30615),X30614)),c_Transitive__Closure_Ortrancl(X30616,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30616,X30616),tc_HOL_Obool)),X30613),X30612)))) )
& ( esk381_5(X30612,X30613,X30614,X30615,X30616) != esk382_5(X30612,X30613,X30614,X30615,X30616)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30616,X30616)),hAPP(hAPP(c_Product__Type_OPair(X30616,X30616),X30615),X30614)),c_Transitive__Closure_Ortrancl(X30616,X30613)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30616,X30616)),hAPP(hAPP(c_Product__Type_OPair(X30616,X30616),X30615),X30614)),c_Transitive__Closure_Ortrancl(X30616,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30616,X30616),tc_HOL_Obool)),X30613),X30612)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separatorE])])])]) ).
fof(i_0_6216,plain,
! [X30567,X30568,X30569,X30570,X30571] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30571,X30571)),hAPP(hAPP(c_Product__Type_OPair(X30571,X30571),esk376_5(X30567,X30568,X30569,X30570,X30571)),X30569)),c_Transitive__Closure_Ortrancl(X30571,X30568)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30571,X30571)),hAPP(hAPP(c_Product__Type_OPair(X30571,X30571),X30570),X30569)),c_Transitive__Closure_Ortrancl(X30571,X30568)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30571,X30571)),hAPP(hAPP(c_Product__Type_OPair(X30571,X30571),X30570),X30569)),c_Transitive__Closure_Ortrancl(X30571,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30571,X30571),tc_HOL_Obool)),X30568),X30567)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30571,X30571)),hAPP(hAPP(c_Product__Type_OPair(X30571,X30571),esk377_5(X30567,X30568,X30569,X30570,X30571)),esk376_5(X30567,X30568,X30569,X30570,X30571))),X30567))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30571,X30571)),hAPP(hAPP(c_Product__Type_OPair(X30571,X30571),X30570),X30569)),c_Transitive__Closure_Ortrancl(X30571,X30568)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30571,X30571)),hAPP(hAPP(c_Product__Type_OPair(X30571,X30571),X30570),X30569)),c_Transitive__Closure_Ortrancl(X30571,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30571,X30571),tc_HOL_Obool)),X30568),X30567)))) )
& ( esk377_5(X30567,X30568,X30569,X30570,X30571) != esk376_5(X30567,X30568,X30569,X30570,X30571)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30571,X30571)),hAPP(hAPP(c_Product__Type_OPair(X30571,X30571),X30570),X30569)),c_Transitive__Closure_Ortrancl(X30571,X30568)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30571,X30571)),hAPP(hAPP(c_Product__Type_OPair(X30571,X30571),X30570),X30569)),c_Transitive__Closure_Ortrancl(X30571,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30571,X30571),tc_HOL_Obool)),X30568),X30567)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separator__converseE])])])]) ).
fof(i_0_6217,plain,
! [X32099,X32100,X32101,X32102,X32103,X32104] : hAPP(hAPP(c_List_Ozip(X32104,X32103),X32102),hAPP(hAPP(c_List_Omap(X32101,X32103),X32100),X32099)) = hAPP(hAPP(c_List_Omap(tc_prod(X32104,X32101),tc_prod(X32104,X32103)),hAPP(c_Product__Type_Oprod_Oprod__case(X32104,X32101,tc_prod(X32104,X32103)),hAPP(hAPP(c_COMBC(X32104,tc_fun(X32101,X32103),tc_fun(X32101,tc_prod(X32104,X32103))),hAPP(hAPP(c_COMBB(tc_fun(X32103,tc_prod(X32104,X32103)),tc_fun(tc_fun(X32101,X32103),tc_fun(X32101,tc_prod(X32104,X32103))),X32104),c_COMBB(X32103,tc_prod(X32104,X32103),X32101)),c_Product__Type_OPair(X32104,X32103))),X32100))),hAPP(hAPP(c_List_Ozip(X32104,X32101),X32102),X32099)),
inference(variable_rename,[status(thm)],[fact_zip__map2]) ).
cnf(i_0_6218,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5269]) ).
cnf(i_0_6219,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_5247]) ).
cnf(i_0_6220,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X1)))))
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_5248]) ).
fof(i_0_6221,plain,
! [X21057,X21058,X21059] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk75_3(X21057,X21058,X21059)),X21059))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21057),hAPP(X21058,X21059)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21058,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21057))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk74_3(X21057,X21058,X21059)),X21059)) )
& ( hAPP(X21058,esk75_3(X21057,X21058,X21059)) = X21057
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21057),hAPP(X21058,X21059)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21058,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21057))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk74_3(X21057,X21058,X21059)),X21059)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk75_3(X21057,X21058,X21059)),X21059))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21057),hAPP(X21058,X21059)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21058,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21057))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X21058,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk74_3(X21057,X21058,X21059)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21058,esk74_3(X21057,X21058,X21059))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( hAPP(X21058,esk75_3(X21057,X21058,X21059)) = X21057
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21057),hAPP(X21058,X21059)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21058,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21057))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X21058,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk74_3(X21057,X21058,X21059)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21058,esk74_3(X21057,X21058,X21059))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat0__intermed__int__val])])])]) ).
fof(i_0_6222,plain,
! [X21052,X21053,X21054] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk73_3(X21052,X21053,X21054)),X21054))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21052),hAPP(X21053,X21054)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21053,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21052))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk72_3(X21052,X21053,X21054)),X21054)) )
& ( hAPP(X21053,esk73_3(X21052,X21053,X21054)) = X21052
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21052),hAPP(X21053,X21054)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21053,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21052))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk72_3(X21052,X21053,X21054)),X21054)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk73_3(X21052,X21053,X21054)),X21054))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21052),hAPP(X21053,X21054)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21053,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X21053,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk72_3(X21052,X21053,X21054)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21053,esk72_3(X21052,X21053,X21054))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( hAPP(X21053,esk73_3(X21052,X21053,X21054)) = X21052
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21052),hAPP(X21053,X21054)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21053,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X21053,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk72_3(X21052,X21053,X21054)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21053,esk72_3(X21052,X21053,X21054))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__val__lemma])])])]) ).
fof(i_0_6223,plain,
! [X30552,X30553,X30554,X30555,X30556] :
( ( X30553 = hAPP(c_Nat_OSuc,esk374_5(X30552,X30553,X30554,X30555,X30556))
| X30553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30556,X30556)),hAPP(hAPP(c_Product__Type_OPair(X30556,X30556),X30555),X30554)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30556,X30556),tc_HOL_Obool),X30553),X30552))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30556,X30556)),hAPP(hAPP(c_Product__Type_OPair(X30556,X30556),X30555),esk373_5(X30552,X30553,X30554,X30555,X30556))),X30552))
| X30553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30556,X30556)),hAPP(hAPP(c_Product__Type_OPair(X30556,X30556),X30555),X30554)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30556,X30556),tc_HOL_Obool),X30553),X30552))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30556,X30556)),hAPP(hAPP(c_Product__Type_OPair(X30556,X30556),esk373_5(X30552,X30553,X30554,X30555,X30556)),X30554)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30556,X30556),tc_HOL_Obool),esk374_5(X30552,X30553,X30554,X30555,X30556)),X30552)))
| X30553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30556,X30556)),hAPP(hAPP(c_Product__Type_OPair(X30556,X30556),X30555),X30554)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30556,X30556),tc_HOL_Obool),X30553),X30552))) )
& ( X30553 = hAPP(c_Nat_OSuc,esk374_5(X30552,X30553,X30554,X30555,X30556))
| X30555 = X30554
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30556,X30556)),hAPP(hAPP(c_Product__Type_OPair(X30556,X30556),X30555),X30554)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30556,X30556),tc_HOL_Obool),X30553),X30552))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30556,X30556)),hAPP(hAPP(c_Product__Type_OPair(X30556,X30556),X30555),esk373_5(X30552,X30553,X30554,X30555,X30556))),X30552))
| X30555 = X30554
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30556,X30556)),hAPP(hAPP(c_Product__Type_OPair(X30556,X30556),X30555),X30554)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30556,X30556),tc_HOL_Obool),X30553),X30552))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30556,X30556)),hAPP(hAPP(c_Product__Type_OPair(X30556,X30556),esk373_5(X30552,X30553,X30554,X30555,X30556)),X30554)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30556,X30556),tc_HOL_Obool),esk374_5(X30552,X30553,X30554,X30555,X30556)),X30552)))
| X30555 = X30554
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30556,X30556)),hAPP(hAPP(c_Product__Type_OPair(X30556,X30556),X30555),X30554)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30556,X30556),tc_HOL_Obool),X30553),X30552))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5270])])])]) ).
fof(i_0_6224,plain,
! [X31695,X31696,X31697,X31698] :
( ~ class_Smallcheck_Osmall(X31698)
| ~ class_Smallcheck_Osmall(X31697)
| hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X31697,X31698)),X31696),X31695) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X31697),hAPP(hAPP(c_COMBC(X31697,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X31698,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X31697),c_Smallcheck_Osmall__class_Osmall(X31698)),hAPP(hAPP(c_COMBB(tc_fun(X31698,tc_prod(X31697,X31698)),tc_fun(X31698,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X31697),hAPP(c_COMBB(tc_prod(X31697,X31698),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X31698),X31696)),c_Product__Type_OPair(X31697,X31698)))),X31695)),X31695) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__prod__def])]) ).
cnf(i_0_6225,plain,
( hAPP(X1,esk434_7(X2,X3,X4,X1,X5,X6,X7)) = hAPP(c_Option_Ooption_OSome(X6),X2)
| c_Map_Omap__comp(X7,X6,X5,X1,X4,X3) != hAPP(c_Option_Ooption_OSome(X6),X2) ),
inference(split_conjunct,[status(thm)],[i_0_5271]) ).
cnf(i_0_6226,plain,
c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X1,c_Option_Ooption_ONone(X2),X4),hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_5272]) ).
cnf(i_0_6227,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),esk434_7(X4,X2,X1,X5,X6,X7,X3))
| c_Map_Omap__comp(X3,X7,X6,X5,X1,X2) != hAPP(c_Option_Ooption_OSome(X7),X4) ),
inference(split_conjunct,[status(thm)],[i_0_5271]) ).
fof(i_0_6228,plain,
! [X28269,X28270,X28271,X28272] :
( ~ c_Fun_Oinj__on(X28272,X28271,X28270,c_Orderings_Otop__class_Otop(tc_fun(X28272,tc_HOL_Obool)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28272,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28272,X28271,X28270),hAPP(hAPP(c_Set_Oinsert(X28271),X28269),c_Orderings_Obot__class_Obot(tc_fun(X28271,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X28272),c_HOL_OThe(X28272,hAPP(hAPP(c_COMBC(X28272,X28271,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X28271,tc_fun(X28271,tc_HOL_Obool),X28272),c_fequal),X28270)),X28269))),c_Orderings_Obot__class_Obot(tc_fun(X28272,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton])]) ).
fof(i_0_6229,plain,
! [X22950,X22951,X22952,X22953,X22954,X22955,X22956] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X22956,X22955,X22954,X22953),X22952),X22951),X22950) = c_New__DSequence_Opos__bind(X22956,X22955,hAPP(hAPP(hAPP(X22954,X22952),X22951),X22950),hAPP(hAPP(c_COMBC(X22956,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X22955))),hAPP(hAPP(c_COMBC(X22956,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X22955)))),hAPP(hAPP(c_COMBC(X22956,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X22955))))),X22953),X22952)),X22951)),X22950)),
inference(variable_rename,[status(thm)],[fact_pos__bind__def]) ).
fof(i_0_6230,plain,
! [X17937,X17938,X17939,X17940,X17941,X17943,X17944,X17945,X17946,X17947,X17948] :
( ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17937),hAPP(c_Natural_Ogetlocs,X17938))),X17941),hAPP(hAPP(c_Natural_Ogetlocs,X17937),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk18_5(X17937,X17938,X17939,X17940,X17941)),hAPP(c_Natural_Ogetlocs,X17938))),X17941),hAPP(hAPP(c_Natural_Ogetlocs,esk18_5(X17937,X17938,X17939,X17940,X17941)),c_Com_ORes))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17941,X17940,X17939)),X17938),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17937),hAPP(c_Natural_Ogetlocs,X17938))),X17941),hAPP(hAPP(c_Natural_Ogetlocs,X17937),c_Com_ORes)))) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17940)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17938),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17939,X17938))),esk18_5(X17937,X17938,X17939,X17940,X17941)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17941,X17940,X17939)),X17938),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17937),hAPP(c_Natural_Ogetlocs,X17938))),X17941),hAPP(hAPP(c_Natural_Ogetlocs,X17937),c_Com_ORes)))) )
& ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17943),hAPP(c_Natural_Ogetlocs,X17944))),X17947),hAPP(hAPP(c_Natural_Ogetlocs,X17943),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17948),hAPP(c_Natural_Ogetlocs,X17944))),X17947),hAPP(hAPP(c_Natural_Ogetlocs,X17948),c_Com_ORes))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17946)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17944),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17945,X17944))),X17948))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17947,X17946,X17945)),X17944),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17943),hAPP(c_Natural_Ogetlocs,X17944))),X17947),hAPP(hAPP(c_Natural_Ogetlocs,X17943),c_Com_ORes)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I10_J])])])])])]) ).
fof(i_0_6231,plain,
! [X25664,X25665] :
( ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25665,X25664) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25665),X25664))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25664),X25665)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25665),X25664))
| c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25665,X25664) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25664),X25665))
| c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25665,X25664) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5273])])]) ).
fof(i_0_6232,plain,
! [X25638,X25639] :
( ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25639,X25638) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25639),X25638))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25638),X25639)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25639),X25638))
| c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25639,X25638) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25638),X25639))
| c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25639,X25638) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5274])])]) ).
fof(i_0_6233,plain,
! [X25662,X25663] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25663,X25662)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25663),X25662))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25662),X25663)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25663),X25662))
| c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25663,X25662) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25662),X25663))
| c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25663,X25662) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5275])])]) ).
fof(i_0_6234,plain,
! [X25640,X25641] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25641,X25640)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25641),X25640))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25640),X25641)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25641),X25640))
| c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25641,X25640) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25640),X25641))
| c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25641,X25640) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5276])])]) ).
fof(i_0_6235,plain,
! [X29350,X29351,X29352,X29353] : c_Nitpick_Oprod(X29353,X29352,X29351,X29350) = hAPP(c_Set_OCollect(tc_prod(X29353,X29352)),hAPP(c_Product__Type_Oprod_Oprod__case(X29353,X29352,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29353,tc_fun(X29352,tc_HOL_Obool),tc_fun(X29352,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29352,tc_HOL_Obool),tc_fun(X29352,tc_HOL_Obool)),X29353),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29352)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29353),c_fconj),hAPP(hAPP(c_COMBC(X29353,tc_fun(X29353,tc_HOL_Obool),tc_HOL_Obool),c_member(X29353)),X29351)))),hAPP(hAPP(c_COMBC(X29352,tc_fun(X29352,tc_HOL_Obool),tc_HOL_Obool),c_member(X29352)),X29350)))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Oprod__def]) ).
fof(i_0_6236,plain,
! [X23456,X23457,X23458,X23459] :
( ~ class_Orderings_Oorder(X23459)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X23459,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X23458)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23457),X23456))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23456),X23457))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23459),hAPP(X23458,X23457)),hAPP(X23458,X23456))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5277])]) ).
fof(i_0_6237,plain,
! [X23475,X23476] :
( ~ class_Orderings_Oorder(X23476)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X23476,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X23475)
| c_Orderings_Oorder_Omono(tc_Nat_Onat,X23476,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23475) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Ostrict__mono__mono])]) ).
cnf(i_0_6238,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5278]) ).
fof(i_0_6239,plain,
! [X28912,X28913,X28914,X28915,X28916,X28917,X28918,X28919,X28920,X28921,X28922] : hAPP(c_Product__Type_Omap__pair(X28922,X28921,X28920,X28919,X28918,X28917),hAPP(c_Product__Type_Omap__pair(X28916,X28922,X28915,X28920,X28914,X28913),X28912)) = hAPP(c_Product__Type_Omap__pair(X28916,X28921,X28915,X28919,hAPP(c_Fun_Ocomp(X28922,X28921,X28916,X28918),X28914),hAPP(c_Fun_Ocomp(X28920,X28919,X28915,X28917),X28913)),X28912),
inference(variable_rename,[status(thm)],[fact_map__pair_Ocompositionality]) ).
fof(i_0_6240,plain,
! [X26766,X26767,X26768,X26769] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26769),X26768)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26767),X26766)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26769),X26766)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26767),X26768))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26769),X26766)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26767),X26768)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26769),X26768)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26767),X26766)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le])]) ).
fof(i_0_6241,plain,
! [X26762,X26763,X26764,X26765] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26765),X26764)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26763),X26762)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26765),X26762)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26763),X26764))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26765),X26762)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26763),X26764)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26765),X26764)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26763),X26762)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less])]) ).
fof(i_0_6242,plain,
! [X26863,X26864,X26865,X26866,X26867,X26868] :
( ( hBOOL(hAPP(hAPP(c_member(X26867),esk240_6(X26863,X26864,X26865,X26866,X26867,X26868)),X26866))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26863,X26868),X26864),hAPP(c_Set_Oimage(X26867,X26863,X26865),X26866)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26867,X26868),hAPP(c_Fun_Ocomp(X26863,X26868,X26867,X26864),X26865)),X26866)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26867),X26866))
| ~ class_Groups_Ocomm__monoid__add(X26868) )
& ( hBOOL(hAPP(hAPP(c_member(X26867),esk241_6(X26863,X26864,X26865,X26866,X26867,X26868)),X26866))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26863,X26868),X26864),hAPP(c_Set_Oimage(X26867,X26863,X26865),X26866)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26867,X26868),hAPP(c_Fun_Ocomp(X26863,X26868,X26867,X26864),X26865)),X26866)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26867),X26866))
| ~ class_Groups_Ocomm__monoid__add(X26868) )
& ( esk240_6(X26863,X26864,X26865,X26866,X26867,X26868) != esk241_6(X26863,X26864,X26865,X26866,X26867,X26868)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26863,X26868),X26864),hAPP(c_Set_Oimage(X26867,X26863,X26865),X26866)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26867,X26868),hAPP(c_Fun_Ocomp(X26863,X26868,X26867,X26864),X26865)),X26866)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26867),X26866))
| ~ class_Groups_Ocomm__monoid__add(X26868) )
& ( hAPP(X26865,esk240_6(X26863,X26864,X26865,X26866,X26867,X26868)) = hAPP(X26865,esk241_6(X26863,X26864,X26865,X26866,X26867,X26868))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26863,X26868),X26864),hAPP(c_Set_Oimage(X26867,X26863,X26865),X26866)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26867,X26868),hAPP(c_Fun_Ocomp(X26863,X26868,X26867,X26864),X26865)),X26866)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26867),X26866))
| ~ class_Groups_Ocomm__monoid__add(X26868) )
& ( hAPP(X26864,hAPP(X26865,esk240_6(X26863,X26864,X26865,X26866,X26867,X26868))) != c_Groups_Ozero__class_Ozero(X26868)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26863,X26868),X26864),hAPP(c_Set_Oimage(X26867,X26863,X26865),X26866)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26867,X26868),hAPP(c_Fun_Ocomp(X26863,X26868,X26867,X26864),X26865)),X26866)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26867),X26866))
| ~ class_Groups_Ocomm__monoid__add(X26868) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex__nonzero])])])]) ).
fof(i_0_6243,plain,
! [X17949,X17950,X17951,X17952,X17953] :
( ( X17949 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk19_5(X17949,X17950,X17951,X17952,X17953)),hAPP(c_Natural_Ogetlocs,X17950))),X17953),hAPP(hAPP(c_Natural_Ogetlocs,esk19_5(X17949,X17950,X17951,X17952,X17953)),c_Com_ORes))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17953,X17952,X17951)),X17950),X17949)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17952)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17950),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17951,X17950))),esk19_5(X17949,X17950,X17951,X17952,X17953)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17953,X17952,X17951)),X17950),X17949)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5279])])])]) ).
fof(i_0_6244,plain,
! [X29262,X29263,X29264,X29265,X29266,X29267] : hAPP(c_Set_Oimage(X29267,X29266,hAPP(hAPP(c_COMBS(X29267,X29266,X29266),hAPP(hAPP(c_COMBS(X29267,X29266,tc_fun(X29266,X29266)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X29266,tc_fun(X29266,X29266)),X29267),c_If(X29266)),X29265)),X29264)),X29263)),X29262) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29266,tc_HOL_Obool)),hAPP(c_Set_Oimage(X29267,X29266,X29264),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29267,tc_HOL_Obool)),X29262),hAPP(c_Set_OCollect(X29267),X29265)))),hAPP(c_Set_Oimage(X29267,X29266,X29263),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29267,tc_HOL_Obool)),X29262),hAPP(c_Set_OCollect(X29267),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29267),c_fNot),X29265))))),
inference(variable_rename,[status(thm)],[fact_if__image__distrib]) ).
cnf(i_0_6245,plain,
hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(c_Product__Type_Oapsnd(X5,X1,X3,X6),X7)) = hAPP(c_Product__Type_Oapsnd(X5,X2,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6)),X7),
inference(split_conjunct,[status(thm)],[i_0_5280]) ).
cnf(i_0_6246,plain,
hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),hAPP(c_Product__Type_Oapfst(X5,X1,X3,X6),X7)) = hAPP(c_Product__Type_Oapfst(X5,X2,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6)),X7),
inference(split_conjunct,[status(thm)],[i_0_5281]) ).
fof(i_0_6247,plain,
! [X26734,X26735,X26736,X26737] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26737),X26736)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26735),X26734)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26737),X26735)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26736),X26734))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26737),X26734)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26736),X26735)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_mult]) ).
fof(i_0_6248,plain,
! [X17701,X17702,X17703,X17704,X17705,X17706,X17708,X17709,X17710,X17711,X17712,X17713,X17714] :
( ( hAPP(hAPP(hAPP(c_Natural_Oupdate,X17701),c_Com_Ovname_OLoc(X17706)),hAPP(hAPP(c_Natural_Ogetlocs,X17703),X17706)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk9_6(X17701,X17702,X17703,X17704,X17705,X17706)),c_Com_Ovname_OLoc(X17706)),hAPP(hAPP(c_Natural_Ogetlocs,X17703),X17706))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X17706,X17705,X17704),X17703,X17702,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17701),c_Com_Ovname_OLoc(X17706)),hAPP(hAPP(c_Natural_Ogetlocs,X17703),X17706))) )
& ( c_Natural_Oevaln(X17704,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17703),c_Com_Ovname_OLoc(X17706)),hAPP(X17705,X17703)),X17702,esk9_6(X17701,X17702,X17703,X17704,X17705,X17706))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X17706,X17705,X17704),X17703,X17702,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17701),c_Com_Ovname_OLoc(X17706)),hAPP(hAPP(c_Natural_Ogetlocs,X17703),X17706))) )
& ( hAPP(hAPP(hAPP(c_Natural_Oupdate,X17708),c_Com_Ovname_OLoc(X17713)),hAPP(hAPP(c_Natural_Ogetlocs,X17710),X17713)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,X17714),c_Com_Ovname_OLoc(X17713)),hAPP(hAPP(c_Natural_Ogetlocs,X17710),X17713))
| ~ c_Natural_Oevaln(X17711,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17710),c_Com_Ovname_OLoc(X17713)),hAPP(X17712,X17710)),X17709,X17714)
| c_Natural_Oevaln(c_Com_Ocom_OLocal(X17713,X17712,X17711),X17710,X17709,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17708),c_Com_Ovname_OLoc(X17713)),hAPP(hAPP(c_Natural_Ogetlocs,X17710),X17713))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I3_J])])])])])]) ).
fof(i_0_6249,plain,
! [X30072,X30073,X30074,X30075,X30076,X30077] :
( ( hBOOL(hAPP(hAPP(c_member(X30076),esk359_6(X30072,X30073,X30074,X30075,X30076,X30077)),X30075))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30077,X30076,c_Groups_Otimes__class_Otimes(X30077)),X30074),X30072),X30075) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30077,X30076,c_Groups_Otimes__class_Otimes(X30077)),X30073),X30072),X30075)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30076),X30075))
| ~ class_Groups_Oab__semigroup__mult(X30077) )
& ( hAPP(X30074,esk359_6(X30072,X30073,X30074,X30075,X30076,X30077)) != hAPP(X30073,esk359_6(X30072,X30073,X30074,X30075,X30076,X30077))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30077,X30076,c_Groups_Otimes__class_Otimes(X30077)),X30074),X30072),X30075) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30077,X30076,c_Groups_Otimes__class_Otimes(X30077)),X30073),X30072),X30075)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30076),X30075))
| ~ class_Groups_Oab__semigroup__mult(X30077) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__cong])])])]) ).
cnf(i_0_6250,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5282]) ).
cnf(i_0_6251,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5282]) ).
fof(i_0_6252,plain,
! [X29631,X29632,X29633,X29634,X29635,X29636,X29637,X29639,X29640,X29641,X29642,X29643,X29644,X29645,X29646] :
( ( hBOOL(hAPP(hAPP(X29634,X29632),esk318_4(X29631,X29632,X29633,X29634)))
| ~ c_Predicate_Opred__comp(X29637,X29636,X29635,X29634,X29633,X29632,X29631) )
& ( hBOOL(hAPP(hAPP(X29633,esk318_4(X29631,X29632,X29633,X29634)),X29631))
| ~ c_Predicate_Opred__comp(X29637,X29636,X29635,X29634,X29633,X29632,X29631) )
& ( ~ hBOOL(hAPP(hAPP(X29642,X29640),X29643))
| ~ hBOOL(hAPP(hAPP(X29641,X29643),X29639))
| c_Predicate_Opred__comp(X29646,X29645,X29644,X29642,X29641,X29640,X29639) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp_Oequations])])])])])]) ).
fof(i_0_6253,plain,
! [X29680,X29681,X29682,X29683] :
( ~ c_Wellfounded_Owf(X29683,X29682)
| ~ c_Fun_Oinj__on(X29683,X29681,X29680,c_Orderings_Otop__class_Otop(tc_fun(X29683,tc_HOL_Obool)))
| c_Wellfounded_Owf(X29681,hAPP(c_Set_Oimage(tc_prod(X29683,X29683),tc_prod(X29681,X29681),c_Product__Type_Omap__pair(X29683,X29681,X29683,X29681,X29680,X29680)),X29682)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__map__pair__image])]) ).
fof(i_0_6254,plain,
! [X31472,X31473,X31474,X31475,X31476,X31477] :
( ( hBOOL(hAPP(hAPP(c_member(X31476),esk412_6(X31472,X31473,X31474,X31475,X31476,X31477)),X31477))
| c_Fun_Oinj__on(X31475,X31474,X31473,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31476,tc_fun(X31475,tc_HOL_Obool)),X31477),X31472))
| X31477 = c_Orderings_Obot__class_Obot(tc_fun(X31476,tc_HOL_Obool)) )
& ( ~ c_Fun_Oinj__on(X31475,X31474,X31473,hAPP(X31472,esk412_6(X31472,X31473,X31474,X31475,X31476,X31477)))
| c_Fun_Oinj__on(X31475,X31474,X31473,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31476,tc_fun(X31475,tc_HOL_Obool)),X31477),X31472))
| X31477 = c_Orderings_Obot__class_Obot(tc_fun(X31476,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__INTER])])])]) ).
fof(i_0_6255,plain,
! [X17879,X17880,X17881,X17882,X17883,X17884] :
( ( X17879 = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk15_6(X17879,X17880,X17881,X17882,X17883,X17884)),c_Com_Ovname_OLoc(X17884)),hAPP(hAPP(c_Natural_Ogetlocs,X17881),X17884))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X17884,X17883,X17882),X17881,X17880,X17879) )
& ( c_Natural_Oevaln(X17882,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17881),c_Com_Ovname_OLoc(X17884)),hAPP(X17883,X17881)),X17880,esk15_6(X17879,X17880,X17881,X17882,X17883,X17884))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X17884,X17883,X17882),X17881,X17880,X17879) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5283])])])]) ).
fof(i_0_6256,plain,
! [X33730,X33731,X33732,X33733,X33734] :
( ( hBOOL(hAPP(hAPP(c_member(X33733),esk471_5(X33730,X33731,X33732,X33733,X33734)),hAPP(c_List_Oset(X33733),X33732)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33734),hAPP(c_List_Omonoid__add__class_Olistsum(X33734),hAPP(hAPP(c_List_Omap(X33733,X33734),X33731),X33732))),hAPP(c_List_Omonoid__add__class_Olistsum(X33734),hAPP(hAPP(c_List_Omap(X33733,X33734),X33730),X33732))))
| ~ class_Groups_Omonoid__add(X33734)
| ~ class_Groups_Oordered__ab__semigroup__add(X33734) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33734),hAPP(X33731,esk471_5(X33730,X33731,X33732,X33733,X33734))),hAPP(X33730,esk471_5(X33730,X33731,X33732,X33733,X33734))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33734),hAPP(c_List_Omonoid__add__class_Olistsum(X33734),hAPP(hAPP(c_List_Omap(X33733,X33734),X33731),X33732))),hAPP(c_List_Omonoid__add__class_Olistsum(X33734),hAPP(hAPP(c_List_Omap(X33733,X33734),X33730),X33732))))
| ~ class_Groups_Omonoid__add(X33734)
| ~ class_Groups_Oordered__ab__semigroup__add(X33734) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mono])])])]) ).
fof(i_0_6257,plain,
! [X26563,X26564,X26565,X26566,X26567] :
( ( hBOOL(hAPP(hAPP(c_member(X26566),esk235_5(X26563,X26564,X26565,X26566,X26567)),X26565))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26567),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26566,X26567),X26564),X26565)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26566,X26567),X26563),X26565)))
| X26565 = c_Orderings_Obot__class_Obot(tc_fun(X26566,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26566),X26565))
| ~ class_Groups_Ocomm__monoid__add(X26567)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X26567) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26567),hAPP(X26564,esk235_5(X26563,X26564,X26565,X26566,X26567))),hAPP(X26563,esk235_5(X26563,X26564,X26565,X26566,X26567))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26567),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26566,X26567),X26564),X26565)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26566,X26567),X26563),X26565)))
| X26565 = c_Orderings_Obot__class_Obot(tc_fun(X26566,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26566),X26565))
| ~ class_Groups_Ocomm__monoid__add(X26567)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X26567) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__strict__mono])])])]) ).
fof(i_0_6258,plain,
! [X29292,X29293,X29294,X29295,X29296,X29297] :
( ~ class_Groups_Ocomm__monoid__add(X29297)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29296),X29295))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29296,X29297),hAPP(hAPP(c_COMBS(X29296,X29297,X29297),hAPP(hAPP(c_COMBS(X29296,X29297,tc_fun(X29297,X29297)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X29297,tc_fun(X29297,X29297)),X29296),c_If(X29297)),X29294)),X29293)),X29292)),X29295) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29297),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29296,X29297),X29293),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29296,tc_HOL_Obool)),X29295),hAPP(c_Set_OCollect(X29296),X29294)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29296,X29297),X29292),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29296,tc_HOL_Obool)),X29295),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29296,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29296),X29294))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cases])]) ).
cnf(i_0_6259,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5264]) ).
cnf(i_0_6260,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5265]) ).
fof(i_0_6261,plain,
! [X29102,X29103,X29104,X29105,X29106] :
( ~ c_Finite__Set_Ofolding__one__idem(X29106,X29105,X29104)
| hAPP(X29103,hAPP(hAPP(X29105,esk305_5(X29102,X29103,X29104,X29105,X29106)),esk306_5(X29102,X29103,X29104,X29105,X29106))) != hAPP(hAPP(X29105,hAPP(X29103,esk305_5(X29102,X29103,X29104,X29105,X29106))),hAPP(X29103,esk306_5(X29102,X29103,X29104,X29105,X29106)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29106),X29102))
| X29102 = c_Orderings_Obot__class_Obot(tc_fun(X29106,tc_HOL_Obool))
| hAPP(X29103,hAPP(X29104,X29102)) = hAPP(X29104,hAPP(c_Set_Oimage(X29106,X29106,X29103),X29102)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute])])]) ).
cnf(i_0_6262,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk488_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))
| c_List_Otranspose(X2,X3) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))
| X3 = c_List_Olist_ONil(tc_List_Olist(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5284]) ).
cnf(i_0_6263,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk488_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))
| c_List_Otranspose(X2,X3) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_5284]) ).
cnf(i_0_6264,plain,
( c_List_Otranspose(X1,X2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))
| X2 = c_List_Olist_ONil(tc_List_Olist(X1))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk488_3(X3,X1,X2))) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_5284]) ).
cnf(i_0_6265,plain,
( c_List_Otranspose(X1,X2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk488_3(X3,X1,X2))) != X3
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_5284]) ).
cnf(i_0_6266,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_5285]) ).
cnf(i_0_6267,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk81_3(X1,X2,X3)),esk82_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk82_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X1,esk81_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk82_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5286]) ).
fof(i_0_6268,plain,
! [X26165,X26166,X26167,X26168,X26169] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X26168),X26166),X26167))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26168,X26169),hAPP(hAPP(c_COMBC(X26168,X26169,X26169),hAPP(hAPP(c_COMBS(X26168,X26169,tc_fun(X26169,X26169)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26169,tc_fun(X26169,X26169)),X26168),c_If(X26169)),hAPP(c_fequal,X26166))),X26165)),c_Groups_Oone__class_Oone(X26169))),X26167) = hAPP(X26165,X26166)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26168),X26167))
| ~ class_Groups_Ocomm__monoid__mult(X26169) )
& ( hBOOL(hAPP(hAPP(c_member(X26168),X26166),X26167))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26168,X26169),hAPP(hAPP(c_COMBC(X26168,X26169,X26169),hAPP(hAPP(c_COMBS(X26168,X26169,tc_fun(X26169,X26169)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26169,tc_fun(X26169,X26169)),X26168),c_If(X26169)),hAPP(c_fequal,X26166))),X26165)),c_Groups_Oone__class_Oone(X26169))),X26167) = c_Groups_Oone__class_Oone(X26169)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26168),X26167))
| ~ class_Groups_Ocomm__monoid__mult(X26169) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5287])])]) ).
fof(i_0_6269,plain,
! [X25337,X25338,X25339,X25340,X25341] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25340),X25338),X25339))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25340,X25341),hAPP(hAPP(c_COMBC(X25340,X25341,X25341),hAPP(hAPP(c_COMBS(X25340,X25341,tc_fun(X25341,X25341)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25341,tc_fun(X25341,X25341)),X25340),c_If(X25341)),hAPP(c_fequal,X25338))),X25337)),c_Groups_Ozero__class_Ozero(X25341))),X25339) = hAPP(X25337,X25338)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25340),X25339))
| ~ class_Groups_Ocomm__monoid__add(X25341) )
& ( hBOOL(hAPP(hAPP(c_member(X25340),X25338),X25339))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25340,X25341),hAPP(hAPP(c_COMBC(X25340,X25341,X25341),hAPP(hAPP(c_COMBS(X25340,X25341,tc_fun(X25341,X25341)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25341,tc_fun(X25341,X25341)),X25340),c_If(X25341)),hAPP(c_fequal,X25338))),X25337)),c_Groups_Ozero__class_Ozero(X25341))),X25339) = c_Groups_Ozero__class_Ozero(X25341)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25340),X25339))
| ~ class_Groups_Ocomm__monoid__add(X25341) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5288])])]) ).
fof(i_0_6270,plain,
! [X28892,X28893,X28894,X28895,X28896,X28897,X28898,X28899,X28900,X28901] : hAPP(c_Fun_Ocomp(tc_prod(X28901,X28900),tc_prod(X28899,X28898),tc_prod(X28897,X28896),c_Product__Type_Omap__pair(X28901,X28899,X28900,X28898,X28895,X28894)),c_Product__Type_Omap__pair(X28897,X28901,X28896,X28900,X28893,X28892)) = c_Product__Type_Omap__pair(X28897,X28899,X28896,X28898,hAPP(c_Fun_Ocomp(X28901,X28899,X28897,X28895),X28893),hAPP(c_Fun_Ocomp(X28900,X28898,X28896,X28894),X28892)),
inference(variable_rename,[status(thm)],[fact_map__pair_Ocomp]) ).
fof(i_0_6271,plain,
! [X28902,X28903,X28904,X28905,X28906,X28907,X28908,X28909,X28910,X28911] : c_Product__Type_Omap__pair(X28911,X28910,X28909,X28908,hAPP(c_Fun_Ocomp(X28907,X28910,X28911,X28906),X28905),hAPP(c_Fun_Ocomp(X28904,X28908,X28909,X28903),X28902)) = hAPP(c_Fun_Ocomp(tc_prod(X28907,X28904),tc_prod(X28910,X28908),tc_prod(X28911,X28909),c_Product__Type_Omap__pair(X28907,X28910,X28904,X28908,X28906,X28903)),c_Product__Type_Omap__pair(X28911,X28907,X28909,X28904,X28905,X28902)),
inference(variable_rename,[status(thm)],[fact_map__pair__compose]) ).
fof(i_0_6272,plain,
! [X32700,X32701,X32702,X32703,X32704,X32705,X32706,X32707,X32708] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32703)),X32702) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32703)),X32701)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32703),tc_List_Olist(X32703))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32703),tc_List_Olist(X32703)),X32702),X32701)),c_List_Olistrel(X32703,X32700))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32704),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32703)),X32702)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32703,X32703)),hAPP(hAPP(c_Product__Type_OPair(X32703,X32703),hAPP(hAPP(c_List_Onth(X32703),X32702),X32704)),hAPP(hAPP(c_List_Onth(X32703),X32701),X32704))),X32700))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32703),tc_List_Olist(X32703))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32703),tc_List_Olist(X32703)),X32702),X32701)),c_List_Olistrel(X32703,X32700))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk454_4(X32705,X32706,X32707,X32708)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32708)),X32707)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32708)),X32707) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32708)),X32706)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32708),tc_List_Olist(X32708))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32708),tc_List_Olist(X32708)),X32707),X32706)),c_List_Olistrel(X32708,X32705))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32708,X32708)),hAPP(hAPP(c_Product__Type_OPair(X32708,X32708),hAPP(hAPP(c_List_Onth(X32708),X32707),esk454_4(X32705,X32706,X32707,X32708))),hAPP(hAPP(c_List_Onth(X32708),X32706),esk454_4(X32705,X32706,X32707,X32708)))),X32705))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32708)),X32707) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32708)),X32706)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32708),tc_List_Olist(X32708))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32708),tc_List_Olist(X32708)),X32707),X32706)),c_List_Olistrel(X32708,X32705))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__iff__nth])])])])])]) ).
cnf(i_0_6273,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk83_3(X1,X2,X3)),esk84_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk84_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X1,esk83_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk84_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5289]) ).
fof(i_0_6274,plain,
! [X32386,X32387,X32388,X32389,X32390] :
( ( X32389 = hAPP(hAPP(c_List_Olist_OCons(X32390),esk445_5(X32386,X32387,X32388,X32389,X32390)),esk446_5(X32386,X32387,X32388,X32389,X32390))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32390),tc_List_Olist(X32390))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32390),tc_List_Olist(X32390)),X32389),hAPP(hAPP(c_List_Olist_OCons(X32390),X32388),X32387))),c_List_Olistrel(X32390,X32386))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32390,X32390)),hAPP(hAPP(c_Product__Type_OPair(X32390,X32390),esk445_5(X32386,X32387,X32388,X32389,X32390)),X32388)),X32386))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32390),tc_List_Olist(X32390))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32390),tc_List_Olist(X32390)),X32389),hAPP(hAPP(c_List_Olist_OCons(X32390),X32388),X32387))),c_List_Olistrel(X32390,X32386))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32390),tc_List_Olist(X32390))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32390),tc_List_Olist(X32390)),esk446_5(X32386,X32387,X32388,X32389,X32390)),X32387)),c_List_Olistrel(X32390,X32386)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32390),tc_List_Olist(X32390))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32390),tc_List_Olist(X32390)),X32389),hAPP(hAPP(c_List_Olist_OCons(X32390),X32388),X32387))),c_List_Olistrel(X32390,X32386))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5290])])])]) ).
cnf(i_0_6275,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5285]) ).
fof(i_0_6276,plain,
! [X30631,X30632,X30633,X30634,X30635] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30635,X30635)),hAPP(hAPP(c_Product__Type_OPair(X30635,X30635),X30634),esk385_5(X30631,X30632,X30633,X30634,X30635))),X30631))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30635,X30635)),hAPP(hAPP(c_Product__Type_OPair(X30635,X30635),X30634),X30633)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30635,X30635),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30632)),X30631))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30635,X30635)),hAPP(hAPP(c_Product__Type_OPair(X30635,X30635),esk385_5(X30631,X30632,X30633,X30634,X30635)),X30633)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30635,X30635),tc_HOL_Obool),X30632),X30631)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30635,X30635)),hAPP(hAPP(c_Product__Type_OPair(X30635,X30635),X30634),X30633)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30635,X30635),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30632)),X30631))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5291])])])]) ).
fof(i_0_6277,plain,
! [X30625,X30626,X30627,X30628,X30629] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30629,X30629)),hAPP(hAPP(c_Product__Type_OPair(X30629,X30629),X30628),esk384_5(X30625,X30626,X30627,X30628,X30629))),X30625))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30629,X30629)),hAPP(hAPP(c_Product__Type_OPair(X30629,X30629),X30628),X30627)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30629,X30629),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30626)),X30625))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30629,X30629)),hAPP(hAPP(c_Product__Type_OPair(X30629,X30629),esk384_5(X30625,X30626,X30627,X30628,X30629)),X30627)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30629,X30629),tc_HOL_Obool),X30626),X30625)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30629,X30629)),hAPP(hAPP(c_Product__Type_OPair(X30629,X30629),X30628),X30627)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30629,X30629),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30626)),X30625))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__D2])])])]) ).
cnf(i_0_6278,plain,
c_Nitpick_Otimes__frac(X1,X2,X3) = hAPP(hAPP(c_Nitpick_Ofrac(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X2)),hAPP(c_Nitpick_Onum(X1),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X1),X2)),hAPP(c_Nitpick_Odenom(X1),X3))),
inference(split_conjunct,[status(thm)],[i_0_5292]) ).
fof(i_0_6279,plain,
! [X30545,X30546,X30547,X30548,X30549] :
( ( X30546 = hAPP(c_Nat_OSuc,esk372_5(X30545,X30546,X30547,X30548,X30549))
| X30546 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),X30548),X30547)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30549,X30549),tc_HOL_Obool),X30546),X30545))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),X30548),esk371_5(X30545,X30546,X30547,X30548,X30549))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30549,X30549),tc_HOL_Obool),esk372_5(X30545,X30546,X30547,X30548,X30549)),X30545)))
| X30546 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),X30548),X30547)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30549,X30549),tc_HOL_Obool),X30546),X30545))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),esk371_5(X30545,X30546,X30547,X30548,X30549)),X30547)),X30545))
| X30546 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),X30548),X30547)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30549,X30549),tc_HOL_Obool),X30546),X30545))) )
& ( X30546 = hAPP(c_Nat_OSuc,esk372_5(X30545,X30546,X30547,X30548,X30549))
| X30548 = X30547
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),X30548),X30547)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30549,X30549),tc_HOL_Obool),X30546),X30545))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),X30548),esk371_5(X30545,X30546,X30547,X30548,X30549))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30549,X30549),tc_HOL_Obool),esk372_5(X30545,X30546,X30547,X30548,X30549)),X30545)))
| X30548 = X30547
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),X30548),X30547)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30549,X30549),tc_HOL_Obool),X30546),X30545))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),esk371_5(X30545,X30546,X30547,X30548,X30549)),X30547)),X30545))
| X30548 = X30547
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),X30548),X30547)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30549,X30549),tc_HOL_Obool),X30546),X30545))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5293])])])]) ).
fof(i_0_6280,plain,
! [X30619,X30620,X30621,X30622,X30623] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30623,X30623)),hAPP(hAPP(c_Product__Type_OPair(X30623,X30623),X30622),esk383_5(X30619,X30620,X30621,X30622,X30623))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30623,X30623),tc_HOL_Obool),X30620),X30619)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30623,X30623)),hAPP(hAPP(c_Product__Type_OPair(X30623,X30623),X30622),X30621)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30623,X30623),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30620)),X30619))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30623,X30623)),hAPP(hAPP(c_Product__Type_OPair(X30623,X30623),esk383_5(X30619,X30620,X30621,X30622,X30623)),X30621)),X30619))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30623,X30623)),hAPP(hAPP(c_Product__Type_OPair(X30623,X30623),X30622),X30621)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30623,X30623),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30620)),X30619))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5294])])])]) ).
cnf(i_0_6281,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
| c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5295]) ).
cnf(i_0_6282,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5296]) ).
cnf(i_0_6283,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
| c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5297]) ).
cnf(i_0_6284,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5298]) ).
cnf(i_0_6285,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5299]) ).
cnf(i_0_6286,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5300]) ).
cnf(i_0_6287,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2)))),
inference(split_conjunct,[status(thm)],[i_0_5301]) ).
cnf(i_0_6288,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_5302]) ).
cnf(i_0_6289,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_5303]) ).
cnf(i_0_6290,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5304]) ).
fof(i_0_6291,plain,
! [X26875,X26876,X26877] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X26877),X26876),X26875) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26877,tc_fun(tc_fun(X26877,tc_HOL_Obool),tc_HOL_Obool)),X26876),hAPP(hAPP(c_COMBC(X26877,tc_fun(tc_fun(X26877,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X26877,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26877,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X26877,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X26877,tc_HOL_Obool),tc_HOL_Obool)),X26877),c_Set_Oinsert(tc_fun(X26877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X26877,tc_HOL_Obool),tc_fun(X26877,tc_HOL_Obool),X26877),c_Relation_OImage(X26877,X26877,X26875)),hAPP(hAPP(c_COMBC(X26877,tc_fun(X26877,tc_HOL_Obool),tc_fun(X26877,tc_HOL_Obool)),c_Set_Oinsert(X26877)),c_Orderings_Obot__class_Obot(tc_fun(X26877,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26877,tc_HOL_Obool),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_quotient__def]) ).
cnf(i_0_6292,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2)))
| ~ class_Rings_Osemiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5305]) ).
cnf(i_0_6293,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5306]) ).
cnf(i_0_6294,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5307]) ).
cnf(i_0_6295,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5308]) ).
cnf(i_0_6296,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5309]) ).
cnf(i_0_6297,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5310]) ).
cnf(i_0_6298,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5311]) ).
cnf(i_0_6299,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5312]) ).
cnf(i_0_6300,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X1),
inference(split_conjunct,[status(thm)],[i_0_5313]) ).
cnf(i_0_6301,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).
fof(i_0_6302,plain,
! [X28434,X28435,X28436,X28437,X28438] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28436,X28438)),hAPP(hAPP(c_Product__Type_OPair(X28436,X28438),esk271_5(X28434,X28435,X28436,X28437,X28438)),X28437)),X28435))
| ~ hBOOL(hAPP(hAPP(c_member(X28438),X28437),hAPP(c_Relation_OImage(X28436,X28438,X28435),X28434))) )
& ( hBOOL(hAPP(hAPP(c_member(X28436),esk271_5(X28434,X28435,X28436,X28437,X28438)),X28434))
| ~ hBOOL(hAPP(hAPP(c_member(X28438),X28437),hAPP(c_Relation_OImage(X28436,X28438,X28435),X28434))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5314])])])]) ).
fof(i_0_6303,plain,
! [X26710,X26711,X26712,X26713,X26714,X26716,X26717,X26718,X26719,X26720,X26721] :
( ( hBOOL(hAPP(hAPP(c_member(X26712),esk237_5(X26710,X26711,X26712,X26713,X26714)),X26710))
| ~ hBOOL(hAPP(hAPP(c_member(X26714),X26713),hAPP(c_Relation_OImage(X26712,X26714,X26711),X26710))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X26712,X26714)),hAPP(hAPP(c_Product__Type_OPair(X26712,X26714),esk237_5(X26710,X26711,X26712,X26713,X26714)),X26713)),X26711))
| ~ hBOOL(hAPP(hAPP(c_member(X26714),X26713),hAPP(c_Relation_OImage(X26712,X26714,X26711),X26710))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X26718),X26721),X26716))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26718,X26720)),hAPP(hAPP(c_Product__Type_OPair(X26718,X26720),X26721),X26719)),X26717))
| hBOOL(hAPP(hAPP(c_member(X26720),X26719),hAPP(c_Relation_OImage(X26718,X26720,X26717),X26716))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__iff])])])])])]) ).
fof(i_0_6304,plain,
! [X31971,X31972,X31973] :
( ~ hBOOL(hAPP(c_List_Odistinct(X31973),hAPP(hAPP(c_List_Omap(tc_prod(X31973,X31972),X31973),c_Product__Type_Ofst(X31973,X31972)),X31971)))
| hAPP(c_List_Oset(tc_prod(X31973,X31972)),X31971) = hAPP(c_Set_OCollect(tc_prod(X31973,X31972)),hAPP(c_Product__Type_Oprod_Oprod__case(X31973,X31972,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X31973,tc_fun(X31972,tc_Option_Ooption(X31972)),tc_fun(X31972,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X31972),tc_HOL_Obool),tc_fun(tc_fun(X31972,tc_Option_Ooption(X31972)),tc_fun(X31972,tc_HOL_Obool)),X31973),c_COMBB(tc_Option_Ooption(X31972),tc_HOL_Obool,X31972)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X31972),tc_fun(tc_Option_Ooption(X31972),tc_HOL_Obool),X31973),c_fequal),c_Map_Omap__of(X31973,X31972,X31971)))),c_Option_Ooption_OSome(X31972)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__map__of__compr])]) ).
fof(i_0_6305,plain,
! [X26003,X26004,X26005,X26006] :
( ~ c_Finite__Set_Ofolding__one(X26006,X26005,X26004)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26006),X26003))
| X26003 = c_Orderings_Obot__class_Obot(tc_fun(X26006,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X26006),hAPP(hAPP(X26005,esk207_4(X26003,X26004,X26005,X26006)),esk208_4(X26003,X26004,X26005,X26006))),hAPP(hAPP(c_Set_Oinsert(X26006),esk207_4(X26003,X26004,X26005,X26006)),hAPP(hAPP(c_Set_Oinsert(X26006),esk208_4(X26003,X26004,X26005,X26006)),c_Orderings_Obot__class_Obot(tc_fun(X26006,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X26006),hAPP(X26004,X26003)),X26003)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oclosed])])]) ).
cnf(i_0_6306,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)),X5)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X1,X2,X3,X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X3),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5)))),
inference(split_conjunct,[status(thm)],[i_0_5315]) ).
cnf(i_0_6307,plain,
( hAPP(c_Code__Numeral_Oint__of,X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(split_conjunct,[status(thm)],[i_0_5237]) ).
fof(i_0_6308,plain,
! [X28181,X28182,X28183,X28184] :
( ~ c_Fun_Oinj__on(X28184,tc_fun(tc_fun(X28184,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28184,tc_fun(tc_prod(X28184,X28184),tc_HOL_Obool),tc_fun(tc_fun(X28184,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28184,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X28184,X28184),tc_HOL_Obool),tc_fun(tc_fun(X28184,tc_HOL_Obool),tc_HOL_Obool)),X28184),c_Equiv__Relations_Oquotient(X28184)),hAPP(hAPP(c_COMBC(X28184,tc_fun(X28184,tc_HOL_Obool),tc_fun(X28184,tc_HOL_Obool)),c_Set_Oinsert(X28184)),c_Orderings_Obot__class_Obot(tc_fun(X28184,tc_HOL_Obool))))),X28183),X28182)
| ~ hBOOL(hAPP(hAPP(c_member(X28184),X28181),X28182))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X28184),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28184,tc_HOL_Obool)),X28182),hAPP(hAPP(c_Set_Oinsert(X28184),X28181),c_Orderings_Obot__class_Obot(tc_fun(X28184,tc_HOL_Obool))))),X28183) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X28184,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X28184),X28182),X28183)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X28184),hAPP(hAPP(c_Set_Oinsert(X28184),X28181),c_Orderings_Obot__class_Obot(tc_fun(X28184,tc_HOL_Obool)))),X28183)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__diff1])]) ).
fof(i_0_6309,plain,
! [X30932,X30933,X30934,X30935] : hAPP(c_Set_OCollect(X30935),hAPP(hAPP(c_COMBB(tc_fun(X30934,tc_HOL_Obool),tc_HOL_Obool,X30935),c_HOL_OAll(X30934)),hAPP(hAPP(c_COMBB(tc_fun(X30934,tc_HOL_Obool),tc_fun(X30934,tc_HOL_Obool),X30935),hAPP(c_COMBS(X30934,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30934),c_fimplies),hAPP(hAPP(c_COMBC(X30934,tc_fun(X30934,tc_HOL_Obool),tc_HOL_Obool),c_member(X30934)),X30933)))),X30932))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30934,tc_fun(X30935,tc_HOL_Obool)),X30933),hAPP(hAPP(c_COMBB(tc_fun(X30935,tc_HOL_Obool),tc_fun(X30935,tc_HOL_Obool),X30934),c_Set_OCollect(X30935)),hAPP(c_COMBC(X30935,X30934,tc_HOL_Obool),X30932))),
inference(variable_rename,[status(thm)],[fact_Collect__ball__eq]) ).
fof(i_0_6310,plain,
! [X33026,X33027,X33028,X33029] : c_List_Osublist(X33029,hAPP(hAPP(c_List_Oappend(X33029),X33028),X33027),X33026) = hAPP(hAPP(c_List_Oappend(X33029),c_List_Osublist(X33029,X33028,X33026)),c_List_Osublist(X33029,X33027,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33029)),X33028)))),X33026)))),
inference(variable_rename,[status(thm)],[fact_sublist__append]) ).
cnf(i_0_6311,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(split_conjunct,[status(thm)],[i_0_5316]) ).
cnf(i_0_6312,plain,
( hAPP(X4,hAPP(c_Product__Type_Osnd(X3,X1),X5)) = hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X1),X5))
| hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),X5) != hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X6),X5) ),
inference(split_conjunct,[status(thm)],[i_0_5317]) ).
cnf(i_0_6313,plain,
( hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X3),X5)) = hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X3),X5))
| hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),X5) != hAPP(c_Product__Type_Oapfst(X1,X2,X3,X6),X5) ),
inference(split_conjunct,[status(thm)],[i_0_5318]) ).
cnf(i_0_6314,plain,
c_Relation_OId(X1) = hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(tc_prod(X1,X1),tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),tc_prod(X1,X1)),c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1)),c_fequal)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))))),
inference(split_conjunct,[status(thm)],[i_0_5319]) ).
cnf(i_0_6315,plain,
hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(c_Product__Type_Oapfst(X5,X3,X1,X6),X7)) = hAPP(hAPP(c_Product__Type_OPair(X3,X2),hAPP(X6,hAPP(c_Product__Type_Ofst(X5,X1),X7))),hAPP(X4,hAPP(c_Product__Type_Osnd(X5,X1),X7))),
inference(split_conjunct,[status(thm)],[i_0_5320]) ).
cnf(i_0_6316,plain,
hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),hAPP(c_Product__Type_Oapsnd(X5,X3,X1,X6),X7)) = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X5),X7))),hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X5),X7))),
inference(split_conjunct,[status(thm)],[i_0_5321]) ).
fof(i_0_6317,plain,
! [X34006,X34007,X34008,X34009,X34010] : hAPP(hAPP(c_List_Omap(X34010,X34009),X34008),hAPP(c_List_Ofilter(X34010,X34007),X34006)) = c_List_Omap__filter(X34010,X34009,hAPP(hAPP(c_COMBC(X34010,tc_Option_Ooption(X34009),tc_Option_Ooption(X34009)),hAPP(hAPP(c_COMBS(X34010,tc_Option_Ooption(X34009),tc_fun(tc_Option_Ooption(X34009),tc_Option_Ooption(X34009))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X34009),tc_fun(tc_Option_Ooption(X34009),tc_Option_Ooption(X34009))),X34010),c_If(tc_Option_Ooption(X34009))),X34007)),hAPP(hAPP(c_COMBB(X34009,tc_Option_Ooption(X34009),X34010),c_Option_Ooption_OSome(X34009)),X34008))),c_Option_Ooption_ONone(X34009)),X34006),
inference(variable_rename,[status(thm)],[fact_map__filter__map__filter]) ).
fof(i_0_6318,plain,
! [X27866,X27867,X27868] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27868),X27867))
| ~ c_Fun_Oinj__on(X27868,tc_fun(tc_fun(X27868,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X27868,tc_fun(tc_prod(X27868,X27868),tc_HOL_Obool),tc_fun(tc_fun(X27868,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27868,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X27868,X27868),tc_HOL_Obool),tc_fun(tc_fun(X27868,tc_HOL_Obool),tc_HOL_Obool)),X27868),c_Equiv__Relations_Oquotient(X27868)),hAPP(hAPP(c_COMBC(X27868,tc_fun(X27868,tc_HOL_Obool),tc_fun(X27868,tc_HOL_Obool)),c_Set_Oinsert(X27868)),c_Orderings_Obot__class_Obot(tc_fun(X27868,tc_HOL_Obool))))),X27866),X27867)
| hAPP(c_Finite__Set_Ocard(tc_fun(X27868,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27868),X27867),X27866)) = hAPP(c_Finite__Set_Ocard(X27868),X27867) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint])]) ).
fof(i_0_6319,plain,
! [X29268,X29269,X29270,X29271,X29272] : c_Map_Odom(X29272,X29271,hAPP(hAPP(c_COMBS(X29272,tc_Option_Ooption(X29271),tc_Option_Ooption(X29271)),hAPP(hAPP(c_COMBS(X29272,tc_Option_Ooption(X29271),tc_fun(tc_Option_Ooption(X29271),tc_Option_Ooption(X29271))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X29271),tc_fun(tc_Option_Ooption(X29271),tc_Option_Ooption(X29271))),X29272),c_If(tc_Option_Ooption(X29271))),X29270)),X29269)),X29268)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29272,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29272,tc_HOL_Obool)),c_Map_Odom(X29272,X29271,X29269)),hAPP(c_Set_OCollect(X29272),X29270))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29272,tc_HOL_Obool)),c_Map_Odom(X29272,X29271,X29268)),hAPP(c_Set_OCollect(X29272),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29272),c_fNot),X29270)))),
inference(variable_rename,[status(thm)],[fact_dom__if]) ).
fof(i_0_6320,plain,
! [X33960,X33961,X33962,X33963] : c_List_Omap__filter(X33963,X33962,X33961,X33960) = hAPP(hAPP(c_List_Omap(X33963,X33962),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X33962),X33962,X33963,c_Option_Othe(X33962)),X33961)),hAPP(c_List_Ofilter(X33963,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33963),c_fNot),hAPP(hAPP(c_COMBC(X33963,tc_Option_Ooption(X33962),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X33962),tc_fun(tc_Option_Ooption(X33962),tc_HOL_Obool),X33963),c_fequal),X33961)),c_Option_Ooption_ONone(X33962)))),X33960)),
inference(variable_rename,[status(thm)],[fact_map__filter__def]) ).
fof(i_0_6321,plain,
! [X23404,X23405,X23406,X23407] :
( ~ class_Rings_Ocomm__semiring__1(X23407)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23407),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23407),c_Groups_Oone__class_Oone(X23407)),c_Groups_Oone__class_Oone(X23407))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23407),hAPP(hAPP(c_COMBB(X23407,X23407,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X23407),X23406)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X23407,X23407),hAPP(hAPP(c_COMBB(X23407,tc_fun(X23407,X23407),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X23407)),c_Nat_Osemiring__1__class_Oof__nat(X23407))),X23405))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X23404))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23407),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23407),X23404)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23407),X23406),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23407),X23406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23407),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23407),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23404),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X23405)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__series__general])]) ).
fof(i_0_6322,plain,
! [X25650,X25651] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25651),X25650))
| c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25650,X25651) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty])]) ).
fof(i_0_6323,plain,
! [X25636,X25637] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25637),X25636))
| c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X25636,X25637) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty])]) ).
fof(i_0_6324,plain,
! [X23678,X23679] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),esk125_2(X23678,X23679)),esk126_2(X23678,X23679)))
| c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X23679,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X23678)
| ~ class_Orderings_Oorder(X23679) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),esk126_2(X23678,X23679)),esk125_2(X23678,X23679)))
| c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X23679,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X23678)
| ~ class_Orderings_Oorder(X23679) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23679),hAPP(X23678,esk125_2(X23678,X23679))),hAPP(X23678,esk126_2(X23678,X23679))))
| c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X23679,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X23678)
| ~ class_Orderings_Oorder(X23679) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5322])])])]) ).
fof(i_0_6325,plain,
! [X24903,X24904] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24904),X24903))
| c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X24903,X24904) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanLessThan__empty])]) ).
cnf(i_0_6326,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5323]) ).
fof(i_0_6327,plain,
! [X29674,X29675] :
( ( c_Wellfounded_Owf(X29675,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool),tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool)),X29674))
| ~ c_FunDef_Oreduction__pair(X29675,X29674) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29675,X29675,X29675),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool),tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool)),X29674)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool),tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool)),X29674))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool),tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool)),X29674)))
| ~ c_FunDef_Oreduction__pair(X29675,X29674) )
& ( ~ c_Wellfounded_Owf(X29675,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool),tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool)),X29674))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29675,X29675,X29675),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool),tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool)),X29674)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool),tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool)),X29674))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool),tc_fun(tc_prod(X29675,X29675),tc_HOL_Obool)),X29674)))
| c_FunDef_Oreduction__pair(X29675,X29674) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__def])])]) ).
cnf(i_0_6328,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X2)))),
inference(split_conjunct,[status(thm)],[i_0_5324]) ).
cnf(i_0_6329,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5325]) ).
cnf(i_0_6330,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X2)))),
inference(split_conjunct,[status(thm)],[i_0_5326]) ).
fof(i_0_6331,plain,
! [X24258,X24259,X24260,X24261,X24262,X24263,X24264,X24265,X24266,X24267,X24268] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24262,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24261,tc_fun(X24262,tc_HOL_Obool)),X24260),X24259)),X24258))
| ~ hBOOL(hAPP(hAPP(c_member(X24261),X24263),X24260))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24262,tc_HOL_Obool)),hAPP(X24259,X24263)),X24258)) )
& ( hBOOL(hAPP(hAPP(c_member(X24267),esk144_5(X24264,X24265,X24266,X24267,X24268)),X24266))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24268,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24267,tc_fun(X24268,tc_HOL_Obool)),X24266),X24265)),X24264)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24268,tc_HOL_Obool)),hAPP(X24265,esk144_5(X24264,X24265,X24266,X24267,X24268))),X24264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24268,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24267,tc_fun(X24268,tc_HOL_Obool)),X24266),X24265)),X24264)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__subset__iff])])])])])]) ).
fof(i_0_6332,plain,
! [X25614,X25615,X25616,X25617,X25618] :
( ( hBOOL(hAPP(hAPP(c_member(X25617),esk189_5(X25614,X25615,X25616,X25617,X25618)),X25616))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25618),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25617,X25618),X25615),X25616)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25618),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25618),hAPP(c_Finite__Set_Ocard(X25617),X25616))),X25614)))
| ~ class_Groups_Oordered__ab__semigroup__add(X25618)
| ~ class_Rings_Osemiring__1(X25618) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25618),hAPP(X25615,esk189_5(X25614,X25615,X25616,X25617,X25618))),X25614))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25618),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25617,X25618),X25615),X25616)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25618),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25618),hAPP(c_Finite__Set_Ocard(X25617),X25616))),X25614)))
| ~ class_Groups_Oordered__ab__semigroup__add(X25618)
| ~ class_Rings_Osemiring__1(X25618) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__bounded])])])]) ).
cnf(i_0_6333,plain,
hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X2,X3)),c_Int_Onat)))),
inference(split_conjunct,[status(thm)],[i_0_5327]) ).
fof(i_0_6334,plain,
! [X28948,X28949,X28950,X28951,X28952,X28953] : c_Product__Type_Omap__pair(X28953,X28952,X28951,X28950,X28949,X28948) = hAPP(c_Product__Type_Oprod_Oprod__case(X28953,X28951,tc_prod(X28952,X28950)),hAPP(hAPP(c_COMBC(X28953,tc_fun(X28951,X28950),tc_fun(X28951,tc_prod(X28952,X28950))),hAPP(hAPP(c_COMBB(tc_fun(X28950,tc_prod(X28952,X28950)),tc_fun(tc_fun(X28951,X28950),tc_fun(X28951,tc_prod(X28952,X28950))),X28953),c_COMBB(X28950,tc_prod(X28952,X28950),X28951)),hAPP(hAPP(c_COMBB(X28952,tc_fun(X28950,tc_prod(X28952,X28950)),X28953),c_Product__Type_OPair(X28952,X28950)),X28949))),X28948)),
inference(variable_rename,[status(thm)],[fact_map__pair__def]) ).
fof(i_0_6335,plain,
! [X20585,X20586,X20587] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20586),X20585))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X20587))),X20585)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__lemma])]) ).
fof(i_0_6336,plain,
! [X24244,X24245,X24246,X24247,X24248,X24249] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24248),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24247,X24248),X24246),X24245)),X24244))
| ~ hBOOL(hAPP(hAPP(c_member(X24247),X24249),X24246))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24248),hAPP(X24245,X24249)),X24244))
| ~ class_Complete__Lattice_Ocomplete__lattice(X24248) )
& ( hBOOL(hAPP(hAPP(c_member(X24247),esk142_5(X24244,X24245,X24246,X24247,X24248)),X24246))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24248),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24247,X24248),X24246),X24245)),X24244))
| ~ class_Complete__Lattice_Ocomplete__lattice(X24248) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24248),hAPP(X24245,esk142_5(X24244,X24245,X24246,X24247,X24248))),X24244))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24248),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24247,X24248),X24246),X24245)),X24244))
| ~ class_Complete__Lattice_Ocomplete__lattice(X24248) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__le__iff])])])])]) ).
cnf(i_0_6337,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5282]) ).
cnf(i_0_6338,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I4_J]) ).
cnf(i_0_6339,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I4_J]) ).
fof(i_0_6340,plain,
! [X33040,X33041,X33042,X33043,X33045,X33046,X33047,X33048,X33049] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk459_4(X33040,X33041,X33042,X33043)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33042)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33041))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33042)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33041)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33043),tc_List_Olist(X33043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33043),tc_List_Olist(X33043)),X33042),X33041)),c_List_Olexord(X33043,X33040))) )
& ( hAPP(hAPP(c_List_Otake(X33043),esk459_4(X33040,X33041,X33042,X33043)),X33042) = hAPP(hAPP(c_List_Otake(X33043),esk459_4(X33040,X33041,X33042,X33043)),X33041)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33042)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33041)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33043),tc_List_Olist(X33043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33043),tc_List_Olist(X33043)),X33042),X33041)),c_List_Olexord(X33043,X33040))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33043,X33043)),hAPP(hAPP(c_Product__Type_OPair(X33043,X33043),hAPP(hAPP(c_List_Onth(X33043),X33042),esk459_4(X33040,X33041,X33042,X33043))),hAPP(hAPP(c_List_Onth(X33043),X33041),esk459_4(X33040,X33041,X33042,X33043)))),X33040))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33042)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33041)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33043),tc_List_Olist(X33043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33043),tc_List_Olist(X33043)),X33042),X33041)),c_List_Olexord(X33043,X33040))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk459_4(X33040,X33041,X33042,X33043)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33042)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33041))))
| hAPP(hAPP(c_List_Otake(X33043),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33042)),X33041) = X33042
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33043),tc_List_Olist(X33043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33043),tc_List_Olist(X33043)),X33042),X33041)),c_List_Olexord(X33043,X33040))) )
& ( hAPP(hAPP(c_List_Otake(X33043),esk459_4(X33040,X33041,X33042,X33043)),X33042) = hAPP(hAPP(c_List_Otake(X33043),esk459_4(X33040,X33041,X33042,X33043)),X33041)
| hAPP(hAPP(c_List_Otake(X33043),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33042)),X33041) = X33042
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33043),tc_List_Olist(X33043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33043),tc_List_Olist(X33043)),X33042),X33041)),c_List_Olexord(X33043,X33040))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33043,X33043)),hAPP(hAPP(c_Product__Type_OPair(X33043,X33043),hAPP(hAPP(c_List_Onth(X33043),X33042),esk459_4(X33040,X33041,X33042,X33043))),hAPP(hAPP(c_List_Onth(X33043),X33041),esk459_4(X33040,X33041,X33042,X33043)))),X33040))
| hAPP(hAPP(c_List_Otake(X33043),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33043)),X33042)),X33041) = X33042
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33043),tc_List_Olist(X33043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33043),tc_List_Olist(X33043)),X33042),X33041)),c_List_Olexord(X33043,X33040))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33048)),X33047)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33048)),X33046)))
| hAPP(hAPP(c_List_Otake(X33048),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33048)),X33047)),X33046) != X33047
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33048),tc_List_Olist(X33048))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33048),tc_List_Olist(X33048)),X33047),X33046)),c_List_Olexord(X33048,X33045))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33049),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33048)),X33047)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33048)),X33046))))
| hAPP(hAPP(c_List_Otake(X33048),X33049),X33047) != hAPP(hAPP(c_List_Otake(X33048),X33049),X33046)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33048,X33048)),hAPP(hAPP(c_Product__Type_OPair(X33048,X33048),hAPP(hAPP(c_List_Onth(X33048),X33047),X33049)),hAPP(hAPP(c_List_Onth(X33048),X33046),X33049))),X33045))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33048),tc_List_Olist(X33048))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33048),tc_List_Olist(X33048)),X33047),X33046)),c_List_Olexord(X33048,X33045))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__take__index__conv])])])])])]) ).
fof(i_0_6341,plain,
! [X29575,X29576,X29577,X29578,X29579,X29580,X29581,X29582] :
( ~ hBOOL(hAPP(hAPP(X29582,X29581),X29580))
| ~ hBOOL(hAPP(hAPP(X29579,X29580),X29578))
| c_Predicate_Opred__comp(X29577,X29576,X29575,X29582,X29579,X29581,X29578) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp_Ointros])]) ).
cnf(i_0_6342,plain,
c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
inference(split_conjunct,[status(thm)],[i_0_5328]) ).
fof(i_0_6343,plain,
! [X29219,X29220,X29221,X29222] : hAPP(c_Set_OCollect(tc_prod(X29222,X29221)),hAPP(c_Product__Type_Oprod_Oprod__case(X29222,X29221,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X29222,tc_fun(X29221,tc_HOL_Obool),tc_fun(X29221,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29221,tc_HOL_Obool),tc_fun(X29221,tc_HOL_Obool)),X29222),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29221)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29222),c_fconj),X29220))),X29219))) = hAPP(hAPP(c_Product__Type_OSigma(X29222,X29221),hAPP(c_Set_OCollect(X29222),X29220)),hAPP(hAPP(c_COMBB(tc_fun(X29221,tc_HOL_Obool),tc_fun(X29221,tc_HOL_Obool),X29222),c_Set_OCollect(X29221)),X29219)),
inference(variable_rename,[status(thm)],[fact_SetCompr__Sigma__eq]) ).
fof(i_0_6344,plain,
! [X29300,X29301] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29301))
| hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X29301))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X29300))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less])]) ).
fof(i_0_6345,plain,
! [X30030,X30031,X30032,X30033] : c_Hilbert__Choice_OEps(tc_prod(X30033,X30032),hAPP(c_Product__Type_Oprod_Oprod__case(X30033,X30032,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X30033,tc_fun(X30032,tc_HOL_Obool),tc_fun(X30032,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X30032,tc_HOL_Obool),tc_fun(X30032,tc_HOL_Obool)),X30033),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X30032)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30033),c_fconj),hAPP(c_fequal,X30031)))),hAPP(c_fequal,X30030)))) = hAPP(hAPP(c_Product__Type_OPair(X30033,X30032),X30031),X30030),
inference(variable_rename,[status(thm)],[fact_Eps__split__eq]) ).
fof(i_0_6346,plain,
! [X22976,X22977,X22978,X22979] : c_HOL_OThe(tc_prod(X22979,X22978),hAPP(c_Product__Type_Oprod_Oprod__case(X22979,X22978,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X22979,tc_fun(X22978,tc_HOL_Obool),tc_fun(X22978,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X22978,tc_HOL_Obool),tc_fun(X22978,tc_HOL_Obool)),X22979),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X22978)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X22979),c_fconj),hAPP(c_fequal,X22977)))),hAPP(c_fequal,X22976)))) = hAPP(hAPP(c_Product__Type_OPair(X22979,X22978),X22977),X22976),
inference(variable_rename,[status(thm)],[fact_The__split__eq]) ).
cnf(i_0_6347,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_5316]) ).
fof(i_0_6348,plain,
! [X23240,X23241,X23242,X23243,X23244,X23245] :
( ~ class_Groups_Ocomm__monoid__add(X23245)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23244,X23245),hAPP(hAPP(c_COMBC(X23244,tc_fun(X23243,tc_HOL_Obool),X23245),hAPP(hAPP(c_COMBB(tc_fun(X23243,X23245),tc_fun(tc_fun(X23243,tc_HOL_Obool),X23245),X23244),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23243,X23245)),X23242)),X23241)),X23240) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23243,X23245),hAPP(hAPP(c_COMBC(X23243,tc_fun(X23244,tc_HOL_Obool),X23245),hAPP(hAPP(c_COMBB(tc_fun(X23244,X23245),tc_fun(tc_fun(X23244,tc_HOL_Obool),X23245),X23243),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23244,X23245)),hAPP(c_COMBC(X23244,X23243,X23245),X23242))),X23240)),X23241) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__commute])]) ).
fof(i_0_6349,plain,
! [X29215,X29216,X29217,X29218] : hAPP(c_Set_OCollect(tc_prod(X29218,X29217)),hAPP(c_Product__Type_Oprod_Oprod__case(X29218,X29217,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29218,tc_fun(X29217,tc_HOL_Obool),tc_fun(X29217,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29217,tc_HOL_Obool),tc_fun(X29217,tc_HOL_Obool)),X29218),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29217)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29218),c_fconj),X29216))),X29215))) = hAPP(hAPP(c_Product__Type_OSigma(X29218,X29217),hAPP(c_Set_OCollect(X29218),X29216)),hAPP(c_COMBK(tc_fun(X29217,tc_HOL_Obool),X29218),hAPP(c_Set_OCollect(X29217),X29215))),
inference(variable_rename,[status(thm)],[fact_Collect__split]) ).
fof(i_0_6350,plain,
! [X28190,X28191,X28192,X28193] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28193),X28192))
| hAPP(c_Set_Oimage(X28193,X28191,X28190),X28192) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X28191,tc_HOL_Obool),X28193,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28191,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X28193,tc_fun(X28191,tc_HOL_Obool),tc_fun(X28191,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X28191,tc_fun(tc_fun(X28191,tc_HOL_Obool),tc_fun(X28191,tc_HOL_Obool)),X28193),c_Set_Oinsert(X28191)),X28190)),c_Orderings_Obot__class_Obot(tc_fun(X28191,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X28191,tc_HOL_Obool))),X28192) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image])]) ).
cnf(i_0_6351,plain,
c_List_Oconcat(tc_List_Olist(X1),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
inference(split_conjunct,[status(thm)],[i_0_5329]) ).
fof(i_0_6352,plain,
! [X25414,X25415,X25416,X25417] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25417),X25416))
| ~ hBOOL(hAPP(hAPP(c_member(X25417),X25415),X25416))
| ~ hBOOL(hAPP(hAPP(c_member(X25417),X25414),X25416))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25417),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25417,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25417,tc_HOL_Obool)),X25416),hAPP(hAPP(c_Set_Oinsert(X25417),X25415),c_Orderings_Obot__class_Obot(tc_fun(X25417,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X25417),X25414),c_Orderings_Obot__class_Obot(tc_fun(X25417,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X25417),X25416))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff2__less])]) ).
cnf(i_0_6353,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Relation_OId(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2)),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5330]) ).
fof(i_0_6354,plain,
! [X26425,X26426] : c_Relation_OId__on(X26426,X26425) = hAPP(c_Product__Type_Oprod_Oprod__case(X26426,X26426,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X26426,tc_HOL_Obool,tc_fun(X26426,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26426,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X26426,tc_HOL_Obool)),X26426),c_COMBC(X26426,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26426,tc_HOL_Obool),tc_fun(X26426,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X26426),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26426),c_fconj)),c_fequal))),X26425)),
inference(variable_rename,[status(thm)],[fact_Id__on__def_H]) ).
fof(i_0_6355,plain,
! [X29354] : c_Int_Oint__ge__less__than(X29354) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29354)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_int__ge__less__than__def]) ).
fof(i_0_6356,plain,
! [X22785,X22786,X22787,X22788,X22789,X22790,X22791,X22792,X22793] : hAPP(hAPP(c_Product__Type_Oscomp(X22793,X22792,X22791,X22790),hAPP(hAPP(c_Product__Type_Oscomp(X22793,X22789,X22788,tc_prod(X22792,X22791)),X22787),X22786)),X22785) = hAPP(hAPP(c_Product__Type_Oscomp(X22793,X22789,X22788,X22790),X22787),hAPP(hAPP(c_COMBC(X22789,tc_fun(X22792,tc_fun(X22791,X22790)),tc_fun(X22788,X22790)),hAPP(hAPP(c_COMBB(tc_fun(X22788,tc_prod(X22792,X22791)),tc_fun(tc_fun(X22792,tc_fun(X22791,X22790)),tc_fun(X22788,X22790)),X22789),c_Product__Type_Oscomp(X22788,X22792,X22791,X22790)),X22786)),X22785)),
inference(variable_rename,[status(thm)],[fact_scomp__scomp]) ).
fof(i_0_6357,plain,
! [X26356,X26357,X26358,X26359] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26359),X26358))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26357),X26359)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X26356),X26358)),c_FunDef_Omax__weak))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26357),X26356)),X26358)),c_FunDef_Omax__weak)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__insertI])]) ).
fof(i_0_6358,plain,
! [X26346,X26347,X26348,X26349] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26349),X26348))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26347),X26349)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X26346),X26348)),c_FunDef_Omax__strict))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26347),X26346)),X26348)),c_FunDef_Omax__strict)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__insertI])]) ).
cnf(i_0_6359,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5302]) ).
cnf(i_0_6360,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5303]) ).
fof(i_0_6361,plain,
! [X34025,X34026,X34027,X34028,X34029] :
( ~ class_Orderings_Olinorder(X34029)
| c_List_Olinorder__class_Osorted(X34029,hAPP(hAPP(c_List_Omap(X34028,X34029),X34027),hAPP(c_List_Ofilter(X34028,hAPP(hAPP(c_COMBC(X34028,X34029,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X34029,tc_fun(X34029,tc_HOL_Obool),X34028),c_fequal),X34027)),hAPP(X34026,X34025))),X34025))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__same])]) ).
fof(i_0_6362,plain,
! [X32379,X32380,X32381,X32382,X32383] :
( ( X32380 = hAPP(hAPP(c_List_Olist_OCons(X32383),esk443_5(X32379,X32380,X32381,X32382,X32383)),esk444_5(X32379,X32380,X32381,X32382,X32383))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32383),tc_List_Olist(X32383))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32383),tc_List_Olist(X32383)),hAPP(hAPP(c_List_Olist_OCons(X32383),X32382),X32381)),X32380)),c_List_Olistrel(X32383,X32379))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32383,X32383)),hAPP(hAPP(c_Product__Type_OPair(X32383,X32383),X32382),esk443_5(X32379,X32380,X32381,X32382,X32383))),X32379))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32383),tc_List_Olist(X32383))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32383),tc_List_Olist(X32383)),hAPP(hAPP(c_List_Olist_OCons(X32383),X32382),X32381)),X32380)),c_List_Olistrel(X32383,X32379))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32383),tc_List_Olist(X32383))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32383),tc_List_Olist(X32383)),X32381),esk444_5(X32379,X32380,X32381,X32382,X32383))),c_List_Olistrel(X32383,X32379)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32383),tc_List_Olist(X32383))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32383),tc_List_Olist(X32383)),hAPP(hAPP(c_List_Olist_OCons(X32383),X32382),X32381)),X32380)),c_List_Olistrel(X32383,X32379))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5331])])])]) ).
cnf(i_0_6363,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5332]) ).
fof(i_0_6364,plain,
! [X26777,X26778,X26779,X26780,X26781] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X26781,X26780,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X26781)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X26781),c_Hoare__Mirabelle_Opeek__and(X26781,X26779,X26778)),X26777),X26779)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X26781),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(X26781,X26780,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X26781)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X26781),X26779),c_Com_Ocom_OWhile(X26778,X26777)),c_Hoare__Mirabelle_Opeek__and(X26781,X26779,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X26778)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X26781),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Loop])]) ).
cnf(i_0_6365,plain,
c_List_Osublist(X1,X2,X3) = hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X3)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))),
inference(split_conjunct,[status(thm)],[i_0_5333]) ).
fof(i_0_6366,plain,
! [X30060,X30061,X30062,X30063,X30064,X30066,X30067,X30068,X30069,X30071] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X30063),X30062))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30063,tc_HOL_Obool),tc_fun(X30063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30063,tc_HOL_Obool),tc_fun(X30063,tc_HOL_Obool)),X30062),X30061)),c_Wellfounded_Omax__ext(X30063,X30060))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X30063),X30061))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30063,tc_HOL_Obool),tc_fun(X30063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30063,tc_HOL_Obool),tc_fun(X30063,tc_HOL_Obool)),X30062),X30061)),c_Wellfounded_Omax__ext(X30063,X30060))) )
& ( X30061 != c_Orderings_Obot__class_Obot(tc_fun(X30063,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30063,tc_HOL_Obool),tc_fun(X30063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30063,tc_HOL_Obool),tc_fun(X30063,tc_HOL_Obool)),X30062),X30061)),c_Wellfounded_Omax__ext(X30063,X30060))) )
& ( hBOOL(hAPP(hAPP(c_member(X30063),esk357_5(X30060,X30061,X30062,X30063,X30064)),X30061))
| ~ hBOOL(hAPP(hAPP(c_member(X30063),X30064),X30062))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30063,tc_HOL_Obool),tc_fun(X30063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30063,tc_HOL_Obool),tc_fun(X30063,tc_HOL_Obool)),X30062),X30061)),c_Wellfounded_Omax__ext(X30063,X30060))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30063,X30063)),hAPP(hAPP(c_Product__Type_OPair(X30063,X30063),X30064),esk357_5(X30060,X30061,X30062,X30063,X30064))),X30060))
| ~ hBOOL(hAPP(hAPP(c_member(X30063),X30064),X30062))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30063,tc_HOL_Obool),tc_fun(X30063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30063,tc_HOL_Obool),tc_fun(X30063,tc_HOL_Obool)),X30062),X30061)),c_Wellfounded_Omax__ext(X30063,X30060))) )
& ( hBOOL(hAPP(hAPP(c_member(X30069),esk358_4(X30066,X30067,X30068,X30069)),X30068))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30069),X30068))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30069),X30067))
| X30067 = c_Orderings_Obot__class_Obot(tc_fun(X30069,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30069,tc_HOL_Obool),tc_fun(X30069,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30069,tc_HOL_Obool),tc_fun(X30069,tc_HOL_Obool)),X30068),X30067)),c_Wellfounded_Omax__ext(X30069,X30066))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X30069),X30071),X30067))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30069,X30069)),hAPP(hAPP(c_Product__Type_OPair(X30069,X30069),esk358_4(X30066,X30067,X30068,X30069)),X30071)),X30066))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30069),X30068))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30069),X30067))
| X30067 = c_Orderings_Obot__class_Obot(tc_fun(X30069,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30069,tc_HOL_Obool),tc_fun(X30069,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30069,tc_HOL_Obool),tc_fun(X30069,tc_HOL_Obool)),X30068),X30067)),c_Wellfounded_Omax__ext(X30069,X30066))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext_Osimps])])])])])]) ).
fof(i_0_6367,plain,
! [X29598,X29599,X29600] :
( ( ~ c_Wellfounded_Owf(X29600,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29600,X29600),tc_HOL_Obool)),X29599),X29598))
| c_Wellfounded_Owf(X29600,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29600,X29600),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29600,X29600),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29600,X29600,X29600),X29599),X29599)),hAPP(hAPP(c_Relation_Orel__comp(X29600,X29600,X29600),X29598),X29599))),X29598)) )
& ( ~ c_Wellfounded_Owf(X29600,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29600,X29600),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29600,X29600),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29600,X29600,X29600),X29599),X29599)),hAPP(hAPP(c_Relation_Orel__comp(X29600,X29600,X29600),X29598),X29599))),X29598))
| c_Wellfounded_Owf(X29600,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29600,X29600),tc_HOL_Obool)),X29599),X29598)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__merge])]) ).
fof(i_0_6368,plain,
! [X28954,X28955,X28956,X28957,X28958,X28959,X28960,X28961,X28962,X28963] :
( hAPP(c_Set_Oimage(X28963,X28962,X28961),X28960) != X28959
| hAPP(c_Set_Oimage(X28958,X28957,X28956),X28955) != X28954
| hAPP(c_Set_Oimage(tc_prod(X28963,X28958),tc_prod(X28962,X28957),c_Product__Type_Omap__pair(X28963,X28962,X28958,X28957,X28961,X28956)),hAPP(hAPP(c_Product__Type_OSigma(X28963,X28958),X28960),hAPP(c_COMBK(tc_fun(X28958,tc_HOL_Obool),X28963),X28955))) = hAPP(hAPP(c_Product__Type_OSigma(X28962,X28957),X28959),hAPP(c_COMBK(tc_fun(X28957,tc_HOL_Obool),X28962),X28954)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj__on])]) ).
fof(i_0_6369,plain,
! [X26360,X26361,X26362,X26363] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26363),X26362))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26363),X26361)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X26362),X26360)),c_FunDef_Omin__weak))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X26362),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26361),X26360))),c_FunDef_Omin__weak)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmin__insertI])]) ).
fof(i_0_6370,plain,
! [X26342,X26343,X26344,X26345] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26345),X26344))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26345),X26343)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X26344),X26342)),c_FunDef_Omin__strict))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X26344),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26343),X26342))),c_FunDef_Omin__strict)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smin__insertI])]) ).
fof(i_0_6371,plain,
! [X28610,X28611,X28612,X28613,X28614] :
( ( hAPP(hAPP(c_Set_Oinsert(X28614),X28612),X28611) = hAPP(hAPP(c_Set_Oinsert(X28614),esk281_5(X28610,X28611,X28612,X28613,X28614)),esk282_5(X28610,X28611,X28612,X28613,X28614))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28614,X28613,hAPP(hAPP(c_Set_Oinsert(X28614),X28612),X28611)),X28610)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28614,X28614,X28613,esk281_5(X28610,X28611,X28612,X28613,X28614),esk282_5(X28610,X28611,X28612,X28613,X28614)),X28610))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28614,X28613,hAPP(hAPP(c_Set_Oinsert(X28614),X28612),X28611)),X28610)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28614),esk281_5(X28610,X28611,X28612,X28613,X28614)),esk282_5(X28610,X28611,X28612,X28613,X28614)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28614,X28613,hAPP(hAPP(c_Set_Oinsert(X28614),X28612),X28611)),X28610)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__fold1SetE])])])]) ).
fof(i_0_6372,plain,
! [X28596,X28597,X28598,X28599,X28600,X28603,X28604,X28605,X28606,X28607,X28608,X28609] :
( ( hAPP(hAPP(c_Set_Oinsert(X28600),X28598),X28597) = hAPP(hAPP(c_Set_Oinsert(X28600),esk279_5(X28596,X28597,X28598,X28599,X28600)),esk280_5(X28596,X28597,X28598,X28599,X28600))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28600,X28599,hAPP(hAPP(c_Set_Oinsert(X28600),X28598),X28597)),X28596)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28600,X28600,X28599,esk279_5(X28596,X28597,X28598,X28599,X28600),esk280_5(X28596,X28597,X28598,X28599,X28600)),X28596))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28600,X28599,hAPP(hAPP(c_Set_Oinsert(X28600),X28598),X28597)),X28596)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28600),esk279_5(X28596,X28597,X28598,X28599,X28600)),esk280_5(X28596,X28597,X28598,X28599,X28600)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28600,X28599,hAPP(hAPP(c_Set_Oinsert(X28600),X28598),X28597)),X28596)) )
& ( hAPP(hAPP(c_Set_Oinsert(X28607),X28605),X28604) != hAPP(hAPP(c_Set_Oinsert(X28607),X28608),X28609)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28607,X28607,X28606,X28608,X28609),X28603))
| hBOOL(hAPP(hAPP(c_member(X28607),X28608),X28609))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28607,X28606,hAPP(hAPP(c_Set_Oinsert(X28607),X28605),X28604)),X28603)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5334])])])])])]) ).
fof(i_0_6373,plain,
! [X33292,X33293,X33294,X33295,X33298,X33299,X33300,X33301,X33302,X33303] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33295,X33295)),hAPP(hAPP(c_Product__Type_OPair(X33295,X33295),hAPP(hAPP(c_List_Onth(X33295),X33294),esk462_4(X33292,X33293,X33294,X33295))),esk461_4(X33292,X33293,X33294,X33295))),X33292))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33295),tc_List_Olist(X33295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33295),tc_List_Olist(X33295)),X33294),X33293)),c_List_Olistrel1(X33295,X33292))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk462_4(X33292,X33293,X33294,X33295)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33295)),X33294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33295),tc_List_Olist(X33295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33295),tc_List_Olist(X33295)),X33294),X33293)),c_List_Olistrel1(X33295,X33292))) )
& ( X33293 = hAPP(hAPP(c_List_Olist__update(X33295,X33294),esk462_4(X33292,X33293,X33294,X33295)),esk461_4(X33292,X33293,X33294,X33295))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33295),tc_List_Olist(X33295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33295),tc_List_Olist(X33295)),X33294),X33293)),c_List_Olistrel1(X33295,X33292))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33301,X33301)),hAPP(hAPP(c_Product__Type_OPair(X33301,X33301),hAPP(hAPP(c_List_Onth(X33301),X33300),X33303)),X33302)),X33298))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33303),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33301)),X33300)))
| X33299 != hAPP(hAPP(c_List_Olist__update(X33301,X33300),X33303),X33302)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33301),tc_List_Olist(X33301))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33301),tc_List_Olist(X33301)),X33300),X33299)),c_List_Olistrel1(X33301,X33298))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__iff__update])])])])])]) ).
fof(i_0_6374,plain,
! [X28857,X28858,X28859,X28860,X28861,X28862] :
( hAPP(c_Set_Oimage(X28862,X28861,X28860),c_Orderings_Otop__class_Otop(tc_fun(X28862,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28861,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X28859,X28858,X28857),c_Orderings_Otop__class_Otop(tc_fun(X28859,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28858,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X28862,X28859),tc_prod(X28861,X28858),c_Product__Type_Omap__pair(X28862,X28861,X28859,X28858,X28860,X28857)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X28862,X28859),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X28861,X28858),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj])]) ).
fof(i_0_6375,plain,
! [X30750,X30751,X30752] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30752),X30751))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30752,tc_HOL_Obool)),X30750),X30751) = hAPP(hAPP(c_Finite__Set_Ofold(X30752,tc_fun(X30752,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30752,tc_HOL_Obool),tc_fun(tc_fun(X30752,tc_HOL_Obool),tc_fun(X30752,tc_HOL_Obool)),X30752),hAPP(c_COMBC(tc_fun(X30752,tc_HOL_Obool),tc_fun(X30752,tc_HOL_Obool),tc_fun(X30752,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X30752,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X30752,tc_fun(X30752,tc_HOL_Obool),tc_fun(X30752,tc_HOL_Obool)),c_Set_Oinsert(X30752)),c_Orderings_Obot__class_Obot(tc_fun(X30752,tc_HOL_Obool))))),X30750),X30751) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__fold__remove])]) ).
fof(i_0_6376,plain,
! [X31706,X31707,X31708,X31709,X31710,X31711,X31712] :
( ~ c_Fun_Oinj__on(X31712,X31711,X31710,c_Orderings_Otop__class_Otop(tc_fun(X31712,tc_HOL_Obool)))
| hAPP(c_Map_Omap__of(X31712,X31709,X31708),X31707) != hAPP(c_Option_Ooption_OSome(X31709),X31706)
| hAPP(c_Map_Omap__of(X31711,X31709,hAPP(hAPP(c_List_Omap(tc_prod(X31712,X31709),tc_prod(X31711,X31709)),hAPP(c_Product__Type_Oprod_Oprod__case(X31712,X31709,tc_prod(X31711,X31709)),hAPP(hAPP(c_COMBB(X31711,tc_fun(X31709,tc_prod(X31711,X31709)),X31712),c_Product__Type_OPair(X31711,X31709)),X31710))),X31708)),hAPP(X31710,X31707)) = hAPP(c_Option_Ooption_OSome(X31709),X31706) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__mapk__SomeI])]) ).
cnf(i_0_6377,plain,
( hAPP(c_Product__Type_Oapsnd(X3,X6,X2,X1),X4) = hAPP(c_Product__Type_Oapsnd(X3,X6,X2,X5),X4)
| hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)) != hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_5317]) ).
cnf(i_0_6378,plain,
( hAPP(c_Product__Type_Oapfst(X2,X6,X3,X1),X4) = hAPP(c_Product__Type_Oapfst(X2,X6,X3,X5),X4)
| hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)) != hAPP(X5,hAPP(c_Product__Type_Ofst(X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_5318]) ).
cnf(i_0_6379,plain,
c_Nitpick_Ouminus__frac(X1,X2) = c_Nitpick_OAbs__Frac(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X2))),hAPP(c_Nitpick_Odenom(X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_5335]) ).
cnf(i_0_6380,plain,
hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Oapsnd(X3,X2,X1,X4),X5)) = hAPP(X4,hAPP(c_Product__Type_Osnd(X1,X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_5336]) ).
cnf(i_0_6381,plain,
hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Oapfst(X3,X1,X2,X4),X5)) = hAPP(X4,hAPP(c_Product__Type_Ofst(X3,X2),X5)),
inference(split_conjunct,[status(thm)],[i_0_5337]) ).
fof(i_0_6382,plain,
! [X28933,X28934,X28935,X28936,X28937,X28938,X28939] : hAPP(c_Product__Type_Ofst(X28939,X28938),hAPP(c_Product__Type_Omap__pair(X28937,X28939,X28936,X28938,X28935,X28934),X28933)) = hAPP(X28935,hAPP(c_Product__Type_Ofst(X28937,X28936),X28933)),
inference(variable_rename,[status(thm)],[fact_fst__map__pair]) ).
fof(i_0_6383,plain,
! [X28926,X28927,X28928,X28929,X28930,X28931,X28932] : hAPP(c_Product__Type_Osnd(X28932,X28931),hAPP(c_Product__Type_Omap__pair(X28930,X28932,X28929,X28931,X28928,X28927),X28926)) = hAPP(X28927,hAPP(c_Product__Type_Osnd(X28930,X28929),X28926)),
inference(variable_rename,[status(thm)],[fact_snd__prod__fun]) ).
cnf(i_0_6384,plain,
hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Oapsnd(X3,X2,X1,X4),X5)) = hAPP(c_Product__Type_Ofst(X1,X3),X5),
inference(split_conjunct,[status(thm)],[i_0_5338]) ).
cnf(i_0_6385,plain,
hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Oapfst(X3,X1,X2,X4),X5)) = hAPP(c_Product__Type_Osnd(X3,X2),X5),
inference(split_conjunct,[status(thm)],[i_0_5339]) ).
fof(i_0_6386,plain,
! [X33768,X33769,X33770,X33771] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33771,X33771)),hAPP(hAPP(c_Product__Type_OPair(X33771,X33771),esk472_4(X33768,X33769,X33770,X33771)),esk473_4(X33768,X33769,X33770,X33771))),X33770))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33771),tc_List_Olist(X33771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33771),tc_List_Olist(X33771)),X33769),X33768)),c_List_Olexord(X33771,X33770)))
| X33769 = X33768
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33771),tc_List_Olist(X33771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33771),tc_List_Olist(X33771)),X33768),X33769)),c_List_Olexord(X33771,X33770))) )
& ( esk472_4(X33768,X33769,X33770,X33771) != esk473_4(X33768,X33769,X33770,X33771)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33771),tc_List_Olist(X33771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33771),tc_List_Olist(X33771)),X33769),X33768)),c_List_Olexord(X33771,X33770)))
| X33769 = X33768
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33771),tc_List_Olist(X33771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33771),tc_List_Olist(X33771)),X33768),X33769)),c_List_Olexord(X33771,X33770))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33771,X33771)),hAPP(hAPP(c_Product__Type_OPair(X33771,X33771),esk473_4(X33768,X33769,X33770,X33771)),esk472_4(X33768,X33769,X33770,X33771))),X33770))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33771),tc_List_Olist(X33771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33771),tc_List_Olist(X33771)),X33769),X33768)),c_List_Olexord(X33771,X33770)))
| X33769 = X33768
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33771),tc_List_Olist(X33771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33771),tc_List_Olist(X33771)),X33768),X33769)),c_List_Olexord(X33771,X33770))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__linear])])])]) ).
fof(i_0_6387,plain,
! [X26755,X26756,X26757,X26758] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26758),X26757)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26756),X26755)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26758),X26756)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26757),X26755))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_add]) ).
fof(i_0_6388,plain,
! [X26423,X26424] : c_Relation_OId__on(X26424,X26423) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26424,tc_fun(tc_prod(X26424,X26424),tc_HOL_Obool)),X26423),hAPP(hAPP(c_COMBC(X26424,tc_fun(tc_prod(X26424,X26424),tc_HOL_Obool),tc_fun(tc_prod(X26424,X26424),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X26424,X26424),tc_fun(tc_fun(tc_prod(X26424,X26424),tc_HOL_Obool),tc_fun(tc_prod(X26424,X26424),tc_HOL_Obool)),X26424),c_Set_Oinsert(tc_prod(X26424,X26424))),hAPP(hAPP(c_COMBS(X26424,X26424,tc_prod(X26424,X26424)),c_Product__Type_OPair(X26424,X26424)),c_COMBI(X26424)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X26424,X26424),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_Id__on__def]) ).
fof(i_0_6389,plain,
! [X31699,X31700,X31701,X31702] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),esk431_4(X31699,X31700,X31701,X31702)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk432_4(X31699,X31700,X31701,X31702)),esk433_4(X31699,X31700,X31701,X31702)))))
| hBOOL(hAPP(hAPP(hAPP(X31699,X31702),X31701),X31700))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X31702),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X31701),X31700)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk432_4(X31699,X31700,X31701,X31702)),esk433_4(X31699,X31700,X31701,X31702)))
| hAPP(esk431_4(X31699,X31700,X31701,X31702),esk433_4(X31699,X31700,X31701,X31702)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
| hBOOL(hAPP(hAPP(hAPP(X31699,esk431_4(X31699,X31700,X31701,X31702)),esk432_4(X31699,X31700,X31701,X31702)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk433_4(X31699,X31700,X31701,X31702)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(hAPP(X31699,X31702),X31701),X31700))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X31702),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X31701),X31700)))) )
& ( ~ hBOOL(hAPP(hAPP(hAPP(X31699,esk431_4(X31699,X31700,X31701,X31702)),esk432_4(X31699,X31700,X31701,X31702)),esk433_4(X31699,X31700,X31701,X31702)))
| hBOOL(hAPP(hAPP(hAPP(X31699,X31702),X31701),X31700))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X31702),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X31701),X31700)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5340])])])]) ).
cnf(i_0_6390,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X3),c_Int_Onat))),
inference(split_conjunct,[status(thm)],[i_0_5341]) ).
cnf(i_0_6391,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1)),c_Int_Onat)))),
inference(split_conjunct,[status(thm)],[i_0_5342]) ).
cnf(i_0_6392,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1)),c_Int_Onat)))),
inference(split_conjunct,[status(thm)],[i_0_5343]) ).
fof(i_0_6393,plain,
! [X32069,X32070,X32071,X32072,X32073,X32074,X32075,X32076] : hAPP(hAPP(c_List_Omap(tc_prod(X32076,X32075),X32074),X32073),hAPP(hAPP(c_List_Ozip(X32076,X32075),hAPP(hAPP(c_List_Omap(X32072,X32076),X32071),X32070)),X32069)) = hAPP(hAPP(c_List_Omap(tc_prod(X32072,X32075),X32074),hAPP(c_Product__Type_Oprod_Oprod__case(X32072,X32075,X32074),hAPP(hAPP(c_COMBB(tc_fun(X32075,tc_prod(X32076,X32075)),tc_fun(X32075,X32074),X32072),hAPP(c_COMBB(tc_prod(X32076,X32075),X32074,X32075),X32073)),hAPP(hAPP(c_COMBB(X32076,tc_fun(X32075,tc_prod(X32076,X32075)),X32072),c_Product__Type_OPair(X32076,X32075)),X32071)))),hAPP(hAPP(c_List_Ozip(X32072,X32075),X32070),X32069)),
inference(variable_rename,[status(thm)],[fact_map__zip__map]) ).
fof(i_0_6394,plain,
! [X32841,X32842,X32843,X32844] : c_List_Osublist(X32844,hAPP(hAPP(c_List_Olist_OCons(X32844),X32843),X32842),X32841) = hAPP(hAPP(c_List_Oappend(X32844),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X32844)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32841)),hAPP(hAPP(c_List_Olist_OCons(X32844),X32843),c_List_Olist_ONil(X32844))),c_List_Olist_ONil(X32844))),c_List_Osublist(X32844,X32842,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X32841)))),
inference(variable_rename,[status(thm)],[fact_sublist__Cons]) ).
cnf(i_0_6395,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5344]) ).
fof(i_0_6396,plain,
! [X29302,X29303,X29304,X29305,X29306] : c_Map_Odom(X29306,X29305,c_Fun_Ooverride__on(X29306,tc_Option_Ooption(X29305),X29304,X29303,X29302)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29306,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29306,tc_HOL_Obool)),c_Map_Odom(X29306,X29305,X29304)),hAPP(c_Set_OCollect(X29306),hAPP(hAPP(c_COMBC(X29306,tc_fun(X29306,tc_HOL_Obool),tc_HOL_Obool),c_member(X29306)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29306,tc_HOL_Obool)),X29302),c_Map_Odom(X29306,X29305,X29303)))))),hAPP(c_Set_OCollect(X29306),hAPP(hAPP(c_COMBC(X29306,tc_fun(X29306,tc_HOL_Obool),tc_HOL_Obool),c_member(X29306)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29306,tc_HOL_Obool)),X29302),c_Map_Odom(X29306,X29305,X29303))))),
inference(variable_rename,[status(thm)],[fact_dom__override__on]) ).
fof(i_0_6397,plain,
! [X34369,X34370,X34371,X34372] :
( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34372),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34372))),X34371)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34370),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34372))),c_List_Otranspose(X34372,X34371))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34369),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34372))),hAPP(c_List_Ofilter(tc_List_Olist(X34372),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34372)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34370)),c_Nat_Osize__class_Osize(tc_List_Olist(X34372)))),X34371))))
| hAPP(hAPP(c_List_Onth(X34372),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34372)),c_List_Otranspose(X34372,X34371)),X34370)),X34369) = hAPP(hAPP(c_List_Onth(X34372),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34372)),X34371),X34369)),X34370) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__nth__transpose__sorted])]) ).
cnf(i_0_6398,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5323]) ).
cnf(i_0_6399,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5345]) ).
cnf(i_0_6400,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5346]) ).
cnf(i_0_6401,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5347]) ).
cnf(i_0_6402,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5348]) ).
cnf(i_0_6403,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5325]) ).
cnf(i_0_6404,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5349]) ).
cnf(i_0_6405,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5350]) ).
cnf(i_0_6406,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5351]) ).
fof(i_0_6407,plain,
! [X31054,X31055,X31056,X31057,X31058,X31060] :
( ( hBOOL(hAPP(hAPP(c_member(X31057),esk393_5(X31054,X31055,X31056,X31057,X31058)),X31056))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31058),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31057,X31058),X31056),X31055)),X31054))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31058)
| ~ class_Orderings_Olinorder(X31058) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31058),hAPP(X31055,esk393_5(X31054,X31055,X31056,X31057,X31058))),X31054))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31058),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31057,X31058),X31056),X31055)),X31054))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31058)
| ~ class_Orderings_Olinorder(X31058) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X31057),X31060),X31056))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31058),hAPP(X31055,X31060)),X31054))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31058),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31057,X31058),X31056),X31055)),X31054))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31058)
| ~ class_Orderings_Olinorder(X31058) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__less__iff])])])])]) ).
fof(i_0_6408,plain,
! [X24204,X24205,X24206,X24207,X24208,X24210,X24211,X24212,X24213,X24214,X24215,X24216,X24219] :
( ( hBOOL(hAPP(hAPP(c_member(X24208),esk139_5(X24204,X24205,X24206,X24207,X24208)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24207,tc_fun(X24208,tc_HOL_Obool)),X24206),X24205)))
| ~ hBOOL(hAPP(hAPP(c_member(X24207),X24210),X24206))
| ~ hBOOL(hAPP(hAPP(c_member(X24208),X24211),hAPP(X24205,X24210)))
| hBOOL(hAPP(X24204,X24211)) )
& ( ~ hBOOL(hAPP(X24204,esk139_5(X24204,X24205,X24206,X24207,X24208)))
| ~ hBOOL(hAPP(hAPP(c_member(X24207),X24210),X24206))
| ~ hBOOL(hAPP(hAPP(c_member(X24208),X24211),hAPP(X24205,X24210)))
| hBOOL(hAPP(X24204,X24211)) )
& ( hBOOL(hAPP(hAPP(c_member(X24215),esk140_5(X24212,X24213,X24214,X24215,X24216)),X24214))
| ~ hBOOL(hAPP(hAPP(c_member(X24216),X24219),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24215,tc_fun(X24216,tc_HOL_Obool)),X24214),X24213)))
| hBOOL(hAPP(X24212,X24219)) )
& ( hBOOL(hAPP(hAPP(c_member(X24216),esk141_5(X24212,X24213,X24214,X24215,X24216)),hAPP(X24213,esk140_5(X24212,X24213,X24214,X24215,X24216))))
| ~ hBOOL(hAPP(hAPP(c_member(X24216),X24219),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24215,tc_fun(X24216,tc_HOL_Obool)),X24214),X24213)))
| hBOOL(hAPP(X24212,X24219)) )
& ( ~ hBOOL(hAPP(X24212,esk141_5(X24212,X24213,X24214,X24215,X24216)))
| ~ hBOOL(hAPP(hAPP(c_member(X24216),X24219),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24215,tc_fun(X24216,tc_HOL_Obool)),X24214),X24213)))
| hBOOL(hAPP(X24212,X24219)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ball__UN])])])])])]) ).
cnf(i_0_6409,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J]) ).
fof(i_0_6410,plain,
! [X26366,X26367,X26368,X26369,X26370,X26371] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X26371,tc_HOL_Obool),tc_fun(X26371,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X26371,tc_HOL_Obool),tc_fun(X26371,tc_HOL_Obool)),X26370),X26369)),c_Wellfounded_Omax__ext(X26371,X26368)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X26371,tc_HOL_Obool),tc_fun(X26371,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X26371,tc_HOL_Obool),tc_fun(X26371,tc_HOL_Obool)),X26367),X26366)),c_Wellfounded_Omax__ext(X26371,X26368)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X26371,tc_HOL_Obool),tc_fun(X26371,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X26371,tc_HOL_Obool),tc_fun(X26371,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26371,tc_HOL_Obool)),X26370),X26367)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26371,tc_HOL_Obool)),X26369),X26366))),c_Wellfounded_Omax__ext(X26371,X26368))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__additive])]) ).
fof(i_0_6411,plain,
! [X28850,X28851,X28852,X28853,X28854] :
( ( hBOOL(hAPP(hAPP(c_member(X28854),esk289_5(X28850,X28851,X28852,X28853,X28854)),X28851))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28854,X28853)),X28852),hAPP(hAPP(c_Product__Type_OSigma(X28854,X28853),X28851),X28850))) )
& ( hBOOL(hAPP(hAPP(c_member(X28853),esk290_5(X28850,X28851,X28852,X28853,X28854)),hAPP(X28850,esk289_5(X28850,X28851,X28852,X28853,X28854))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28854,X28853)),X28852),hAPP(hAPP(c_Product__Type_OSigma(X28854,X28853),X28851),X28850))) )
& ( X28852 = hAPP(hAPP(c_Product__Type_OPair(X28854,X28853),esk289_5(X28850,X28851,X28852,X28853,X28854)),esk290_5(X28850,X28851,X28852,X28853,X28854))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28854,X28853)),X28852),hAPP(hAPP(c_Product__Type_OSigma(X28854,X28853),X28851),X28850))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaE])])])]) ).
fof(i_0_6412,plain,
! [X33577,X33578,X33579,X33580,X33581,X33582,X33583] : hAPP(c_List_Ofoldl(X33583,X33582,X33581,X33580),hAPP(hAPP(c_List_Omap(X33579,X33582),X33578),X33577)) = hAPP(c_List_Ofoldl(X33583,X33579,hAPP(hAPP(c_COMBC(X33583,tc_fun(X33579,X33582),tc_fun(X33579,X33583)),hAPP(hAPP(c_COMBB(tc_fun(X33582,X33583),tc_fun(tc_fun(X33579,X33582),tc_fun(X33579,X33583)),X33583),c_COMBB(X33582,X33583,X33579)),X33581)),X33578),X33580),X33577),
inference(variable_rename,[status(thm)],[fact_foldl__map]) ).
fof(i_0_6413,plain,
! [X29536,X29537,X29538,X29539,X29540,X29541,X29542] : hAPP(hAPP(c_Relation_Orel__comp(X29542,X29541,X29540),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29539,tc_fun(tc_prod(X29542,X29541),tc_HOL_Obool)),X29538),X29537)),X29536) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29539,tc_fun(tc_prod(X29542,X29540),tc_HOL_Obool)),X29538),hAPP(hAPP(c_COMBC(X29539,tc_fun(tc_prod(X29541,X29540),tc_HOL_Obool),tc_fun(tc_prod(X29542,X29540),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29542,X29541),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X29541,X29540),tc_HOL_Obool),tc_fun(tc_prod(X29542,X29540),tc_HOL_Obool)),X29539),c_Relation_Orel__comp(X29542,X29541,X29540)),X29537)),X29536)),
inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib2]) ).
fof(i_0_6414,plain,
! [X21824,X21825] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21825),c_Int_OPls))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21824)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21825)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21824) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21825),c_Int_OPls))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21824)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21825)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21824),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21825)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5352])]) ).
fof(i_0_6415,plain,
! [X29170,X29171,X29172] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X29172),hAPP(c_Set_OCollect(X29172),X29171)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29172),hAPP(c_Set_OCollect(X29172),hAPP(hAPP(c_COMBS(X29172,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29172),c_fdisj),X29171)),X29170)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X29172),hAPP(c_Set_OCollect(X29172),X29170)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29172),hAPP(c_Set_OCollect(X29172),hAPP(hAPP(c_COMBS(X29172,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29172),c_fdisj),X29171)),X29170)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29172),hAPP(c_Set_OCollect(X29172),X29171)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29172),hAPP(c_Set_OCollect(X29172),X29170)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29172),hAPP(c_Set_OCollect(X29172),hAPP(hAPP(c_COMBS(X29172,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29172),c_fdisj),X29171)),X29170)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI])])]) ).
fof(i_0_6416,plain,
! [X21861,X21862] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X21862))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X21861)),hAPP(c_Int_Onat,X21862)) = hAPP(c_Int_Onat,X21861) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X21862))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X21861)),hAPP(c_Int_Onat,X21862)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21861),X21862)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5353])]) ).
fof(i_0_6417,plain,
! [X28495,X28496,X28497,X28498,X28499] :
( ~ class_Groups_Oab__semigroup__mult(X28499)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28499,X28499,c_Groups_Otimes__class_Otimes(X28499),X28498,X28497),X28496))
| ~ hBOOL(hAPP(hAPP(c_member(X28499),X28495),X28497))
| hBOOL(hAPP(hAPP(c_member(X28499),X28498),X28497))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28499,X28499,c_Groups_Otimes__class_Otimes(X28499),X28495,hAPP(hAPP(c_Set_Oinsert(X28499),X28498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28499,tc_HOL_Obool)),X28497),hAPP(hAPP(c_Set_Oinsert(X28499),X28495),c_Orderings_Obot__class_Obot(tc_fun(X28499,tc_HOL_Obool)))))),X28496)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5354])]) ).
fof(i_0_6418,plain,
! [X26957,X26958,X26959,X26960,X26961,X26962,X26963,X26964,X26965,X26966] :
( ~ c_Equiv__Relations_Oequiv(X26966,X26965,X26964)
| ~ c_Equiv__Relations_Oequiv(X26963,X26962,X26961)
| ~ c_Equiv__Relations_Ocongruent2(X26966,X26963,tc_fun(X26960,tc_HOL_Obool),X26964,X26961,X26959)
| ~ hBOOL(hAPP(hAPP(c_member(X26966),X26958),X26965))
| ~ hBOOL(hAPP(hAPP(c_member(X26963),X26957),X26962))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26966,tc_fun(X26960,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26966,X26966,X26964),hAPP(hAPP(c_Set_Oinsert(X26966),X26958),c_Orderings_Obot__class_Obot(tc_fun(X26966,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X26963,tc_fun(X26960,tc_HOL_Obool)),tc_fun(X26960,tc_HOL_Obool),X26966),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26963,tc_fun(X26960,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26963,X26963,X26961),hAPP(hAPP(c_Set_Oinsert(X26963),X26957),c_Orderings_Obot__class_Obot(tc_fun(X26963,tc_HOL_Obool)))))),X26959)) = hAPP(hAPP(X26959,X26958),X26957) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class2])]) ).
fof(i_0_6419,plain,
! [X32393,X32394,X32395] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32395)),c_List_Osublist(X32395,X32394,X32393)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32395)),X32394)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X32393)))),
inference(variable_rename,[status(thm)],[fact_length__sublist]) ).
cnf(i_0_6420,plain,
c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(X2,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(X2,tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_OCons(X1)),X3)),c_List_Olist_ONil(X1))),X4)) = hAPP(hAPP(c_List_Omap(X2,X1),X3),X4),
inference(split_conjunct,[status(thm)],[i_0_5355]) ).
fof(i_0_6421,plain,
! [X33957,X33958,X33959] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33959)),hAPP(c_List_Ofilter(X33959,X33958),X33957)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33959)),X33957)))),hAPP(hAPP(c_COMBB(X33959,tc_HOL_Obool,tc_Nat_Onat),X33958),hAPP(c_List_Onth(X33959),X33957))))),
inference(variable_rename,[status(thm)],[fact_length__filter__conv__card]) ).
fof(i_0_6422,plain,
! [X28129,X28130,X28131,X28132,X28133] :
( ~ class_Groups_Ocomm__monoid__mult(X28133)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28132),X28131))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28133,X28132,c_Groups_Otimes__class_Otimes(X28133)),hAPP(hAPP(c_COMBS(X28132,X28133,X28133),hAPP(hAPP(c_COMBB(X28133,tc_fun(X28133,X28133),X28132),c_Groups_Otimes__class_Otimes(X28133)),X28130)),X28129)),c_Groups_Oone__class_Oone(X28133)),X28131) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28133),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28133,X28132,c_Groups_Otimes__class_Otimes(X28133)),X28130),c_Groups_Oone__class_Oone(X28133)),X28131)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28133,X28132,c_Groups_Otimes__class_Otimes(X28133)),X28129),c_Groups_Oone__class_Oone(X28133)),X28131)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__distrib])]) ).
fof(i_0_6423,plain,
! [X33195,X33196,X33197,X33198,X33199,X33200] :
( ( X33199 = X33197
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33200),tc_List_Olist(X33200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33200),tc_List_Olist(X33200)),X33199),X33197)),c_List_Olistrel1(X33200,X33195)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33200),tc_List_Olist(X33200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33200),tc_List_Olist(X33200)),hAPP(hAPP(c_List_Oappend(X33200),X33199),hAPP(hAPP(c_List_Olist_OCons(X33200),X33198),c_List_Olist_ONil(X33200)))),hAPP(hAPP(c_List_Oappend(X33200),X33197),hAPP(hAPP(c_List_Olist_OCons(X33200),X33196),c_List_Olist_ONil(X33200))))),c_List_Olistrel1(X33200,X33195))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33200,X33200)),hAPP(hAPP(c_Product__Type_OPair(X33200,X33200),X33198),X33196)),X33195))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33200),tc_List_Olist(X33200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33200),tc_List_Olist(X33200)),X33199),X33197)),c_List_Olistrel1(X33200,X33195)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33200),tc_List_Olist(X33200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33200),tc_List_Olist(X33200)),hAPP(hAPP(c_List_Oappend(X33200),X33199),hAPP(hAPP(c_List_Olist_OCons(X33200),X33198),c_List_Olist_ONil(X33200)))),hAPP(hAPP(c_List_Oappend(X33200),X33197),hAPP(hAPP(c_List_Olist_OCons(X33200),X33196),c_List_Olist_ONil(X33200))))),c_List_Olistrel1(X33200,X33195))) )
& ( X33199 = X33197
| X33198 = X33196
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33200),tc_List_Olist(X33200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33200),tc_List_Olist(X33200)),hAPP(hAPP(c_List_Oappend(X33200),X33199),hAPP(hAPP(c_List_Olist_OCons(X33200),X33198),c_List_Olist_ONil(X33200)))),hAPP(hAPP(c_List_Oappend(X33200),X33197),hAPP(hAPP(c_List_Olist_OCons(X33200),X33196),c_List_Olist_ONil(X33200))))),c_List_Olistrel1(X33200,X33195))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33200,X33200)),hAPP(hAPP(c_Product__Type_OPair(X33200,X33200),X33198),X33196)),X33195))
| X33198 = X33196
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33200),tc_List_Olist(X33200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33200),tc_List_Olist(X33200)),hAPP(hAPP(c_List_Oappend(X33200),X33199),hAPP(hAPP(c_List_Olist_OCons(X33200),X33198),c_List_Olist_ONil(X33200)))),hAPP(hAPP(c_List_Oappend(X33200),X33197),hAPP(hAPP(c_List_Olist_OCons(X33200),X33196),c_List_Olist_ONil(X33200))))),c_List_Olistrel1(X33200,X33195))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33200),tc_List_Olist(X33200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33200),tc_List_Olist(X33200)),X33199),X33197)),c_List_Olistrel1(X33200,X33195)))
| X33198 != X33196
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33200),tc_List_Olist(X33200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33200),tc_List_Olist(X33200)),hAPP(hAPP(c_List_Oappend(X33200),X33199),hAPP(hAPP(c_List_Olist_OCons(X33200),X33198),c_List_Olist_ONil(X33200)))),hAPP(hAPP(c_List_Oappend(X33200),X33197),hAPP(hAPP(c_List_Olist_OCons(X33200),X33196),c_List_Olist_ONil(X33200))))),c_List_Olistrel1(X33200,X33195))) )
& ( X33199 != X33197
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33200,X33200)),hAPP(hAPP(c_Product__Type_OPair(X33200,X33200),X33198),X33196)),X33195))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33200),tc_List_Olist(X33200))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33200),tc_List_Olist(X33200)),hAPP(hAPP(c_List_Oappend(X33200),X33199),hAPP(hAPP(c_List_Olist_OCons(X33200),X33198),c_List_Olist_ONil(X33200)))),hAPP(hAPP(c_List_Oappend(X33200),X33197),hAPP(hAPP(c_List_Olist_OCons(X33200),X33196),c_List_Olist_ONil(X33200))))),c_List_Olistrel1(X33200,X33195))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])]) ).
fof(i_0_6424,plain,
! [X24352,X24353,X24354,X24355] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24355,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk150_4(X24352,X24353,X24354,X24355))),X24354) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24355,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk150_4(X24352,X24353,X24354,X24355)),X24353))),X24352)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24355,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X24354) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24355,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X24352) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__eq])])]) ).
fof(i_0_6425,plain,
! [X28579,X28580,X28581,X28582,X28584] :
( ( hBOOL(hAPP(hAPP(c_member(X28582),esk278_4(X28579,X28580,X28581,X28582)),X28581))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28582,tc_HOL_Obool),tc_fun(X28582,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28582,tc_HOL_Obool),tc_fun(X28582,tc_HOL_Obool)),X28581),X28580)),c_Wellfounded_Omax__ext(X28582,X28579)))
| X28580 = c_Orderings_Obot__class_Obot(tc_fun(X28582,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28582),X28580))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28582),X28581)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28582),X28584),X28580))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28582,X28582)),hAPP(hAPP(c_Product__Type_OPair(X28582,X28582),esk278_4(X28579,X28580,X28581,X28582)),X28584)),X28579))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28582,tc_HOL_Obool),tc_fun(X28582,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28582,tc_HOL_Obool),tc_fun(X28582,tc_HOL_Obool)),X28581),X28580)),c_Wellfounded_Omax__ext(X28582,X28579)))
| X28580 = c_Orderings_Obot__class_Obot(tc_fun(X28582,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28582),X28580))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28582),X28581)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext_Ointros])])])])]) ).
fof(i_0_6426,plain,
! [X29377,X29378,X29379] : c_Map_Oran(X29379,X29378,X29377) = hAPP(c_Set_OCollect(X29378),hAPP(hAPP(c_COMBB(tc_fun(X29379,tc_HOL_Obool),tc_HOL_Obool,X29378),c_HOL_OEx(X29379)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X29378),tc_fun(X29379,tc_HOL_Obool),X29378),hAPP(c_COMBC(X29379,tc_Option_Ooption(X29378),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X29378),tc_fun(tc_Option_Ooption(X29378),tc_HOL_Obool),X29379),c_fequal),X29377))),c_Option_Ooption_OSome(X29378)))),
inference(variable_rename,[status(thm)],[fact_ran__def]) ).
fof(i_0_6427,plain,
! [X30094,X30095,X30096] :
( ~ c_Wellfounded_Owf(X30096,X30095)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30096,X30096)),hAPP(hAPP(c_Product__Type_OPair(X30096,X30096),hAPP(X30094,hAPP(c_Nat_OSuc,esk363_3(X30094,X30095,X30096)))),hAPP(X30094,esk363_3(X30094,X30095,X30096)))),X30095)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__infinite__down__chainE])])]) ).
fof(i_0_6428,plain,
! [X29659,X29660,X29661,X29663,X29664,X29666] :
( ( ~ c_Wellfounded_Owf(X29660,X29659)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29660,X29660)),hAPP(hAPP(c_Product__Type_OPair(X29660,X29660),hAPP(X29661,hAPP(c_Nat_OSuc,esk319_3(X29659,X29660,X29661)))),hAPP(X29661,esk319_3(X29659,X29660,X29661)))),X29659)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29664,X29664)),hAPP(hAPP(c_Product__Type_OPair(X29664,X29664),hAPP(esk320_2(X29663,X29664),hAPP(c_Nat_OSuc,X29666))),hAPP(esk320_2(X29663,X29664),X29666))),X29663))
| c_Wellfounded_Owf(X29664,X29663) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__iff__no__infinite__down__chain])])])])]) ).
fof(i_0_6429,plain,
! [X27658,X27659,X27660,X27661,X27662,X27663,X27664,X27665,X27666] :
( ~ c_Equiv__Relations_Oequiv(X27666,X27665,X27664)
| ~ c_Equiv__Relations_Oequiv(X27663,X27662,X27661)
| ~ c_Equiv__Relations_Ocongruent2(X27666,X27663,tc_fun(X27660,tc_HOL_Obool),X27664,X27661,X27659)
| ~ hBOOL(hAPP(hAPP(c_member(X27663),X27658),X27662))
| c_Equiv__Relations_Ocongruent(X27666,tc_fun(X27660,tc_HOL_Obool),X27664,hAPP(hAPP(c_COMBB(tc_fun(X27663,tc_fun(X27660,tc_HOL_Obool)),tc_fun(X27660,tc_HOL_Obool),X27666),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27663,tc_fun(X27660,tc_HOL_Obool)),hAPP(c_Relation_OImage(X27663,X27663,X27661),hAPP(hAPP(c_Set_Oinsert(X27663),X27658),c_Orderings_Obot__class_Obot(tc_fun(X27663,tc_HOL_Obool)))))),X27659)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent__UN])]) ).
cnf(i_0_6430,plain,
( c_Nitpick_Oless__eq__frac(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_5356]) ).
cnf(i_0_6431,plain,
( c_Nitpick_Oless__frac(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_5357]) ).
fof(i_0_6432,plain,
! [X28555,X28556,X28557,X28558,X28559,X28560,X28561] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28561,X28560,X28559,X28558,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28561,tc_HOL_Obool)),X28557),hAPP(hAPP(c_Set_Oinsert(X28561),X28556),c_Orderings_Obot__class_Obot(tc_fun(X28561,tc_HOL_Obool))))),X28555))
| ~ hBOOL(hAPP(hAPP(c_member(X28561),X28556),X28557))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28561,X28560,X28559,X28558,X28557),hAPP(hAPP(X28559,X28556),X28555))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph])]) ).
fof(i_0_6433,plain,
! [X24603,X24604,X24605,X24606,X24607] :
( ( hBOOL(hAPP(hAPP(c_member(X24606),esk162_5(X24603,X24604,X24605,X24606,X24607)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24606,tc_HOL_Obool)),X24605),X24604)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24607),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24606,X24607),X24603),X24604)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24606,X24607),X24603),X24605)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24606,tc_HOL_Obool)),X24604),X24605))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24606),X24605))
| ~ class_Groups_Ocomm__monoid__add(X24607)
| ~ class_Groups_Oordered__ab__semigroup__add(X24607) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24607),c_Groups_Ozero__class_Ozero(X24607)),hAPP(X24603,esk162_5(X24603,X24604,X24605,X24606,X24607))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24607),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24606,X24607),X24603),X24604)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24606,X24607),X24603),X24605)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24606,tc_HOL_Obool)),X24604),X24605))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24606),X24605))
| ~ class_Groups_Ocomm__monoid__add(X24607)
| ~ class_Groups_Oordered__ab__semigroup__add(X24607) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono3])])])]) ).
fof(i_0_6434,plain,
! [X25573,X25574,X25575,X25576,X25577] :
( ( hBOOL(hAPP(hAPP(c_member(X25576),esk188_5(X25573,X25574,X25575,X25576,X25577)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25576,tc_HOL_Obool)),X25575),X25574)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25577),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25576,X25577),X25573),X25574)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25576,X25577),X25573),X25575)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25576,tc_HOL_Obool)),X25574),X25575))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25576),X25575))
| ~ class_Groups_Oordered__comm__monoid__add(X25577) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25577),c_Groups_Ozero__class_Ozero(X25577)),hAPP(X25573,esk188_5(X25573,X25574,X25575,X25576,X25577))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25577),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25576,X25577),X25573),X25574)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25576,X25577),X25573),X25575)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25576,tc_HOL_Obool)),X25574),X25575))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25576),X25575))
| ~ class_Groups_Oordered__comm__monoid__add(X25577) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono2])])])]) ).
fof(i_0_6435,plain,
! [X31066,X31067,X31068,X31069] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31069,tc_fun(X31068,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X31069,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X31068,tc_HOL_Obool),tc_fun(X31068,tc_HOL_Obool),X31069),hAPP(c_COMBC(X31068,tc_fun(X31068,tc_HOL_Obool),tc_HOL_Obool),c_member(X31068))),X31067)),X31066))
| hBOOL(hAPP(hAPP(c_member(X31068),X31066),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31069,tc_fun(X31068,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X31069,tc_HOL_Obool))),X31067))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X31068),X31066),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31069,tc_fun(X31068,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X31069,tc_HOL_Obool))),X31067)))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31069,tc_fun(X31068,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X31069,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X31068,tc_HOL_Obool),tc_fun(X31068,tc_HOL_Obool),X31069),hAPP(c_COMBC(X31068,tc_fun(X31068,tc_HOL_Obool),tc_HOL_Obool),c_member(X31068))),X31067)),X31066)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq])]) ).
fof(i_0_6436,plain,
! [X25313,X25314,X25315,X25316] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25316,tc_fun(X25315,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X25316,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25315,tc_HOL_Obool),tc_fun(X25315,tc_HOL_Obool),X25316),hAPP(c_COMBC(X25315,tc_fun(X25315,tc_HOL_Obool),tc_HOL_Obool),c_member(X25315))),X25314)),X25313))
| hBOOL(hAPP(hAPP(c_member(X25315),X25313),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25316,tc_fun(X25315,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X25316,tc_HOL_Obool))),X25314))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25315),X25313),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25316,tc_fun(X25315,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X25316,tc_HOL_Obool))),X25314)))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25316,tc_fun(X25315,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X25316,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25315,tc_HOL_Obool),tc_fun(X25315,tc_HOL_Obool),X25316),hAPP(c_COMBC(X25315,tc_fun(X25315,tc_HOL_Obool),tc_HOL_Obool),c_member(X25315))),X25314)),X25313)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq])]) ).
fof(i_0_6437,plain,
! [X20473,X20474,X20475,X20476,X20477,X20478] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20478),X20477),X20476)),X20475)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20478),X20474),X20476)),X20473)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20478),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20478),X20477),X20474)),X20476)),X20475)),X20473))
| ~ class_Rings_Oordered__ring(X20478) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20478),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20478),X20477),X20474)),X20476)),X20475)),X20473))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20478),X20477),X20476)),X20475)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20478),X20474),X20476)),X20473)))
| ~ class_Rings_Oordered__ring(X20478) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).
fof(i_0_6438,plain,
! [X20485,X20486,X20487,X20488,X20489,X20490] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20490),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20490),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20490),X20489),X20488)),X20487)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20490),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20490),X20486),X20488)),X20485)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20490),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20490),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20490),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20490),X20489),X20486)),X20488)),X20487)),X20485))
| ~ class_Rings_Oordered__ring(X20490) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20490),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20490),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20490),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20490),X20489),X20486)),X20488)),X20487)),X20485))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20490),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20490),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20490),X20489),X20488)),X20487)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20490),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20490),X20486),X20488)),X20485)))
| ~ class_Rings_Oordered__ring(X20490) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).
cnf(i_0_6439,plain,
( X2 = X3
| ~ class_Rings_Olinordered__semidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_5358]) ).
fof(i_0_6440,plain,
! [X25566,X25567,X25568,X25569,X25570,X25571,X25572] :
( ~ hBOOL(hAPP(hAPP(c_member(X25572),X25571),X25570))
| ~ c_Nitpick_Ofold__graph_H(X25572,X25569,X25568,X25567,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25572,tc_HOL_Obool)),X25570),hAPP(hAPP(c_Set_Oinsert(X25572),X25571),c_Orderings_Obot__class_Obot(tc_fun(X25572,tc_HOL_Obool)))),X25566)
| c_Nitpick_Ofold__graph_H(X25572,X25569,X25568,X25567,X25570,hAPP(hAPP(X25568,X25571),X25566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J])]) ).
fof(i_0_6441,plain,
! [X30976,X30977,X30978,X30979,X30980,X30981,X30982,X30983,X30984,X30985,X30986] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30980,tc_HOL_Obool)),X30979),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30978,tc_fun(X30980,tc_HOL_Obool)),X30977),X30976)))
| ~ hBOOL(hAPP(hAPP(c_member(X30978),X30981),X30977))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30980,tc_HOL_Obool)),X30979),hAPP(X30976,X30981))) )
& ( hBOOL(hAPP(hAPP(c_member(X30984),esk391_5(X30982,X30983,X30984,X30985,X30986)),X30983))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30986,tc_HOL_Obool)),X30985),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30984,tc_fun(X30986,tc_HOL_Obool)),X30983),X30982))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30986,tc_HOL_Obool)),X30985),hAPP(X30982,esk391_5(X30982,X30983,X30984,X30985,X30986))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30986,tc_HOL_Obool)),X30985),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30984,tc_fun(X30986,tc_HOL_Obool)),X30983),X30982))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__subset__iff])])])])])]) ).
fof(i_0_6442,plain,
! [X22223,X22224,X22225,X22226] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22226,X22225),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22224),X22223)))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22226),X22225),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X22223),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22224)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22224)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X22223),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22225),X22223))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zminus1__lemma])]) ).
cnf(i_0_6443,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(split_conjunct,[status(thm)],[i_0_5359]) ).
fof(i_0_6444,plain,
! [X31042,X31043,X31044,X31045,X31046,X31047,X31048,X31049,X31050,X31051,X31052] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X31046),X31045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31044,tc_fun(X31046,tc_HOL_Obool)),X31043),X31042)))
| ~ hBOOL(hAPP(hAPP(c_member(X31044),X31047),X31043))
| hBOOL(hAPP(hAPP(c_member(X31046),X31045),hAPP(X31042,X31047))) )
& ( hBOOL(hAPP(hAPP(c_member(X31050),esk392_5(X31048,X31049,X31050,X31051,X31052)),X31049))
| hBOOL(hAPP(hAPP(c_member(X31052),X31051),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31050,tc_fun(X31052,tc_HOL_Obool)),X31049),X31048))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X31052),X31051),hAPP(X31048,esk392_5(X31048,X31049,X31050,X31051,X31052))))
| hBOOL(hAPP(hAPP(c_member(X31052),X31051),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31050,tc_fun(X31052,tc_HOL_Obool)),X31049),X31048))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__iff])])])])])]) ).
fof(i_0_6445,plain,
! [X28808,X28809,X28810,X28811,X28812,X28813] : hAPP(c_Set_Ovimage(X28813,tc_prod(X28812,X28811),X28810),hAPP(hAPP(c_Product__Type_OSigma(X28812,X28811),X28809),hAPP(c_COMBK(tc_fun(X28811,tc_HOL_Obool),X28812),X28808))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28813,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28813,X28812,hAPP(c_Fun_Ocomp(tc_prod(X28812,X28811),X28812,X28813,c_Product__Type_Ofst(X28812,X28811)),X28810)),X28809)),hAPP(c_Set_Ovimage(X28813,X28811,hAPP(c_Fun_Ocomp(tc_prod(X28812,X28811),X28811,X28813,c_Product__Type_Osnd(X28812,X28811)),X28810)),X28808)),
inference(variable_rename,[status(thm)],[fact_vimage__Times]) ).
fof(i_0_6446,plain,
! [X25907,X25908,X25909,X25910,X25911,X25912,X25913,X25914] :
( ( X25912 = X25910
| hBOOL(hAPP(hAPP(c_member(tc_prod(X25914,X25914)),hAPP(hAPP(c_Product__Type_OPair(X25914,X25914),X25912),X25910)),X25908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X25914,X25913),tc_prod(X25914,X25913))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X25914,X25913),tc_prod(X25914,X25913)),hAPP(hAPP(c_Product__Type_OPair(X25914,X25913),X25912),X25911)),hAPP(hAPP(c_Product__Type_OPair(X25914,X25913),X25910),X25909))),c_Wellfounded_Olex__prod(X25914,X25913,X25908,X25907))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X25913,X25913)),hAPP(hAPP(c_Product__Type_OPair(X25913,X25913),X25911),X25909)),X25907))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X25914,X25914)),hAPP(hAPP(c_Product__Type_OPair(X25914,X25914),X25912),X25910)),X25908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X25914,X25913),tc_prod(X25914,X25913))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X25914,X25913),tc_prod(X25914,X25913)),hAPP(hAPP(c_Product__Type_OPair(X25914,X25913),X25912),X25911)),hAPP(hAPP(c_Product__Type_OPair(X25914,X25913),X25910),X25909))),c_Wellfounded_Olex__prod(X25914,X25913,X25908,X25907))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25914,X25914)),hAPP(hAPP(c_Product__Type_OPair(X25914,X25914),X25912),X25910)),X25908))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X25914,X25913),tc_prod(X25914,X25913))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X25914,X25913),tc_prod(X25914,X25913)),hAPP(hAPP(c_Product__Type_OPair(X25914,X25913),X25912),X25911)),hAPP(hAPP(c_Product__Type_OPair(X25914,X25913),X25910),X25909))),c_Wellfounded_Olex__prod(X25914,X25913,X25908,X25907))) )
& ( X25912 != X25910
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25913,X25913)),hAPP(hAPP(c_Product__Type_OPair(X25913,X25913),X25911),X25909)),X25907))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X25914,X25913),tc_prod(X25914,X25913))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X25914,X25913),tc_prod(X25914,X25913)),hAPP(hAPP(c_Product__Type_OPair(X25914,X25913),X25912),X25911)),hAPP(hAPP(c_Product__Type_OPair(X25914,X25913),X25910),X25909))),c_Wellfounded_Olex__prod(X25914,X25913,X25908,X25907))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_6447,plain,
! [X31234,X31235,X31236,X31237,X31238,X31239,X31240,X31241,X31242,X31243,X31244] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31238,tc_fun(X31237,tc_HOL_Obool)),X31236),X31235),X31234))
| ~ hBOOL(hAPP(hAPP(c_member(X31238),X31239),X31236))
| hBOOL(hAPP(hAPP(X31235,X31239),X31234)) )
& ( hBOOL(hAPP(hAPP(c_member(X31244),esk396_5(X31240,X31241,X31242,X31243,X31244)),X31242))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31244,tc_fun(X31243,tc_HOL_Obool)),X31242),X31241),X31240)) )
& ( ~ hBOOL(hAPP(hAPP(X31241,esk396_5(X31240,X31241,X31242,X31243,X31244)),X31240))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31244,tc_fun(X31243,tc_HOL_Obool)),X31242),X31241),X31240)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF1__iff])])])])])]) ).
fof(i_0_6448,plain,
! [X29253,X29254] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),X29254)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X29253))))),
inference(variable_rename,[status(thm)],[fact_finite__M__bounded__by__nat]) ).
fof(i_0_6449,plain,
! [X20588,X20589,X20590] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20590))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20589),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20588),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20588),X20589))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X20590)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])]) ).
fof(i_0_6450,plain,
! [X30969,X30970,X30971,X30972,X30973,X30974] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30973),X30972),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30971,X30973),X30970),X30969)))
| ~ hBOOL(hAPP(hAPP(c_member(X30971),X30974),X30970))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30973),X30972),hAPP(X30969,X30974)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X30973) )
& ( hBOOL(hAPP(hAPP(c_member(X30971),esk390_5(X30969,X30970,X30971,X30972,X30973)),X30970))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30973),X30972),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30971,X30973),X30970),X30969)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X30973) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30973),X30972),hAPP(X30969,esk390_5(X30969,X30970,X30971,X30972,X30973))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30973),X30972),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30971,X30973),X30970),X30969)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X30973) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__INF__iff])])])])]) ).
fof(i_0_6451,plain,
! [X26319,X26320,X26321,X26322,X26323] :
( ( hBOOL(hAPP(hAPP(c_member(X26322),esk214_5(X26319,X26320,X26321,X26322,X26323)),X26321))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26322,X26323),X26320),X26321) != c_Groups_Ozero__class_Ozero(X26323)
| ~ hBOOL(hAPP(hAPP(c_member(X26322),X26319),X26321))
| hAPP(X26320,X26319) = c_Groups_Ozero__class_Ozero(X26323)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26322),X26321))
| ~ class_Groups_Oordered__ab__group__add(X26323) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26323),c_Groups_Ozero__class_Ozero(X26323)),hAPP(X26320,esk214_5(X26319,X26320,X26321,X26322,X26323))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26322,X26323),X26320),X26321) != c_Groups_Ozero__class_Ozero(X26323)
| ~ hBOOL(hAPP(hAPP(c_member(X26322),X26319),X26321))
| hAPP(X26320,X26319) = c_Groups_Ozero__class_Ozero(X26323)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26322),X26321))
| ~ class_Groups_Oordered__ab__group__add(X26323) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__0])])])]) ).
cnf(i_0_6452,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(split_conjunct,[status(thm)],[i_0_5360]) ).
fof(i_0_6453,plain,
! [X28418,X28419,X28420,X28421,X28422] : hAPP(c_Fun_Othe__inv__into(X28422,X28421,X28420,X28419),X28418) = c_HOL_OThe(X28422,hAPP(hAPP(c_COMBS(X28422,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28422),c_fconj),hAPP(hAPP(c_COMBC(X28422,tc_fun(X28422,tc_HOL_Obool),tc_HOL_Obool),c_member(X28422)),X28420))),hAPP(hAPP(c_COMBC(X28422,X28421,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X28421,tc_fun(X28421,tc_HOL_Obool),X28422),c_fequal),X28419)),X28418))),
inference(variable_rename,[status(thm)],[fact_the__inv__into__def]) ).
cnf(i_0_6454,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5361]) ).
fof(i_0_6455,plain,
! [X33304,X33305,X33306,X33307] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33307,X33307)),hAPP(hAPP(c_Product__Type_OPair(X33307,X33307),esk463_4(X33304,X33305,X33306,X33307)),esk464_4(X33304,X33305,X33306,X33307))),X33304))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33307),tc_List_Olist(X33307))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33307),tc_List_Olist(X33307)),X33306),X33305)),c_List_Olistrel1(X33307,X33304))) )
& ( X33306 = hAPP(hAPP(c_List_Oappend(X33307),esk465_4(X33304,X33305,X33306,X33307)),hAPP(hAPP(c_List_Olist_OCons(X33307),esk463_4(X33304,X33305,X33306,X33307)),esk466_4(X33304,X33305,X33306,X33307)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33307),tc_List_Olist(X33307))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33307),tc_List_Olist(X33307)),X33306),X33305)),c_List_Olistrel1(X33307,X33304))) )
& ( X33305 = hAPP(hAPP(c_List_Oappend(X33307),esk465_4(X33304,X33305,X33306,X33307)),hAPP(hAPP(c_List_Olist_OCons(X33307),esk464_4(X33304,X33305,X33306,X33307)),esk466_4(X33304,X33305,X33306,X33307)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33307),tc_List_Olist(X33307))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33307),tc_List_Olist(X33307)),X33306),X33305)),c_List_Olistrel1(X33307,X33304))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1E])])])]) ).
fof(i_0_6456,plain,
! [X26574,X26575,X26576,X26577,X26578,X26579] :
( ~ class_Groups_Ocomm__monoid__add(X26579)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26578),X26577))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26576),X26575))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(X26578,X26576),X26579),X26574),c_Sum__Type_OPlus(X26578,X26576,X26577,X26575)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26579),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26578,X26579),hAPP(c_Fun_Ocomp(tc_sum(X26578,X26576),X26579,X26578,X26574),c_Sum__Type_OInl(X26578,X26576))),X26577)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26576,X26579),hAPP(c_Fun_Ocomp(tc_sum(X26578,X26576),X26579,X26576,X26574),c_Sum__Type_OInr(X26576,X26578))),X26575)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Plus])]) ).
fof(i_0_6457,plain,
! [X30804,X30805,X30806,X30807,X30808,X30809,X30810] :
( ~ c_Finite__Set_Ofun__left__comm(X30810,X30809,X30808)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30810,X30809,X30808,X30807,X30806),X30805))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30810,X30809,X30808,X30807,X30806),X30804))
| X30804 = X30805 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ])]) ).
fof(i_0_6458,plain,
! [X32423,X32424,X32425,X32426,X32427] :
( ~ class_Groups_Oab__group__add(X32427)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32427),hAPP(hAPP(c_List_Omap(X32426,X32427),hAPP(hAPP(c_COMBS(X32426,X32427,X32427),hAPP(hAPP(c_COMBB(X32427,tc_fun(X32427,X32427),X32426),c_Groups_Ominus__class_Ominus(X32427)),X32425)),X32424)),X32423)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X32427),hAPP(c_List_Omonoid__add__class_Olistsum(X32427),hAPP(hAPP(c_List_Omap(X32426,X32427),X32425),X32423))),hAPP(c_List_Omonoid__add__class_Olistsum(X32427),hAPP(hAPP(c_List_Omap(X32426,X32427),X32424),X32423))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__subtractf])]) ).
fof(i_0_6459,plain,
! [X32438,X32439,X32440,X32441,X32442] :
( ~ class_Groups_Ocomm__monoid__add(X32442)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32442),hAPP(hAPP(c_List_Omap(X32441,X32442),hAPP(hAPP(c_COMBS(X32441,X32442,X32442),hAPP(hAPP(c_COMBB(X32442,tc_fun(X32442,X32442),X32441),c_Groups_Oplus__class_Oplus(X32442)),X32440)),X32439)),X32438)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32442),hAPP(c_List_Omonoid__add__class_Olistsum(X32442),hAPP(hAPP(c_List_Omap(X32441,X32442),X32440),X32438))),hAPP(c_List_Omonoid__add__class_Olistsum(X32442),hAPP(hAPP(c_List_Omap(X32441,X32442),X32439),X32438))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__addf])]) ).
fof(i_0_6460,plain,
! [X26530,X26531,X26532,X26533] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X26533,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26532,tc_fun(tc_fun(X26533,tc_HOL_Obool),tc_HOL_Obool)),X26531),hAPP(hAPP(c_COMBB(tc_fun(X26533,tc_HOL_Obool),tc_fun(tc_fun(X26533,tc_HOL_Obool),tc_HOL_Obool),X26532),c_Set_OPow(X26533)),X26530))),hAPP(c_Set_OPow(X26533),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26532,tc_fun(X26533,tc_HOL_Obool)),X26531),X26530)))),
inference(variable_rename,[status(thm)],[fact_UN__Pow__subset]) ).
fof(i_0_6461,plain,
! [X20543,X20544,X20545,X20546,X20547] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20546),X20545)),X20544)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20547),X20545)),X20543)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20546),X20547)),X20545)),X20544)),X20543))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20547),X20546)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20546),X20547)),X20545)),X20544)),X20543))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20546),X20545)),X20544)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20547),X20545)),X20543)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20547),X20546)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).
fof(i_0_6462,plain,
! [X20565,X20566,X20567,X20568,X20569] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20568),X20567)),X20566)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20569),X20567)),X20565)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20568),X20569)),X20567)),X20566)),X20565))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20569),X20568)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20568),X20569)),X20567)),X20566)),X20565))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20568),X20567)),X20566)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20569),X20567)),X20565)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20569),X20568)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])]) ).
fof(i_0_6463,plain,
! [X32433,X32434,X32435,X32436,X32437] :
( ~ class_Rings_Osemiring__0(X32437)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32437),hAPP(hAPP(c_List_Omap(X32436,X32437),hAPP(hAPP(c_COMBC(X32436,X32437,X32437),hAPP(hAPP(c_COMBB(X32437,tc_fun(X32437,X32437),X32436),c_Groups_Otimes__class_Otimes(X32437)),X32435)),X32434)),X32433)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32437),hAPP(c_List_Omonoid__add__class_Olistsum(X32437),hAPP(hAPP(c_List_Omap(X32436,X32437),X32435),X32433))),X32434) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mult__const])]) ).
fof(i_0_6464,plain,
! [X29355] : c_Int_Oint__ge__less__than2(X29355) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29355)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_int__ge__less__than2__def]) ).
fof(i_0_6465,plain,
! [X28213,X28214,X28215,X28216,X28217] :
( ( hBOOL(hAPP(hAPP(c_member(X28216),esk270_5(X28213,X28214,X28215,X28216,X28217)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28216,tc_HOL_Obool)),X28215),X28214)))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28217,X28216,c_Groups_Otimes__class_Otimes(X28217)),X28213),c_Groups_Oone__class_Oone(X28217)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28216,tc_HOL_Obool)),X28215),X28214)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28217),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28217,X28216,c_Groups_Otimes__class_Otimes(X28217)),X28213),c_Groups_Oone__class_Oone(X28217)),X28215)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28217,X28216,c_Groups_Otimes__class_Otimes(X28217)),X28213),c_Groups_Oone__class_Oone(X28217)),X28214))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28216),X28214))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28216),X28215))
| ~ class_Groups_Ocomm__monoid__mult(X28217) )
& ( hAPP(X28213,esk270_5(X28213,X28214,X28215,X28216,X28217)) != c_Groups_Oone__class_Oone(X28217)
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28217,X28216,c_Groups_Otimes__class_Otimes(X28217)),X28213),c_Groups_Oone__class_Oone(X28217)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28216,tc_HOL_Obool)),X28215),X28214)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28217),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28217,X28216,c_Groups_Otimes__class_Otimes(X28217)),X28213),c_Groups_Oone__class_Oone(X28217)),X28215)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28217,X28216,c_Groups_Otimes__class_Otimes(X28217)),X28213),c_Groups_Oone__class_Oone(X28217)),X28214))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28216),X28214))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28216),X28215))
| ~ class_Groups_Ocomm__monoid__mult(X28217) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__Un__one])])])]) ).
fof(i_0_6466,plain,
! [X27074,X27075,X27076,X27077] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27077,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X27077,tc_fun(X27077,tc_HOL_Obool),tc_HOL_Obool),c_member(X27077)),X27076)),hAPP(hAPP(c_COMBC(X27077,tc_fun(X27077,tc_HOL_Obool),tc_HOL_Obool),c_member(X27077)),X27075)),X27074))
| hBOOL(hAPP(hAPP(c_member(X27077),X27074),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27077,tc_HOL_Obool)),X27076),X27075))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X27077),X27074),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27077,tc_HOL_Obool)),X27076),X27075)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27077,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X27077,tc_fun(X27077,tc_HOL_Obool),tc_HOL_Obool),c_member(X27077)),X27076)),hAPP(hAPP(c_COMBC(X27077,tc_fun(X27077,tc_HOL_Obool),tc_HOL_Obool),c_member(X27077)),X27075)),X27074)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq])]) ).
fof(i_0_6467,plain,
! [X25108,X25109,X25110,X25111] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25111,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X25111,tc_fun(X25111,tc_HOL_Obool),tc_HOL_Obool),c_member(X25111)),X25110)),hAPP(hAPP(c_COMBC(X25111,tc_fun(X25111,tc_HOL_Obool),tc_HOL_Obool),c_member(X25111)),X25109)),X25108))
| hBOOL(hAPP(hAPP(c_member(X25111),X25108),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25111,tc_HOL_Obool)),X25110),X25109))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25111),X25108),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25111,tc_HOL_Obool)),X25110),X25109)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25111,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X25111,tc_fun(X25111,tc_HOL_Obool),tc_HOL_Obool),c_member(X25111)),X25110)),hAPP(hAPP(c_COMBC(X25111,tc_fun(X25111,tc_HOL_Obool),tc_HOL_Obool),c_member(X25111)),X25109)),X25108)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq])]) ).
fof(i_0_6468,plain,
! [X29178,X29179,X29180] : hAPP(hAPP(c_Set_Oinsert(X29180),X29179),hAPP(c_Set_OCollect(X29180),X29178)) = hAPP(c_Set_OCollect(X29180),hAPP(hAPP(c_COMBS(X29180,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29180),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29180),c_fNot),hAPP(hAPP(c_COMBC(X29180,X29180,tc_HOL_Obool),c_fequal),X29179)))),X29178)),
inference(variable_rename,[status(thm)],[fact_insert__Collect]) ).
cnf(i_0_6469,plain,
( c_Nitpick_Oof__frac(X2,X1,X3) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nitpick_Onum(X2),X3))),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nitpick_Odenom(X2),X3)))
| ~ class_Rings_Oinverse(X1)
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5362]) ).
fof(i_0_6470,plain,
! [X26967,X26968,X26969,X26970,X26971,X26972] :
( ~ c_Equiv__Relations_Oequiv(X26972,X26971,X26970)
| ~ hBOOL(hAPP(hAPP(c_member(X26972),X26969),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26972,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26972,X26972,X26970),hAPP(hAPP(c_Set_Oinsert(X26972),X26968),c_Orderings_Obot__class_Obot(tc_fun(X26972,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X26972,X26972,X26970),hAPP(hAPP(c_Set_Oinsert(X26972),X26967),c_Orderings_Obot__class_Obot(tc_fun(X26972,tc_HOL_Obool)))))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26972,X26972)),hAPP(hAPP(c_Product__Type_OPair(X26972,X26972),X26968),X26967)),X26970)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint])]) ).
fof(i_0_6471,plain,
! [X22012,X22013,X22014,X22015,X22016,X22017,X22018] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22018,X22017),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22016),X22015)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22014,X22017),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22013),X22012)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22017))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22018),X22014),X22017),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22016),X22013)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22015),X22012)),X22017))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22015),X22012),X22017)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__add1__eq])]) ).
fof(i_0_6472,plain,
! [X26871,X26872,X26873,X26874] : c_Random__Sequence_Omap(X26874,X26873,X26872,X26871) = c_Random__Sequence_Obind(X26874,X26873,X26871,hAPP(c_Fun_Ocomp(X26873,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X26873)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X26874,c_Random__Sequence_Osingle(X26873)),X26872)),
inference(variable_rename,[status(thm)],[fact_Random__Sequence_Omap__def]) ).
fof(i_0_6473,plain,
! [X27707,X27708,X27709,X27710,X27711] :
( ( hBOOL(hAPP(hAPP(c_member(X27710),esk251_5(X27707,X27708,X27709,X27710,X27711)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27710,tc_HOL_Obool)),X27709),X27708)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27710,X27711),X27707),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27710,tc_HOL_Obool)),X27709),X27708)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27711),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27710,X27711),X27707),X27709)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27710,X27711),X27707),X27708))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27710,X27711),X27707),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27710,tc_HOL_Obool)),X27709),X27708)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27710),X27708))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27710),X27709))
| ~ class_Fields_Ofield(X27711) )
& ( hAPP(X27707,esk251_5(X27707,X27708,X27709,X27710,X27711)) = c_Groups_Ozero__class_Ozero(X27711)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27710,X27711),X27707),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27710,tc_HOL_Obool)),X27709),X27708)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27711),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27710,X27711),X27707),X27709)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27710,X27711),X27707),X27708))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27710,X27711),X27707),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27710,tc_HOL_Obool)),X27709),X27708)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27710),X27708))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27710),X27709))
| ~ class_Fields_Ofield(X27711) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un])])])]) ).
fof(i_0_6474,plain,
! [X22216,X22217,X22218,X22219,X22220,X22221,X22222] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22222,X22221),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22220),X22219)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22218,X22221),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22217),X22216)))
| X22221 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22222),X22218),X22221),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22220),X22217)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22219),X22216)),X22221))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22219),X22216),X22221)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd1__lemma])]) ).
fof(i_0_6475,plain,
! [X28676,X28677,X28678,X28679,X28680,X28681] :
( ~ class_Groups_Ocomm__monoid__mult(X28681)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28680,X28681),hAPP(hAPP(c_COMBC(X28680,tc_fun(X28679,tc_HOL_Obool),X28681),hAPP(hAPP(c_COMBB(tc_fun(X28679,X28681),tc_fun(tc_fun(X28679,tc_HOL_Obool),X28681),X28680),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28679,X28681)),X28678)),X28677)),X28676) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X28680,X28679),X28681),hAPP(c_Product__Type_Oprod_Oprod__case(X28680,X28679,X28681),X28678)),hAPP(hAPP(c_Product__Type_OSigma(X28680,X28679),X28676),hAPP(c_COMBK(tc_fun(X28679,tc_HOL_Obool),X28680),X28677))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product])]) ).
fof(i_0_6476,plain,
! [X28657,X28658,X28659,X28660,X28661,X28662] :
( ~ class_Groups_Ocomm__monoid__add(X28662)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28661,X28662),hAPP(hAPP(c_COMBC(X28661,tc_fun(X28660,tc_HOL_Obool),X28662),hAPP(hAPP(c_COMBB(tc_fun(X28660,X28662),tc_fun(tc_fun(X28660,tc_HOL_Obool),X28662),X28661),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28660,X28662)),X28659)),X28658)),X28657) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X28661,X28660),X28662),hAPP(c_Product__Type_Oprod_Oprod__case(X28661,X28660,X28662),X28659)),hAPP(hAPP(c_Product__Type_OSigma(X28661,X28660),X28657),hAPP(c_COMBK(tc_fun(X28660,tc_HOL_Obool),X28661),X28658))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product])]) ).
fof(i_0_6477,plain,
! [X31581,X31582,X31583,X31584] :
( ( X31582 = hAPP(hAPP(c_Product__Type_OPair(X31584,X31583),esk427_4(X31581,X31582,X31583,X31584)),esk426_4(X31581,X31582,X31583,X31584))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31584,X31583)),X31582),hAPP(c_Relation_Oconverse(X31583,X31584),X31581))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31583,X31584)),hAPP(hAPP(c_Product__Type_OPair(X31583,X31584),esk426_4(X31581,X31582,X31583,X31584)),esk427_4(X31581,X31582,X31583,X31584))),X31581))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31584,X31583)),X31582),hAPP(c_Relation_Oconverse(X31583,X31584),X31581))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5363])])])]) ).
fof(i_0_6478,plain,
! [X28863,X28864,X28865,X28866,X28867,X28868,X28869,X28870] :
( ~ c_Fun_Oinj__on(X28870,X28869,X28868,X28867)
| ~ c_Fun_Oinj__on(X28866,X28865,X28864,X28863)
| c_Fun_Oinj__on(tc_prod(X28870,X28866),tc_prod(X28869,X28865),c_Product__Type_Omap__pair(X28870,X28869,X28866,X28865,X28868,X28864),hAPP(hAPP(c_Product__Type_OSigma(X28870,X28866),X28867),hAPP(c_COMBK(tc_fun(X28866,tc_HOL_Obool),X28870),X28863))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__inj__on])]) ).
fof(i_0_6479,plain,
! [X21954,X21955,X21956,X21957,X21958] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21958,X21957),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21956),X21955)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21957))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21954),X21958),X21957),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21954),X21956)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21954),X21955)),X21957))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21954),X21955),X21957)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult1__eq])]) ).
fof(i_0_6480,plain,
! [X18509,X18510,X18511,X18512] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18512),hAPP(X18511,X18510)),hAPP(X18511,X18509)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18510),X18509))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18512),hAPP(X18511,esk38_4(X18509,X18510,X18511,X18512))),hAPP(X18511,hAPP(c_Nat_OSuc,esk38_4(X18509,X18510,X18511,X18512)))))
| ~ class_Orderings_Oorder(X18512) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18510),X18509))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18512),hAPP(X18511,X18510)),hAPP(X18511,X18509)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18512),hAPP(X18511,esk38_4(X18509,X18510,X18511,X18512))),hAPP(X18511,hAPP(c_Nat_OSuc,esk38_4(X18509,X18510,X18511,X18512)))))
| ~ class_Orderings_Oorder(X18512) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__less__iff])])])]) ).
fof(i_0_6481,plain,
! [X18504,X18505,X18506,X18507] :
( ~ class_Orderings_Oorder(X18507)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18507),hAPP(X18506,esk37_4(X18504,X18505,X18506,X18507))),hAPP(X18506,hAPP(c_Nat_OSuc,esk37_4(X18504,X18505,X18506,X18507)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18505),X18504))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18507),hAPP(X18506,X18505)),hAPP(X18506,X18504))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__less])])]) ).
fof(i_0_6482,plain,
! [X28500,X28501,X28502,X28503,X28504] :
( ( hBOOL(hAPP(hAPP(c_member(X28502),esk274_5(X28500,X28501,X28502,X28503,X28504)),X28500))
| ~ hBOOL(hAPP(hAPP(c_member(X28504),X28503),c_Map_Oran(X28502,X28504,c_Map_Orestrict__map(X28502,X28504,X28501,X28500)))) )
& ( hAPP(X28501,esk274_5(X28500,X28501,X28502,X28503,X28504)) = hAPP(c_Option_Ooption_OSome(X28504),X28503)
| ~ hBOOL(hAPP(hAPP(c_member(X28504),X28503),c_Map_Oran(X28502,X28504,c_Map_Orestrict__map(X28502,X28504,X28501,X28500)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__restrictD])])])]) ).
fof(i_0_6483,plain,
! [X22237,X22238,X22239,X22240,X22241] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22241,X22240),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22239),X22238)))
| X22240 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22237),X22241),X22240),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22237),X22239)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22237),X22238)),X22240))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22237),X22238),X22240)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult1__lemma])]) ).
fof(i_0_6484,plain,
! [X23467,X23468,X23469,X23470] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23469),X23468))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23470),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X23470,X23470),hAPP(hAPP(c_COMBB(X23470,tc_fun(X23470,X23470),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X23470)),X23467)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23470,tc_Nat_Onat),X23467),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23469,X23468)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23470),hAPP(X23467,X23469)),hAPP(X23467,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23468),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Oab__group__add(X23470) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23469),X23468))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23470),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X23470,X23470),hAPP(hAPP(c_COMBB(X23470,tc_fun(X23470,X23470),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X23470)),X23467)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23470,tc_Nat_Onat),X23467),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23469,X23468)) = c_Groups_Ozero__class_Ozero(X23470)
| ~ class_Groups_Oab__group__add(X23470) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5364])])]) ).
fof(i_0_6485,plain,
! [X33131,X33132,X33133,X33134,X33135,X33136,X33137] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X33137),X33136),hAPP(c_List_Oset(X33137),hAPP(hAPP(c_List_Otake(X33137),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33135)),X33134)),X33133))))
| c_Map_Omap__upds(X33137,X33135,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X33137,tc_Option_Ooption(X33135)),X33132),X33136),hAPP(c_Option_Ooption_OSome(X33135),X33131)),X33133,X33134) = c_Map_Omap__upds(X33137,X33135,X33132,X33133,X33134) )
& ( hBOOL(hAPP(hAPP(c_member(X33137),X33136),hAPP(c_List_Oset(X33137),hAPP(hAPP(c_List_Otake(X33137),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33135)),X33134)),X33133))))
| c_Map_Omap__upds(X33137,X33135,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X33137,tc_Option_Ooption(X33135)),X33132),X33136),hAPP(c_Option_Ooption_OSome(X33135),X33131)),X33133,X33134) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X33137,tc_Option_Ooption(X33135)),c_Map_Omap__upds(X33137,X33135,X33132,X33133,X33134)),X33136),hAPP(c_Option_Ooption_OSome(X33135),X33131)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5365])]) ).
fof(i_0_6486,plain,
! [X28814,X28815,X28816,X28817] :
( c_Fun_Oinj__on(X28817,tc_prod(X28816,X28817),esk283_4(X28814,X28815,X28816,X28817),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28816,tc_fun(X28817,tc_HOL_Obool)),X28815),X28814))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28816,X28817),tc_HOL_Obool)),hAPP(c_Set_Oimage(X28817,tc_prod(X28816,X28817),esk283_4(X28814,X28815,X28816,X28817)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28816,tc_fun(X28817,tc_HOL_Obool)),X28815),X28814))),hAPP(hAPP(c_Product__Type_OSigma(X28816,X28817),X28815),X28814))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_Ex__inj__on__UNION__Sigma])]) ).
fof(i_0_6487,plain,
! [X28538,X28539,X28540,X28541,X28542] :
( ~ class_Groups_Oab__semigroup__mult(X28542)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28542,X28542,c_Groups_Otimes__class_Otimes(X28542),X28541,X28540),X28539))
| hBOOL(hAPP(hAPP(c_member(X28542),X28541),X28540))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28542,X28542,c_Groups_Otimes__class_Otimes(X28542),X28538,hAPP(hAPP(c_Set_Oinsert(X28542),X28541),X28540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28542),X28538),X28539))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5366])]) ).
fof(i_0_6488,plain,
! [X33993,X33994,X33995,X33996] : hAPP(hAPP(c_List_Omap(tc_prod(X33996,tc_Nat_Onat),X33996),c_Product__Type_Ofst(X33996,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X33996,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X33996,tc_Nat_Onat)),X33995),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X33996,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X33996,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X33996,tc_Nat_Onat),X33994),X33993))) = hAPP(hAPP(c_List_Omap(tc_prod(X33996,tc_Nat_Onat),X33996),c_Product__Type_Ofst(X33996,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X33996,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X33996,tc_Nat_Onat)),X33995),c_Product__Type_Osnd(X33996,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X33996,tc_Nat_Onat),X33994),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X33993)))),
inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma__Suc]) ).
fof(i_0_6489,plain,
! [X28880,X28881,X28882,X28883,X28884,X28885] : hAPP(c_Fun_Ocomp(tc_prod(X28885,X28884),X28885,tc_prod(X28883,X28882),c_Product__Type_Ofst(X28885,X28884)),c_Product__Type_Omap__pair(X28883,X28885,X28882,X28884,X28881,X28880)) = hAPP(c_Fun_Ocomp(X28883,X28885,tc_prod(X28883,X28882),X28881),c_Product__Type_Ofst(X28883,X28882)),
inference(variable_rename,[status(thm)],[fact_fst__comp__map__pair]) ).
fof(i_0_6490,plain,
! [X28886,X28887,X28888,X28889,X28890,X28891] : hAPP(c_Fun_Ocomp(tc_prod(X28891,X28890),X28890,tc_prod(X28889,X28888),c_Product__Type_Osnd(X28891,X28890)),c_Product__Type_Omap__pair(X28889,X28891,X28888,X28890,X28887,X28886)) = hAPP(c_Fun_Ocomp(X28888,X28890,tc_prod(X28889,X28888),X28886),c_Product__Type_Osnd(X28889,X28888)),
inference(variable_rename,[status(thm)],[fact_snd__comp__map__pair]) ).
fof(i_0_6491,plain,
! [X30916,X30917,X30918,X30919,X30920,X30921] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30921,tc_fun(X30920,tc_HOL_Obool)),X30919),hAPP(hAPP(c_COMBC(X30921,tc_fun(X30918,tc_fun(X30920,tc_HOL_Obool)),tc_fun(X30920,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30918,tc_HOL_Obool),tc_fun(tc_fun(X30918,tc_fun(X30920,tc_HOL_Obool)),tc_fun(X30920,tc_HOL_Obool)),X30921),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30918,tc_fun(X30920,tc_HOL_Obool))),X30917)),X30916)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30918,tc_fun(X30920,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30921,tc_fun(X30918,tc_HOL_Obool)),X30919),X30917)),X30916),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I9_J]) ).
fof(i_0_6492,plain,
! [X24226,X24227,X24228,X24229,X24230,X24231] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24231,tc_fun(X24230,tc_HOL_Obool)),X24229),hAPP(hAPP(c_COMBC(X24231,tc_fun(X24228,tc_fun(X24230,tc_HOL_Obool)),tc_fun(X24230,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24228,tc_HOL_Obool),tc_fun(tc_fun(X24228,tc_fun(X24230,tc_HOL_Obool)),tc_fun(X24230,tc_HOL_Obool)),X24231),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24228,tc_fun(X24230,tc_HOL_Obool))),X24227)),X24226)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24228,tc_fun(X24230,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24231,tc_fun(X24228,tc_HOL_Obool)),X24229),X24227)),X24226),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I9_J]) ).
fof(i_0_6493,plain,
! [X30910,X30911,X30912,X30913,X30914,X30915] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30915,tc_fun(X30914,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30913,tc_fun(X30915,tc_HOL_Obool)),X30912),X30911)),X30910) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30913,tc_fun(X30914,tc_HOL_Obool)),X30912),hAPP(hAPP(c_COMBC(X30913,tc_fun(X30915,tc_fun(X30914,tc_HOL_Obool)),tc_fun(X30914,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30915,tc_HOL_Obool),tc_fun(tc_fun(X30915,tc_fun(X30914,tc_HOL_Obool)),tc_fun(X30914,tc_HOL_Obool)),X30913),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30915,tc_fun(X30914,tc_HOL_Obool))),X30911)),X30910)),
inference(variable_rename,[status(thm)],[fact_INT__simps_I9_J]) ).
fof(i_0_6494,plain,
! [X24238,X24239,X24240,X24241,X24242,X24243] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24243,tc_fun(X24242,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24241,tc_fun(X24243,tc_HOL_Obool)),X24240),X24239)),X24238) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24241,tc_fun(X24242,tc_HOL_Obool)),X24240),hAPP(hAPP(c_COMBC(X24241,tc_fun(X24243,tc_fun(X24242,tc_HOL_Obool)),tc_fun(X24242,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24243,tc_HOL_Obool),tc_fun(tc_fun(X24243,tc_fun(X24242,tc_HOL_Obool)),tc_fun(X24242,tc_HOL_Obool)),X24241),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24243,tc_fun(X24242,tc_HOL_Obool))),X24239)),X24238)),
inference(variable_rename,[status(thm)],[fact_UN__UN__flatten]) ).
fof(i_0_6495,plain,
! [X24232,X24233,X24234,X24235,X24236,X24237] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24237,tc_fun(X24236,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24235,tc_fun(X24237,tc_HOL_Obool)),X24234),X24233)),X24232) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24235,tc_fun(X24236,tc_HOL_Obool)),X24234),hAPP(hAPP(c_COMBC(X24235,tc_fun(X24237,tc_fun(X24236,tc_HOL_Obool)),tc_fun(X24236,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24237,tc_HOL_Obool),tc_fun(tc_fun(X24237,tc_fun(X24236,tc_HOL_Obool)),tc_fun(X24236,tc_HOL_Obool)),X24235),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24237,tc_fun(X24236,tc_HOL_Obool))),X24233)),X24232)),
inference(variable_rename,[status(thm)],[fact_UN__simps_I9_J]) ).
fof(i_0_6496,plain,
! [X28528,X28529,X28530,X28531,X28532,X28533,X28534] :
( hBOOL(hAPP(hAPP(c_member(X28534),X28533),X28532))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28534,X28531,X28530,X28529,X28532),X28528))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28534,X28531,X28530,X28529,hAPP(hAPP(c_Set_Oinsert(X28534),X28533),X28532)),hAPP(hAPP(X28530,X28533),X28528))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5367])]) ).
cnf(i_0_6497,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),esk435_6(X2,X1,X4,X5,X6,X3))
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| c_Map_Omap__comp(X3,X6,X5,X4,X1,X2) != c_Option_Ooption_ONone(X6) ),
inference(split_conjunct,[status(thm)],[i_0_5368]) ).
cnf(i_0_6498,plain,
( hAPP(X1,esk435_6(X2,X3,X1,X4,X5,X6)) = c_Option_Ooption_ONone(X5)
| hAPP(X3,X2) = c_Option_Ooption_ONone(X6)
| c_Map_Omap__comp(X6,X5,X4,X1,X3,X2) != c_Option_Ooption_ONone(X5) ),
inference(split_conjunct,[status(thm)],[i_0_5368]) ).
fof(i_0_6499,plain,
! [X27632,X27633,X27634,X27635,X27636,X27637,X27638,X27639,X27640,X27641] :
( ~ c_Equiv__Relations_Ocongruent2(X27641,X27640,X27639,X27638,X27637,X27636)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27641,X27641)),hAPP(hAPP(c_Product__Type_OPair(X27641,X27641),X27635),X27634)),X27638))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27640,X27640)),hAPP(hAPP(c_Product__Type_OPair(X27640,X27640),X27633),X27632)),X27637))
| hAPP(hAPP(X27636,X27635),X27633) = hAPP(hAPP(X27636,X27634),X27632) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2D])]) ).
fof(i_0_6500,plain,
! [X31565,X31566,X31567,X31568,X31569] :
( ( hBOOL(hAPP(hAPP(c_member(X31569),esk424_5(X31565,X31566,X31567,X31568,X31569)),X31568))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31569,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31569,tc_HOL_Obool)),X31568),hAPP(c_Set_OCollect(X31569),X31566))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31569,tc_HOL_Obool)),X31567),hAPP(c_Set_OCollect(X31569),X31565))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31569,tc_HOL_Obool)),X31568),X31567)) )
& ( hBOOL(hAPP(X31566,esk424_5(X31565,X31566,X31567,X31568,X31569)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31569,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31569,tc_HOL_Obool)),X31568),hAPP(c_Set_OCollect(X31569),X31566))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31569,tc_HOL_Obool)),X31567),hAPP(c_Set_OCollect(X31569),X31565))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31569,tc_HOL_Obool)),X31568),X31567)) )
& ( ~ hBOOL(hAPP(X31565,esk424_5(X31565,X31566,X31567,X31568,X31569)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31569,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31569,tc_HOL_Obool)),X31568),hAPP(c_Set_OCollect(X31569),X31566))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31569,tc_HOL_Obool)),X31567),hAPP(c_Set_OCollect(X31569),X31565))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31569,tc_HOL_Obool)),X31568),X31567)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__Collect__mono])])])]) ).
fof(i_0_6501,plain,
! [X33034,X33035,X33036,X33037,X33038,X33039] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33039)),X33038)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33037)),X33036)))
| c_Map_Omap__upds(X33039,X33037,X33035,hAPP(hAPP(c_List_Oappend(X33039),X33038),hAPP(hAPP(c_List_Olist_OCons(X33039),X33034),c_List_Olist_ONil(X33039))),X33036) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X33039,tc_Option_Ooption(X33037)),c_Map_Omap__upds(X33039,X33037,X33035,X33038,X33036)),X33034),hAPP(c_Option_Ooption_OSome(X33037),hAPP(hAPP(c_List_Onth(X33037),X33036),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33039)),X33038)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upds__append1])]) ).
fof(i_0_6502,plain,
! [X24357,X24358,X24359] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24359,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24359,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk151_3(X24357,X24358,X24359))),X24358)),X24357))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24359,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24359,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X24358)),X24357)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite__subset])])]) ).
fof(i_0_6503,plain,
! [X29233,X29234,X29235] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29235,tc_HOL_Obool)),X29234),X29233) = hAPP(c_Set_OCollect(X29235),hAPP(hAPP(c_COMBS(X29235,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29235),c_fconj),hAPP(hAPP(c_COMBC(X29235,tc_fun(X29235,tc_HOL_Obool),tc_HOL_Obool),c_member(X29235)),X29234))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29235),c_fNot),hAPP(hAPP(c_COMBC(X29235,tc_fun(X29235,tc_HOL_Obool),tc_HOL_Obool),c_member(X29235)),X29233)))),
inference(variable_rename,[status(thm)],[fact_set__diff__eq]) ).
fof(i_0_6504,plain,
! [X29149,X29150,X29151] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29151),hAPP(c_Set_OCollect(X29151),X29150)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29151),hAPP(c_Set_OCollect(X29151),hAPP(hAPP(c_COMBS(X29151,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29151),c_fconj),X29150)),X29149)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29151),hAPP(c_Set_OCollect(X29151),X29149)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29151),hAPP(c_Set_OCollect(X29151),hAPP(hAPP(c_COMBS(X29151,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29151),c_fconj),X29150)),X29149)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI])])]) ).
fof(i_0_6505,plain,
! [X17689,X17690,X17691,X17692,X17693,X17695,X17696,X17697,X17698,X17699,X17700] :
( ( hAPP(hAPP(hAPP(c_Natural_Oupdate,X17689),c_Com_Ovname_OLoc(X17693)),hAPP(hAPP(c_Natural_Ogetlocs,X17690),X17693)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk8_5(X17689,X17690,X17691,X17692,X17693)),c_Com_Ovname_OLoc(X17693)),hAPP(hAPP(c_Natural_Ogetlocs,X17690),X17693))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17693,X17692,X17691)),X17690),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17689),c_Com_Ovname_OLoc(X17693)),hAPP(hAPP(c_Natural_Ogetlocs,X17690),X17693)))) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17691),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17690),c_Com_Ovname_OLoc(X17693)),hAPP(X17692,X17690))),esk8_5(X17689,X17690,X17691,X17692,X17693)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17693,X17692,X17691)),X17690),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17689),c_Com_Ovname_OLoc(X17693)),hAPP(hAPP(c_Natural_Ogetlocs,X17690),X17693)))) )
& ( hAPP(hAPP(hAPP(c_Natural_Oupdate,X17695),c_Com_Ovname_OLoc(X17699)),hAPP(hAPP(c_Natural_Ogetlocs,X17696),X17699)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,X17700),c_Com_Ovname_OLoc(X17699)),hAPP(hAPP(c_Natural_Ogetlocs,X17696),X17699))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17697),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17696),c_Com_Ovname_OLoc(X17699)),hAPP(X17698,X17696))),X17700))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17699,X17698,X17697)),X17696),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17695),c_Com_Ovname_OLoc(X17699)),hAPP(hAPP(c_Natural_Ogetlocs,X17696),X17699)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I3_J])])])])])]) ).
fof(i_0_6506,plain,
! [X24345,X24346] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24346,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X24346,tc_HOL_Obool)),tc_fun(X24346,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X24346,tc_HOL_Obool)),tc_fun(X24346,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24346,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X24345)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24346,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X24345),
inference(variable_rename,[status(thm)],[fact_UN__UN__finite__eq]) ).
cnf(i_0_6507,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk387_4(X2,X3,X4,X1)),X3)),c_Transitive__Closure_Ortrancl(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5369]) ).
cnf(i_0_6508,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk386_4(X2,X3,X4,X1)),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5370]) ).
fof(i_0_6509,plain,
! [X28940,X28941,X28942,X28943,X28944,X28945,X28946,X28947] : hAPP(c_Product__Type_Omap__pair(X28947,X28946,X28945,X28944,X28943,X28942),hAPP(hAPP(c_Product__Type_OPair(X28947,X28945),X28941),X28940)) = hAPP(hAPP(c_Product__Type_OPair(X28946,X28944),hAPP(X28943,X28941)),hAPP(X28942,X28940)),
inference(variable_rename,[status(thm)],[fact_map__pair__simp]) ).
cnf(i_0_6510,plain,
hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X5),X6)) = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,X5)),X6),
inference(split_conjunct,[status(thm)],[i_0_5371]) ).
cnf(i_0_6511,plain,
hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X6)) = hAPP(hAPP(c_Product__Type_OPair(X3,X2),X5),hAPP(X4,X6)),
inference(split_conjunct,[status(thm)],[i_0_5372]) ).
fof(i_0_6512,plain,
! [X28923,X28924,X28925] : hAPP(c_Product__Type_Omap__pair(X28925,X28925,X28924,X28924,c_COMBI(X28925),c_COMBI(X28924)),X28923) = X28923,
inference(variable_rename,[status(thm)],[fact_map__pair__ident]) ).
fof(i_0_6513,plain,
! [X23666,X23667,X23668,X23669,X23670] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk123_5(X23666,X23667,X23668,X23669,X23670)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23668)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23670),X23666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23670),X23668)),X23666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23669),X23668)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk124_5(X23666,X23667,X23668,X23669,X23670)),X23667))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23670),X23666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23670),X23668)),X23666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23669),X23668)) )
& ( X23670 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk124_5(X23666,X23667,X23668,X23669,X23670)),esk123_5(X23666,X23667,X23668,X23669,X23670))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23670),X23666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23670),X23668)),X23666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23669),X23668)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5373])])])])]) ).
fof(i_0_6514,plain,
! [X23659,X23660,X23661,X23662,X23663] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk121_5(X23659,X23660,X23661,X23662,X23663)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23661)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23663),X23659)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23663),X23661)),X23659)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23662),X23661)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk122_5(X23659,X23660,X23661,X23662,X23663)),X23660))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23663),X23659)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23663),X23661)),X23659)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23662),X23661)) )
& ( X23663 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk122_5(X23659,X23660,X23661,X23662,X23663)),esk121_5(X23659,X23660,X23661,X23662,X23663))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23663),X23659)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23663),X23661)),X23659)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23662),X23661)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5374])])])])]) ).
fof(i_0_6515,plain,
! [X33175,X33176,X33177,X33178,X33179,X33180,X33181] :
( hBOOL(hAPP(hAPP(c_member(X33181),X33180),hAPP(c_List_Oset(X33181),X33179)))
| c_Map_Omap__upds(X33181,X33178,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X33181,tc_Option_Ooption(X33178)),X33177),X33180),hAPP(c_Option_Ooption_OSome(X33178),X33176)),X33179,X33175) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X33181,tc_Option_Ooption(X33178)),c_Map_Omap__upds(X33181,X33178,X33177,X33179,X33175)),X33180),hAPP(c_Option_Ooption_OSome(X33178),X33176)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5375])]) ).
fof(i_0_6516,plain,
! [X23652,X23653,X23654,X23655,X23656] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk119_5(X23652,X23653,X23654,X23655,X23656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23654)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23656),X23652)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23656),X23654)),X23652)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23655),X23654)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk120_5(X23652,X23653,X23654,X23655,X23656)),X23653))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23656),X23652)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23656),X23654)),X23652)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23655),X23654)) )
& ( X23656 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk120_5(X23652,X23653,X23654,X23655,X23656)),esk119_5(X23652,X23653,X23654,X23655,X23656))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23656),X23652)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23656),X23654)),X23652)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23655),X23654)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I9_J])])])])]) ).
fof(i_0_6517,plain,
! [X23645,X23646,X23647,X23648,X23649] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk117_5(X23645,X23646,X23647,X23648,X23649)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23647)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23648),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23649),X23645)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23648),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23649),X23647)),X23645)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23648),X23647)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk118_5(X23645,X23646,X23647,X23648,X23649)),X23646))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23648),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23649),X23645)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23648),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23649),X23647)),X23645)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23648),X23647)) )
& ( X23649 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk118_5(X23645,X23646,X23647,X23648,X23649)),esk117_5(X23645,X23646,X23647,X23648,X23649))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23648),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23649),X23645)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23648),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23649),X23647)),X23645)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23648),X23647)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I9_J])])])])]) ).
fof(i_0_6518,plain,
! [X27508,X27509,X27510,X27511,X27512,X27513,X27514,X27515] :
( ~ c_Finite__Set_Ofolding__image__simple(X27515,X27514,X27513,X27512,X27511,X27510)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27514),X27509))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27514),X27508))
| hAPP(hAPP(X27513,hAPP(X27510,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27514,tc_HOL_Obool)),X27509),X27508))),hAPP(X27510,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27514,tc_HOL_Obool)),X27509),X27508))) = hAPP(hAPP(X27513,hAPP(X27510,X27509)),hAPP(X27510,X27508)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter])]) ).
fof(i_0_6519,plain,
! [X27744,X27745,X27746,X27747,X27748] :
( ( hBOOL(hAPP(hAPP(c_member(X27747),esk253_5(X27744,X27745,X27746,X27747,X27748)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27747,tc_HOL_Obool)),X27746),X27745)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27747,X27748),X27744),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27747,tc_HOL_Obool)),X27746),X27745)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27748),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27747,X27748),X27744),X27746)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27747,X27748),X27744),X27745))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27747),X27745))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27747),X27746))
| ~ class_Groups_Ocomm__monoid__mult(X27748) )
& ( hAPP(X27744,esk253_5(X27744,X27745,X27746,X27747,X27748)) != c_Groups_Oone__class_Oone(X27748)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27747,X27748),X27744),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27747,tc_HOL_Obool)),X27746),X27745)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27748),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27747,X27748),X27744),X27746)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27747,X27748),X27744),X27745))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27747),X27745))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27747),X27746))
| ~ class_Groups_Ocomm__monoid__mult(X27748) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__one])])])]) ).
fof(i_0_6520,plain,
! [X27738,X27739,X27740,X27741,X27742] :
( ( hBOOL(hAPP(hAPP(c_member(X27741),esk252_5(X27738,X27739,X27740,X27741,X27742)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27741,tc_HOL_Obool)),X27740),X27739)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27741,X27742),X27738),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27741,tc_HOL_Obool)),X27740),X27739)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27742),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27741,X27742),X27738),X27740)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27741,X27742),X27738),X27739))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27741),X27739))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27741),X27740))
| ~ class_Groups_Ocomm__monoid__mult(X27742) )
& ( hAPP(X27738,esk252_5(X27738,X27739,X27740,X27741,X27742)) != c_Groups_Oone__class_Oone(X27742)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27741,X27742),X27738),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27741,tc_HOL_Obool)),X27740),X27739)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27742),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27741,X27742),X27738),X27740)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27741,X27742),X27738),X27739))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27741),X27739))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27741),X27740))
| ~ class_Groups_Ocomm__monoid__mult(X27742) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter__neutral])])])]) ).
fof(i_0_6521,plain,
! [X27756,X27757,X27758,X27759,X27760] :
( ( hBOOL(hAPP(hAPP(c_member(X27759),esk255_5(X27756,X27757,X27758,X27759,X27760)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27759,tc_HOL_Obool)),X27758),X27757)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27759,X27760),X27756),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27759,tc_HOL_Obool)),X27758),X27757)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27760),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27759,X27760),X27756),X27758)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27759,X27760),X27756),X27757))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27759),X27757))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27759),X27758))
| ~ class_Groups_Ocomm__monoid__add(X27760) )
& ( hAPP(X27756,esk255_5(X27756,X27757,X27758,X27759,X27760)) != c_Groups_Ozero__class_Ozero(X27760)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27759,X27760),X27756),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27759,tc_HOL_Obool)),X27758),X27757)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27760),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27759,X27760),X27756),X27758)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27759,X27760),X27756),X27757))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27759),X27757))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27759),X27758))
| ~ class_Groups_Ocomm__monoid__add(X27760) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Ounion__inter__neutral])])])]) ).
fof(i_0_6522,plain,
! [X27750,X27751,X27752,X27753,X27754] :
( ( hBOOL(hAPP(hAPP(c_member(X27753),esk254_5(X27750,X27751,X27752,X27753,X27754)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27753,tc_HOL_Obool)),X27752),X27751)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27753,X27754),X27750),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27753,tc_HOL_Obool)),X27752),X27751)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27753,X27754),X27750),X27752)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27753,X27754),X27750),X27751))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27753),X27751))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27753),X27752))
| ~ class_Groups_Ocomm__monoid__add(X27754) )
& ( hAPP(X27750,esk254_5(X27750,X27751,X27752,X27753,X27754)) != c_Groups_Ozero__class_Ozero(X27754)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27753,X27754),X27750),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27753,tc_HOL_Obool)),X27752),X27751)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27753,X27754),X27750),X27752)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27753,X27754),X27750),X27751))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27753),X27751))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27753),X27752))
| ~ class_Groups_Ocomm__monoid__add(X27754) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__zero])])])]) ).
fof(i_0_6523,plain,
! [X29288,X29289,X29290,X29291] : hAPP(c_Relation_OImage(X29291,X29290,X29289),hAPP(hAPP(c_Set_Oinsert(X29291),X29288),c_Orderings_Obot__class_Obot(tc_fun(X29291,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X29290),hAPP(hAPP(c_COMBC(X29290,tc_fun(tc_prod(X29291,X29290),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X29291,X29290),tc_fun(tc_fun(tc_prod(X29291,X29290),tc_HOL_Obool),tc_HOL_Obool),X29290),c_member(tc_prod(X29291,X29290))),hAPP(c_Product__Type_OPair(X29291,X29290),X29288))),X29289)),
inference(variable_rename,[status(thm)],[fact_Image__singleton]) ).
fof(i_0_6524,plain,
! [X17873,X17874,X17875,X17876,X17877] :
( ( X17873 = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk14_5(X17873,X17874,X17875,X17876,X17877)),c_Com_Ovname_OLoc(X17877)),hAPP(hAPP(c_Natural_Ogetlocs,X17874),X17877))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17877,X17876,X17875)),X17874),X17873)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17875),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17874),c_Com_Ovname_OLoc(X17877)),hAPP(X17876,X17874))),esk14_5(X17873,X17874,X17875,X17876,X17877)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17877,X17876,X17875)),X17874),X17873)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5376])])])]) ).
cnf(i_0_6525,plain,
c_List_Ofoldr(tc_List_Olist(X1),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),c_List_Otranspose(X1,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
inference(split_conjunct,[status(thm)],[i_0_5377]) ).
fof(i_0_6526,plain,
! [X25294,X25295,X25296,X25297,X25298,X25299,X25300,X25301] :
( ~ c_Finite__Set_Ofolding__image__simple(X25301,X25300,X25299,X25298,X25297,X25296)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25300),X25295))
| ~ hBOOL(hAPP(hAPP(c_member(X25300),X25294),X25295))
| hAPP(X25296,X25295) = hAPP(hAPP(X25299,hAPP(X25297,X25294)),hAPP(X25296,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25300,tc_HOL_Obool)),X25295),hAPP(hAPP(c_Set_Oinsert(X25300),X25294),c_Orderings_Obot__class_Obot(tc_fun(X25300,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove])]) ).
fof(i_0_6527,plain,
! [X23700,X23701,X23702,X23703,X23704,X23706,X23707,X23708,X23709,X23710,X23711] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23702,tc_HOL_Obool)),esk127_5(X23700,X23701,X23702,X23703,X23704)),X23700))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23704,tc_HOL_Obool)),X23703),hAPP(c_Set_Oimage(X23702,X23704,X23701),X23700))) )
& ( X23703 = hAPP(c_Set_Oimage(X23702,X23704,X23701),esk127_5(X23700,X23701,X23702,X23703,X23704))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23704,tc_HOL_Obool)),X23703),hAPP(c_Set_Oimage(X23702,X23704,X23701),X23700))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23708,tc_HOL_Obool)),X23711),X23706))
| X23709 != hAPP(c_Set_Oimage(X23708,X23710,X23707),X23711)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23710,tc_HOL_Obool)),X23709),hAPP(c_Set_Oimage(X23708,X23710,X23707),X23706))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__image__iff])])])])])]) ).
fof(i_0_6528,plain,
! [X25205,X25206,X25207,X25208,X25209,X25211,X25212,X25213,X25214,X25215,X25216] :
( ( hBOOL(hAPP(hAPP(c_member(X25207),esk168_5(X25205,X25206,X25207,X25208,X25209)),X25206))
| ~ hBOOL(hAPP(hAPP(c_member(X25209),X25208),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25207,tc_fun(X25209,tc_HOL_Obool)),X25206),X25205))) )
& ( hBOOL(hAPP(hAPP(c_member(X25209),X25208),hAPP(X25205,esk168_5(X25205,X25206,X25207,X25208,X25209))))
| ~ hBOOL(hAPP(hAPP(c_member(X25209),X25208),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25207,tc_fun(X25209,tc_HOL_Obool)),X25206),X25205))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25213),X25216),X25212))
| ~ hBOOL(hAPP(hAPP(c_member(X25215),X25214),hAPP(X25211,X25216)))
| hBOOL(hAPP(hAPP(c_member(X25215),X25214),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25213,tc_fun(X25215,tc_HOL_Obool)),X25212),X25211))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__iff])])])])])]) ).
fof(i_0_6529,plain,
! [X24921,X24922,X24923,X24924,X24925,X24926,X24927,X24928] :
( ~ c_Finite__Set_Ofolding__image__simple(X24928,X24927,X24926,X24925,X24924,X24923)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24927),X24922))
| hAPP(X24923,hAPP(hAPP(c_Set_Oinsert(X24927),X24921),X24922)) = hAPP(hAPP(X24926,hAPP(X24924,X24921)),hAPP(X24923,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24927,tc_HOL_Obool)),X24922),hAPP(hAPP(c_Set_Oinsert(X24927),X24921),c_Orderings_Obot__class_Obot(tc_fun(X24927,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert__remove])]) ).
fof(i_0_6530,plain,
! [X28256,X28257,X28258,X28259,X28260,X28261,X28262] :
( ~ c_Fun_Oinj__on(X28262,X28261,X28260,hAPP(c_Set_Oimage(X28259,X28262,X28258),X28257))
| ~ c_Fun_Oinj__on(X28259,X28262,X28258,X28257)
| ~ hBOOL(hAPP(hAPP(c_member(X28261),X28256),hAPP(c_Set_Oimage(X28262,X28261,X28260),hAPP(c_Set_Oimage(X28259,X28262,X28258),X28257))))
| hAPP(c_Fun_Othe__inv__into(X28259,X28261,X28257,hAPP(c_Fun_Ocomp(X28262,X28261,X28259,X28260),X28258)),X28256) = hAPP(hAPP(c_Fun_Ocomp(X28262,X28259,X28261,c_Fun_Othe__inv__into(X28259,X28262,X28257,X28258)),c_Fun_Othe__inv__into(X28262,X28261,hAPP(c_Set_Oimage(X28259,X28262,X28258),X28257),X28260)),X28256) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__comp])]) ).
cnf(i_0_6531,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))),
inference(split_conjunct,[status(thm)],[i_0_5378]) ).
fof(i_0_6532,plain,
! [X26460,X26461,X26462,X26463,X26464] :
( ( hBOOL(hAPP(hAPP(c_member(X26463),esk228_5(X26460,X26461,X26462,X26463,X26464)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26463,tc_HOL_Obool)),X26462),X26461)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26463,X26464),X26460),X26462) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26463,X26464),X26460),X26461)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26463,tc_HOL_Obool)),X26461),X26462))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26463),X26462))
| ~ class_Groups_Ocomm__monoid__mult(X26464) )
& ( hAPP(X26460,esk228_5(X26460,X26461,X26462,X26463,X26464)) != c_Groups_Oone__class_Oone(X26464)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26463,X26464),X26460),X26462) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26463,X26464),X26460),X26461)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26463,tc_HOL_Obool)),X26461),X26462))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26463),X26462))
| ~ class_Groups_Ocomm__monoid__mult(X26464) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__right])])])]) ).
fof(i_0_6533,plain,
! [X26454,X26455,X26456,X26457,X26458] :
( ( hBOOL(hAPP(hAPP(c_member(X26457),esk227_5(X26454,X26455,X26456,X26457,X26458)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26457,tc_HOL_Obool)),X26456),X26455)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26457,X26458),X26454),X26455) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26457,X26458),X26454),X26456)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26457,tc_HOL_Obool)),X26455),X26456))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26457),X26456))
| ~ class_Groups_Ocomm__monoid__mult(X26458) )
& ( hAPP(X26454,esk227_5(X26454,X26455,X26456,X26457,X26458)) != c_Groups_Oone__class_Oone(X26458)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26457,X26458),X26454),X26455) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26457,X26458),X26454),X26456)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26457,tc_HOL_Obool)),X26455),X26456))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26457),X26456))
| ~ class_Groups_Ocomm__monoid__mult(X26458) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__left])])])]) ).
fof(i_0_6534,plain,
! [X26472,X26473,X26474,X26475,X26476] :
( ( hBOOL(hAPP(hAPP(c_member(X26475),esk230_5(X26472,X26473,X26474,X26475,X26476)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26475,tc_HOL_Obool)),X26474),X26473)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26475,X26476),X26472),X26473) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26475,X26476),X26472),X26474)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26475,tc_HOL_Obool)),X26473),X26474))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26475),X26474))
| ~ class_Groups_Ocomm__monoid__add(X26476) )
& ( hAPP(X26472,esk230_5(X26472,X26473,X26474,X26475,X26476)) != c_Groups_Ozero__class_Ozero(X26476)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26475,X26476),X26472),X26473) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26475,X26476),X26472),X26474)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26475,tc_HOL_Obool)),X26473),X26474))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26475),X26474))
| ~ class_Groups_Ocomm__monoid__add(X26476) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__left])])])]) ).
fof(i_0_6535,plain,
! [X26466,X26467,X26468,X26469,X26470] :
( ( hBOOL(hAPP(hAPP(c_member(X26469),esk229_5(X26466,X26467,X26468,X26469,X26470)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26469,tc_HOL_Obool)),X26468),X26467)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26469,X26470),X26466),X26468) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26469,X26470),X26466),X26467)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26469,tc_HOL_Obool)),X26467),X26468))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26469),X26468))
| ~ class_Groups_Ocomm__monoid__add(X26470) )
& ( hAPP(X26466,esk229_5(X26466,X26467,X26468,X26469,X26470)) != c_Groups_Ozero__class_Ozero(X26470)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26469,X26470),X26466),X26468) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26469,X26470),X26466),X26467)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26469,tc_HOL_Obool)),X26467),X26468))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26469),X26468))
| ~ class_Groups_Ocomm__monoid__add(X26470) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__right])])])]) ).
cnf(i_0_6536,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__eq__frac(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_5356]) ).
cnf(i_0_6537,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__frac(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_5357]) ).
fof(i_0_6538,plain,
! [X24148,X24149,X24150,X24151,X24152,X24154,X24155,X24156,X24157,X24158,X24159] :
( ( hBOOL(hAPP(hAPP(c_member(X24152),esk138_5(X24148,X24149,X24150,X24151,X24152)),X24150))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24152,tc_fun(X24151,tc_HOL_Obool)),X24150),X24149),X24148)) )
& ( hBOOL(hAPP(hAPP(X24149,esk138_5(X24148,X24149,X24150,X24151,X24152)),X24148))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24152,tc_fun(X24151,tc_HOL_Obool)),X24150),X24149),X24148)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24158),X24159),X24156))
| ~ hBOOL(hAPP(hAPP(X24155,X24159),X24154))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24158,tc_fun(X24157,tc_HOL_Obool)),X24156),X24155),X24154)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP1__iff])])])])])]) ).
fof(i_0_6539,plain,
! [X30447,X30448,X30449] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30449,X30449)),X30448),c_Transitive__Closure_Ortrancl(X30449,X30447)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30449,X30449)),X30448),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X30449,X30449),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X30449,X30449),tc_HOL_Obool),tc_fun(tc_prod(X30449,X30449),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X30449,X30449),tc_HOL_Obool)),X30447)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__imp__UN__rel__pow])]) ).
fof(i_0_6540,plain,
! [X31390,X31391,X31392,X31393,X31394] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31394,tc_fun(X31393,tc_HOL_Obool)),X31392),hAPP(hAPP(c_COMBS(X31394,tc_fun(X31393,tc_HOL_Obool),tc_fun(X31393,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31393,tc_HOL_Obool),tc_fun(tc_fun(X31393,tc_HOL_Obool),tc_fun(X31393,tc_HOL_Obool)),X31394),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31393,tc_HOL_Obool))),X31391)),X31390)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31393,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31393,tc_HOL_Obool),hAPP(c_Set_Oimage(X31394,tc_fun(X31393,tc_HOL_Obool),X31391),X31392))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31393,tc_HOL_Obool),hAPP(c_Set_Oimage(X31394,tc_fun(X31393,tc_HOL_Obool),X31390),X31392))),
inference(variable_rename,[status(thm)],[fact_Int__Inter__image]) ).
fof(i_0_6541,plain,
! [X31406,X31407,X31408,X31409,X31410] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31410,tc_fun(X31409,tc_HOL_Obool)),X31408),hAPP(hAPP(c_COMBS(X31410,tc_fun(X31409,tc_HOL_Obool),tc_fun(X31409,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31409,tc_HOL_Obool),tc_fun(tc_fun(X31409,tc_HOL_Obool),tc_fun(X31409,tc_HOL_Obool)),X31410),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31409,tc_HOL_Obool))),X31407)),X31406)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31409,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31409,tc_HOL_Obool),hAPP(c_Set_Oimage(X31410,tc_fun(X31409,tc_HOL_Obool),X31407),X31408))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31409,tc_HOL_Obool),hAPP(c_Set_Oimage(X31410,tc_fun(X31409,tc_HOL_Obool),X31406),X31408))),
inference(variable_rename,[status(thm)],[fact_Un__Union__image]) ).
fof(i_0_6542,plain,
! [X32907,X32908,X32909,X32910,X32911,X32912,X32913] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32913,X32913)),hAPP(hAPP(c_Product__Type_OPair(X32913,X32913),X32912),X32911)),X32910))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32913),tc_List_Olist(X32913))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32913),tc_List_Olist(X32913)),hAPP(hAPP(c_List_Oappend(X32913),X32909),hAPP(hAPP(c_List_Olist_OCons(X32913),X32912),X32908))),hAPP(hAPP(c_List_Oappend(X32913),X32909),hAPP(hAPP(c_List_Olist_OCons(X32913),X32911),X32907)))),c_List_Olexord(X32913,X32910))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI])]) ).
fof(i_0_6543,plain,
! [X26378,X26379,X26380,X26381] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26381),X26380)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26379),X26378))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26381),X26378) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26379),X26380) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26381),X26378) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26379),X26380)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26381),X26380)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26379),X26378))),c_Int_Ointrel)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_intrel__iff])]) ).
fof(i_0_6544,plain,
! [X25934,X25935,X25936,X25937,X25938,X25939,X25940] :
( ~ hBOOL(hAPP(X25940,X25939))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25938,X25938)),hAPP(hAPP(c_Product__Type_OPair(X25938,X25938),X25937),X25936)),hAPP(X25935,X25939)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X25934,X25938),tc_prod(X25934,X25938))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X25934,X25938),tc_prod(X25934,X25938)),hAPP(hAPP(c_Product__Type_OPair(X25934,X25938),X25939),X25937)),hAPP(hAPP(c_Product__Type_OPair(X25934,X25938),X25939),X25936))),c_Recdef_Osame__fst(X25934,X25938,X25940,X25935))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
fof(i_0_6545,plain,
! [X24251,X24252,X24253,X24254,X24255,X24257] :
( ( hBOOL(hAPP(hAPP(c_member(X24253),esk143_5(X24251,X24252,X24253,X24254,X24255)),X24252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),X24254),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24253,X24255),X24252),X24251)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X24255)
| ~ class_Orderings_Olinorder(X24255) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),X24254),hAPP(X24251,esk143_5(X24251,X24252,X24253,X24254,X24255))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),X24254),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24253,X24255),X24252),X24251)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X24255)
| ~ class_Orderings_Olinorder(X24255) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24253),X24257),X24252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),X24254),hAPP(X24251,X24257)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),X24254),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24253,X24255),X24252),X24251)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X24255)
| ~ class_Orderings_Olinorder(X24255) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SUP__iff])])])])]) ).
fof(i_0_6546,plain,
! [X22112,X22113,X22114,X22115,X22116,X22117,X22118,X22119] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22119,X22118,X22117),X22116),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22115,X22114,tc_prod(X22119,X22118)),X22113),X22112)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22115,X22114,X22117),hAPP(hAPP(c_COMBB(tc_fun(X22114,tc_prod(X22119,X22118)),tc_fun(X22114,X22117),X22115),hAPP(c_COMBB(tc_prod(X22119,X22118),X22117,X22114),hAPP(c_Product__Type_Oprod_Oprod__case(X22119,X22118,X22117),X22116))),X22113)),X22112),
inference(variable_rename,[status(thm)],[fact_split__twice]) ).
cnf(i_0_6547,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5379]) ).
cnf(i_0_6548,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5380]) ).
cnf(i_0_6549,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[i_0_5381]) ).
fof(i_0_6550,plain,
! [X26557,X26558,X26559,X26560] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26560),esk234_4(X26557,X26558,X26559,X26560)))
| hBOOL(hAPP(X26557,X26559))
| ~ hBOOL(hAPP(X26557,c_Orderings_Obot__class_Obot(tc_fun(X26560,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26560,tc_HOL_Obool)),X26559),X26558))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26560),X26559)) )
& ( hBOOL(hAPP(hAPP(c_member(X26560),esk233_4(X26557,X26558,X26559,X26560)),X26558))
| hBOOL(hAPP(X26557,X26559))
| ~ hBOOL(hAPP(X26557,c_Orderings_Obot__class_Obot(tc_fun(X26560,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26560,tc_HOL_Obool)),X26559),X26558))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26560),X26559)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X26560),esk233_4(X26557,X26558,X26559,X26560)),esk234_4(X26557,X26558,X26559,X26560)))
| hBOOL(hAPP(X26557,X26559))
| ~ hBOOL(hAPP(X26557,c_Orderings_Obot__class_Obot(tc_fun(X26560,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26560,tc_HOL_Obool)),X26559),X26558))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26560),X26559)) )
& ( hBOOL(hAPP(X26557,esk234_4(X26557,X26558,X26559,X26560)))
| hBOOL(hAPP(X26557,X26559))
| ~ hBOOL(hAPP(X26557,c_Orderings_Obot__class_Obot(tc_fun(X26560,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26560,tc_HOL_Obool)),X26559),X26558))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26560),X26559)) )
& ( ~ hBOOL(hAPP(X26557,hAPP(hAPP(c_Set_Oinsert(X26560),esk233_4(X26557,X26558,X26559,X26560)),esk234_4(X26557,X26558,X26559,X26560))))
| hBOOL(hAPP(X26557,X26559))
| ~ hBOOL(hAPP(X26557,c_Orderings_Obot__class_Obot(tc_fun(X26560,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26560,tc_HOL_Obool)),X26559),X26558))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26560),X26559)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5382])])])]) ).
fof(i_0_6551,plain,
! [X33788,X33789,X33790,X33791] :
( ( hBOOL(hAPP(hAPP(c_member(X33791),esk477_4(X33788,X33789,X33790,X33791)),hAPP(c_List_Oset(X33791),X33790)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X33791,X33789,X33790)),c_List_Olist_Olist__size(X33791,X33788,X33790))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X33789,esk477_4(X33788,X33789,X33790,X33791))),hAPP(X33788,esk477_4(X33788,X33789,X33790,X33791))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X33791,X33789,X33790)),c_List_Olist_Olist__size(X33791,X33788,X33790))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__pointwise])])])]) ).
fof(i_0_6552,plain,
! [X29334,X29335] : c_Fun_Oinj__on(tc_fun(X29335,X29334),tc_fun(tc_prod(X29335,X29334),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29335,X29334),tc_HOL_Obool),tc_fun(tc_prod(X29335,X29334),tc_HOL_Obool),tc_fun(X29335,X29334)),c_Set_OCollect(tc_prod(X29335,X29334))),hAPP(hAPP(c_COMBB(tc_fun(X29335,tc_fun(X29334,tc_HOL_Obool)),tc_fun(tc_prod(X29335,X29334),tc_HOL_Obool),tc_fun(X29335,X29334)),c_Product__Type_Oprod_Oprod__case(X29335,X29334,tc_HOL_Obool)),hAPP(c_COMBB(X29334,tc_fun(X29334,tc_HOL_Obool),X29335),hAPP(c_COMBC(X29334,X29334,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X29335,X29334),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_inj__graph]) ).
cnf(i_0_6553,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(split_conjunct,[status(thm)],[fact_numeral__3__eq__3]) ).
cnf(i_0_6554,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5383]) ).
cnf(i_0_6555,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J]) ).
cnf(i_0_6556,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1),
inference(split_conjunct,[status(thm)],[i_0_5384]) ).
cnf(i_0_6557,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[i_0_5385]) ).
fof(i_0_6558,plain,
! [X28567,X28568,X28569,X28570,X28571,X28573,X28574,X28575,X28576,X28578] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28570),X28568))
| ~ c_Wellfounded_Omax__extp(X28570,X28569,X28568,X28567) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28570),X28567))
| ~ c_Wellfounded_Omax__extp(X28570,X28569,X28568,X28567) )
& ( X28567 != c_Orderings_Obot__class_Obot(tc_fun(X28570,tc_HOL_Obool))
| ~ c_Wellfounded_Omax__extp(X28570,X28569,X28568,X28567) )
& ( hBOOL(hAPP(hAPP(c_member(X28570),esk276_5(X28567,X28568,X28569,X28570,X28571)),X28567))
| ~ hBOOL(hAPP(hAPP(c_member(X28570),X28571),X28568))
| ~ c_Wellfounded_Omax__extp(X28570,X28569,X28568,X28567) )
& ( hBOOL(hAPP(hAPP(X28569,X28571),esk276_5(X28567,X28568,X28569,X28570,X28571)))
| ~ hBOOL(hAPP(hAPP(c_member(X28570),X28571),X28568))
| ~ c_Wellfounded_Omax__extp(X28570,X28569,X28568,X28567) )
& ( hBOOL(hAPP(hAPP(c_member(X28576),esk277_4(X28573,X28574,X28575,X28576)),X28574))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28576),X28574))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28576),X28573))
| X28573 = c_Orderings_Obot__class_Obot(tc_fun(X28576,tc_HOL_Obool))
| c_Wellfounded_Omax__extp(X28576,X28575,X28574,X28573) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28576),X28578),X28573))
| ~ hBOOL(hAPP(hAPP(X28575,esk277_4(X28573,X28574,X28575,X28576)),X28578))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28576),X28574))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28576),X28573))
| X28573 = c_Orderings_Obot__class_Obot(tc_fun(X28576,tc_HOL_Obool))
| c_Wellfounded_Omax__extp(X28576,X28575,X28574,X28573) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp_Oequations])])])])])]) ).
fof(i_0_6559,plain,
! [X29227,X29228,X29229] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29229,tc_HOL_Obool)),X29228),X29227) = hAPP(c_Set_OCollect(X29229),hAPP(hAPP(c_COMBS(X29229,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29229),c_fconj),hAPP(hAPP(c_COMBC(X29229,tc_fun(X29229,tc_HOL_Obool),tc_HOL_Obool),c_member(X29229)),X29228))),hAPP(hAPP(c_COMBC(X29229,tc_fun(X29229,tc_HOL_Obool),tc_HOL_Obool),c_member(X29229)),X29227))),
inference(variable_rename,[status(thm)],[fact_Int__def]) ).
fof(i_0_6560,plain,
! [X29230,X29231,X29232] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29232,tc_HOL_Obool)),X29231),X29230) = hAPP(c_Set_OCollect(X29232),hAPP(hAPP(c_COMBS(X29232,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29232),c_fdisj),hAPP(hAPP(c_COMBC(X29232,tc_fun(X29232,tc_HOL_Obool),tc_HOL_Obool),c_member(X29232)),X29231))),hAPP(hAPP(c_COMBC(X29232,tc_fun(X29232,tc_HOL_Obool),tc_HOL_Obool),c_member(X29232)),X29230))),
inference(variable_rename,[status(thm)],[fact_Un__def]) ).
fof(i_0_6561,plain,
! [X27561,X27562,X27563,X27564,X27565,X27566,X27567,X27568] :
( ~ c_Finite__Set_Ofolding__image__simple(X27568,X27567,X27566,X27565,X27564,X27563)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27567),X27562))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27567),X27561))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27567,tc_HOL_Obool)),X27562),X27561) != c_Orderings_Obot__class_Obot(tc_fun(X27567,tc_HOL_Obool))
| hAPP(X27563,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27567,tc_HOL_Obool)),X27562),X27561)) = hAPP(hAPP(X27566,hAPP(X27563,X27562)),hAPP(X27563,X27561)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__disjoint])]) ).
fof(i_0_6562,plain,
! [X26304,X26305,X26306,X26307,X26308,X26309] :
( ~ hBOOL(hAPP(hAPP(c_member(X26309),X26308),X26307))
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26309,tc_Option_Ooption(X26306)),c_Map_Orestrict__map(X26309,X26306,X26305,X26307)),X26308),X26304) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26309,tc_Option_Ooption(X26306)),c_Map_Orestrict__map(X26309,X26306,X26305,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26309,tc_HOL_Obool)),X26307),hAPP(hAPP(c_Set_Oinsert(X26309),X26308),c_Orderings_Obot__class_Obot(tc_fun(X26309,tc_HOL_Obool)))))),X26308),X26304) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__restrict__conv])]) ).
fof(i_0_6563,plain,
! [X20467,X20468,X20469,X20470,X20471,X20472] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20472),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20472),X20471),X20470)),X20469)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20472),X20468),X20470)),X20467)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20472),X20469),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20472),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20472),X20468),X20471)),X20470)),X20467)))
| ~ class_Rings_Oordered__ring(X20472) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20472),X20469),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20472),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20472),X20468),X20471)),X20470)),X20467)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20472),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20472),X20471),X20470)),X20469)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20472),X20468),X20470)),X20467)))
| ~ class_Rings_Oordered__ring(X20472) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).
fof(i_0_6564,plain,
! [X20479,X20480,X20481,X20482,X20483,X20484] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20484),X20483),X20482)),X20481)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20484),X20480),X20482)),X20479)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20484),X20481),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20484),X20480),X20483)),X20482)),X20479)))
| ~ class_Rings_Oordered__ring(X20484) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20484),X20481),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20484),X20480),X20483)),X20482)),X20479)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20484),X20483),X20482)),X20481)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20484),X20480),X20482)),X20479)))
| ~ class_Rings_Oordered__ring(X20484) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).
fof(i_0_6565,plain,
! [X30958,X30959,X30960,X30961,X30962,X30963] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30963,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30962,X30963,X30961),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30960,tc_fun(X30962,tc_HOL_Obool)),X30959),X30958))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30960,tc_fun(X30963,tc_HOL_Obool)),X30959),hAPP(hAPP(c_COMBB(tc_fun(X30962,tc_HOL_Obool),tc_fun(X30963,tc_HOL_Obool),X30960),c_Relation_OImage(X30962,X30963,X30961)),X30958)))),
inference(variable_rename,[status(thm)],[fact_Image__INT__subset]) ).
fof(i_0_6566,plain,
! [X31557,X31558,X31559,X31560,X31561,X31562,X31563,X31564] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X31564,X31563,X31562,X31561,X31560,X31559)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31563),X31558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31563,tc_HOL_Obool)),X31557),X31558))
| hAPP(hAPP(X31562,hAPP(X31559,X31557)),hAPP(X31559,X31558)) = hAPP(X31559,X31558) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).
fof(i_0_6567,plain,
! [X19090,X19091,X19092,X19093,X19094] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19092,X19093)),X19091),X19090))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19093),hAPP(X19091,X19094)),hAPP(X19090,X19094)))
| ~ class_Orderings_Oord(X19093) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19093),hAPP(X19091,esk42_4(X19090,X19091,X19092,X19093))),hAPP(X19090,esk42_4(X19090,X19091,X19092,X19093))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19092,X19093)),X19091),X19090))
| ~ class_Orderings_Oord(X19093) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__fun__def])])])])]) ).
fof(i_0_6568,plain,
! [X26290,X26291,X26292,X26293,X26294,X26295] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26295,tc_Option_Ooption(X26294)),c_Map_Orestrict__map(X26295,X26294,X26293,X26292)),X26291),X26290) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26295,tc_Option_Ooption(X26294)),c_Map_Orestrict__map(X26295,X26294,X26293,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26295,tc_HOL_Obool)),X26292),hAPP(hAPP(c_Set_Oinsert(X26295),X26291),c_Orderings_Obot__class_Obot(tc_fun(X26295,tc_HOL_Obool)))))),X26291),X26290),
inference(variable_rename,[status(thm)],[fact_fun__upd__restrict]) ).
fof(i_0_6569,plain,
! [X28022,X28023,X28024,X28025,X28026,X28027,X28028] :
( ~ c_Finite__Set_Ofolding__image__simple(X28028,X28027,X28026,X28025,X28024,X28023)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28027),X28022))
| hAPP(X28023,X28022) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28028,X28027,X28026),X28024),X28025),X28022) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).
fof(i_0_6570,plain,
! [X31839,X31840,X31841,X31842,X31843,X31844,X31845,X31846,X31847,X31848,X31849] :
( ( hAPP(hAPP(c_List_Omap(X31843,X31842),X31841),X31840) != hAPP(hAPP(c_List_Omap(X31843,X31842),X31839),X31840)
| ~ hBOOL(hAPP(hAPP(c_member(X31843),X31844),hAPP(c_List_Oset(X31843),X31840)))
| hAPP(X31841,X31844) = hAPP(X31839,X31844) )
& ( hBOOL(hAPP(hAPP(c_member(X31849),esk436_5(X31845,X31846,X31847,X31848,X31849)),hAPP(c_List_Oset(X31849),X31846)))
| hAPP(hAPP(c_List_Omap(X31849,X31848),X31847),X31846) = hAPP(hAPP(c_List_Omap(X31849,X31848),X31845),X31846) )
& ( hAPP(X31847,esk436_5(X31845,X31846,X31847,X31848,X31849)) != hAPP(X31845,esk436_5(X31845,X31846,X31847,X31848,X31849))
| hAPP(hAPP(c_List_Omap(X31849,X31848),X31847),X31846) = hAPP(hAPP(c_List_Omap(X31849,X31848),X31845),X31846) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__eq__conv])])])])])]) ).
fof(i_0_6571,plain,
! [X31523,X31524,X31525,X31526,X31527,X31528,X31529,X31530] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X31530,X31529,X31528,X31527,X31526,X31525)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31529),X31524))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31529),X31523))
| hAPP(X31525,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31529,tc_HOL_Obool)),X31524),X31523)) = hAPP(hAPP(X31528,hAPP(X31525,X31524)),hAPP(X31525,X31523)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem])]) ).
fof(i_0_6572,plain,
! [X27410,X27411,X27412,X27413,X27414,X27415,X27416,X27417] :
( ~ c_Equiv__Relations_Oequiv(X27417,X27416,X27415)
| ~ c_Equiv__Relations_Ocongruent2(X27417,X27414,X27413,X27415,X27412,X27411)
| ~ hBOOL(hAPP(hAPP(c_member(X27417),X27410),X27416))
| c_Equiv__Relations_Ocongruent(X27414,X27413,X27412,hAPP(X27411,X27410)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent])]) ).
fof(i_0_6573,plain,
! [X32943,X32944,X32945,X32946,X32947,X32950,X32951,X32952,X32953,X32954,X32955,X32956] :
( ( hAPP(hAPP(c_List_Oappend(X32947),X32946),esk458_5(X32943,X32944,X32945,X32946,X32947)) = X32944
| X32946 = hAPP(hAPP(c_List_Oappend(X32947),X32944),esk457_5(X32943,X32944,X32945,X32946,X32947))
| hAPP(hAPP(c_List_Oappend(X32947),X32946),X32945) != hAPP(hAPP(c_List_Oappend(X32947),X32944),X32943) )
& ( X32945 = hAPP(hAPP(c_List_Oappend(X32947),esk458_5(X32943,X32944,X32945,X32946,X32947)),X32943)
| X32946 = hAPP(hAPP(c_List_Oappend(X32947),X32944),esk457_5(X32943,X32944,X32945,X32946,X32947))
| hAPP(hAPP(c_List_Oappend(X32947),X32946),X32945) != hAPP(hAPP(c_List_Oappend(X32947),X32944),X32943) )
& ( hAPP(hAPP(c_List_Oappend(X32947),X32946),esk458_5(X32943,X32944,X32945,X32946,X32947)) = X32944
| hAPP(hAPP(c_List_Oappend(X32947),esk457_5(X32943,X32944,X32945,X32946,X32947)),X32945) = X32943
| hAPP(hAPP(c_List_Oappend(X32947),X32946),X32945) != hAPP(hAPP(c_List_Oappend(X32947),X32944),X32943) )
& ( X32945 = hAPP(hAPP(c_List_Oappend(X32947),esk458_5(X32943,X32944,X32945,X32946,X32947)),X32943)
| hAPP(hAPP(c_List_Oappend(X32947),esk457_5(X32943,X32944,X32945,X32946,X32947)),X32945) = X32943
| hAPP(hAPP(c_List_Oappend(X32947),X32946),X32945) != hAPP(hAPP(c_List_Oappend(X32947),X32944),X32943) )
& ( X32953 != hAPP(hAPP(c_List_Oappend(X32954),X32951),X32955)
| hAPP(hAPP(c_List_Oappend(X32954),X32955),X32952) != X32950
| hAPP(hAPP(c_List_Oappend(X32954),X32953),X32952) = hAPP(hAPP(c_List_Oappend(X32954),X32951),X32950) )
& ( hAPP(hAPP(c_List_Oappend(X32954),X32953),X32956) != X32951
| X32952 != hAPP(hAPP(c_List_Oappend(X32954),X32956),X32950)
| hAPP(hAPP(c_List_Oappend(X32954),X32953),X32952) = hAPP(hAPP(c_List_Oappend(X32954),X32951),X32950) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv2])])])])])]) ).
fof(i_0_6574,plain,
! [X25197,X25198,X25199,X25200,X25201,X25202,X25203,X25204] :
( ~ c_Finite__Set_Ofolding__image__simple(X25204,X25203,X25202,X25201,X25200,X25199)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25203),X25198))
| hBOOL(hAPP(hAPP(c_member(X25203),X25197),X25198))
| hAPP(X25199,hAPP(hAPP(c_Set_Oinsert(X25203),X25197),X25198)) = hAPP(hAPP(X25202,hAPP(X25200,X25197)),hAPP(X25199,X25198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5386])]) ).
fof(i_0_6575,plain,
! [X28175,X28176,X28177,X28178,X28179] :
( ( ~ c_Fun_Oinj__on(X28178,X28176,X28179,X28177)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28176,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28178,X28176,X28179),X28177)),X28175))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X28178),X28177)),hAPP(c_Finite__Set_Ocard(X28176),X28175)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28176),X28175))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28178),X28177)) )
& ( c_Fun_Oinj__on(X28178,X28176,esk269_4(X28175,X28176,X28177,X28178),X28177)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X28178),X28177)),hAPP(c_Finite__Set_Ocard(X28176),X28175)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28176),X28175))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28178),X28177)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28176,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28178,X28176,esk269_4(X28175,X28176,X28177,X28178)),X28177)),X28175))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X28178),X28177)),hAPP(c_Finite__Set_Ocard(X28176),X28175)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28176),X28175))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28178),X28177)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__card__le])])])])]) ).
fof(i_0_6576,plain,
! [X31541,X31542,X31543,X31544,X31545,X31546,X31547,X31548] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X31548,X31547,X31546,X31545,X31544,X31543)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31547),X31542))
| ~ hBOOL(hAPP(hAPP(c_member(X31547),X31541),X31542))
| hAPP(hAPP(X31546,hAPP(X31544,X31541)),hAPP(X31543,X31542)) = hAPP(X31543,X31542) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).
fof(i_0_6577,plain,
! [X31549,X31550,X31551,X31552,X31553,X31554,X31555,X31556] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X31556,X31555,X31554,X31553,X31552,X31551)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31555),X31550))
| hAPP(X31551,hAPP(hAPP(c_Set_Oinsert(X31555),X31549),X31550)) = hAPP(hAPP(X31554,hAPP(X31552,X31549)),hAPP(X31551,X31550)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).
fof(i_0_6578,plain,
! [X31021,X31022,X31023,X31024,X31025] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31025,tc_fun(X31024,tc_HOL_Obool)),X31023),hAPP(hAPP(c_COMBS(X31025,tc_fun(X31024,tc_HOL_Obool),tc_fun(X31024,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31024,tc_HOL_Obool),tc_fun(tc_fun(X31024,tc_HOL_Obool),tc_fun(X31024,tc_HOL_Obool)),X31025),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31024,tc_HOL_Obool))),X31022)),X31021)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31024,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31025,tc_fun(X31024,tc_HOL_Obool)),X31023),X31022)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31025,tc_fun(X31024,tc_HOL_Obool)),X31023),X31021)),
inference(variable_rename,[status(thm)],[fact_INT__Int__distrib]) ).
fof(i_0_6579,plain,
! [X24293,X24294,X24295,X24296,X24297] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24297,tc_fun(X24296,tc_HOL_Obool)),X24295),hAPP(hAPP(c_COMBS(X24297,tc_fun(X24296,tc_HOL_Obool),tc_fun(X24296,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24296,tc_HOL_Obool),tc_fun(tc_fun(X24296,tc_HOL_Obool),tc_fun(X24296,tc_HOL_Obool)),X24297),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24296,tc_HOL_Obool))),X24294)),X24293)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24296,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24297,tc_fun(X24296,tc_HOL_Obool)),X24295),X24294)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24297,tc_fun(X24296,tc_HOL_Obool)),X24295),X24293)),
inference(variable_rename,[status(thm)],[fact_UN__Un__distrib]) ).
fof(i_0_6580,plain,
! [X25217,X25218,X25219,X25220,X25221,X25222] :
( ~ c_Finite__Set_Ofolding__image__simple(X25222,X25221,X25220,X25219,X25218,X25217)
| hAPP(X25217,c_Orderings_Obot__class_Obot(tc_fun(X25221,tc_HOL_Obool))) = X25219 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty])]) ).
fof(i_0_6581,plain,
! [X31534,X31535,X31536,X31537,X31538,X31539,X31540] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X31540,X31539,X31538,X31537,X31536,X31535)
| hAPP(hAPP(X31538,X31534),X31534) = X31534 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).
fof(i_0_6582,plain,
! [X26351] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26351))
| X26351 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X26351)),c_FunDef_Omax__strict)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__emptyI])]) ).
fof(i_0_6583,plain,
! [X33920,X33921,X33922] : hAPP(c_List_Oset(X33922),hAPP(c_List_Ofilter(X33922,X33921),X33920)) = hAPP(c_Set_OCollect(X33922),hAPP(hAPP(c_COMBS(X33922,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33922),c_fconj),hAPP(hAPP(c_COMBC(X33922,tc_fun(X33922,tc_HOL_Obool),tc_HOL_Obool),c_member(X33922)),hAPP(c_List_Oset(X33922),X33920)))),X33921)),
inference(variable_rename,[status(thm)],[fact_set__filter]) ).
fof(i_0_6584,plain,
! [X23531,X23532,X23533] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X23533,esk100_3(X23531,X23532,X23533))),hAPP(X23532,esk100_3(X23531,X23532,X23533))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X23532),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X23531))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X23533),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X23531))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23532)),X23533)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X23531)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib])])]) ).
fof(i_0_6585,plain,
! [X28029,X28030,X28031,X28032,X28033,X28035] :
( ( ~ c_Fun_Oinj__on(X28031,X28030,X28033,X28032)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28030,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28031,X28030,X28033),X28032)),X28029))
| hAPP(c_Set_Oimage(X28030,X28031,esk267_4(X28029,X28030,X28031,X28032)),X28029) = X28032
| X28032 = c_Orderings_Obot__class_Obot(tc_fun(X28031,tc_HOL_Obool)) )
& ( c_Fun_Oinj__on(X28031,X28030,esk268_4(X28029,X28030,X28031,X28032),X28032)
| hAPP(c_Set_Oimage(X28030,X28031,X28035),X28029) != X28032
| X28032 = c_Orderings_Obot__class_Obot(tc_fun(X28031,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28030,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28031,X28030,esk268_4(X28029,X28030,X28031,X28032)),X28032)),X28029))
| hAPP(c_Set_Oimage(X28030,X28031,X28035),X28029) != X28032
| X28032 = c_Orderings_Obot__class_Obot(tc_fun(X28031,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__surj])])])])]) ).
fof(i_0_6586,plain,
! [X29757,X29758,X29759,X29760] :
( ~ hBOOL(hAPP(hAPP(c_member(X29760),X29759),hAPP(c_Relation_ORange(X29758,X29760),X29757)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29758,X29760)),hAPP(hAPP(c_Product__Type_OPair(X29758,X29760),esk324_4(X29757,X29758,X29759,X29760)),X29759)),X29757)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5387])])]) ).
fof(i_0_6587,plain,
! [X29730,X29731,X29732,X29733,X29735,X29736,X29737,X29738,X29739] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X29733),X29732),hAPP(c_Relation_ORange(X29731,X29733),X29730)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29731,X29733)),hAPP(hAPP(c_Product__Type_OPair(X29731,X29733),esk323_4(X29730,X29731,X29732,X29733)),X29732)),X29730)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29736,X29738)),hAPP(hAPP(c_Product__Type_OPair(X29736,X29738),X29739),X29737)),X29735))
| hBOOL(hAPP(hAPP(c_member(X29738),X29737),hAPP(c_Relation_ORange(X29736,X29738),X29735))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__iff])])])])]) ).
fof(i_0_6588,plain,
! [X26365] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26365))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X26365)),c_FunDef_Omax__weak)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__emptyI])]) ).
fof(i_0_6589,plain,
! [X31153,X31154,X31155,X31156,X31157] :
( ( X31157 != c_Orderings_Obot__class_Obot(tc_fun(X31156,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31156,tc_fun(X31155,tc_HOL_Obool)),X31157),hAPP(hAPP(c_COMBC(X31156,tc_fun(X31155,tc_HOL_Obool),tc_fun(X31155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31155,tc_HOL_Obool),tc_fun(tc_fun(X31155,tc_HOL_Obool),tc_fun(X31155,tc_HOL_Obool)),X31156),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31155,tc_HOL_Obool))),X31154)),X31153)) = c_Orderings_Otop__class_Otop(tc_fun(X31155,tc_HOL_Obool)) )
& ( X31157 = c_Orderings_Obot__class_Obot(tc_fun(X31156,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31156,tc_fun(X31155,tc_HOL_Obool)),X31157),hAPP(hAPP(c_COMBC(X31156,tc_fun(X31155,tc_HOL_Obool),tc_fun(X31155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31155,tc_HOL_Obool),tc_fun(tc_fun(X31155,tc_HOL_Obool),tc_fun(X31155,tc_HOL_Obool)),X31156),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31155,tc_HOL_Obool))),X31154)),X31153)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31155,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31156,tc_fun(X31155,tc_HOL_Obool)),X31157),X31154)),X31153) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J])]) ).
fof(i_0_6590,plain,
! [X31163,X31164,X31165,X31166,X31167] :
( ( X31167 != c_Orderings_Obot__class_Obot(tc_fun(X31166,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31166,tc_fun(X31165,tc_HOL_Obool)),X31167),hAPP(hAPP(c_COMBC(X31166,tc_fun(X31165,tc_HOL_Obool),tc_fun(X31165,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31165,tc_HOL_Obool),tc_fun(tc_fun(X31165,tc_HOL_Obool),tc_fun(X31165,tc_HOL_Obool)),X31166),c_Groups_Ominus__class_Ominus(tc_fun(X31165,tc_HOL_Obool))),X31164)),X31163)) = c_Orderings_Otop__class_Otop(tc_fun(X31165,tc_HOL_Obool)) )
& ( X31167 = c_Orderings_Obot__class_Obot(tc_fun(X31166,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31166,tc_fun(X31165,tc_HOL_Obool)),X31167),hAPP(hAPP(c_COMBC(X31166,tc_fun(X31165,tc_HOL_Obool),tc_fun(X31165,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31165,tc_HOL_Obool),tc_fun(tc_fun(X31165,tc_HOL_Obool),tc_fun(X31165,tc_HOL_Obool)),X31166),c_Groups_Ominus__class_Ominus(tc_fun(X31165,tc_HOL_Obool))),X31164)),X31163)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31165,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31166,tc_fun(X31165,tc_HOL_Obool)),X31167),X31164)),X31163) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J])]) ).
fof(i_0_6591,plain,
! [X24825,X24826,X24827,X24828,X24829] :
( ( X24829 != c_Orderings_Obot__class_Obot(tc_fun(X24828,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24828,tc_fun(X24827,tc_HOL_Obool)),X24829),hAPP(hAPP(c_COMBC(X24828,tc_fun(X24827,tc_HOL_Obool),tc_fun(X24827,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24827,tc_HOL_Obool),tc_fun(tc_fun(X24827,tc_HOL_Obool),tc_fun(X24827,tc_HOL_Obool)),X24828),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24827,tc_HOL_Obool))),X24826)),X24825)) = c_Orderings_Obot__class_Obot(tc_fun(X24827,tc_HOL_Obool)) )
& ( X24829 = c_Orderings_Obot__class_Obot(tc_fun(X24828,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24828,tc_fun(X24827,tc_HOL_Obool)),X24829),hAPP(hAPP(c_COMBC(X24828,tc_fun(X24827,tc_HOL_Obool),tc_fun(X24827,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24827,tc_HOL_Obool),tc_fun(tc_fun(X24827,tc_HOL_Obool),tc_fun(X24827,tc_HOL_Obool)),X24828),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24827,tc_HOL_Obool))),X24826)),X24825)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24827,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24828,tc_fun(X24827,tc_HOL_Obool)),X24829),X24826)),X24825) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J])]) ).
fof(i_0_6592,plain,
! [X30937,X30938,X30939,X30940,X30941] :
( ( X30941 != c_Orderings_Obot__class_Obot(tc_fun(X30940,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30939,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30940,tc_fun(X30939,tc_HOL_Obool)),X30941),X30938)),X30937) = X30937 )
& ( X30941 = c_Orderings_Obot__class_Obot(tc_fun(X30940,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30939,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30940,tc_fun(X30939,tc_HOL_Obool)),X30941),X30938)),X30937) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30940,tc_fun(X30939,tc_HOL_Obool)),X30941),hAPP(hAPP(c_COMBC(X30940,tc_fun(X30939,tc_HOL_Obool),tc_fun(X30939,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30939,tc_HOL_Obool),tc_fun(tc_fun(X30939,tc_HOL_Obool),tc_fun(X30939,tc_HOL_Obool)),X30940),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30939,tc_HOL_Obool))),X30938)),X30937)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J])]) ).
fof(i_0_6593,plain,
! [X24835,X24836,X24837,X24838,X24839] :
( ( X24839 != c_Orderings_Obot__class_Obot(tc_fun(X24838,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24838,tc_fun(X24837,tc_HOL_Obool)),X24839),X24836)),X24835) = X24835 )
& ( X24839 = c_Orderings_Obot__class_Obot(tc_fun(X24838,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24837,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24838,tc_fun(X24837,tc_HOL_Obool)),X24839),X24836)),X24835) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24838,tc_fun(X24837,tc_HOL_Obool)),X24839),hAPP(hAPP(c_COMBC(X24838,tc_fun(X24837,tc_HOL_Obool),tc_fun(X24837,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24837,tc_HOL_Obool),tc_fun(tc_fun(X24837,tc_HOL_Obool),tc_fun(X24837,tc_HOL_Obool)),X24838),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24837,tc_HOL_Obool))),X24836)),X24835)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J])]) ).
fof(i_0_6594,plain,
! [X31168,X31169,X31170,X31171,X31172] :
( ( X31172 != c_Orderings_Obot__class_Obot(tc_fun(X31171,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31170,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31171,tc_fun(X31170,tc_HOL_Obool)),X31172),X31169)),X31168) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31170,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X31170,tc_HOL_Obool))),X31168) )
& ( X31172 = c_Orderings_Obot__class_Obot(tc_fun(X31171,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31170,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31171,tc_fun(X31170,tc_HOL_Obool)),X31172),X31169)),X31168) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31171,tc_fun(X31170,tc_HOL_Obool)),X31172),hAPP(hAPP(c_COMBC(X31171,tc_fun(X31170,tc_HOL_Obool),tc_fun(X31170,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31170,tc_HOL_Obool),tc_fun(tc_fun(X31170,tc_HOL_Obool),tc_fun(X31170,tc_HOL_Obool)),X31171),c_Groups_Ominus__class_Ominus(tc_fun(X31170,tc_HOL_Obool))),X31169)),X31168)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J])]) ).
fof(i_0_6595,plain,
! [X31129,X31130,X31131,X31132,X31133] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31133,tc_fun(X31132,tc_HOL_Obool)),X31131),hAPP(hAPP(c_COMBC(X31133,tc_fun(X31132,tc_HOL_Obool),tc_fun(X31132,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31132,tc_HOL_Obool),tc_fun(tc_fun(X31132,tc_HOL_Obool),tc_fun(X31132,tc_HOL_Obool)),X31133),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31132,tc_HOL_Obool))),X31130)),X31129)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31132,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31133,tc_fun(X31132,tc_HOL_Obool)),X31131),X31130)),X31129),
inference(variable_rename,[status(thm)],[fact_INT__simps_I6_J]) ).
fof(i_0_6596,plain,
! [X27276,X27277,X27278,X27279,X27280] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27280,tc_fun(X27279,tc_HOL_Obool)),X27278),hAPP(hAPP(c_COMBC(X27280,tc_fun(X27279,tc_HOL_Obool),tc_fun(X27279,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27279,tc_HOL_Obool),tc_fun(tc_fun(X27279,tc_HOL_Obool),tc_fun(X27279,tc_HOL_Obool)),X27280),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27279,tc_HOL_Obool))),X27277)),X27276)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27279,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27280,tc_fun(X27279,tc_HOL_Obool)),X27278),X27277)),X27276),
inference(variable_rename,[status(thm)],[fact_UN__simps_I4_J]) ).
fof(i_0_6597,plain,
! [X24188,X24189,X24190,X24191,X24192] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24192,tc_fun(X24191,tc_HOL_Obool)),X24190),hAPP(hAPP(c_COMBC(X24192,tc_fun(X24191,tc_HOL_Obool),tc_fun(X24191,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24191,tc_HOL_Obool),tc_fun(tc_fun(X24191,tc_HOL_Obool),tc_fun(X24191,tc_HOL_Obool)),X24192),c_Groups_Ominus__class_Ominus(tc_fun(X24191,tc_HOL_Obool))),X24189)),X24188)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24191,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24192,tc_fun(X24191,tc_HOL_Obool)),X24190),X24189)),X24188),
inference(variable_rename,[status(thm)],[fact_UN__simps_I6_J]) ).
fof(i_0_6598,plain,
! [X27291,X27292,X27293,X27294,X27295] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27295,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27294,tc_fun(X27295,tc_HOL_Obool)),X27293),X27292)),X27291) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27294,tc_fun(X27295,tc_HOL_Obool)),X27293),hAPP(hAPP(c_COMBC(X27294,tc_fun(X27295,tc_HOL_Obool),tc_fun(X27295,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27295,tc_HOL_Obool),tc_fun(tc_fun(X27295,tc_HOL_Obool),tc_fun(X27295,tc_HOL_Obool)),X27294),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27295,tc_HOL_Obool))),X27292)),X27291)),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I4_J]) ).
fof(i_0_6599,plain,
! [X31114,X31115,X31116,X31117,X31118] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31118,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31117,tc_fun(X31118,tc_HOL_Obool)),X31116),X31115)),X31114) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31117,tc_fun(X31118,tc_HOL_Obool)),X31116),hAPP(hAPP(c_COMBC(X31117,tc_fun(X31118,tc_HOL_Obool),tc_fun(X31118,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31118,tc_HOL_Obool),tc_fun(tc_fun(X31118,tc_HOL_Obool),tc_fun(X31118,tc_HOL_Obool)),X31117),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31118,tc_HOL_Obool))),X31115)),X31114)),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I6_J]) ).
fof(i_0_6600,plain,
! [X24193,X24194,X24195,X24196,X24197] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24197,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24196,tc_fun(X24197,tc_HOL_Obool)),X24195),X24194)),X24193) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24196,tc_fun(X24197,tc_HOL_Obool)),X24195),hAPP(hAPP(c_COMBC(X24196,tc_fun(X24197,tc_HOL_Obool),tc_fun(X24197,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24197,tc_HOL_Obool),tc_fun(tc_fun(X24197,tc_HOL_Obool),tc_fun(X24197,tc_HOL_Obool)),X24196),c_Groups_Ominus__class_Ominus(tc_fun(X24197,tc_HOL_Obool))),X24194)),X24193)),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I6_J]) ).
fof(i_0_6601,plain,
! [X29551,X29552,X29553,X29554,X29555,X29556,X29557,X29558] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29558,X29557),tc_HOL_Obool)),X29556),hAPP(hAPP(c_Product__Type_OSigma(X29558,X29557),X29555),hAPP(c_COMBK(tc_fun(X29557,tc_HOL_Obool),X29558),X29554))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29557,X29553),tc_HOL_Obool)),X29552),hAPP(hAPP(c_Product__Type_OSigma(X29557,X29553),X29554),hAPP(c_COMBK(tc_fun(X29553,tc_HOL_Obool),X29557),X29551))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29558,X29553),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29558,X29557,X29553),X29556),X29552)),hAPP(hAPP(c_Product__Type_OSigma(X29558,X29553),X29555),hAPP(c_COMBK(tc_fun(X29553,tc_HOL_Obool),X29558),X29551)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__subset__Sigma])]) ).
fof(i_0_6602,plain,
! [X33264,X33265,X33266,X33267,X33268,X33269] :
( ( X33268 = X33266
| hBOOL(hAPP(hAPP(c_member(tc_prod(X33269,X33269)),hAPP(hAPP(c_Product__Type_OPair(X33269,X33269),X33268),X33266)),X33264))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33269),tc_List_Olist(X33269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33269),tc_List_Olist(X33269)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33268),X33267)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33266),X33265))),c_List_Olistrel1(X33269,X33264))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33269),tc_List_Olist(X33269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33269),tc_List_Olist(X33269)),X33267),X33265)),c_List_Olistrel1(X33269,X33264)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X33269,X33269)),hAPP(hAPP(c_Product__Type_OPair(X33269,X33269),X33268),X33266)),X33264))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33269),tc_List_Olist(X33269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33269),tc_List_Olist(X33269)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33268),X33267)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33266),X33265))),c_List_Olistrel1(X33269,X33264))) )
& ( X33268 = X33266
| X33267 = X33265
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33269),tc_List_Olist(X33269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33269),tc_List_Olist(X33269)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33268),X33267)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33266),X33265))),c_List_Olistrel1(X33269,X33264))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33269),tc_List_Olist(X33269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33269),tc_List_Olist(X33269)),X33267),X33265)),c_List_Olistrel1(X33269,X33264)))
| X33267 = X33265
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33269),tc_List_Olist(X33269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33269),tc_List_Olist(X33269)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33268),X33267)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33266),X33265))),c_List_Olistrel1(X33269,X33264))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33269,X33269)),hAPP(hAPP(c_Product__Type_OPair(X33269,X33269),X33268),X33266)),X33264))
| X33267 != X33265
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33269),tc_List_Olist(X33269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33269),tc_List_Olist(X33269)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33268),X33267)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33266),X33265))),c_List_Olistrel1(X33269,X33264))) )
& ( X33268 != X33266
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33269),tc_List_Olist(X33269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33269),tc_List_Olist(X33269)),X33267),X33265)),c_List_Olistrel1(X33269,X33264)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33269),tc_List_Olist(X33269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33269),tc_List_Olist(X33269)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33268),X33267)),hAPP(hAPP(c_List_Olist_OCons(X33269),X33266),X33265))),c_List_Olistrel1(X33269,X33264))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])]) ).
fof(i_0_6603,plain,
! [X32845,X32846,X32847,X32848,X32849,X32850] :
( ( X32849 = X32847
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32850,X32850)),hAPP(hAPP(c_Product__Type_OPair(X32850,X32850),X32849),X32847)),X32845))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32850),tc_List_Olist(X32850))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32850),tc_List_Olist(X32850)),hAPP(hAPP(c_List_Olist_OCons(X32850),X32849),X32848)),hAPP(hAPP(c_List_Olist_OCons(X32850),X32847),X32846))),c_List_Olexord(X32850,X32845))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32850),tc_List_Olist(X32850))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32850),tc_List_Olist(X32850)),X32848),X32846)),c_List_Olexord(X32850,X32845)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32850,X32850)),hAPP(hAPP(c_Product__Type_OPair(X32850,X32850),X32849),X32847)),X32845))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32850),tc_List_Olist(X32850))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32850),tc_List_Olist(X32850)),hAPP(hAPP(c_List_Olist_OCons(X32850),X32849),X32848)),hAPP(hAPP(c_List_Olist_OCons(X32850),X32847),X32846))),c_List_Olexord(X32850,X32845))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32850,X32850)),hAPP(hAPP(c_Product__Type_OPair(X32850,X32850),X32849),X32847)),X32845))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32850),tc_List_Olist(X32850))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32850),tc_List_Olist(X32850)),hAPP(hAPP(c_List_Olist_OCons(X32850),X32849),X32848)),hAPP(hAPP(c_List_Olist_OCons(X32850),X32847),X32846))),c_List_Olexord(X32850,X32845))) )
& ( X32849 != X32847
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32850),tc_List_Olist(X32850))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32850),tc_List_Olist(X32850)),X32848),X32846)),c_List_Olexord(X32850,X32845)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32850),tc_List_Olist(X32850))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32850),tc_List_Olist(X32850)),hAPP(hAPP(c_List_Olist_OCons(X32850),X32849),X32848)),hAPP(hAPP(c_List_Olist_OCons(X32850),X32847),X32846))),c_List_Olexord(X32850,X32845))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons])])]) ).
fof(i_0_6604,plain,
! [X32366,X32367,X32368,X32369,X32370,X32371] :
( ( X32370 = X32368
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32371,X32371)),hAPP(hAPP(c_Product__Type_OPair(X32371,X32371),X32370),X32368)),X32366))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32371),tc_List_Olist(X32371))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32371),tc_List_Olist(X32371)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32370),X32369)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32368),X32367))),c_List_Olex(X32371,X32366))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32371),tc_List_Olist(X32371))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32371),tc_List_Olist(X32371)),X32369),X32367)),c_List_Olex(X32371,X32366)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32371,X32371)),hAPP(hAPP(c_Product__Type_OPair(X32371,X32371),X32370),X32368)),X32366))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32371),tc_List_Olist(X32371))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32371),tc_List_Olist(X32371)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32370),X32369)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32368),X32367))),c_List_Olex(X32371,X32366))) )
& ( X32370 = X32368
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32371)),X32369) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32371)),X32367)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32371),tc_List_Olist(X32371))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32371),tc_List_Olist(X32371)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32370),X32369)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32368),X32367))),c_List_Olex(X32371,X32366))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32371),tc_List_Olist(X32371))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32371),tc_List_Olist(X32371)),X32369),X32367)),c_List_Olex(X32371,X32366)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32371)),X32369) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32371)),X32367)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32371),tc_List_Olist(X32371))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32371),tc_List_Olist(X32371)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32370),X32369)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32368),X32367))),c_List_Olex(X32371,X32366))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32371,X32371)),hAPP(hAPP(c_Product__Type_OPair(X32371,X32371),X32370),X32368)),X32366))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32371)),X32369) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32371)),X32367)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32371),tc_List_Olist(X32371))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32371),tc_List_Olist(X32371)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32370),X32369)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32368),X32367))),c_List_Olex(X32371,X32366))) )
& ( X32370 != X32368
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32371),tc_List_Olist(X32371))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32371),tc_List_Olist(X32371)),X32369),X32367)),c_List_Olex(X32371,X32366)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32371),tc_List_Olist(X32371))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32371),tc_List_Olist(X32371)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32370),X32369)),hAPP(hAPP(c_List_Olist_OCons(X32371),X32368),X32367))),c_List_Olex(X32371,X32366))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])]) ).
fof(i_0_6605,plain,
! [X28718,X28719,X28720,X28721,X28722] : hAPP(hAPP(c_Product__Type_OSigma(X28722,X28721),X28720),hAPP(hAPP(c_COMBS(X28722,tc_fun(X28721,tc_HOL_Obool),tc_fun(X28721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28721,tc_HOL_Obool),tc_fun(tc_fun(X28721,tc_HOL_Obool),tc_fun(X28721,tc_HOL_Obool)),X28722),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28721,tc_HOL_Obool))),X28719)),X28718)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28722,X28721),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28722,X28721),X28720),X28719)),hAPP(hAPP(c_Product__Type_OSigma(X28722,X28721),X28720),X28718)),
inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib2]) ).
fof(i_0_6606,plain,
! [X28692,X28693,X28694,X28695,X28696] : hAPP(hAPP(c_Product__Type_OSigma(X28696,X28695),X28694),hAPP(hAPP(c_COMBS(X28696,tc_fun(X28695,tc_HOL_Obool),tc_fun(X28695,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28695,tc_HOL_Obool),tc_fun(tc_fun(X28695,tc_HOL_Obool),tc_fun(X28695,tc_HOL_Obool)),X28696),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28695,tc_HOL_Obool))),X28693)),X28692)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28696,X28695),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28696,X28695),X28694),X28693)),hAPP(hAPP(c_Product__Type_OSigma(X28696,X28695),X28694),X28692)),
inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib2]) ).
fof(i_0_6607,plain,
! [X28629,X28630,X28631,X28632,X28633] : hAPP(hAPP(c_Product__Type_OSigma(X28633,X28632),X28631),hAPP(hAPP(c_COMBS(X28633,tc_fun(X28632,tc_HOL_Obool),tc_fun(X28632,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28632,tc_HOL_Obool),tc_fun(tc_fun(X28632,tc_HOL_Obool),tc_fun(X28632,tc_HOL_Obool)),X28633),c_Groups_Ominus__class_Ominus(tc_fun(X28632,tc_HOL_Obool))),X28630)),X28629)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28633,X28632),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28633,X28632),X28631),X28630)),hAPP(hAPP(c_Product__Type_OSigma(X28633,X28632),X28631),X28629)),
inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib2]) ).
fof(i_0_6608,plain,
! [X20793,X20794,X20795,X20796,X20797] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20797)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20797),hAPP(c_Groups_Oabs__class_Oabs(X20797),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20797),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20797),X20796),X20795)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20797),X20794),X20793)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20797),hAPP(c_Groups_Oabs__class_Oabs(X20797),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20797),X20796),X20794))),hAPP(c_Groups_Oabs__class_Oabs(X20797),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20797),X20795),X20793))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])]) ).
fof(i_0_6609,plain,
! [X20528,X20529,X20530,X20531,X20532] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20532),X20530)),X20529)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20531),X20530)),X20528)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20529),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20531),X20532)),X20530)),X20528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20532),X20531)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20529),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20531),X20532)),X20530)),X20528)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20532),X20530)),X20529)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20531),X20530)),X20528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20532),X20531)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).
fof(i_0_6610,plain,
! [X20560,X20561,X20562,X20563,X20564] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20564),X20562)),X20561)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20563),X20562)),X20560)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20561),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20563),X20564)),X20562)),X20560)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20564),X20563)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20561),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20563),X20564)),X20562)),X20560)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20564),X20562)),X20561)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20563),X20562)),X20560)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20564),X20563)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])]) ).
fof(i_0_6611,plain,
! [X28234,X28235,X28236,X28237,X28238,X28239,X28240,X28241] :
( ~ c_Finite__Set_Ofolding__image(X28241,X28240,X28239,X28238,X28237)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28240),X28236))
| hAPP(hAPP(X28237,hAPP(hAPP(c_COMBS(X28240,X28241,X28241),hAPP(hAPP(c_COMBB(X28241,tc_fun(X28241,X28241),X28240),X28239),X28235)),X28234)),X28236) = hAPP(hAPP(X28239,hAPP(hAPP(X28237,X28235),X28236)),hAPP(hAPP(X28237,X28234),X28236)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Odistrib])]) ).
cnf(i_0_6612,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Otrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5388]) ).
fof(i_0_6613,plain,
! [X28185,X28186,X28187,X28188,X28189] :
( ~ class_Groups_Ocomm__monoid__mult(X28189)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28188),X28187))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28188),X28186))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28189),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28189,X28188,c_Groups_Otimes__class_Otimes(X28189)),X28185),c_Groups_Oone__class_Oone(X28189)),X28187)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28189,X28188,c_Groups_Otimes__class_Otimes(X28189)),X28185),c_Groups_Oone__class_Oone(X28189)),X28186)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28189),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28189,X28188,c_Groups_Otimes__class_Otimes(X28189)),X28185),c_Groups_Oone__class_Oone(X28189)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28188,tc_HOL_Obool)),X28187),X28186))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28189,X28188,c_Groups_Otimes__class_Otimes(X28189)),X28185),c_Groups_Oone__class_Oone(X28189)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28188,tc_HOL_Obool)),X28187),X28186))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int])]) ).
fof(i_0_6614,plain,
! [X23460,X23461,X23462] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23462)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X23461))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X23460))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23460),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23462),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23460),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X23461)))),
inference(variable_rename,[status(thm)],[fact_arith__series__nat]) ).
fof(i_0_6615,plain,
! [X27090,X27091,X27092,X27093] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27093,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27093,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27093,tc_HOL_Obool)),X27092),X27091)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27093,tc_HOL_Obool)),X27091),X27090))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27093,tc_HOL_Obool)),X27090),X27092)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27093,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27093,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27093,tc_HOL_Obool)),X27092),X27091)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27093,tc_HOL_Obool)),X27091),X27090))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27093,tc_HOL_Obool)),X27090),X27092)),
inference(variable_rename,[status(thm)],[fact_Un__Int__crazy]) ).
fof(i_0_6616,plain,
! [X17908,X17909,X17910,X17911,X17912] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17912)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17911),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17910,X17911))),X17909))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17908,X17912,X17910)),X17911),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17909),hAPP(c_Natural_Ogetlocs,X17911))),X17908),hAPP(hAPP(c_Natural_Ogetlocs,X17909),c_Com_ORes)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OCall])]) ).
fof(i_0_6617,plain,
! [X33286,X33287,X33288,X33289,X33290,X33291] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33291,X33291)),hAPP(hAPP(c_Product__Type_OPair(X33291,X33291),X33290),X33289)),c_Transitive__Closure_Ortrancl(X33291,X33288)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33291),tc_List_Olist(X33291))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33291),tc_List_Olist(X33291)),X33287),X33286)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33291),c_List_Olistrel1(X33291,X33288))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33291),tc_List_Olist(X33291))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33291),tc_List_Olist(X33291)),hAPP(hAPP(c_List_Olist_OCons(X33291),X33290),X33287)),hAPP(hAPP(c_List_Olist_OCons(X33291),X33289),X33286))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33291),c_List_Olistrel1(X33291,X33288)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2])]) ).
fof(i_0_6618,plain,
! [X23717,X23718,X23719,X23720,X23721] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23721,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23721,tc_HOL_Obool)),hAPP(c_Set_Oimage(X23720,X23721,X23719),X23718)),hAPP(c_Set_Oimage(X23720,X23721,X23719),X23717))),hAPP(c_Set_Oimage(X23720,X23721,X23719),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23720,tc_HOL_Obool)),X23718),X23717)))),
inference(variable_rename,[status(thm)],[fact_image__diff__subset]) ).
cnf(i_0_6619,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_5389]) ).
cnf(i_0_6620,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_5390]) ).
fof(i_0_6621,plain,
! [X26298,X26299,X26300,X26301,X26302,X26303] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X26303),X26302),X26301))
| c_Map_Orestrict__map(X26303,X26300,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26303,tc_Option_Ooption(X26300)),X26299),X26302),X26298),X26301) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26303,tc_Option_Ooption(X26300)),c_Map_Orestrict__map(X26303,X26300,X26299,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26303,tc_HOL_Obool)),X26301),hAPP(hAPP(c_Set_Oinsert(X26303),X26302),c_Orderings_Obot__class_Obot(tc_fun(X26303,tc_HOL_Obool)))))),X26302),X26298) )
& ( hBOOL(hAPP(hAPP(c_member(X26303),X26302),X26301))
| c_Map_Orestrict__map(X26303,X26300,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26303,tc_Option_Ooption(X26300)),X26299),X26302),X26298),X26301) = c_Map_Orestrict__map(X26303,X26300,X26299,X26301) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5391])]) ).
fof(i_0_6622,plain,
! [X29349] : hAPP(c_Set_OCollect(tc_Nat_Onat),X29349) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X29349),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).
fof(i_0_6623,plain,
! [X32211,X32212] : c_List_Olenlex(X32212,X32211) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X32212)),tc_List_Olist(X32212)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X32212),c_Wellfounded_Oless__than,c_List_Olex(X32212,X32211))),hAPP(hAPP(c_COMBS(tc_List_Olist(X32212),tc_List_Olist(X32212),tc_prod(tc_Nat_Onat,tc_List_Olist(X32212))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X32212),tc_prod(tc_Nat_Onat,tc_List_Olist(X32212))),tc_List_Olist(X32212)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X32212))),c_Nat_Osize__class_Osize(tc_List_Olist(X32212)))),c_COMBI(tc_List_Olist(X32212)))),
inference(variable_rename,[status(thm)],[fact_lenlex__def]) ).
fof(i_0_6624,plain,
! [X29009,X29010,X29011] :
( ( hBOOL(hAPP(hAPP(c_member(X29011),esk294_3(X29009,X29010,X29011)),X29009))
| c_Relation_Orefl__on(X29011,X29009,X29010)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29011,X29011),tc_HOL_Obool)),X29010),hAPP(hAPP(c_Product__Type_OSigma(X29011,X29011),X29009),hAPP(c_COMBK(tc_fun(X29011,tc_HOL_Obool),X29011),X29009)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29011,X29011)),hAPP(hAPP(c_Product__Type_OPair(X29011,X29011),esk294_3(X29009,X29010,X29011)),esk294_3(X29009,X29010,X29011))),X29010))
| c_Relation_Orefl__on(X29011,X29009,X29010)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29011,X29011),tc_HOL_Obool)),X29010),hAPP(hAPP(c_Product__Type_OSigma(X29011,X29011),X29009),hAPP(c_COMBK(tc_fun(X29011,tc_HOL_Obool),X29011),X29009)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onI])])])]) ).
fof(i_0_6625,plain,
! [X28974,X28975,X28976,X28977,X28978,X28979,X28980] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28976,X28976),tc_HOL_Obool)),X28974),hAPP(hAPP(c_Product__Type_OSigma(X28976,X28976),X28975),hAPP(c_COMBK(tc_fun(X28976,tc_HOL_Obool),X28976),X28975))))
| ~ c_Relation_Orefl__on(X28976,X28975,X28974) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28976),X28977),X28975))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X28976,X28976)),hAPP(hAPP(c_Product__Type_OPair(X28976,X28976),X28977),X28977)),X28974))
| ~ c_Relation_Orefl__on(X28976,X28975,X28974) )
& ( hBOOL(hAPP(hAPP(c_member(X28980),esk293_3(X28978,X28979,X28980)),X28979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28980,X28980),tc_HOL_Obool)),X28978),hAPP(hAPP(c_Product__Type_OSigma(X28980,X28980),X28979),hAPP(c_COMBK(tc_fun(X28980,tc_HOL_Obool),X28980),X28979))))
| c_Relation_Orefl__on(X28980,X28979,X28978) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28980,X28980)),hAPP(hAPP(c_Product__Type_OPair(X28980,X28980),esk293_3(X28978,X28979,X28980)),esk293_3(X28978,X28979,X28980))),X28978))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28980,X28980),tc_HOL_Obool)),X28978),hAPP(hAPP(c_Product__Type_OSigma(X28980,X28980),X28979),hAPP(c_COMBK(tc_fun(X28980,tc_HOL_Obool),X28980),X28979))))
| c_Relation_Orefl__on(X28980,X28979,X28978) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__def])])])])])]) ).
fof(i_0_6626,plain,
! [X31829,X31830,X31831,X31832] :
( hAPP(c_List_Oset(X31832),X31831) != c_Map_Odom(X31832,X31830,X31829)
| c_Map_Omap__of(X31832,X31830,hAPP(hAPP(c_List_Omap(X31832,tc_prod(X31832,X31830)),hAPP(hAPP(c_COMBS(X31832,X31830,tc_prod(X31832,X31830)),c_Product__Type_OPair(X31832,X31830)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X31830),X31830,X31832),c_Option_Othe(X31830)),X31829))),X31831)) = X31829 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__map__keys])]) ).
fof(i_0_6627,plain,
! [X29167,X29168,X29169] : hAPP(hAPP(c_Set_Oinsert(X29169),X29168),X29167) = hAPP(c_Set_OCollect(X29169),hAPP(hAPP(c_COMBS(X29169,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29169),c_fdisj),hAPP(hAPP(c_COMBC(X29169,X29169,tc_HOL_Obool),c_fequal),X29168))),hAPP(hAPP(c_COMBC(X29169,tc_fun(X29169,tc_HOL_Obool),tc_HOL_Obool),c_member(X29169)),X29167))),
inference(variable_rename,[status(thm)],[fact_insert__compr__raw]) ).
fof(i_0_6628,plain,
! [X29164,X29165,X29166] : hAPP(hAPP(c_Set_Oinsert(X29166),X29165),X29164) = hAPP(c_Set_OCollect(X29166),hAPP(hAPP(c_COMBS(X29166,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29166),c_fdisj),hAPP(hAPP(c_COMBC(X29166,X29166,tc_HOL_Obool),c_fequal),X29165))),hAPP(hAPP(c_COMBC(X29166,tc_fun(X29166,tc_HOL_Obool),tc_HOL_Obool),c_member(X29166)),X29164))),
inference(variable_rename,[status(thm)],[fact_insert__compr]) ).
cnf(i_0_6629,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk386_4(X3,X4,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Otrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_5370]) ).
fof(i_0_6630,plain,
! [X32356,X32357,X32358,X32359,X32360,X32361] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32361,X32361)),hAPP(hAPP(c_Product__Type_OPair(X32361,X32361),X32360),X32359)),X32358))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32361),tc_List_Olist(X32361))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32361),tc_List_Olist(X32361)),X32357),X32356)),c_List_Olistrel(X32361,X32358)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32361),tc_List_Olist(X32361))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32361),tc_List_Olist(X32361)),hAPP(hAPP(c_List_Olist_OCons(X32361),X32360),X32357)),hAPP(hAPP(c_List_Olist_OCons(X32361),X32359),X32356))),c_List_Olistrel(X32361,X32358))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel_OCons])]) ).
cnf(i_0_6631,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk387_4(X3,X4,X2,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Otrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_5369]) ).
fof(i_0_6632,plain,
! [X28562,X28563,X28564,X28565,X28566] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28566,X28566,X28565,X28564,X28563),X28562))
| hBOOL(hAPP(hAPP(c_member(X28566),X28564),X28563))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28566,X28565,hAPP(hAPP(c_Set_Oinsert(X28566),X28564),X28563)),X28562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5392])]) ).
fof(i_0_6633,plain,
! [X29250,X29251,X29252] : c_Map_Odom(X29252,X29251,X29250) = hAPP(c_Set_OCollect(X29252),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29252),c_fNot),hAPP(hAPP(c_COMBC(X29252,tc_Option_Ooption(X29251),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X29251),tc_fun(tc_Option_Ooption(X29251),tc_HOL_Obool),X29252),c_fequal),X29250)),c_Option_Ooption_ONone(X29251)))),
inference(variable_rename,[status(thm)],[fact_dom__def]) ).
cnf(i_0_6634,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5393]) ).
cnf(i_0_6635,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5394]) ).
fof(i_0_6636,plain,
! [X26350] :
( X26350 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X26350),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smin__emptyI])]) ).
fof(i_0_6637,plain,
! [X26752,X26753] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26753),X26752)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26752),X26753)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_minus]) ).
fof(i_0_6638,plain,
! [X26364] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X26364),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
inference(variable_rename,[status(thm)],[fact_wmin__emptyI]) ).
fof(i_0_6639,plain,
! [X30822,X30823,X30824,X30825,X30826,X30827] :
( ~ c_Finite__Set_Ofun__left__comm(X30827,X30826,X30825)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30827,X30826,X30825,X30824,X30823),X30822))
| hAPP(hAPP(c_Finite__Set_Ofold(X30827,X30826,X30825),X30824),X30823) = X30822 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality])]) ).
fof(i_0_6640,plain,
! [X28515,X28516,X28517,X28518,X28519] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28519,X28518,X28517,X28516,c_Orderings_Obot__class_Obot(tc_fun(X28519,tc_HOL_Obool))),X28515))
| X28515 = X28516 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE])]) ).
fof(i_0_6641,plain,
! [X26893,X26894,X26895,X26896,X26897] :
( ~ c_Equiv__Relations_Oequiv(X26897,X26896,X26895)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26897,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26897,X26897,X26895),hAPP(hAPP(c_Set_Oinsert(X26897),X26894),c_Orderings_Obot__class_Obot(tc_fun(X26897,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X26897,X26897,X26895),hAPP(hAPP(c_Set_Oinsert(X26897),X26893),c_Orderings_Obot__class_Obot(tc_fun(X26897,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X26897),X26894),X26896))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26897,X26897)),hAPP(hAPP(c_Product__Type_OPair(X26897,X26897),X26893),X26894)),X26895)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__equiv__class])]) ).
fof(i_0_6642,plain,
! [X25642,X25643,X25644,X25645,X25646,X25647] :
( ( hBOOL(hAPP(hAPP(X25645,X25643),X25646))
| ~ hBOOL(hAPP(hAPP(c_member(X25647),X25646),c_SetInterval_Oord_OatLeastLessThan(X25647,X25645,X25644,X25643,X25642))) )
& ( hBOOL(hAPP(hAPP(X25644,X25646),X25642))
| ~ hBOOL(hAPP(hAPP(c_member(X25647),X25646),c_SetInterval_Oord_OatLeastLessThan(X25647,X25645,X25644,X25643,X25642))) )
& ( ~ hBOOL(hAPP(hAPP(X25645,X25643),X25646))
| ~ hBOOL(hAPP(hAPP(X25644,X25646),X25642))
| hBOOL(hAPP(hAPP(c_member(X25647),X25646),c_SetInterval_Oord_OatLeastLessThan(X25647,X25645,X25644,X25643,X25642))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff])])]) ).
fof(i_0_6643,plain,
! [X25630,X25631,X25632,X25633,X25634,X25635] :
( ( hBOOL(hAPP(hAPP(X25632,X25631),X25634))
| ~ hBOOL(hAPP(hAPP(c_member(X25635),X25634),c_SetInterval_Oord_OgreaterThanAtMost(X25635,X25633,X25632,X25631,X25630))) )
& ( hBOOL(hAPP(hAPP(X25633,X25634),X25630))
| ~ hBOOL(hAPP(hAPP(c_member(X25635),X25634),c_SetInterval_Oord_OgreaterThanAtMost(X25635,X25633,X25632,X25631,X25630))) )
& ( ~ hBOOL(hAPP(hAPP(X25632,X25631),X25634))
| ~ hBOOL(hAPP(hAPP(X25633,X25634),X25630))
| hBOOL(hAPP(hAPP(c_member(X25635),X25634),c_SetInterval_Oord_OgreaterThanAtMost(X25635,X25633,X25632,X25631,X25630))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff])])]) ).
fof(i_0_6644,plain,
! [X26580,X26581,X26582,X26583,X26584] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk236_5(X26580,X26581,X26582,X26583,X26584)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26584),X26581),X26583) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26584),X26580),X26582)
| ~ c_Nat__Transfer_Onat__set(X26582)
| X26583 != X26582
| ~ class_Groups_Ocomm__monoid__add(X26584)
| ~ class_Groups_Ocomm__monoid__mult(X26584) )
& ( hAPP(X26581,esk236_5(X26580,X26581,X26582,X26583,X26584)) != hAPP(X26580,esk236_5(X26580,X26581,X26582,X26583,X26584))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26584),X26581),X26583) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26584),X26580),X26582)
| ~ c_Nat__Transfer_Onat__set(X26582)
| X26583 != X26582
| ~ class_Groups_Ocomm__monoid__add(X26584)
| ~ class_Groups_Ocomm__monoid__mult(X26584) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I2_J])])])]) ).
fof(i_0_6645,plain,
! [X23824,X23825,X23826,X23827,X23828] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk131_5(X23824,X23825,X23826,X23827,X23828)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X23828),X23825),X23827) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X23828),X23824),X23826)
| ~ c_Nat__Transfer_Onat__set(X23826)
| X23827 != X23826
| ~ class_Groups_Ocomm__monoid__add(X23828)
| ~ class_Groups_Ocomm__monoid__mult(X23828) )
& ( hAPP(X23825,esk131_5(X23824,X23825,X23826,X23827,X23828)) != hAPP(X23824,esk131_5(X23824,X23825,X23826,X23827,X23828))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X23828),X23825),X23827) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X23828),X23824),X23826)
| ~ c_Nat__Transfer_Onat__set(X23826)
| X23827 != X23826
| ~ class_Groups_Ocomm__monoid__add(X23828)
| ~ class_Groups_Ocomm__monoid__mult(X23828) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I1_J])])])]) ).
fof(i_0_6646,plain,
! [X33997,X33998] : c_Random_Oselect__weight(X33998,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X33998),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X33998,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X33998,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X33998)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X33997)) = c_Random_Oselect__weight(X33998,X33997),
inference(variable_rename,[status(thm)],[fact_select__weigth__drop__zero]) ).
fof(i_0_6647,plain,
! [X33999,X34000] : c_Random_Opick(X34000,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X34000),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X34000,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X34000,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X34000)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X33999)) = c_Random_Opick(X34000,X33999),
inference(variable_rename,[status(thm)],[fact_pick__drop__zero]) ).
cnf(i_0_6648,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I3_J]) ).
cnf(i_0_6649,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I3_J]) ).
fof(i_0_6650,plain,
! [X31659,X31660,X31661,X31662] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X31662)),hAPP(c_Set_Oimage(X31661,tc_Option_Ooption(X31662),X31660),c_Orderings_Otop__class_Otop(tc_fun(X31661,tc_HOL_Obool)))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X31662)),hAPP(c_Set_Oimage(X31661,tc_Option_Ooption(X31662),c_Map_Omap__add(X31661,X31662,X31660,c_Map_Omap__of(X31661,X31662,X31659))),c_Orderings_Otop__class_Otop(tc_fun(X31661,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__map__of__map__add])]) ).
fof(i_0_6651,plain,
! [X29836,X29837,X29838,X29839] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29839,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29839,X29838),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29839,X29838),tc_HOL_Obool)),X29837),X29836))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29839,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29839,X29838),X29837)),hAPP(c_Relation_ODomain(X29839,X29838),X29836)))),
inference(variable_rename,[status(thm)],[fact_Domain__Int__subset]) ).
fof(i_0_6652,plain,
! [X29745,X29746,X29747,X29748] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29748,tc_HOL_Obool)),hAPP(c_Relation_ORange(X29747,X29748),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29747,X29748),tc_HOL_Obool)),X29746),X29745))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29748,tc_HOL_Obool)),hAPP(c_Relation_ORange(X29747,X29748),X29746)),hAPP(c_Relation_ORange(X29747,X29748),X29745)))),
inference(variable_rename,[status(thm)],[fact_Range__Int__subset]) ).
fof(i_0_6653,plain,
! [X26145,X26146,X26147,X26148,X26149] :
( ~ class_Fields_Ofield__inverse__zero(X26149)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26148),X26147))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26148,X26149),hAPP(hAPP(c_COMBS(X26148,X26149,X26149),hAPP(hAPP(c_COMBB(X26149,tc_fun(X26149,X26149),X26148),c_Rings_Oinverse__class_Odivide(X26149)),X26146)),X26145)),X26147) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26149),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26148,X26149),X26146),X26147)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26148,X26149),X26145),X26147)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__dividef])]) ).
fof(i_0_6654,plain,
! [X26140,X26141,X26142,X26143,X26144] :
( ~ class_Groups_Ocomm__monoid__mult(X26144)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26143),X26142))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26143,X26144),hAPP(hAPP(c_COMBS(X26143,X26144,X26144),hAPP(hAPP(c_COMBB(X26144,tc_fun(X26144,X26144),X26143),c_Groups_Otimes__class_Otimes(X26144)),X26141)),X26140)),X26142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26144),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26143,X26144),X26141),X26142)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26143,X26144),X26140),X26142)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib])]) ).
fof(i_0_6655,plain,
! [X24463,X24464,X24465,X24466,X24467] :
( ~ class_Groups_Ocomm__monoid__add(X24467)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24466),X24465))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24466,X24467),hAPP(hAPP(c_COMBS(X24466,X24467,X24467),hAPP(hAPP(c_COMBB(X24467,tc_fun(X24467,X24467),X24466),c_Groups_Oplus__class_Oplus(X24467)),X24464)),X24463)),X24465) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24467),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24466,X24467),X24464),X24465)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24466,X24467),X24463),X24465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib])]) ).
fof(i_0_6656,plain,
! [X32122,X32123,X32124,X32125,X32126,X32127,X32128,X32129] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32129)),X32128) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32127)),X32126)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32129)),X32125) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32127)),X32126)
| hBOOL(hAPP(hAPP(c_member(X32127),X32124),hAPP(c_List_Oset(X32127),X32126)))
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32127,tc_Option_Ooption(X32129)),c_Map_Omap__of(X32127,X32129,hAPP(hAPP(c_List_Ozip(X32127,X32129),X32126),X32128))),X32124),hAPP(c_Option_Ooption_OSome(X32129),X32123)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32127,tc_Option_Ooption(X32129)),c_Map_Omap__of(X32127,X32129,hAPP(hAPP(c_List_Ozip(X32127,X32129),X32126),X32125))),X32124),hAPP(c_Option_Ooption_OSome(X32129),X32122))
| c_Map_Omap__of(X32127,X32129,hAPP(hAPP(c_List_Ozip(X32127,X32129),X32126),X32128)) = c_Map_Omap__of(X32127,X32129,hAPP(hAPP(c_List_Ozip(X32127,X32129),X32126),X32125)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5395])]) ).
fof(i_0_6657,plain,
! [X28509,X28510,X28511,X28512,X28513,X28514] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28514,X28513,X28512,X28511,X28510),X28509))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28514),X28510)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite])]) ).
fof(i_0_6658,plain,
! [X33312,X33313] : hAPP(c_List_Orotate1(X33313),X33312) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X33313),X33313,c_List_Olist_ONil(X33313),hAPP(hAPP(c_COMBB(tc_List_Olist(X33313),tc_fun(tc_List_Olist(X33313),tc_List_Olist(X33313)),X33313),hAPP(c_COMBC(tc_List_Olist(X33313),tc_List_Olist(X33313),tc_List_Olist(X33313)),c_List_Oappend(X33313))),hAPP(hAPP(c_COMBC(X33313,tc_List_Olist(X33313),tc_List_Olist(X33313)),c_List_Olist_OCons(X33313)),c_List_Olist_ONil(X33313)))),X33312),
inference(variable_rename,[status(thm)],[fact_rotate1__def]) ).
fof(i_0_6659,plain,
! [X26056,X26057,X26058,X26059,X26060] :
( ~ class_Groups_Ocomm__monoid__mult(X26060)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26059,X26060),hAPP(hAPP(c_COMBS(X26059,X26060,X26060),hAPP(hAPP(c_COMBB(X26060,tc_fun(X26060,X26060),X26059),c_Groups_Otimes__class_Otimes(X26060)),X26058)),X26057)),X26056) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26060),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26059,X26060),X26058),X26056)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26059,X26060),X26057),X26056)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__timesf])]) ).
fof(i_0_6660,plain,
! [X23273,X23274,X23275,X23276,X23277] :
( ~ class_Groups_Oab__group__add(X23277)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23276,X23277),hAPP(hAPP(c_COMBS(X23276,X23277,X23277),hAPP(hAPP(c_COMBB(X23277,tc_fun(X23277,X23277),X23276),c_Groups_Ominus__class_Ominus(X23277)),X23275)),X23274)),X23273) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23277),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23276,X23277),X23275),X23273)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23276,X23277),X23274),X23273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__subtractf])]) ).
fof(i_0_6661,plain,
! [X23251,X23252,X23253,X23254,X23255] :
( ~ class_Groups_Ocomm__monoid__add(X23255)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23254,X23255),hAPP(hAPP(c_COMBS(X23254,X23255,X23255),hAPP(hAPP(c_COMBB(X23255,tc_fun(X23255,X23255),X23254),c_Groups_Oplus__class_Oplus(X23255)),X23253)),X23252)),X23251) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23255),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23254,X23255),X23253),X23251)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23254,X23255),X23252),X23251)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__addf])]) ).
fof(i_0_6662,plain,
! [X21949,X21950,X21951,X21952,X21953] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21953,X21952),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21951),X21950)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21952))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21949))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21953,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21952),X21949)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21951),X21949)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21952),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21951,X21949))),X21950)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult2__eq])]) ).
fof(i_0_6663,plain,
! [X32454,X32455] : c_Random_Oselect__weight(X32455,X32454) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X32455,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X32455),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32455)),X32454)))),hAPP(hAPP(c_COMBB(X32455,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X32455,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X32455,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X32455,X32454))),
inference(variable_rename,[status(thm)],[fact_select__weight__def]) ).
fof(i_0_6664,plain,
! [X28783,X28784,X28785,X28786,X28787,X28788] : hAPP(hAPP(c_Product__Type_OSigma(X28788,X28787),hAPP(hAPP(c_Set_Oinsert(X28788),X28786),X28785)),hAPP(c_COMBK(tc_fun(X28787,tc_HOL_Obool),X28788),hAPP(hAPP(c_Set_Oinsert(X28787),X28784),X28783))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X28788,X28787)),hAPP(hAPP(c_Product__Type_OPair(X28788,X28787),X28786),X28784)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28788,X28787),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28788,X28787),X28785),hAPP(c_COMBK(tc_fun(X28787,tc_HOL_Obool),X28788),hAPP(hAPP(c_Set_Oinsert(X28787),X28784),X28783)))),hAPP(hAPP(c_Product__Type_OSigma(X28788,X28787),hAPP(hAPP(c_Set_Oinsert(X28788),X28786),X28785)),hAPP(c_COMBK(tc_fun(X28787,tc_HOL_Obool),X28788),X28783)))),
inference(variable_rename,[status(thm)],[fact_insert__times__insert]) ).
fof(i_0_6665,plain,
! [X23282,X23283,X23284,X23285,X23286] :
( ~ class_Fields_Ofield(X23286)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23286),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23285,X23286),X23284),X23283)),X23282) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23285,X23286),hAPP(hAPP(c_COMBC(X23285,X23286,X23286),hAPP(hAPP(c_COMBB(X23286,tc_fun(X23286,X23286),X23285),c_Rings_Oinverse__class_Odivide(X23286)),X23284)),X23282)),X23283) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib])]) ).
fof(i_0_6666,plain,
! [X23263,X23264,X23265,X23266,X23267] :
( ~ class_Rings_Osemiring__0(X23267)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23267),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23266,X23267),X23265),X23264)),X23263) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23266,X23267),hAPP(hAPP(c_COMBC(X23266,X23267,X23267),hAPP(hAPP(c_COMBB(X23267,tc_fun(X23267,X23267),X23266),c_Groups_Otimes__class_Otimes(X23267)),X23265)),X23263)),X23264) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib])]) ).
fof(i_0_6667,plain,
! [X22128,X22129,X22130,X22131,X22132] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22132,X22131),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22130),X22129)))
| X22131 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22128))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22132,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22131),X22128)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22130),X22128)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22131),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22130,X22128))),X22129)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma])]) ).
fof(i_0_6668,plain,
! [X32265,X32266,X32267,X32268,X32269] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32269),tc_List_Olist(X32269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32269),tc_List_Olist(X32269)),X32268),X32267)),c_List_Olistrel(X32269,c_Transitive__Closure_Ortrancl(X32269,X32266))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32269),tc_List_Olist(X32269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32269),tc_List_Olist(X32269)),X32267),X32265)),c_List_Olistrel(X32269,c_Transitive__Closure_Ortrancl(X32269,X32266))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32269),tc_List_Olist(X32269))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32269),tc_List_Olist(X32269)),X32268),X32265)),c_List_Olistrel(X32269,c_Transitive__Closure_Ortrancl(X32269,X32266)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__trans])]) ).
cnf(i_0_6669,plain,
hAPP(c_List_Orotate(X1,X2),hAPP(c_List_Orev(X1),X3)) = hAPP(c_List_Orev(X1),hAPP(c_List_Orotate(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))),X3)),
inference(split_conjunct,[status(thm)],[i_0_5396]) ).
cnf(i_0_6670,plain,
c_List_Orotate(X1,X2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),
inference(split_conjunct,[status(thm)],[i_0_5397]) ).
fof(i_0_6671,plain,
! [X25105,X25106,X25107] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25107,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X25107,tc_fun(X25107,tc_HOL_Obool),tc_HOL_Obool),c_member(X25107)),X25106)),hAPP(hAPP(c_COMBC(X25107,tc_fun(X25107,tc_HOL_Obool),tc_HOL_Obool),c_member(X25107)),X25105)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25107,tc_HOL_Obool)),X25106),X25105)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25107,tc_HOL_Obool)),X25106),X25105))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25107,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X25107,tc_fun(X25107,tc_HOL_Obool),tc_HOL_Obool),c_member(X25107)),X25106)),hAPP(hAPP(c_COMBC(X25107,tc_fun(X25107,tc_HOL_Obool),tc_HOL_Obool),c_member(X25107)),X25105))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
cnf(i_0_6672,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Otrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5398]) ).
cnf(i_0_6673,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5399]) ).
fof(i_0_6674,plain,
! [X29676,X29677,X29678,X29679] :
( ~ c_FunDef_Oreduction__pair(X29679,X29678)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29679,X29679),tc_HOL_Obool)),X29677),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29679,X29679),tc_HOL_Obool),tc_fun(tc_prod(X29679,X29679),tc_HOL_Obool)),X29678)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29679,X29679),tc_HOL_Obool)),X29676),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X29679,X29679),tc_HOL_Obool),tc_fun(tc_prod(X29679,X29679),tc_HOL_Obool)),X29678)))
| ~ c_Wellfounded_Owf(X29679,X29676)
| c_Wellfounded_Owf(X29679,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29679,X29679),tc_HOL_Obool)),X29677),X29676)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma])]) ).
fof(i_0_6675,plain,
! [X31411,X31412,X31413] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31413,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31413,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X31413,tc_HOL_Obool),tc_HOL_Obool)),X31412),X31411))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31413,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31413,tc_HOL_Obool),X31412)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31413,tc_HOL_Obool),X31411)))),
inference(variable_rename,[status(thm)],[fact_Union__Int__subset]) ).
fof(i_0_6676,plain,
! [X30428,X30429,X30430,X30431,X30432] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30432,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30431,X30432,X30430),X30429)),X30428))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30431,tc_HOL_Obool)),X30429),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30431,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30432,X30431,hAPP(c_Relation_Oconverse(X30431,X30432),X30430)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30432,tc_HOL_Obool)),X30428))))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30431,tc_HOL_Obool)),X30429),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30431,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30432,X30431,hAPP(c_Relation_Oconverse(X30431,X30432),X30430)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30432,tc_HOL_Obool)),X30428)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30432,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30431,X30432,X30430),X30429)),X30428)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset__eq])]) ).
cnf(i_0_6677,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Otrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5400]) ).
cnf(i_0_6678,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_5401]) ).
fof(i_0_6679,plain,
! [X24846,X24847,X24848,X24849] : hAPP(c_Set_Oimage(X24849,X24848,X24847),X24846) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24849,tc_fun(X24848,tc_HOL_Obool)),X24846),hAPP(hAPP(c_COMBC(X24849,tc_fun(X24848,tc_HOL_Obool),tc_fun(X24848,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X24848,tc_fun(tc_fun(X24848,tc_HOL_Obool),tc_fun(X24848,tc_HOL_Obool)),X24849),c_Set_Oinsert(X24848)),X24847)),c_Orderings_Obot__class_Obot(tc_fun(X24848,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_image__eq__UN]) ).
fof(i_0_6680,plain,
! [X29154,X29155,X29156] :
( ( ~ hBOOL(hAPP(X29156,X29155))
| hAPP(c_Set_OCollect(X29154),hAPP(hAPP(c_COMBS(X29154,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29154),c_fconj),hAPP(hAPP(c_COMBC(X29154,X29154,tc_HOL_Obool),c_fequal),X29155))),X29156)) = hAPP(hAPP(c_Set_Oinsert(X29154),X29155),c_Orderings_Obot__class_Obot(tc_fun(X29154,tc_HOL_Obool))) )
& ( hBOOL(hAPP(X29156,X29155))
| hAPP(c_Set_OCollect(X29154),hAPP(hAPP(c_COMBS(X29154,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29154),c_fconj),hAPP(hAPP(c_COMBC(X29154,X29154,tc_HOL_Obool),c_fequal),X29155))),X29156)) = c_Orderings_Obot__class_Obot(tc_fun(X29154,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5402])]) ).
fof(i_0_6681,plain,
! [X31868,X31869,X31870,X31871,X31872,X31873,X31874] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31874),tc_Option_Ooption(X31873),tc_sum(X31872,X31871),hAPP(c_Option_Omap(X31874,X31873),X31870)),c_Sum__Type_Osum_Osum__case(X31872,tc_Option_Ooption(X31874),X31871,X31869,X31868)) = c_Sum__Type_Osum_Osum__case(X31872,tc_Option_Ooption(X31873),X31871,hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31874),tc_Option_Ooption(X31873),X31872,hAPP(c_Option_Omap(X31874,X31873),X31870)),X31869),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31874),tc_Option_Ooption(X31873),X31871,hAPP(c_Option_Omap(X31874,X31873),X31870)),X31868)),
inference(variable_rename,[status(thm)],[fact_option__map__o__sum__case]) ).
fof(i_0_6682,plain,
! [X33227,X33228,X33229,X33230,X33231] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33231),tc_List_Olist(X33231))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33231),tc_List_Olist(X33231)),X33230),X33229)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33231),c_List_Olistrel1(X33231,X33228))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33231),tc_List_Olist(X33231))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33231),tc_List_Olist(X33231)),hAPP(hAPP(c_List_Olist_OCons(X33231),X33227),X33230)),hAPP(hAPP(c_List_Olist_OCons(X33231),X33227),X33229))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33231),c_List_Olistrel1(X33231,X33228)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1])]) ).
fof(i_0_6683,plain,
! [X31911,X31912,X31913,X31914,X31915,X31916,X31917] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31917),tc_Option_Ooption(X31916),X31915,hAPP(c_Option_Omap(X31917,X31916),X31914)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31915,tc_Option_Ooption(X31917)),X31913),X31912),hAPP(c_Option_Ooption_OSome(X31917),X31911))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31915,tc_Option_Ooption(X31916)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31917),tc_Option_Ooption(X31916),X31915,hAPP(c_Option_Omap(X31917,X31916),X31914)),X31913)),X31912),hAPP(c_Option_Ooption_OSome(X31916),hAPP(X31914,X31911))),
inference(variable_rename,[status(thm)],[fact_option__map__o__map__upd]) ).
fof(i_0_6684,plain,
! [X26338,X26339,X26340,X26341] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26341),X26340))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26339),X26338))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26341),X26339)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26340),X26338))),c_FunDef_Opair__leq)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI2])]) ).
fof(i_0_6685,plain,
! [X26325,X26326,X26327,X26328] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26328),X26327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26326),X26325))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26328),X26326)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26327),X26325))),c_FunDef_Opair__less)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI2])]) ).
fof(i_0_6686,plain,
! [X30234,X30235,X30236] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30236,X30236),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30236,X30236),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30236,X30235)),c_Transitive__Closure_Ortrancl(X30236,X30234))),c_Transitive__Closure_Ortrancl(X30236,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30236,X30236),tc_HOL_Obool)),X30235),X30234)))),
inference(variable_rename,[status(thm)],[fact_rtrancl__Un__subset]) ).
fof(i_0_6687,plain,
! [X27384,X27385,X27386,X27387,X27388] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27388,tc_HOL_Obool)),hAPP(c_Relation_OImage(X27387,X27388,X27386),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27387,tc_HOL_Obool)),X27385),X27384))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27388,tc_HOL_Obool)),hAPP(c_Relation_OImage(X27387,X27388,X27386),X27385)),hAPP(c_Relation_OImage(X27387,X27388,X27386),X27384)))),
inference(variable_rename,[status(thm)],[fact_Image__Int__subset]) ).
fof(i_0_6688,plain,
! [X27348,X27349,X27350,X27351,X27352] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27352,tc_HOL_Obool)),hAPP(c_Set_Oimage(X27351,X27352,X27350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27351,tc_HOL_Obool)),X27349),X27348))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27352,tc_HOL_Obool)),hAPP(c_Set_Oimage(X27351,X27352,X27350),X27349)),hAPP(c_Set_Oimage(X27351,X27352,X27350),X27348)))),
inference(variable_rename,[status(thm)],[fact_image__Int__subset]) ).
fof(i_0_6689,plain,
! [X31531,X31532] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk423_2(X31531,X31532)))
| hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X31532)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X31531)) )
& ( ~ hBOOL(hAPP(X31532,esk423_2(X31531,X31532)))
| ~ hBOOL(hAPP(X31531,esk423_2(X31531,X31532)))
| hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X31532)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X31531)) )
& ( hBOOL(hAPP(X31532,esk423_2(X31531,X31532)))
| hBOOL(hAPP(X31531,esk423_2(X31531,X31532)))
| hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X31532)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X31531)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__cong])])])]) ).
cnf(i_0_6690,plain,
c_List_Ofoldr(X1,X2,X3,hAPP(hAPP(c_List_Omap(X4,X1),X5),X6),X7) = c_List_Ofoldr(X4,X2,hAPP(c_Fun_Ocomp(X1,tc_fun(X2,X2),X4,X3),X5),X6,X7),
inference(split_conjunct,[status(thm)],[i_0_5403]) ).
fof(i_0_6691,plain,
! [X26352,X26353,X26354,X26355] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26355),X26354))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26355),X26353)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26354),X26352))),c_FunDef_Opair__leq)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI1])]) ).
fof(i_0_6692,plain,
! [X26334,X26335,X26336,X26337] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26337),X26336))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26337),X26335)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26336),X26334))),c_FunDef_Opair__less)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI1])]) ).
fof(i_0_6693,plain,
! [X33704,X33705] : c_List_Olists(X33705,X33704) = hAPP(c_Set_OCollect(tc_List_Olist(X33705)),hAPP(hAPP(c_COMBC(tc_List_Olist(X33705),tc_fun(X33705,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X33705,tc_HOL_Obool),tc_fun(tc_fun(X33705,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X33705)),c_Orderings_Oord__class_Oless__eq(tc_fun(X33705,tc_HOL_Obool))),c_List_Oset(X33705))),X33704)),
inference(variable_rename,[status(thm)],[fact_lists__eq__set]) ).
fof(i_0_6694,plain,
! [X33246,X33247,X33248,X33249,X33250,X33251] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33251),tc_List_Olist(X33251))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33251),tc_List_Olist(X33251)),X33250),X33249)),c_List_Olistrel1(X33251,X33248)))
| X33247 != X33246
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33251),tc_List_Olist(X33251))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33251),tc_List_Olist(X33251)),hAPP(hAPP(c_List_Oappend(X33251),X33250),X33247)),hAPP(hAPP(c_List_Oappend(X33251),X33249),X33246))),c_List_Olistrel1(X33251,X33248))) )
& ( X33250 != X33249
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33251),tc_List_Olist(X33251))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33251),tc_List_Olist(X33251)),X33247),X33246)),c_List_Olistrel1(X33251,X33248)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33251),tc_List_Olist(X33251))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33251),tc_List_Olist(X33251)),hAPP(hAPP(c_List_Oappend(X33251),X33250),X33247)),hAPP(hAPP(c_List_Oappend(X33251),X33249),X33246))),c_List_Olistrel1(X33251,X33248))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])]) ).
fof(i_0_6695,plain,
! [X32981,X32982,X32983,X32984,X32985] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32985),tc_List_Olist(X32985))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32985),tc_List_Olist(X32985)),X32984),X32983)),c_List_Olexord(X32985,X32982)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32985),tc_List_Olist(X32985))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32985),tc_List_Olist(X32985)),hAPP(hAPP(c_List_Oappend(X32985),X32981),X32984)),hAPP(hAPP(c_List_Oappend(X32985),X32981),X32983))),c_List_Olexord(X32985,X32982))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI])]) ).
fof(i_0_6696,plain,
! [X33222,X33223,X33224,X33225,X33226] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33226),tc_List_Olist(X33226))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33226),tc_List_Olist(X33226)),X33225),X33224)),c_List_Olistrel1(X33226,X33223)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33226),tc_List_Olist(X33226))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33226),tc_List_Olist(X33226)),hAPP(hAPP(c_List_Olist_OCons(X33226),X33222),X33225)),hAPP(hAPP(c_List_Olist_OCons(X33226),X33222),X33224))),c_List_Olistrel1(X33226,X33223))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I2])]) ).
cnf(i_0_6697,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_5404]) ).
fof(i_0_6698,plain,
! [X29336] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X29336))),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).
fof(i_0_6699,plain,
! [X26204,X26205,X26206,X26207,X26208] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X26208)),hAPP(c_Set_Oimage(X26207,tc_Option_Ooption(X26208),X26206),c_Orderings_Otop__class_Otop(tc_fun(X26207,tc_HOL_Obool)))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X26208)),hAPP(c_Set_Oimage(X26207,tc_Option_Ooption(X26208),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26207,tc_Option_Ooption(X26208)),X26206),X26205),hAPP(c_Option_Ooption_OSome(X26208),X26204))),c_Orderings_Otop__class_Otop(tc_fun(X26207,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__updI])]) ).
fof(i_0_6700,plain,
! [X32105,X32106,X32107,X32108,X32109,X32110] : hAPP(hAPP(c_List_Ozip(X32110,X32109),hAPP(hAPP(c_List_Omap(X32108,X32110),X32107),X32106)),X32105) = hAPP(hAPP(c_List_Omap(tc_prod(X32108,X32109),tc_prod(X32110,X32109)),hAPP(c_Product__Type_Oprod_Oprod__case(X32108,X32109,tc_prod(X32110,X32109)),hAPP(hAPP(c_COMBB(X32110,tc_fun(X32109,tc_prod(X32110,X32109)),X32108),c_Product__Type_OPair(X32110,X32109)),X32107))),hAPP(hAPP(c_List_Ozip(X32108,X32109),X32106),X32105)),
inference(variable_rename,[status(thm)],[fact_zip__map1]) ).
fof(i_0_6701,plain,
! [X26382,X26383,X26384] : c_Wellfounded_Omlex__prod(X26384,X26383,X26382) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X26384),X26384),c_Wellfounded_Olex__prod(tc_Nat_Onat,X26384,c_Wellfounded_Oless__than,X26382)),hAPP(hAPP(c_COMBS(X26384,X26384,tc_prod(tc_Nat_Onat,X26384)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X26384,tc_prod(tc_Nat_Onat,X26384)),X26384),c_Product__Type_OPair(tc_Nat_Onat,X26384)),X26383)),c_COMBI(X26384))),
inference(variable_rename,[status(thm)],[fact_mlex__prod__def]) ).
fof(i_0_6702,plain,
! [X26480,X26481,X26482] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26482),esk232_3(X26480,X26481,X26482)))
| hBOOL(hAPP(X26480,c_Orderings_Obot__class_Obot(tc_fun(X26482,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X26480,X26481))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26482),X26481)) )
& ( hBOOL(hAPP(hAPP(c_member(X26482),esk231_3(X26480,X26481,X26482)),esk232_3(X26480,X26481,X26482)))
| hBOOL(hAPP(X26480,c_Orderings_Obot__class_Obot(tc_fun(X26482,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X26480,X26481))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26482),X26481)) )
& ( hBOOL(hAPP(X26480,esk232_3(X26480,X26481,X26482)))
| hBOOL(hAPP(X26480,c_Orderings_Obot__class_Obot(tc_fun(X26482,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X26480,X26481))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26482),X26481)) )
& ( ~ hBOOL(hAPP(X26480,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26482,tc_HOL_Obool)),esk232_3(X26480,X26481,X26482)),hAPP(hAPP(c_Set_Oinsert(X26482),esk231_3(X26480,X26481,X26482)),c_Orderings_Obot__class_Obot(tc_fun(X26482,tc_HOL_Obool))))))
| hBOOL(hAPP(X26480,c_Orderings_Obot__class_Obot(tc_fun(X26482,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X26480,X26481))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26482),X26481)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__empty__induct])])])]) ).
fof(i_0_6703,plain,
! [X28755,X28756,X28757,X28758,X28759,X28760] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28757,X28760),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28757,X28760),X28756),hAPP(c_COMBK(tc_fun(X28760,tc_HOL_Obool),X28757),X28758))),hAPP(hAPP(c_Product__Type_OSigma(X28757,X28760),X28755),hAPP(c_COMBK(tc_fun(X28760,tc_HOL_Obool),X28757),X28758))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28757,tc_HOL_Obool)),X28756),X28755))
| ~ hBOOL(hAPP(hAPP(c_member(X28760),X28759),X28758)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28757,tc_HOL_Obool)),X28756),X28755))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28757,X28760),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28757,X28760),X28756),hAPP(c_COMBK(tc_fun(X28760,tc_HOL_Obool),X28757),X28758))),hAPP(hAPP(c_Product__Type_OSigma(X28757,X28760),X28755),hAPP(c_COMBK(tc_fun(X28760,tc_HOL_Obool),X28757),X28758))))
| ~ hBOOL(hAPP(hAPP(c_member(X28760),X28759),X28758)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__subset__cancel2])])]) ).
cnf(i_0_6704,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = hAPP(hAPP(c_HOL_OLet(X2,X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Otimes__class_Otimes(X2)),hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)))),c_COMBI(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5405]) ).
fof(i_0_6705,plain,
! [X30509,X30510,X30511,X30512,X30513,X30514] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30514,X30514)),hAPP(hAPP(c_Product__Type_OPair(X30514,X30514),X30513),X30512)),X30511))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30514,X30514)),hAPP(hAPP(c_Product__Type_OPair(X30514,X30514),X30512),X30510)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30514,X30514),tc_HOL_Obool),X30509),X30511)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30514,X30514)),hAPP(hAPP(c_Product__Type_OPair(X30514,X30514),X30513),X30510)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30514,X30514),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30509)),X30511))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I2])]) ).
fof(i_0_6706,plain,
! [X30503,X30504,X30505,X30506,X30507,X30508] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30508,X30508)),hAPP(hAPP(c_Product__Type_OPair(X30508,X30508),X30507),X30506)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30508,X30508),tc_HOL_Obool),X30505),X30504)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30508,X30508)),hAPP(hAPP(c_Product__Type_OPair(X30508,X30508),X30506),X30503)),X30504))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30508,X30508)),hAPP(hAPP(c_Product__Type_OPair(X30508,X30508),X30507),X30503)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30508,X30508),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30505)),X30504))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I])]) ).
fof(i_0_6707,plain,
! [X26534,X26535,X26536,X26537,X26538] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26538,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26537,X26538,X26536),X26535)),X26534))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X26538,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X26537,tc_HOL_Obool),tc_fun(X26538,tc_HOL_Obool),c_Set_Oimage(X26537,X26538,X26536)),hAPP(c_Set_OPow(X26537),X26535))),hAPP(c_Set_OPow(X26538),X26534))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__mono])]) ).
fof(i_0_6708,plain,
! [X22025,X22026] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Onorm__frac(X22026,X22025) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22026),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22025))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22026),X22025))) )
& ( X22026 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X22026,X22025) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22026),X22025))) )
& ( X22025 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X22026,X22025) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22026),X22025))) )
& ( X22026 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X22025 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X22026,X22025) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X22026),X22025)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22026))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22025)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22026),X22025))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5406])])]) ).
cnf(i_0_6709,plain,
c_List_Ofoldr(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X5),X6) = c_List_Ofoldr(X1,X2,X3,X4,c_List_Ofoldr(X1,X2,X3,X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_5407]) ).
fof(i_0_6710,plain,
! [X32477,X32478,X32479] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X32479),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32479)),X32478))))
| hBOOL(hAPP(hAPP(c_member(X32479),hAPP(c_Product__Type_Ofst(X32479,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X32479,X32478),X32477))),hAPP(c_List_Oset(X32479),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X32479),X32479),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X32479)),X32478)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weight__member])]) ).
fof(i_0_6711,plain,
! [X23047,X23048,X23049,X23050] :
( ~ class_Groups_Oordered__ab__group__add__abs(X23050)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23050),hAPP(c_Groups_Oabs__class_Oabs(X23050),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23049,X23050),X23048),X23047))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23049,X23050),hAPP(hAPP(c_COMBB(X23050,X23050,X23049),c_Groups_Oabs__class_Oabs(X23050)),X23048)),X23047))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs])]) ).
fof(i_0_6712,plain,
! [X33938,X33939,X33940] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X33940,tc_HOL_Obool)),hAPP(c_List_Oset(X33940),X33939)),hAPP(hAPP(c_Set_Oinsert(X33940),X33938),c_Orderings_Obot__class_Obot(tc_fun(X33940,tc_HOL_Obool)))) = hAPP(c_List_Oset(X33940),hAPP(c_List_Ofilter(X33940,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33940),c_fNot),hAPP(hAPP(c_COMBC(X33940,X33940,tc_HOL_Obool),c_fequal),X33938))),X33939)),
inference(variable_rename,[status(thm)],[fact_set__minus__filter__out]) ).
fof(i_0_6713,plain,
! [X33903,X33904,X33905,X33906] : hAPP(c_List_Ofilter(X33906,X33905),hAPP(c_List_Ofilter(X33906,X33904),X33903)) = hAPP(c_List_Ofilter(X33906,hAPP(hAPP(c_COMBS(X33906,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33906),c_fconj),X33904)),X33905)),X33903),
inference(variable_rename,[status(thm)],[fact_filter__filter]) ).
fof(i_0_6714,plain,
! [X29840,X29841,X29842,X29843] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29843,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29843,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29843,X29842),X29841)),hAPP(c_Relation_ODomain(X29843,X29842),X29840))),hAPP(c_Relation_ODomain(X29843,X29842),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X29843,X29842),tc_HOL_Obool)),X29841),X29840)))),
inference(variable_rename,[status(thm)],[fact_Domain__Diff__subset]) ).
fof(i_0_6715,plain,
! [X29749,X29750,X29751,X29752] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29752,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29752,tc_HOL_Obool)),hAPP(c_Relation_ORange(X29751,X29752),X29750)),hAPP(c_Relation_ORange(X29751,X29752),X29749))),hAPP(c_Relation_ORange(X29751,X29752),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X29751,X29752),tc_HOL_Obool)),X29750),X29749)))),
inference(variable_rename,[status(thm)],[fact_Range__Diff__subset]) ).
fof(i_0_6716,plain,
! [X25380,X25381,X25382,X25383] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),X25380))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25382))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),c_Orderings_Obot__class_Obot(tc_fun(X25383,tc_HOL_Obool))))),X25380))
| hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25380))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25382))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25383,tc_HOL_Obool)),X25382),X25380))
| hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25380))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25380))
| hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25382))
| hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25382))
| hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25383,tc_HOL_Obool)),X25382),X25380))
| hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25382))
| hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),c_Orderings_Obot__class_Obot(tc_fun(X25383,tc_HOL_Obool))))),X25380))
| hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25383,tc_HOL_Obool)),X25382),X25380))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),c_Orderings_Obot__class_Obot(tc_fun(X25383,tc_HOL_Obool))))),X25380))
| hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25380))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),X25380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25382))
| hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),X25380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25383,tc_HOL_Obool)),X25382),X25380))
| hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),X25380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25383),X25381),X25382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),c_Orderings_Obot__class_Obot(tc_fun(X25383,tc_HOL_Obool))))),X25380))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),X25380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25383,tc_HOL_Obool)),X25382),X25380))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),c_Orderings_Obot__class_Obot(tc_fun(X25383,tc_HOL_Obool))))),X25380))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),X25380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25383,tc_HOL_Obool)),X25382),hAPP(hAPP(c_Set_Oinsert(X25383),X25381),X25380))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5408])])]) ).
fof(i_0_6717,plain,
! [X33774,X33775,X33776] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X33776,X33776)),hAPP(hAPP(c_Product__Type_OPair(X33776,X33776),esk474_3(X33774,X33775,X33776)),esk474_3(X33774,X33775,X33776))),X33775))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33776),tc_List_Olist(X33776))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33776),tc_List_Olist(X33776)),X33774),X33774)),c_List_Olexord(X33776,X33775))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5409])])]) ).
fof(i_0_6718,plain,
! [X29114] : c_Finite__Set_Ofun__left__comm__idem(X29114,tc_fun(X29114,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29114,tc_HOL_Obool),tc_fun(tc_fun(X29114,tc_HOL_Obool),tc_fun(X29114,tc_HOL_Obool)),X29114),hAPP(c_COMBC(tc_fun(X29114,tc_HOL_Obool),tc_fun(X29114,tc_HOL_Obool),tc_fun(X29114,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X29114,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X29114,tc_fun(X29114,tc_HOL_Obool),tc_fun(X29114,tc_HOL_Obool)),c_Set_Oinsert(X29114)),c_Orderings_Obot__class_Obot(tc_fun(X29114,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__remove]) ).
cnf(i_0_6719,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X1)),X2)),
inference(split_conjunct,[status(thm)],[i_0_5410]) ).
fof(i_0_6720,plain,
! [X25411,X25412,X25413] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25413),X25412))
| ~ hBOOL(hAPP(hAPP(c_member(X25413),X25411),X25412))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25413),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25413,tc_HOL_Obool)),X25412),hAPP(hAPP(c_Set_Oinsert(X25413),X25411),c_Orderings_Obot__class_Obot(tc_fun(X25413,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X25413),X25412))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__less])]) ).
fof(i_0_6721,plain,
! [X22407,X22408,X22409,X22410,X22411,X22412] : hAPP(hAPP(c_COMBS(tc_prod(X22412,X22411),X22411,X22410),hAPP(hAPP(c_COMBB(X22409,tc_fun(X22411,X22410),tc_prod(X22412,X22411)),X22408),hAPP(hAPP(c_COMBB(X22412,X22409,tc_prod(X22412,X22411)),X22407),c_Product__Type_Ofst(X22412,X22411)))),c_Product__Type_Osnd(X22412,X22411)) = hAPP(c_Product__Type_Oprod_Oprod__case(X22412,X22411,X22410),hAPP(hAPP(c_COMBB(X22409,tc_fun(X22411,X22410),X22412),X22408),X22407)),
inference(variable_rename,[status(thm)],[fact_split__comp__eq]) ).
fof(i_0_6722,plain,
! [X34011,X34012,X34013,X34014,X34015] :
( ~ class_Orderings_Olinorder(X34015)
| ~ hBOOL(hAPP(hAPP(c_member(X34014),X34013),hAPP(c_List_Oset(X34014),X34012)))
| ~ c_List_Olinorder__class_Osorted(X34015,hAPP(hAPP(c_List_Omap(X34014,X34015),X34011),X34012))
| hAPP(c_List_Ohd(X34014),hAPP(c_List_Ofilter(X34014,hAPP(hAPP(c_COMBB(X34015,tc_HOL_Obool,X34014),hAPP(c_fequal,hAPP(X34011,X34013))),X34011)),X34012)) != X34013
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34014,X34015,X34011),X34013),c_List_Oremove1(X34014,X34013,X34012)) = X34012 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__remove1])]) ).
fof(i_0_6723,plain,
! [X18429,X18430,X18431,X18432,X18433,X18434] : c_Sum__Type_Osum_Osum__rec(X18434,X18433,X18432,X18431,X18430,hAPP(c_Sum__Type_OInl(X18434,X18432),X18429)) = hAPP(X18431,X18429),
inference(variable_rename,[status(thm)],[fact_sum_Orecs_I1_J]) ).
fof(i_0_6724,plain,
! [X18435,X18436,X18437,X18438,X18439,X18440] : c_Sum__Type_Osum_Osum__rec(X18440,X18439,X18438,X18437,X18436,hAPP(c_Sum__Type_OInr(X18438,X18440),X18435)) = hAPP(X18436,X18435),
inference(variable_rename,[status(thm)],[fact_sum_Orecs_I2_J]) ).
fof(i_0_6725,plain,
! [X26572,X26573] :
( ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26573),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26572),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26573),X26572)),c_Int_Ointrel)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26573),X26572)),c_Int_Ointrel))
| hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26573),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X26572),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__intrel__iff])]) ).
fof(i_0_6726,plain,
! [X25583,X25584,X25585,X25586] : c_Nitpick_Ofold__graph_H(X25586,X25585,X25584,X25583,c_Orderings_Obot__class_Obot(tc_fun(X25586,tc_HOL_Obool)),X25583),
inference(variable_rename,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).
fof(i_0_6727,plain,
! [X25579,X25580,X25581,X25582] : c_Nitpick_Ofold__graph_H(X25582,X25581,X25580,X25579,c_Orderings_Obot__class_Obot(tc_fun(X25582,tc_HOL_Obool)),X25579),
inference(variable_rename,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).
fof(i_0_6728,plain,
! [X28160,X28161,X28162,X28163,X28164] :
( ( c_Fun_Oinj__on(X28164,X28163,X28162,X28160)
| ~ c_Fun_Oinj__on(X28164,X28163,X28162,hAPP(hAPP(c_Set_Oinsert(X28164),X28161),X28160)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28163),hAPP(X28162,X28161)),hAPP(c_Set_Oimage(X28164,X28163,X28162),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28164,tc_HOL_Obool)),X28160),hAPP(hAPP(c_Set_Oinsert(X28164),X28161),c_Orderings_Obot__class_Obot(tc_fun(X28164,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(X28164,X28163,X28162,hAPP(hAPP(c_Set_Oinsert(X28164),X28161),X28160)) )
& ( ~ c_Fun_Oinj__on(X28164,X28163,X28162,X28160)
| hBOOL(hAPP(hAPP(c_member(X28163),hAPP(X28162,X28161)),hAPP(c_Set_Oimage(X28164,X28163,X28162),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28164,tc_HOL_Obool)),X28160),hAPP(hAPP(c_Set_Oinsert(X28164),X28161),c_Orderings_Obot__class_Obot(tc_fun(X28164,tc_HOL_Obool)))))))
| c_Fun_Oinj__on(X28164,X28163,X28162,hAPP(hAPP(c_Set_Oinsert(X28164),X28161),X28160)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5411])])]) ).
fof(i_0_6729,plain,
! [X29447,X29448] : c_Product__Type_Omap__pair(X29448,X29448,X29447,X29447,c_Fun_Oid(X29448),c_Fun_Oid(X29447)) = c_Fun_Oid(tc_prod(X29448,X29447)),
inference(variable_rename,[status(thm)],[fact_map__pair_Oid]) ).
cnf(i_0_6730,plain,
c_Product__Type_Oapfst(X1,X1,X2,c_Fun_Oid(X1)) = c_Fun_Oid(tc_prod(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_5412]) ).
fof(i_0_6731,plain,
! [X29445,X29446] : c_Product__Type_Omap__pair(X29446,X29446,X29445,X29445,c_COMBI(X29446),c_COMBI(X29445)) = c_Fun_Oid(tc_prod(X29446,X29445)),
inference(variable_rename,[status(thm)],[fact_map__pair_Oidentity]) ).
cnf(i_0_6732,plain,
c_Product__Type_Oapsnd(X1,X1,X2,c_Fun_Oid(X1)) = c_Fun_Oid(tc_prod(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_5413]) ).
fof(i_0_6733,plain,
! [X30828,X30829,X30830,X30831,X30832] :
( ~ c_Finite__Set_Ofun__left__comm(X30832,X30831,X30830)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30832),X30829))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30832,X30831,X30830,X30828,X30829),hAPP(hAPP(c_Finite__Set_Ofold(X30832,X30831,X30830),X30828),X30829))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold])]) ).
cnf(i_0_6734,plain,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_negateSnd__def]) ).
fof(i_0_6735,plain,
! [X24883,X24884,X24885] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24885),X24884))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24885),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24885,tc_HOL_Obool)),X24884),hAPP(hAPP(c_Set_Oinsert(X24885),X24883),c_Orderings_Obot__class_Obot(tc_fun(X24885,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X24885),X24884))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__le])]) ).
fof(i_0_6736,plain,
! [X29502,X29503,X29504,X29505,X29506,X29507,X29508] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29508,X29507),tc_HOL_Obool)),X29506),X29505))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29507,X29504),tc_HOL_Obool)),X29503),X29502))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29508,X29504),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29508,X29507,X29504),X29506),X29503)),hAPP(hAPP(c_Relation_Orel__comp(X29508,X29507,X29504),X29505),X29502))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__mono])]) ).
fof(i_0_6737,plain,
! [X26946,X26947,X26948,X26949,X26950] :
( ~ c_Equiv__Relations_Oequiv(X26950,X26949,X26948)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26950,X26950)),hAPP(hAPP(c_Product__Type_OPair(X26950,X26950),X26947),X26946)),X26948))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26950,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26950,X26950,X26948),hAPP(hAPP(c_Set_Oinsert(X26950),X26947),c_Orderings_Obot__class_Obot(tc_fun(X26950,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X26950,X26950,X26948),hAPP(hAPP(c_Set_Oinsert(X26950),X26946),c_Orderings_Obot__class_Obot(tc_fun(X26950,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__subset])]) ).
fof(i_0_6738,plain,
! [X28263,X28264,X28265,X28266,X28267,X28268] :
( ~ c_Fun_Oinj__on(X28268,X28267,X28266,X28265)
| ~ hBOOL(hAPP(hAPP(c_member(X28267),X28264),hAPP(c_Set_Oimage(X28268,X28267,X28266),X28265)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28268,tc_HOL_Obool)),X28265),X28263))
| hBOOL(hAPP(hAPP(c_member(X28268),hAPP(c_Fun_Othe__inv__into(X28268,X28267,X28265,X28266),X28264)),X28263)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__into])]) ).
fof(i_0_6739,plain,
! [X24574,X24575,X24576,X24577,X24578] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24578),hAPP(c_Set_Oimage(X24577,X24578,X24576),c_Orderings_Otop__class_Otop(tc_fun(X24577,tc_HOL_Obool)))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24575),hAPP(c_Set_Oimage(X24577,X24575,hAPP(hAPP(c_COMBB(X24578,X24575,X24577),X24574),X24576)),c_Orderings_Otop__class_Otop(tc_fun(X24577,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).
fof(i_0_6740,plain,
! [X31417,X31418,X31419] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31419,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31419,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31419,tc_HOL_Obool),X31418)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31419,tc_HOL_Obool),X31417))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31419,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X31419,tc_HOL_Obool),tc_HOL_Obool)),X31418),X31417)))),
inference(variable_rename,[status(thm)],[fact_Inter__Un__subset]) ).
fof(i_0_6741,plain,
! [X33670,X33671,X33672] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33672,X33672),tc_HOL_Obool)),X33671),hAPP(hAPP(c_Product__Type_OSigma(X33672,X33672),X33670),hAPP(c_COMBK(tc_fun(X33672,tc_HOL_Obool),X33672),X33670))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X33672),tc_List_Olist(X33672)),tc_HOL_Obool)),c_List_Olistrel(X33672,X33671)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X33672),tc_List_Olist(X33672)),c_List_Olists(X33672,X33670)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X33672),tc_HOL_Obool),tc_List_Olist(X33672)),c_List_Olists(X33672,X33670))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__subset])]) ).
fof(i_0_6742,plain,
! [X27968,X27969,X27970,X27971,X27972,X27973,X27974] :
( ~ class_Groups_Oab__semigroup__mult(X27974)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27973),X27972))
| ~ c_Fun_Oinj__on(X27973,X27971,X27970,X27972)
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27974,X27971,c_Groups_Otimes__class_Otimes(X27974)),X27969),X27968),hAPP(c_Set_Oimage(X27973,X27971,X27970),X27972)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27974,X27973,c_Groups_Otimes__class_Otimes(X27974)),hAPP(c_Fun_Ocomp(X27971,X27974,X27973,X27969),X27970)),X27968),X27972) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__reindex])]) ).
fof(i_0_6743,plain,
! [X19748,X19749,X19750,X19751] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19750),X19749))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19749),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19748,X19751))),X19750)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19749),X19751))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4])]) ).
fof(i_0_6744,plain,
! [X33186,X33187,X33188,X33189,X33190,X33191] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33191)),X33190) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33189)),X33188)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33191,tc_HOL_Obool)),hAPP(c_List_Oset(X33191),X33190)),X33187))
| c_Map_Orestrict__map(X33191,X33189,c_Map_Omap__upds(X33191,X33189,X33186,X33190,X33188),X33187) = c_Map_Omap__upds(X33191,X33189,c_Map_Orestrict__map(X33191,X33189,X33186,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X33191,tc_HOL_Obool)),X33187),hAPP(c_List_Oset(X33191),X33190))),X33190,X33188) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrict__map__upds])]) ).
fof(i_0_6745,plain,
! [X31506,X31507,X31508,X31509] :
( ( hBOOL(hAPP(hAPP(c_member(X31509),esk418_4(X31506,X31507,X31508,X31509)),X31508))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31509),hAPP(hAPP(c_Finite__Set_Ofold(X31509,X31509,c_Lattices_Osemilattice__sup__class_Osup(X31509)),X31506),X31508)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X31509),X31507),X31506)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31509),X31508))
| ~ class_Lattices_Osemilattice__sup(X31509) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31509),esk418_4(X31506,X31507,X31508,X31509)),X31507))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31509),hAPP(hAPP(c_Finite__Set_Ofold(X31509,X31509,c_Lattices_Osemilattice__sup__class_Osup(X31509)),X31506),X31508)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X31509),X31507),X31506)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31509),X31508))
| ~ class_Lattices_Osemilattice__sup(X31509) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__sup__le__sup])])])]) ).
fof(i_0_6746,plain,
! [X31487,X31488,X31489,X31490] :
( ( hBOOL(hAPP(hAPP(c_member(X31490),esk414_4(X31487,X31488,X31489,X31490)),X31489))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31490),hAPP(hAPP(c_Finite__Set_Ofold(X31490,X31490,c_Orderings_Oord__class_Omax(X31490)),X31487),X31489)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X31490),X31488),X31487)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31490),X31489))
| ~ class_Orderings_Olinorder(X31490) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31490),esk414_4(X31487,X31488,X31489,X31490)),X31488))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31490),hAPP(hAPP(c_Finite__Set_Ofold(X31490,X31490,c_Orderings_Oord__class_Omax(X31490)),X31487),X31489)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X31490),X31488),X31487)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31490),X31489))
| ~ class_Orderings_Olinorder(X31490) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__le__sup])])])]) ).
cnf(i_0_6747,plain,
c_Transitive__Closure_Otrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_5414]) ).
fof(i_0_6748,plain,
! [X25363,X25364,X25365,X25366] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25366),X25364),X25365))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25366,tc_HOL_Obool)),X25365),hAPP(hAPP(c_Set_Oinsert(X25366),X25364),c_Orderings_Obot__class_Obot(tc_fun(X25366,tc_HOL_Obool))))),X25363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),X25365),hAPP(hAPP(c_Set_Oinsert(X25366),X25364),X25363))) )
& ( hBOOL(hAPP(hAPP(c_member(X25366),X25364),X25365))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),X25365),X25363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),X25365),hAPP(hAPP(c_Set_Oinsert(X25366),X25364),X25363))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25366),X25364),X25365))
| hBOOL(hAPP(hAPP(c_member(X25366),X25364),X25365))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),X25365),hAPP(hAPP(c_Set_Oinsert(X25366),X25364),X25363))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),X25365),X25363))
| hBOOL(hAPP(hAPP(c_member(X25366),X25364),X25365))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),X25365),hAPP(hAPP(c_Set_Oinsert(X25366),X25364),X25363))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25366),X25364),X25365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25366,tc_HOL_Obool)),X25365),hAPP(hAPP(c_Set_Oinsert(X25366),X25364),c_Orderings_Obot__class_Obot(tc_fun(X25366,tc_HOL_Obool))))),X25363))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),X25365),hAPP(hAPP(c_Set_Oinsert(X25366),X25364),X25363))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),X25365),X25363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25366,tc_HOL_Obool)),X25365),hAPP(hAPP(c_Set_Oinsert(X25366),X25364),c_Orderings_Obot__class_Obot(tc_fun(X25366,tc_HOL_Obool))))),X25363))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25366,tc_HOL_Obool)),X25365),hAPP(hAPP(c_Set_Oinsert(X25366),X25364),X25363))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5415])])]) ).
fof(i_0_6749,plain,
! [X33270,X33271,X33272,X33273,X33274] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33274,X33274)),hAPP(hAPP(c_Product__Type_OPair(X33274,X33274),X33273),X33272)),X33271))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33274),tc_List_Olist(X33274))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33274),tc_List_Olist(X33274)),hAPP(hAPP(c_List_Olist_OCons(X33274),X33273),X33270)),hAPP(hAPP(c_List_Olist_OCons(X33274),X33272),X33270))),c_List_Olistrel1(X33274,X33271))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I1])]) ).
cnf(i_0_6750,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Oone__class_Oone(X1)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5416]) ).
cnf(i_0_6751,plain,
( c_Groups_Oone__class_Oone(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5417]) ).
fof(i_0_6752,plain,
! [X34209,X34210,X34211] :
( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34211),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34211))),X34210)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34209),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34211))),X34210)))
| hAPP(hAPP(c_List_Omap(tc_List_Olist(X34211),X34211),hAPP(hAPP(c_COMBC(tc_List_Olist(X34211),tc_Nat_Onat,X34211),c_List_Onth(X34211)),X34209)),hAPP(c_List_Ofilter(tc_List_Olist(X34211),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34211)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34209)),c_Nat_Osize__class_Osize(tc_List_Olist(X34211)))),c_List_Otranspose(X34211,X34210))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X34211)),X34210),X34209) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column])]) ).
fof(i_0_6753,plain,
! [X30027,X30028,X30029] : c_Hilbert__Choice_OEps(tc_prod(X30029,X30028),X30027) = c_Hilbert__Choice_OEps(tc_prod(X30029,X30028),hAPP(c_Product__Type_Oprod_Oprod__case(X30029,X30028,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30028,tc_prod(X30029,X30028)),tc_fun(X30028,tc_HOL_Obool),X30029),hAPP(c_COMBB(tc_prod(X30029,X30028),tc_HOL_Obool,X30028),X30027)),c_Product__Type_OPair(X30029,X30028)))),
inference(variable_rename,[status(thm)],[fact_split__paired__Eps]) ).
fof(i_0_6754,plain,
! [X22980,X22981,X22982] : c_HOL_OThe(tc_prod(X22982,X22981),X22980) = c_HOL_OThe(tc_prod(X22982,X22981),hAPP(c_Product__Type_Oprod_Oprod__case(X22982,X22981,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X22981,tc_prod(X22982,X22981)),tc_fun(X22981,tc_HOL_Obool),X22982),hAPP(c_COMBB(tc_prod(X22982,X22981),tc_HOL_Obool,X22981),X22980)),c_Product__Type_OPair(X22982,X22981)))),
inference(variable_rename,[status(thm)],[fact_split__paired__The]) ).
fof(i_0_6755,plain,
! [X25689,X25690,X25691,X25692,X25693,X25694,X25695] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X25695,X25694,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25695)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25695),X25693),X25692),X25691)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25695),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X25695,X25694,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25695)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25695),X25691),X25690),X25689)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25695),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(X25695,X25694,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25695)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25695),X25693),c_Com_Ocom_OSemi(X25692,X25690)),X25689)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25695),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Comp])]) ).
fof(i_0_6756,plain,
! [X30532,X30533,X30534,X30535,X30536,X30537,X30538,X30539] :
( ( ~ c_Relation_Ototal__on(X30534,X30533,X30532)
| ~ hBOOL(hAPP(hAPP(c_member(X30534),X30535),X30533))
| ~ hBOOL(hAPP(hAPP(c_member(X30534),X30536),X30533))
| X30535 = X30536
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30534,X30534)),hAPP(hAPP(c_Product__Type_OPair(X30534,X30534),X30535),X30536)),X30532))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30534,X30534)),hAPP(hAPP(c_Product__Type_OPair(X30534,X30534),X30536),X30535)),X30532)) )
& ( hBOOL(hAPP(hAPP(c_member(X30539),esk369_3(X30537,X30538,X30539)),X30538))
| c_Relation_Ototal__on(X30539,X30538,X30537) )
& ( hBOOL(hAPP(hAPP(c_member(X30539),esk370_3(X30537,X30538,X30539)),X30538))
| c_Relation_Ototal__on(X30539,X30538,X30537) )
& ( esk369_3(X30537,X30538,X30539) != esk370_3(X30537,X30538,X30539)
| c_Relation_Ototal__on(X30539,X30538,X30537) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30539,X30539)),hAPP(hAPP(c_Product__Type_OPair(X30539,X30539),esk369_3(X30537,X30538,X30539)),esk370_3(X30537,X30538,X30539))),X30537))
| c_Relation_Ototal__on(X30539,X30538,X30537) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30539,X30539)),hAPP(hAPP(c_Product__Type_OPair(X30539,X30539),esk370_3(X30537,X30538,X30539)),esk369_3(X30537,X30538,X30539))),X30537))
| c_Relation_Ototal__on(X30539,X30538,X30537) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__def])])])])])]) ).
fof(i_0_6757,plain,
! [X20180,X20181,X20182,X20183] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20183))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20182),X20181))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20181),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20180,X20183))),X20182)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20181),X20183))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__lemma])]) ).
fof(i_0_6758,plain,
! [X31690,X31691,X31692] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31691),X31690))
| c_Smallcheck_Osmall_H(X31692,X31691,X31690) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X31692),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X31691),X31690)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31691),X31690))
| c_Smallcheck_Osmall_H(X31692,X31691,X31690) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X31692,X31691,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X31690),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X31692,X31690))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X31692),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X31691),X31690)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5418])])]) ).
fof(i_0_6759,plain,
! [X30607,X30608,X30609,X30610,X30611] :
( ~ c_Relation_Osingle__valued(X30611,X30611,X30610)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30611,X30611)),hAPP(hAPP(c_Product__Type_OPair(X30611,X30611),X30609),X30608)),c_Transitive__Closure_Ortrancl(X30611,X30610)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30611,X30611)),hAPP(hAPP(c_Product__Type_OPair(X30611,X30611),X30609),X30607)),c_Transitive__Closure_Ortrancl(X30611,X30610)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30611,X30611)),hAPP(hAPP(c_Product__Type_OPair(X30611,X30611),X30608),X30607)),c_Transitive__Closure_Ortrancl(X30611,X30610)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30611,X30611)),hAPP(hAPP(c_Product__Type_OPair(X30611,X30611),X30607),X30608)),c_Transitive__Closure_Ortrancl(X30611,X30610))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__confluent])]) ).
fof(i_0_6760,plain,
! [X29572,X29573,X29574] :
( ~ c_Wellfounded_Owf(X29574,X29573)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29574,X29574),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29574,X29574,X29574),X29573),X29572)),X29573))
| c_FunDef_Oreduction__pair(X29574,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X29574,X29574),tc_HOL_Obool),tc_fun(tc_prod(X29574,X29574),tc_HOL_Obool)),X29573),X29572)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pairI])]) ).
fof(i_0_6761,plain,
! [X19916,X19917,X19918,X19919] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19919))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19918),X19917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19917),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19918),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19916,X19919))),X19917)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux2])]) ).
fof(i_0_6762,plain,
! [X32616,X32617] : c_Random_Oselect(X32617,X32616) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X32617,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32617)),X32616)))),hAPP(hAPP(c_COMBB(X32617,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X32617,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X32617,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X32617,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X32617),X32616)),c_Code__Numeral_Onat__of))),
inference(variable_rename,[status(thm)],[fact_select__def]) ).
fof(i_0_6763,plain,
! [X21909,X21910] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21910),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Onorm__frac(X21909,X21910) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21909),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21910)) )
& ( X21909 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X21909,X21910) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21910),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( X21910 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X21909,X21910) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21910),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( X21909 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X21910 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X21909,X21910) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X21909),X21910)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21909))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21910)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21910),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5419])])]) ).
fof(i_0_6764,plain,
! [X26731,X26732,X26733] :
( ~ class_Rings_Oring__1(X26733)
| hAPP(c_Int_Oring__1__class_Oof__int(X26733),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26732),X26731)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26733),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26733),X26732)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26733),X26731)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int])]) ).
fof(i_0_6765,plain,
! [X31875,X31876,X31877,X31878,X31879] : c_Map_Odom(X31879,X31878,hAPP(hAPP(c_COMBS(X31879,tc_Option_Ooption(X31877),tc_Option_Ooption(X31878)),hAPP(hAPP(c_COMBB(tc_fun(X31877,X31878),tc_fun(tc_Option_Ooption(X31877),tc_Option_Ooption(X31878)),X31879),c_Option_Omap(X31877,X31878)),X31876)),X31875)) = c_Map_Odom(X31879,X31877,X31875),
inference(variable_rename,[status(thm)],[fact_dom__option__map]) ).
cnf(i_0_6766,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5420]) ).
cnf(i_0_6767,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_5421]) ).
fof(i_0_6768,plain,
! [X25367,X25368,X25369,X25370] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25370,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25370,tc_HOL_Obool)),X25369),hAPP(hAPP(c_Set_Oinsert(X25370),X25368),c_Orderings_Obot__class_Obot(tc_fun(X25370,tc_HOL_Obool))))),X25367))
| ~ hBOOL(hAPP(hAPP(c_member(X25370),X25368),X25369))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25370,tc_HOL_Obool)),X25369),hAPP(hAPP(c_Set_Oinsert(X25370),X25368),X25367))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__single__insert])]) ).
fof(i_0_6769,plain,
! [X26759,X26760] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26760),X26759)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26760),X26759),
inference(variable_rename,[status(thm)],[fact_nat]) ).
cnf(i_0_6770,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = hAPP(hAPP(c_HOL_OLet(X2,X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Otimes__class_Otimes(X2)),hAPP(c_Groups_Otimes__class_Otimes(X2),X3))),c_COMBI(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5422]) ).
cnf(i_0_6771,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Groups_Omonoid__mult(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5423]) ).
cnf(i_0_6772,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_5424]) ).
fof(i_0_6773,plain,
! [X28165,X28166,X28167,X28168,X28169] :
( ( c_Fun_Oinj__on(X28169,X28168,X28167,X28166)
| ~ c_Fun_Oinj__on(X28169,X28168,X28167,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28169,tc_HOL_Obool)),X28166),X28165)) )
& ( c_Fun_Oinj__on(X28169,X28168,X28167,X28165)
| ~ c_Fun_Oinj__on(X28169,X28168,X28167,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28169,tc_HOL_Obool)),X28166),X28165)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28168,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28169,X28168,X28167),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28169,tc_HOL_Obool)),X28166),X28165))),hAPP(c_Set_Oimage(X28169,X28168,X28167),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28169,tc_HOL_Obool)),X28165),X28166))) = c_Orderings_Obot__class_Obot(tc_fun(X28168,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(X28169,X28168,X28167,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28169,tc_HOL_Obool)),X28166),X28165)) )
& ( ~ c_Fun_Oinj__on(X28169,X28168,X28167,X28166)
| ~ c_Fun_Oinj__on(X28169,X28168,X28167,X28165)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28168,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28169,X28168,X28167),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28169,tc_HOL_Obool)),X28166),X28165))),hAPP(c_Set_Oimage(X28169,X28168,X28167),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28169,tc_HOL_Obool)),X28165),X28166))) != c_Orderings_Obot__class_Obot(tc_fun(X28168,tc_HOL_Obool))
| c_Fun_Oinj__on(X28169,X28168,X28167,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28169,tc_HOL_Obool)),X28166),X28165)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un])])]) ).
fof(i_0_6774,plain,
! [X25915,X25916,X25917] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25917,tc_HOL_Obool)),X25916),X25915))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X25917,tc_HOL_Obool),tc_fun(X25917,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X25917,tc_HOL_Obool),tc_fun(X25917,tc_HOL_Obool)),X25916),X25915)),c_Wellfounded_Ofinite__psubset(X25917))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X25917),X25915))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X25917,tc_HOL_Obool),tc_fun(X25917,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X25917,tc_HOL_Obool),tc_fun(X25917,tc_HOL_Obool)),X25916),X25915)),c_Wellfounded_Ofinite__psubset(X25917))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25917,tc_HOL_Obool)),X25916),X25915))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25917),X25915))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X25917,tc_HOL_Obool),tc_fun(X25917,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X25917,tc_HOL_Obool),tc_fun(X25917,tc_HOL_Obool)),X25916),X25915)),c_Wellfounded_Ofinite__psubset(X25917))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).
fof(i_0_6775,plain,
! [X29857,X29858,X29859,X29860] :
( ~ hBOOL(hAPP(hAPP(c_member(X29860),X29859),hAPP(c_Relation_ODomain(X29860,X29858),X29857)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29860,X29858)),hAPP(hAPP(c_Product__Type_OPair(X29860,X29858),X29859),esk328_4(X29857,X29858,X29859,X29860))),X29857)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5425])])]) ).
fof(i_0_6776,plain,
! [X29821,X29822,X29823,X29824,X29826,X29827,X29828,X29829,X29830] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X29824),X29823),hAPP(c_Relation_ODomain(X29824,X29822),X29821)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29824,X29822)),hAPP(hAPP(c_Product__Type_OPair(X29824,X29822),X29823),esk327_4(X29821,X29822,X29823,X29824))),X29821)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29829,X29827)),hAPP(hAPP(c_Product__Type_OPair(X29829,X29827),X29828),X29830)),X29826))
| hBOOL(hAPP(hAPP(c_member(X29829),X29828),hAPP(c_Relation_ODomain(X29829,X29827),X29826))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__iff])])])])]) ).
fof(i_0_6777,plain,
! [X26501,X26502,X26503] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X26503,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X26503,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X26503),X26502)),hAPP(c_Set_OPow(X26503),X26501))),hAPP(c_Set_OPow(X26503),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26503,tc_HOL_Obool)),X26502),X26501)))),
inference(variable_rename,[status(thm)],[fact_Un__Pow__subset]) ).
fof(i_0_6778,plain,
! [X20538,X20539,X20540,X20541,X20542] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20542),X20541))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20541),X20540)),X20539)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20542),X20540)),X20538)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20541),X20542)),X20540)),X20539)),X20538) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])]) ).
cnf(i_0_6779,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X1,
inference(split_conjunct,[status(thm)],[i_0_5426]) ).
fof(i_0_6780,plain,
! [X32417,X32418,X32419] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X32419),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X32418),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32418)),X32417))))
| hBOOL(hAPP(hAPP(c_member(X32418),hAPP(c_Random_Opick(X32418,X32417),X32419)),hAPP(c_List_Oset(X32418),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X32418),X32418),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X32418)),X32417)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__member])]) ).
fof(i_0_6781,plain,
! [X24175,X24176,X24177,X24178] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24176),X24178))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24178),X24177))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24178,X24177)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24176,X24175))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24177),X24175))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24178),X24177))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24178,X24177)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24176,X24175))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24178),X24177))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24178,X24177)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24176,X24175))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24176),X24178))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24177),X24175))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24178,X24177)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24176,X24175))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5427])])]) ).
fof(i_0_6782,plain,
! [X29487,X29488,X29489,X29490,X29491,X29492,X29493,X29494] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29494,X29493)),hAPP(hAPP(c_Product__Type_OPair(X29494,X29493),X29492),X29491)),X29490))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29493,X29489)),hAPP(hAPP(c_Product__Type_OPair(X29493,X29489),X29491),X29488)),X29487))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29494,X29489)),hAPP(hAPP(c_Product__Type_OPair(X29494,X29489),X29492),X29488)),hAPP(hAPP(c_Relation_Orel__comp(X29494,X29493,X29489),X29490),X29487))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__compI])]) ).
fof(i_0_6783,plain,
! [X34134,X34135,X34136,X34137,X34138] :
( ~ class_Orderings_Olinorder(X34138)
| ~ c_List_Olinorder__class_Osorted(X34138,hAPP(hAPP(c_List_Omap(X34137,X34138),X34136),X34135))
| c_List_Olinorder__class_Osorted(X34138,hAPP(hAPP(c_List_Omap(X34137,X34138),X34136),c_List_Olinorder__class_Oinsort__insert__key(X34137,X34138,X34136,X34134,X34135))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert__key])]) ).
fof(i_0_6784,plain,
! [X23878,X23879,X23880,X23881,X23882,X23885,X23886,X23887,X23888,X23889,X23890] :
( ( hBOOL(hAPP(hAPP(c_member(X23881),esk136_4(X23878,X23879,X23880,X23881)),X23879))
| hBOOL(hAPP(hAPP(c_member(X23881),esk135_4(X23878,X23879,X23880,X23881)),X23880))
| ~ hBOOL(hAPP(hAPP(c_member(X23881),X23882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23881,tc_HOL_Obool)),X23880),X23879)))
| ~ hBOOL(hAPP(X23878,X23882)) )
& ( hBOOL(hAPP(X23878,esk136_4(X23878,X23879,X23880,X23881)))
| hBOOL(hAPP(hAPP(c_member(X23881),esk135_4(X23878,X23879,X23880,X23881)),X23880))
| ~ hBOOL(hAPP(hAPP(c_member(X23881),X23882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23881,tc_HOL_Obool)),X23880),X23879)))
| ~ hBOOL(hAPP(X23878,X23882)) )
& ( hBOOL(hAPP(hAPP(c_member(X23881),esk136_4(X23878,X23879,X23880,X23881)),X23879))
| hBOOL(hAPP(X23878,esk135_4(X23878,X23879,X23880,X23881)))
| ~ hBOOL(hAPP(hAPP(c_member(X23881),X23882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23881,tc_HOL_Obool)),X23880),X23879)))
| ~ hBOOL(hAPP(X23878,X23882)) )
& ( hBOOL(hAPP(X23878,esk136_4(X23878,X23879,X23880,X23881)))
| hBOOL(hAPP(X23878,esk135_4(X23878,X23879,X23880,X23881)))
| ~ hBOOL(hAPP(hAPP(c_member(X23881),X23882),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23881,tc_HOL_Obool)),X23880),X23879)))
| ~ hBOOL(hAPP(X23878,X23882)) )
& ( hBOOL(hAPP(hAPP(c_member(X23888),esk137_4(X23885,X23886,X23887,X23888)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23888,tc_HOL_Obool)),X23887),X23886)))
| ~ hBOOL(hAPP(hAPP(c_member(X23888),X23889),X23887))
| ~ hBOOL(hAPP(X23885,X23889)) )
& ( hBOOL(hAPP(X23885,esk137_4(X23885,X23886,X23887,X23888)))
| ~ hBOOL(hAPP(hAPP(c_member(X23888),X23889),X23887))
| ~ hBOOL(hAPP(X23885,X23889)) )
& ( hBOOL(hAPP(hAPP(c_member(X23888),esk137_4(X23885,X23886,X23887,X23888)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23888,tc_HOL_Obool)),X23887),X23886)))
| ~ hBOOL(hAPP(hAPP(c_member(X23888),X23890),X23886))
| ~ hBOOL(hAPP(X23885,X23890)) )
& ( hBOOL(hAPP(X23885,esk137_4(X23885,X23886,X23887,X23888)))
| ~ hBOOL(hAPP(hAPP(c_member(X23888),X23890),X23886))
| ~ hBOOL(hAPP(X23885,X23890)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__Un])])])])])]) ).
cnf(i_0_6785,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5428]) ).
fof(i_0_6786,plain,
! [X23864,X23865,X23866,X23867,X23869,X23870,X23871,X23872,X23873,X23874,X23877] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23867),X23869),X23866))
| hBOOL(hAPP(X23864,X23869))
| hBOOL(hAPP(hAPP(c_member(X23867),esk132_4(X23864,X23865,X23866,X23867)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23867,tc_HOL_Obool)),X23866),X23865))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23867),X23870),X23865))
| hBOOL(hAPP(X23864,X23870))
| hBOOL(hAPP(hAPP(c_member(X23867),esk132_4(X23864,X23865,X23866,X23867)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23867,tc_HOL_Obool)),X23866),X23865))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23867),X23869),X23866))
| hBOOL(hAPP(X23864,X23869))
| ~ hBOOL(hAPP(X23864,esk132_4(X23864,X23865,X23866,X23867))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23867),X23870),X23865))
| hBOOL(hAPP(X23864,X23870))
| ~ hBOOL(hAPP(X23864,esk132_4(X23864,X23865,X23866,X23867))) )
& ( hBOOL(hAPP(hAPP(c_member(X23874),esk134_4(X23871,X23872,X23873,X23874)),X23872))
| hBOOL(hAPP(hAPP(c_member(X23874),esk133_4(X23871,X23872,X23873,X23874)),X23873))
| ~ hBOOL(hAPP(hAPP(c_member(X23874),X23877),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23874,tc_HOL_Obool)),X23873),X23872)))
| hBOOL(hAPP(X23871,X23877)) )
& ( ~ hBOOL(hAPP(X23871,esk134_4(X23871,X23872,X23873,X23874)))
| hBOOL(hAPP(hAPP(c_member(X23874),esk133_4(X23871,X23872,X23873,X23874)),X23873))
| ~ hBOOL(hAPP(hAPP(c_member(X23874),X23877),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23874,tc_HOL_Obool)),X23873),X23872)))
| hBOOL(hAPP(X23871,X23877)) )
& ( hBOOL(hAPP(hAPP(c_member(X23874),esk134_4(X23871,X23872,X23873,X23874)),X23872))
| ~ hBOOL(hAPP(X23871,esk133_4(X23871,X23872,X23873,X23874)))
| ~ hBOOL(hAPP(hAPP(c_member(X23874),X23877),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23874,tc_HOL_Obool)),X23873),X23872)))
| hBOOL(hAPP(X23871,X23877)) )
& ( ~ hBOOL(hAPP(X23871,esk134_4(X23871,X23872,X23873,X23874)))
| ~ hBOOL(hAPP(X23871,esk133_4(X23871,X23872,X23873,X23874)))
| ~ hBOOL(hAPP(hAPP(c_member(X23874),X23877),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23874,tc_HOL_Obool)),X23873),X23872)))
| hBOOL(hAPP(X23871,X23877)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ball__Un])])])])])]) ).
cnf(i_0_6787,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5429]) ).
cnf(i_0_6788,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5430]) ).
cnf(i_0_6789,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X2)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5393]) ).
fof(i_0_6790,plain,
! [X30889,X30890,X30891,X30892,X30893,X30894,X30895,X30896] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30896,tc_fun(X30895,tc_fun(X30894,tc_HOL_Obool))),X30893),X30892),X30891),X30890))
| ~ hBOOL(hAPP(hAPP(c_member(X30896),X30889),X30893))
| hBOOL(hAPP(hAPP(hAPP(X30892,X30889),X30891),X30890)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__D])]) ).
fof(i_0_6791,plain,
! [X30881,X30882,X30883,X30884,X30885,X30886,X30887,X30888] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30888,tc_fun(X30887,tc_fun(X30886,tc_HOL_Obool))),X30885),X30884),X30883),X30882))
| hBOOL(hAPP(hAPP(hAPP(X30884,X30881),X30883),X30882))
| ~ hBOOL(hAPP(hAPP(c_member(X30888),X30881),X30885)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5431])]) ).
cnf(i_0_6792,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1),
inference(split_conjunct,[status(thm)],[i_0_5432]) ).
cnf(i_0_6793,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[i_0_5433]) ).
cnf(i_0_6794,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5434]) ).
cnf(i_0_6795,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5435]) ).
cnf(i_0_6796,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5393]) ).
cnf(i_0_6797,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5394]) ).
cnf(i_0_6798,plain,
hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[fact_nat__2]) ).
fof(i_0_6799,plain,
! [X26681,X26682,X26683,X26684,X26685,X26686,X26687] : hAPP(c_Fun_Ocomp(X26687,X26686,X26685,X26684),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26685,X26687),X26683),X26682),X26681)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26685,X26686),hAPP(c_Fun_Ocomp(X26687,X26686,X26685,X26684),X26683)),X26682),hAPP(X26684,X26681)),
inference(variable_rename,[status(thm)],[fact_fun__upd__comp]) ).
cnf(i_0_6800,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J]) ).
fof(i_0_6801,plain,
! [X29243,X29244,X29245,X29246] : hAPP(c_Set_Ovimage(X29246,X29245,X29244),X29243) = hAPP(c_Set_OCollect(X29246),hAPP(hAPP(c_COMBC(X29246,tc_fun(X29245,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X29245,tc_fun(tc_fun(X29245,tc_HOL_Obool),tc_HOL_Obool),X29246),c_member(X29245)),X29244)),X29243)),
inference(variable_rename,[status(thm)],[fact_vimage__def]) ).
fof(i_0_6802,plain,
! [X33432,X33433,X33434,X33435,X33436] : hAPP(hAPP(c_List_Ozip(X33436,X33435),X33434),hAPP(hAPP(c_List_Oappend(X33435),X33433),X33432)) = hAPP(hAPP(c_List_Oappend(tc_prod(X33436,X33435)),hAPP(hAPP(c_List_Ozip(X33436,X33435),hAPP(hAPP(c_List_Otake(X33436),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33435)),X33433)),X33434)),X33433)),hAPP(hAPP(c_List_Ozip(X33436,X33435),hAPP(hAPP(c_List_Odrop(X33436),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33435)),X33433)),X33434)),X33432)),
inference(variable_rename,[status(thm)],[fact_zip__append2]) ).
fof(i_0_6803,plain,
! [X33252,X33253,X33254,X33255] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33255),tc_List_Olist(X33255))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33255),tc_List_Olist(X33255)),X33254),X33253)),c_List_Olistrel1(X33255,hAPP(c_Relation_Oconverse(X33255,X33255),X33252))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33255),tc_List_Olist(X33255))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33255),tc_List_Olist(X33255)),X33254),X33253)),hAPP(c_Relation_Oconverse(tc_List_Olist(X33255),tc_List_Olist(X33255)),c_List_Olistrel1(X33255,X33252)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33255),tc_List_Olist(X33255))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33255),tc_List_Olist(X33255)),X33254),X33253)),hAPP(c_Relation_Oconverse(tc_List_Olist(X33255),tc_List_Olist(X33255)),c_List_Olistrel1(X33255,X33252))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33255),tc_List_Olist(X33255))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33255),tc_List_Olist(X33255)),X33254),X33253)),c_List_Olistrel1(X33255,hAPP(c_Relation_Oconverse(X33255,X33255),X33252)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__listrel1__converse])]) ).
fof(i_0_6804,plain,
! [X33976,X33977,X33978,X33979,X33980] : c_List_Omap__filter(X33980,X33979,X33978,hAPP(hAPP(c_List_Olist_OCons(X33980),X33977),X33976)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X33979),X33979,c_List_Omap__filter(X33980,X33979,X33978,X33976),hAPP(hAPP(c_COMBC(X33979,tc_List_Olist(X33979),tc_List_Olist(X33979)),c_List_Olist_OCons(X33979)),c_List_Omap__filter(X33980,X33979,X33978,X33976))),hAPP(X33978,X33977)),
inference(variable_rename,[status(thm)],[fact_map__filter__simps_I1_J]) ).
fof(i_0_6805,plain,
! [X32883,X32884,X32885,X32886,X32887,X32889,X32890,X32891,X32892,X32893,X32894] :
( ( hAPP(hAPP(c_List_Olist_OCons(X32887),X32886),esk455_5(X32883,X32884,X32885,X32886,X32887)) = X32884
| X32884 = c_List_Olist_ONil(X32887)
| hAPP(hAPP(c_List_Olist_OCons(X32887),X32886),X32885) != hAPP(hAPP(c_List_Oappend(X32887),X32884),X32883) )
& ( X32885 = hAPP(hAPP(c_List_Oappend(X32887),esk455_5(X32883,X32884,X32885,X32886,X32887)),X32883)
| X32884 = c_List_Olist_ONil(X32887)
| hAPP(hAPP(c_List_Olist_OCons(X32887),X32886),X32885) != hAPP(hAPP(c_List_Oappend(X32887),X32884),X32883) )
& ( hAPP(hAPP(c_List_Olist_OCons(X32887),X32886),esk455_5(X32883,X32884,X32885,X32886,X32887)) = X32884
| hAPP(hAPP(c_List_Olist_OCons(X32887),X32886),X32885) = X32883
| hAPP(hAPP(c_List_Olist_OCons(X32887),X32886),X32885) != hAPP(hAPP(c_List_Oappend(X32887),X32884),X32883) )
& ( X32885 = hAPP(hAPP(c_List_Oappend(X32887),esk455_5(X32883,X32884,X32885,X32886,X32887)),X32883)
| hAPP(hAPP(c_List_Olist_OCons(X32887),X32886),X32885) = X32883
| hAPP(hAPP(c_List_Olist_OCons(X32887),X32886),X32885) != hAPP(hAPP(c_List_Oappend(X32887),X32884),X32883) )
& ( X32890 != c_List_Olist_ONil(X32893)
| hAPP(hAPP(c_List_Olist_OCons(X32893),X32892),X32891) != X32889
| hAPP(hAPP(c_List_Olist_OCons(X32893),X32892),X32891) = hAPP(hAPP(c_List_Oappend(X32893),X32890),X32889) )
& ( hAPP(hAPP(c_List_Olist_OCons(X32893),X32892),X32894) != X32890
| X32891 != hAPP(hAPP(c_List_Oappend(X32893),X32894),X32889)
| hAPP(hAPP(c_List_Olist_OCons(X32893),X32892),X32891) = hAPP(hAPP(c_List_Oappend(X32893),X32890),X32889) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__append__conv])])])])])]) ).
fof(i_0_6806,plain,
! [X32895,X32896,X32897,X32898,X32899,X32901,X32902,X32903,X32904,X32905,X32906] :
( ( X32898 = hAPP(hAPP(c_List_Olist_OCons(X32899),X32896),esk456_5(X32895,X32896,X32897,X32898,X32899))
| X32898 = c_List_Olist_ONil(X32899)
| hAPP(hAPP(c_List_Oappend(X32899),X32898),X32897) != hAPP(hAPP(c_List_Olist_OCons(X32899),X32896),X32895) )
& ( hAPP(hAPP(c_List_Oappend(X32899),esk456_5(X32895,X32896,X32897,X32898,X32899)),X32897) = X32895
| X32898 = c_List_Olist_ONil(X32899)
| hAPP(hAPP(c_List_Oappend(X32899),X32898),X32897) != hAPP(hAPP(c_List_Olist_OCons(X32899),X32896),X32895) )
& ( X32898 = hAPP(hAPP(c_List_Olist_OCons(X32899),X32896),esk456_5(X32895,X32896,X32897,X32898,X32899))
| X32897 = hAPP(hAPP(c_List_Olist_OCons(X32899),X32896),X32895)
| hAPP(hAPP(c_List_Oappend(X32899),X32898),X32897) != hAPP(hAPP(c_List_Olist_OCons(X32899),X32896),X32895) )
& ( hAPP(hAPP(c_List_Oappend(X32899),esk456_5(X32895,X32896,X32897,X32898,X32899)),X32897) = X32895
| X32897 = hAPP(hAPP(c_List_Olist_OCons(X32899),X32896),X32895)
| hAPP(hAPP(c_List_Oappend(X32899),X32898),X32897) != hAPP(hAPP(c_List_Olist_OCons(X32899),X32896),X32895) )
& ( X32904 != c_List_Olist_ONil(X32905)
| X32903 != hAPP(hAPP(c_List_Olist_OCons(X32905),X32902),X32901)
| hAPP(hAPP(c_List_Oappend(X32905),X32904),X32903) = hAPP(hAPP(c_List_Olist_OCons(X32905),X32902),X32901) )
& ( X32904 != hAPP(hAPP(c_List_Olist_OCons(X32905),X32902),X32906)
| hAPP(hAPP(c_List_Oappend(X32905),X32906),X32903) != X32901
| hAPP(hAPP(c_List_Oappend(X32905),X32904),X32903) = hAPP(hAPP(c_List_Olist_OCons(X32905),X32902),X32901) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__Cons__conv])])])])])]) ).
fof(i_0_6807,plain,
! [X25999,X26000] :
( ~ class_Orderings_Olinorder(X26000)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26000),X25999))
| X25999 = c_Orderings_Obot__class_Obot(tc_fun(X26000,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X26000),hAPP(hAPP(c_Orderings_Oord__class_Omin(X26000),esk205_2(X25999,X26000)),esk206_2(X25999,X26000))),hAPP(hAPP(c_Set_Oinsert(X26000),esk205_2(X25999,X26000)),hAPP(hAPP(c_Set_Oinsert(X26000),esk206_2(X25999,X26000)),c_Orderings_Obot__class_Obot(tc_fun(X26000,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X26000),c_Big__Operators_Olattice_OInf__fin(X26000,c_Orderings_Oord__class_Omin(X26000),X25999)),X25999)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oclosed])])]) ).
fof(i_0_6808,plain,
! [X25995,X25996] :
( ~ class_Orderings_Olinorder(X25996)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25996),X25995))
| X25995 = c_Orderings_Obot__class_Obot(tc_fun(X25996,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25996),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25996),esk203_2(X25995,X25996)),esk204_2(X25995,X25996))),hAPP(hAPP(c_Set_Oinsert(X25996),esk203_2(X25995,X25996)),hAPP(hAPP(c_Set_Oinsert(X25996),esk204_2(X25995,X25996)),c_Orderings_Obot__class_Obot(tc_fun(X25996,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X25996),c_Big__Operators_Olattice_OSup__fin(X25996,c_Orderings_Oord__class_Omax(X25996),X25995)),X25995)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oclosed])])]) ).
fof(i_0_6809,plain,
! [X25918,X25919,X25920,X25921,X25922,X25923,X25924,X25925,X25926,X25927,X25928,X25929,X25933] :
( ( ~ c_Hoare__Mirabelle_Otriple__valid(X25922,X25921,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25922),X25920),X25919),X25918))
| ~ hBOOL(hAPP(hAPP(X25920,X25923),X25924))
| ~ c_Natural_Oevaln(X25919,X25924,X25921,X25925)
| hBOOL(hAPP(hAPP(X25918,X25923),X25925)) )
& ( hBOOL(hAPP(hAPP(X25928,esk200_4(X25926,X25927,X25928,X25929)),esk201_4(X25926,X25927,X25928,X25929)))
| c_Hoare__Mirabelle_Otriple__valid(X25933,X25929,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25933),X25928),X25927),X25926)) )
& ( c_Natural_Oevaln(X25927,esk201_4(X25926,X25927,X25928,X25929),X25929,esk202_4(X25926,X25927,X25928,X25929))
| c_Hoare__Mirabelle_Otriple__valid(X25933,X25929,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25933),X25928),X25927),X25926)) )
& ( ~ hBOOL(hAPP(hAPP(X25926,esk200_4(X25926,X25927,X25928,X25929)),esk202_4(X25926,X25927,X25928,X25929)))
| c_Hoare__Mirabelle_Otriple__valid(X25933,X25929,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25933),X25928),X25927),X25926)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triple__valid__def2])])])])])]) ).
fof(i_0_6810,plain,
! [X31964,X31965,X31966,X31967] : c_Map_Omap__of(X31967,X31966,hAPP(hAPP(c_List_Omap(X31967,tc_prod(X31967,X31966)),hAPP(hAPP(c_COMBS(X31967,X31966,tc_prod(X31967,X31966)),c_Product__Type_OPair(X31967,X31966)),X31965)),X31964)) = c_Map_Orestrict__map(X31967,X31966,hAPP(c_Fun_Ocomp(X31966,tc_Option_Ooption(X31966),X31967,c_Option_Ooption_OSome(X31966)),X31965),hAPP(c_List_Oset(X31967),X31964)),
inference(variable_rename,[status(thm)],[fact_map__of__map__restrict]) ).
fof(i_0_6811,plain,
! [X28845,X28846,X28847,X28848] :
( ( hBOOL(hAPP(hAPP(c_member(X28848),esk288_4(X28845,X28846,X28847,X28848)),X28847))
| hAPP(c_Finite__Set_Ocard(tc_prod(X28848,X28846)),hAPP(hAPP(c_Product__Type_OSigma(X28848,X28846),X28847),X28845)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28848,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X28846,tc_HOL_Obool),tc_Nat_Onat,X28848),c_Finite__Set_Ocard(X28846)),X28845)),X28847)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28848),X28847)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28846),hAPP(X28845,esk288_4(X28845,X28846,X28847,X28848))))
| hAPP(c_Finite__Set_Ocard(tc_prod(X28848,X28846)),hAPP(hAPP(c_Product__Type_OSigma(X28848,X28846),X28847),X28845)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28848,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X28846,tc_HOL_Obool),tc_Nat_Onat,X28848),c_Finite__Set_Ocard(X28846)),X28845)),X28847)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28848),X28847)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__SigmaI])])])]) ).
fof(i_0_6812,plain,
! [X28524,X28525,X28526,X28527] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28527,X28526,X28525,X28524,c_Orderings_Obot__class_Obot(tc_fun(X28527,tc_HOL_Obool))),X28524)),
inference(variable_rename,[status(thm)],[fact_fold__graph_Oequations_I1_J]) ).
fof(i_0_6813,plain,
! [X28520,X28521,X28522,X28523] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28523,X28522,X28521,X28520,c_Orderings_Obot__class_Obot(tc_fun(X28523,tc_HOL_Obool))),X28520)),
inference(variable_rename,[status(thm)],[fact_fold__graph_OemptyI]) ).
fof(i_0_6814,plain,
! [X29670,X29671,X29672] :
( ~ c_Wellfounded_Owf(X29672,X29671)
| ~ c_Wellfounded_Owf(X29672,X29670)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29672,X29672),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29672,X29672,X29672),X29671),X29670)),X29671))
| c_Wellfounded_Owf(X29672,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29672,X29672),tc_HOL_Obool)),X29671),X29670)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__compatible])]) ).
fof(i_0_6815,plain,
! [X29089,X29090] :
( ~ class_Groups_Oab__semigroup__mult(X29090)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29090),X29089))
| X29089 = c_Orderings_Obot__class_Obot(tc_fun(X29090,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X29090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29090),esk300_2(X29089,X29090)),esk301_2(X29089,X29090))),hAPP(hAPP(c_Set_Oinsert(X29090),esk300_2(X29089,X29090)),hAPP(hAPP(c_Set_Oinsert(X29090),esk301_2(X29089,X29090)),c_Orderings_Obot__class_Obot(tc_fun(X29090,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X29090),hAPP(c_Finite__Set_Ofold1(X29090,c_Groups_Otimes__class_Otimes(X29090)),X29089)),X29089)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__in])])]) ).
cnf(i_0_6816,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2))),c_COMBI(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5436]) ).
fof(i_0_6817,plain,
! [X19690,X19691,X19692,X19693,X19694] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19694),X19693)),X19692)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19694),X19691)),X19690)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19692))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19692),X19694))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19690),X19694))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19693),X19691)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).
fof(i_0_6818,plain,
! [X19679,X19680,X19681,X19682,X19683] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19683),X19682)),X19681)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19683),X19680)),X19679)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19679),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19683),X19679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19683),X19681))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19680),X19682)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).
fof(i_0_6819,plain,
! [X32769,X32770,X32771,X32772,X32773] :
( ~ class_Orderings_Olinorder(X32773)
| ~ hBOOL(hAPP(c_List_Odistinct(X32772),X32771))
| hBOOL(hAPP(c_List_Odistinct(X32772),c_List_Olinorder__class_Oinsort__insert__key(X32772,X32773,X32770,X32769,X32771))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insort__insert])]) ).
fof(i_0_6820,plain,
! [X34001,X34002,X34003] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34003),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34002))),c_List_Otranspose(X34002,X34001))))
| hAPP(hAPP(c_List_Onth(tc_List_Olist(X34002)),c_List_Otranspose(X34002,X34001)),X34003) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X34002),X34002),hAPP(hAPP(c_COMBC(tc_List_Olist(X34002),tc_Nat_Onat,X34002),c_List_Onth(X34002)),X34003)),hAPP(c_List_Ofilter(tc_List_Olist(X34002),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34002)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34003)),c_Nat_Osize__class_Osize(tc_List_Olist(X34002)))),X34001)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__transpose])]) ).
fof(i_0_6821,plain,
! [X26554,X26555,X26556] :
( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X26556,hAPP(hAPP(c_COMBC(X26556,tc_fun(X26556,tc_HOL_Obool),tc_HOL_Obool),c_member(X26556)),X26555)),X26554))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26556,tc_HOL_Obool)),X26554),hAPP(c_Set_OPow(X26556),X26555))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26556,tc_HOL_Obool)),X26554),hAPP(c_Set_OPow(X26556),X26555)))
| hBOOL(hAPP(c_Predicate_OPowp(X26556,hAPP(hAPP(c_COMBC(X26556,tc_fun(X26556,tc_HOL_Obool),tc_HOL_Obool),c_member(X26556)),X26555)),X26554)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq])]) ).
fof(i_0_6822,plain,
! [X28118,X28119,X28120,X28121,X28122,X28123] :
( ~ c_Fun_Oinj__on(X28123,X28122,X28121,X28120)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28122,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28123,X28122,X28121),X28120)),X28119))
| ~ c_Fun_Oinj__on(X28122,X28123,X28118,X28119)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28123,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28122,X28123,X28118),X28119)),X28120))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28123),X28120))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28122),X28119))
| hAPP(c_Finite__Set_Ocard(X28123),X28120) = hAPP(c_Finite__Set_Ocard(X28122),X28119) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).
fof(i_0_6823,plain,
! [X30001,X30002,X30003] : c_Hilbert__Choice_OEps(tc_prod(X30003,X30002),hAPP(c_Product__Type_Oprod_Oprod__case(X30003,X30002,tc_HOL_Obool),X30001)) = c_Hilbert__Choice_OEps(tc_prod(X30003,X30002),hAPP(hAPP(c_COMBS(tc_prod(X30003,X30002),X30002,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X30003,tc_fun(X30002,tc_HOL_Obool),tc_prod(X30003,X30002)),X30001),c_Product__Type_Ofst(X30003,X30002))),c_Product__Type_Osnd(X30003,X30002))),
inference(variable_rename,[status(thm)],[fact_Eps__split]) ).
fof(i_0_6824,plain,
! [X22957,X22958,X22959] : c_HOL_OThe(tc_prod(X22959,X22958),hAPP(c_Product__Type_Oprod_Oprod__case(X22959,X22958,tc_HOL_Obool),X22957)) = c_HOL_OThe(tc_prod(X22959,X22958),hAPP(hAPP(c_COMBS(tc_prod(X22959,X22958),X22958,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X22959,tc_fun(X22958,tc_HOL_Obool),tc_prod(X22959,X22958)),X22957),c_Product__Type_Ofst(X22959,X22958))),c_Product__Type_Osnd(X22959,X22958))),
inference(variable_rename,[status(thm)],[fact_The__split]) ).
fof(i_0_6825,plain,
! [X23421,X23422,X23423,X23424,X23425,X23426] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23424),X23423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23424),X23425),X23421)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23424),X23423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23424),X23425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23424),X23426),X23422))),X23421)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23424),X23423),X23422))
| ~ class_Rings_Ocomm__ring(X23424)
| ~ class_Rings_Odvd(X23424) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23424),X23423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23424),X23425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23424),X23426),X23422))),X23421)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23424),X23423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23424),X23425),X23421)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23424),X23423),X23422))
| ~ class_Rings_Ocomm__ring(X23424)
| ~ class_Rings_Odvd(X23424) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J])])])]) ).
fof(i_0_6826,plain,
! [X23415,X23416,X23417,X23418,X23419,X23420] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23418),X23417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23418),X23419),X23415)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23418),X23417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23418),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23418),X23419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23418),X23420),X23416))),X23415)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23418),X23417),X23416))
| ~ class_Rings_Ocomm__ring(X23418)
| ~ class_Rings_Odvd(X23418) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23418),X23417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23418),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23418),X23419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23418),X23420),X23416))),X23415)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23418),X23417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23418),X23419),X23415)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23418),X23417),X23416))
| ~ class_Rings_Ocomm__ring(X23418)
| ~ class_Rings_Odvd(X23418) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J])])])]) ).
fof(i_0_6827,plain,
! [X20156,X20157,X20158,X20159] :
( ~ class_Divides_Osemiring__div(X20159)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20159),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20159),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20159),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20159),X20158),X20157)),X20157)),c_Divides_Odiv__class_Omod(X20159,X20158,X20157))),X20156) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20159),X20158),X20156) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality])]) ).
fof(i_0_6828,plain,
! [X27869,X27870,X27871,X27872,X27873] :
( ~ class_Groups_Ocomm__monoid__mult(X27873)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27872),X27871))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27872),X27870))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27872,tc_HOL_Obool)),X27871),X27870) != c_Orderings_Obot__class_Obot(tc_fun(X27872,tc_HOL_Obool))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27873,X27872,c_Groups_Otimes__class_Otimes(X27873)),X27869),c_Groups_Oone__class_Oone(X27873)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27872,tc_HOL_Obool)),X27871),X27870)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27873),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27873,X27872,c_Groups_Otimes__class_Otimes(X27873)),X27869),c_Groups_Oone__class_Oone(X27873)),X27871)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27873,X27872,c_Groups_Otimes__class_Otimes(X27873)),X27869),c_Groups_Oone__class_Oone(X27873)),X27870)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__Un__disjoint])]) ).
cnf(i_0_6829,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_5437]) ).
fof(i_0_6830,plain,
! [X32448,X32449,X32450,X32451] :
( ~ class_Groups_Oab__group__add(X32451)
| hAPP(c_Groups_Ouminus__class_Ouminus(X32451),hAPP(c_List_Omonoid__add__class_Olistsum(X32451),hAPP(hAPP(c_List_Omap(X32450,X32451),X32449),X32448))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32451),hAPP(hAPP(c_List_Omap(X32450,X32451),hAPP(c_Fun_Ocomp(X32451,X32451,X32450,c_Groups_Ouminus__class_Ouminus(X32451)),X32449)),X32448)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__listsum__map])]) ).
fof(i_0_6831,plain,
! [X29902,X29903,X29904,X29905] : c_New__Random__Sequence_Oneg__map(X29905,X29904,X29903,X29902) = c_New__Random__Sequence_Oneg__bind(X29905,X29904,X29902,hAPP(c_Fun_Ocomp(X29904,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X29904)))))),X29905,c_New__Random__Sequence_Oneg__single(X29904)),X29903)),
inference(variable_rename,[status(thm)],[fact_neg__map__def]) ).
fof(i_0_6832,plain,
! [X23051,X23052,X23053,X23054] :
( ~ class_Groups_Oordered__ab__group__add__abs(X23054)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23054),c_Groups_Ozero__class_Ozero(X23054)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23053,X23054),hAPP(hAPP(c_COMBB(X23054,X23054,X23053),c_Groups_Oabs__class_Oabs(X23054)),X23052)),X23051))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero])]) ).
fof(i_0_6833,plain,
! [X29314,X29315] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29315),X29314))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29315,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X29315,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X29315,tc_HOL_Obool),tc_fun(X29315,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X29315,tc_HOL_Obool))),X29314)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets])]) ).
fof(i_0_6834,plain,
! [X19607,X19608,X19609] :
( ( X19608 = c_Groups_Ozero__class_Ozero(X19609)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19609),X19608),X19608)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19609),X19607),X19607))),c_Groups_Ozero__class_Ozero(X19609)))
| ~ class_Rings_Olinordered__ring__strict(X19609) )
& ( X19607 = c_Groups_Ozero__class_Ozero(X19609)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19609),X19608),X19608)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19609),X19607),X19607))),c_Groups_Ozero__class_Ozero(X19609)))
| ~ class_Rings_Olinordered__ring__strict(X19609) )
& ( X19608 != c_Groups_Ozero__class_Ozero(X19609)
| X19607 != c_Groups_Ozero__class_Ozero(X19609)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19609),X19608),X19608)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19609),X19607),X19607))),c_Groups_Ozero__class_Ozero(X19609)))
| ~ class_Rings_Olinordered__ring__strict(X19609) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).
fof(i_0_6835,plain,
! [X27801,X27802] :
( ~ class_Lattices_Olattice(X27802)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27802),X27801))
| X27801 = c_Orderings_Obot__class_Obot(tc_fun(X27802,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X27802),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27802),esk257_2(X27801,X27802)),esk258_2(X27801,X27802))),hAPP(hAPP(c_Set_Oinsert(X27802),esk257_2(X27801,X27802)),hAPP(hAPP(c_Set_Oinsert(X27802),esk258_2(X27801,X27802)),c_Orderings_Obot__class_Obot(tc_fun(X27802,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X27802),c_Big__Operators_Olattice__class_OInf__fin(X27802,X27801)),X27801)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed])])]) ).
fof(i_0_6836,plain,
! [X25885,X25886] :
( ~ class_Orderings_Olinorder(X25886)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25886),X25885))
| X25885 = c_Orderings_Obot__class_Obot(tc_fun(X25886,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25886),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25886),esk196_2(X25885,X25886)),esk197_2(X25885,X25886))),hAPP(hAPP(c_Set_Oinsert(X25886),esk196_2(X25885,X25886)),hAPP(hAPP(c_Set_Oinsert(X25886),esk197_2(X25885,X25886)),c_Orderings_Obot__class_Obot(tc_fun(X25886,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X25886),c_Big__Operators_Olinorder__class_OMin(X25886,X25885)),X25885)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oclosed])])]) ).
fof(i_0_6837,plain,
! [X25881,X25882] :
( ~ class_Orderings_Olinorder(X25882)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25882),X25881))
| X25881 = c_Orderings_Obot__class_Obot(tc_fun(X25882,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25882),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25882),esk194_2(X25881,X25882)),esk195_2(X25881,X25882))),hAPP(hAPP(c_Set_Oinsert(X25882),esk194_2(X25881,X25882)),hAPP(hAPP(c_Set_Oinsert(X25882),esk195_2(X25881,X25882)),c_Orderings_Obot__class_Obot(tc_fun(X25882,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X25882),c_Big__Operators_Olinorder__class_OMax(X25882,X25881)),X25881)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oclosed])])]) ).
fof(i_0_6838,plain,
! [X25809,X25810] :
( ~ class_Lattices_Olattice(X25810)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25810),X25809))
| X25809 = c_Orderings_Obot__class_Obot(tc_fun(X25810,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25810),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25810),esk192_2(X25809,X25810)),esk193_2(X25809,X25810))),hAPP(hAPP(c_Set_Oinsert(X25810),esk192_2(X25809,X25810)),hAPP(hAPP(c_Set_Oinsert(X25810),esk193_2(X25809,X25810)),c_Orderings_Obot__class_Obot(tc_fun(X25810,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X25810),c_Big__Operators_Olattice__class_OSup__fin(X25810,X25809)),X25809)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed])])]) ).
fof(i_0_6839,plain,
! [X18964,X18965,X18966] :
( ~ class_Rings_Olinordered__ring(X18966)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18966),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18966),X18965),X18965)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18966),X18964),X18964))),c_Groups_Ozero__class_Ozero(X18966))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5438])]) ).
fof(i_0_6840,plain,
! [X28205,X28206,X28207,X28208,X28209,X28210,X28211,X28212] :
( ~ c_Finite__Set_Ofolding__image(X28212,X28211,X28210,X28209,X28208)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28211),X28207))
| ~ c_Fun_Oinj__on(X28211,X28211,X28206,X28207)
| hAPP(hAPP(X28208,X28205),hAPP(c_Set_Oimage(X28211,X28211,X28206),X28207)) = hAPP(hAPP(X28208,hAPP(c_Fun_Ocomp(X28211,X28212,X28211,X28205),X28206)),X28207) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oreindex])]) ).
fof(i_0_6841,plain,
! [X34364,X34365,X34366] :
( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34366),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34366))),X34365)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34364),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34366))),X34365)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34366))),hAPP(c_List_Ofilter(tc_List_Olist(X34366),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34366)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34364)),c_Nat_Osize__class_Osize(tc_List_Olist(X34366)))),c_List_Otranspose(X34366,X34365))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34366)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34366)),X34365),X34364)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column__length])]) ).
fof(i_0_6842,plain,
! [X25001,X25002,X25003,X25004,X25005,X25006,X25007] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25007,X25006)),hAPP(hAPP(c_Product__Type_OPair(X25007,X25006),X25005),X25004)),X25003))
| hBOOL(hAPP(hAPP(c_member(X25002),hAPP(hAPP(X25001,X25005),X25004)),hAPP(c_Set_Oimage(tc_prod(X25007,X25006),X25002,hAPP(c_Product__Type_Oprod_Oprod__case(X25007,X25006,X25002),X25001)),X25003))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__imageI])]) ).
fof(i_0_6843,plain,
! [X31999,X32000,X32001,X32002,X32003] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32003,X32002)),hAPP(hAPP(c_Product__Type_OPair(X32003,X32002),X32001),X32000)),hAPP(c_List_Oset(tc_prod(X32003,X32002)),X31999)))
| hAPP(c_Map_Omap__of(X32003,X32002,X31999),X32001) = hAPP(c_Option_Ooption_OSome(X32002),esk439_5(X31999,X32000,X32001,X32002,X32003)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weak__map__of__SomeI])])]) ).
fof(i_0_6844,plain,
! [X33856,X33857,X33858,X33859,X33860] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33860)),hAPP(c_List_Ofilter(X33860,X33859),hAPP(hAPP(c_List_Omap(X33858,X33860),X33857),X33856))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33858)),hAPP(c_List_Ofilter(X33858,hAPP(c_Fun_Ocomp(X33860,tc_HOL_Obool,X33858,X33859),X33857)),X33856)),
inference(variable_rename,[status(thm)],[fact_length__filter__map]) ).
cnf(i_0_6845,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),hAPP(c_Relation_OField(X1),X2)),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_Relation_OField(X1),X2))))),
inference(split_conjunct,[status(thm)],[i_0_5439]) ).
fof(i_0_6846,plain,
! [X30327,X30328,X30329,X30330,X30331] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30331,X30331)),hAPP(hAPP(c_Product__Type_OPair(X30331,X30331),X30330),X30329)),c_Transitive__Closure_Ortrancl(X30331,X30328)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30331,X30331),tc_HOL_Obool)),X30328),hAPP(hAPP(c_Product__Type_OSigma(X30331,X30331),X30327),hAPP(c_COMBK(tc_fun(X30331,tc_HOL_Obool),X30331),X30327))))
| X30330 = X30329
| hBOOL(hAPP(hAPP(c_member(X30331),X30330),X30327)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux])]) ).
fof(i_0_6847,plain,
! [X25452,X25453,X25454,X25455,X25456,X25457] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25457,tc_fun(X25456,tc_HOL_Obool))),X25455),X25454),X25453),X25452))
| hBOOL(hAPP(hAPP(X25455,X25453),X25452))
| hBOOL(hAPP(hAPP(X25454,X25453),X25452)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5440])]) ).
fof(i_0_6848,plain,
! [X33871,X33872,X33873] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33873)),hAPP(c_List_Ofilter(X33873,X33872),X33871))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33873)),hAPP(c_List_Ofilter(X33873,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33873),c_fNot),X33872)),X33871))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33873)),X33871),
inference(variable_rename,[status(thm)],[fact_sum__length__filter__compl]) ).
fof(i_0_6849,plain,
! [X30239,X30240,X30241,X30242,X30243] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30243,X30243)),hAPP(hAPP(c_Product__Type_OPair(X30243,X30243),X30242),X30241)),c_Transitive__Closure_Ortrancl(X30243,X30240)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30243,X30243)),hAPP(hAPP(c_Product__Type_OPair(X30243,X30243),X30241),X30239)),c_Transitive__Closure_Ortrancl(X30243,X30240)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30243,X30243)),hAPP(hAPP(c_Product__Type_OPair(X30243,X30243),X30242),X30239)),c_Transitive__Closure_Ortrancl(X30243,X30240))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trans])]) ).
cnf(i_0_6850,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Otrancl(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5441]) ).
cnf(i_0_6851,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5442]) ).
fof(i_0_6852,plain,
! [X20036,X20037,X20038] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20038),X20037)),X20036) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20038),X20036)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20037),X20036))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20038,X20036)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20037,X20036))),X20036)),
inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq]) ).
fof(i_0_6853,plain,
! [X19956,X19957,X19958] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19958),X19957)),X19956) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19958),X19956)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19957),X19956))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19958,X19956)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19957,X19956))),X19956)),
inference(variable_rename,[status(thm)],[fact_div__add1__eq]) ).
fof(i_0_6854,plain,
! [X27713,X27714,X27715,X27716,X27717,X27718] :
( ( hBOOL(hAPP(hAPP(X27716,X27714),X27713))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27718,tc_fun(X27717,tc_HOL_Obool))),X27716),X27715),X27714),X27713)) )
& ( hBOOL(hAPP(hAPP(X27715,X27714),X27713))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27718,tc_fun(X27717,tc_HOL_Obool))),X27716),X27715),X27714),X27713)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5443])])]) ).
fof(i_0_6855,plain,
! [X27731,X27732,X27733,X27734,X27735,X27736] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27736,tc_fun(X27735,tc_HOL_Obool))),X27734),X27733),X27732),X27731))
| hBOOL(hAPP(hAPP(X27734,X27732),X27731)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D1])]) ).
fof(i_0_6856,plain,
! [X27725,X27726,X27727,X27728,X27729,X27730] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27730,tc_fun(X27729,tc_HOL_Obool))),X27728),X27727),X27726),X27725))
| hBOOL(hAPP(hAPP(X27727,X27726),X27725)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])]) ).
cnf(i_0_6857,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk492_3(X2,X3,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2))))
| X3 = X2
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)
| c_List_Oconcat(X1,X3) != c_List_Oconcat(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_5240]) ).
cnf(i_0_6858,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk491_3(X3,X2,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3))))
| c_List_Oconcat(X1,X2) != c_List_Oconcat(X1,X3)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3) ),
inference(split_conjunct,[status(thm)],[i_0_5241]) ).
cnf(i_0_6859,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5444]) ).
cnf(i_0_6860,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5445]) ).
cnf(i_0_6861,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5446]) ).
cnf(i_0_6862,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5447]) ).
fof(i_0_6863,plain,
! [X30249,X30250,X30251,X30252,X30253] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30253,X30253)),hAPP(hAPP(c_Product__Type_OPair(X30253,X30253),X30252),X30251)),X30250))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30253,X30253)),hAPP(hAPP(c_Product__Type_OPair(X30253,X30253),X30251),X30249)),c_Transitive__Closure_Ortrancl(X30253,X30250)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30253,X30253)),hAPP(hAPP(c_Product__Type_OPair(X30253,X30253),X30252),X30249)),c_Transitive__Closure_Ortrancl(X30253,X30250))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl])]) ).
fof(i_0_6864,plain,
! [X30244,X30245,X30246,X30247,X30248] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30248,X30248)),hAPP(hAPP(c_Product__Type_OPair(X30248,X30248),X30247),X30246)),c_Transitive__Closure_Ortrancl(X30248,X30245)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30248,X30248)),hAPP(hAPP(c_Product__Type_OPair(X30248,X30248),X30246),X30244)),X30245))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30248,X30248)),hAPP(hAPP(c_Product__Type_OPair(X30248,X30248),X30247),X30244)),c_Transitive__Closure_Ortrancl(X30248,X30245))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])]) ).
fof(i_0_6865,plain,
! [X33256,X33257,X33258,X33259] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33259),tc_List_Olist(X33259))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33259),tc_List_Olist(X33259)),X33258),X33257)),c_List_Olistrel(X33259,X33256)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33259),tc_List_Olist(X33259))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33259),tc_List_Olist(X33259)),X33258),X33257)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33259),c_List_Olistrel1(X33259,X33256)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel])]) ).
fof(i_0_6866,plain,
! [X26818,X26819,X26820,X26821,X26822,X26823,X26824,X26825,X26826,X26827,X26828] :
( ~ c_Finite__Set_Ofolding(X26828,X26827,X26826,X26825)
| hAPP(c_Fun_Ocomp(X26824,X26823,X26822,X26821),hAPP(c_Fun_Ocomp(X26820,X26824,X26822,X26819),X26818)) = hAPP(c_Fun_Ocomp(X26820,X26823,X26822,hAPP(c_Fun_Ocomp(X26824,X26823,X26820,X26821),X26819)),X26818) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comps_I1_J])]) ).
fof(i_0_6867,plain,
! [X19673,X19674,X19675,X19676,X19677,X19678] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19678),X19677)),X19676) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19675),X19674)),X19673)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19675),X19674)),X19673)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19676),X19678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19673))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19675),X19678))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19674),X19677)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).
fof(i_0_6868,plain,
! [X29348] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X29348)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X29348),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J]) ).
fof(i_0_6869,plain,
! [X33260,X33261,X33262,X33263] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33263),tc_List_Olist(X33263))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33263),tc_List_Olist(X33263)),X33262),X33261)),c_List_Olistrel1(X33263,X33260)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33263),tc_List_Olist(X33263))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33263),tc_List_Olist(X33263)),X33262),X33261)),c_List_Olistrel(X33263,c_Transitive__Closure_Ortrancl(X33263,X33260)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1])]) ).
fof(i_0_6870,plain,
! [X33030,X33031,X33032,X33033] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33033),tc_List_Olist(X33033))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33033),tc_List_Olist(X33033)),X33032),X33031)),c_List_Olexord(X33033,X33030)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33033),tc_List_Olist(X33033))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33033),tc_List_Olist(X33033)),X33032),X33031)),c_List_Olex(X33033,X33030))) )
& ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33033)),X33032) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33033)),X33031)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33033),tc_List_Olist(X33033))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33033),tc_List_Olist(X33033)),X33032),X33031)),c_List_Olex(X33033,X33030))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33033),tc_List_Olist(X33033))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33033),tc_List_Olist(X33033)),X33032),X33031)),c_List_Olexord(X33033,X33030)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33033)),X33032) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33033)),X33031)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33033),tc_List_Olist(X33033))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33033),tc_List_Olist(X33033)),X33032),X33031)),c_List_Olex(X33033,X33030))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])]) ).
fof(i_0_6871,plain,
! [X33929,X33930,X33931,X33932,X33933] : hAPP(c_List_Ofilter(X33933,X33932),hAPP(hAPP(c_List_Omap(X33931,X33933),X33930),X33929)) = hAPP(hAPP(c_List_Omap(X33931,X33933),X33930),hAPP(c_List_Ofilter(X33931,hAPP(c_Fun_Ocomp(X33933,tc_HOL_Obool,X33931,X33932),X33930)),X33929)),
inference(variable_rename,[status(thm)],[fact_filter__map]) ).
fof(i_0_6872,plain,
! [X29975,X29976,X29977] :
( ( hAPP(X29976,esk343_3(X29975,X29976,X29977)) != hAPP(X29976,esk344_3(X29975,X29976,X29977))
| c_Wellfounded_OwfP(X29977,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29975,tc_fun(X29977,tc_fun(X29977,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X29975,tc_HOL_Obool))),X29976))
| ~ c_Wellfounded_OwfP(X29977,hAPP(X29976,esk342_3(X29975,X29976,X29977))) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29977,tc_HOL_Obool)),c_Predicate_ODomainP(X29977,X29977,hAPP(X29976,esk343_3(X29975,X29976,X29977)))),c_Predicate_ORangeP(X29977,X29977,hAPP(X29976,esk344_3(X29975,X29976,X29977)))) != c_Orderings_Obot__class_Obot(tc_fun(X29977,tc_HOL_Obool))
| c_Wellfounded_OwfP(X29977,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29975,tc_fun(X29977,tc_fun(X29977,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X29975,tc_HOL_Obool))),X29976))
| ~ c_Wellfounded_OwfP(X29977,hAPP(X29976,esk342_3(X29975,X29976,X29977))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__SUP])])])]) ).
fof(i_0_6873,plain,
! [X33923,X33924,X33925] : c_List_Opartition(X33925,X33924,X33923) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33925),tc_List_Olist(X33925)),hAPP(c_List_Ofilter(X33925,X33924),X33923)),hAPP(c_List_Ofilter(X33925,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X33925,c_fNot),X33924)),X33923)),
inference(variable_rename,[status(thm)],[fact_partition__filter__conv]) ).
fof(i_0_6874,plain,
! [X24302,X24303,X24304] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk147_3(X24302,X24303,X24304)),esk148_3(X24302,X24303,X24304))))
| hBOOL(hAPP(hAPP(X24302,X24304),X24303))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X24304),X24303))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk147_3(X24302,X24303,X24304)),esk148_3(X24302,X24303,X24304)))
| hBOOL(hAPP(hAPP(X24302,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk147_3(X24302,X24303,X24304)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk148_3(X24302,X24303,X24304)))
| hBOOL(hAPP(hAPP(X24302,X24304),X24303))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X24304),X24303))) )
& ( ~ hBOOL(hAPP(hAPP(X24302,esk147_3(X24302,X24303,X24304)),esk148_3(X24302,X24303,X24304)))
| hBOOL(hAPP(hAPP(X24302,X24304),X24303))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X24304),X24303))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto_Opinduct])])])]) ).
fof(i_0_6875,plain,
! [X33093,X33094,X33095,X33096,X33097,X33098] : c_Map_Omap__add(X33098,X33097,X33096,c_Map_Omap__upds(X33098,X33097,X33095,X33094,X33093)) = c_Map_Omap__upds(X33098,X33097,c_Map_Omap__add(X33098,X33097,X33096,X33095),X33094,X33093),
inference(variable_rename,[status(thm)],[fact_map__add__upds]) ).
cnf(i_0_6876,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X1),X2)),c_Transitive__Closure_Ortrancl(X1,X2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5448]) ).
fof(i_0_6877,plain,
! [X25674,X25675] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25675),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25675),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25675),c_Groups_Oone__class_Oone(X25675)),X25674)),X25674)),c_Groups_Ozero__class_Ozero(X25675)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25675),X25674),c_Groups_Ozero__class_Ozero(X25675)))
| ~ hBOOL(hAPP(hAPP(c_member(X25675),X25674),c_Int_Oring__1__class_OInts(X25675)))
| ~ class_Rings_Olinordered__idom(X25675) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25675),X25674),c_Groups_Ozero__class_Ozero(X25675)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25675),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25675),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25675),c_Groups_Oone__class_Oone(X25675)),X25674)),X25674)),c_Groups_Ozero__class_Ozero(X25675)))
| ~ hBOOL(hAPP(hAPP(c_member(X25675),X25674),c_Int_Oring__1__class_OInts(X25675)))
| ~ class_Rings_Olinordered__idom(X25675) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).
fof(i_0_6878,plain,
! [X20126,X20127,X20128] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20128),X20127)),X20127)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20128,X20127))),X20126) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20128),X20126),
inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality2]) ).
fof(i_0_6879,plain,
! [X23374,X23375,X23376,X23377,X23378] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23378),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23376),X23375)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23378),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23374),X23377))),X23375)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23378),X23377)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23378),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23374),X23377))),X23375)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23378),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23376),X23375)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23378),X23377)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__period])])]) ).
fof(i_0_6880,plain,
! [X33138,X33139,X33140,X33141,X33142] : c_Map_Odom(X33142,X33141,c_Map_Omap__upds(X33142,X33141,X33140,X33139,X33138)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33142,tc_HOL_Obool)),hAPP(c_List_Oset(X33142),hAPP(hAPP(c_List_Otake(X33142),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33141)),X33138)),X33139))),c_Map_Odom(X33142,X33141,X33140)),
inference(variable_rename,[status(thm)],[fact_dom__map__upds]) ).
cnf(i_0_6881,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)) = c_List_Ofoldr(tc_List_Olist(X1),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_5449]) ).
cnf(i_0_6882,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk368_3(X3,X2,X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_5450]) ).
fof(i_0_6883,plain,
! [X33646,X33647,X33648,X33649] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33649)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33648,X33649),hAPP(c_List_Oset(X33648),X33647)),X33646) = hAPP(c_List_Ofoldl(X33649,X33648,hAPP(c_COMBC(X33648,X33649,X33649),hAPP(hAPP(c_COMBB(X33649,tc_fun(X33649,X33649),X33648),c_Lattices_Osemilattice__inf__class_Oinf(X33649)),X33646)),c_Orderings_Otop__class_Otop(X33649)),X33647) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__set__fold])]) ).
fof(i_0_6884,plain,
! [X33642,X33643,X33644,X33645] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33645)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33644,X33645),hAPP(c_List_Oset(X33644),X33643)),X33642) = hAPP(c_List_Ofoldl(X33645,X33644,hAPP(c_COMBC(X33644,X33645,X33645),hAPP(hAPP(c_COMBB(X33645,tc_fun(X33645,X33645),X33644),c_Lattices_Osemilattice__sup__class_Osup(X33645)),X33642)),c_Orderings_Obot__class_Obot(X33645)),X33643) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__set__fold])]) ).
cnf(i_0_6885,plain,
c_List_Oconcat(X1,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X1)),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),c_List_Oconcat(X1,X2)),c_List_Oconcat(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_5451]) ).
fof(i_0_6886,plain,
! [X29967,X29968,X29969,X29970] :
( ( hBOOL(hAPP(hAPP(c_member(X29970),esk340_4(X29967,X29968,X29969,X29970)),X29969))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29968),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29970,tc_fun(X29968,tc_HOL_Obool)),X29969),X29967)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29970),X29969)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29968),hAPP(X29967,esk340_4(X29967,X29968,X29969,X29970))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29968),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29970,tc_fun(X29968,tc_HOL_Obool)),X29969),X29967)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29970),X29969)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UN__I])])])]) ).
fof(i_0_6887,plain,
! [X24553,X24554,X24555,X24556,X24557] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24554),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24556,tc_fun(X24554,tc_HOL_Obool)),X24555),X24553)))
| ~ hBOOL(hAPP(hAPP(c_member(X24556),X24557),X24555))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24554),hAPP(X24553,X24557)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24556),X24555)) )
& ( hBOOL(hAPP(hAPP(c_member(X24556),esk161_4(X24553,X24554,X24555,X24556)),X24555))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24554),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24556,tc_fun(X24554,tc_HOL_Obool)),X24555),X24553)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24556),X24555)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24554),hAPP(X24553,esk161_4(X24553,X24554,X24555,X24556))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24554),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24556,tc_fun(X24554,tc_HOL_Obool)),X24555),X24553)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24556),X24555)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UN])])])])]) ).
fof(i_0_6888,plain,
! [X29529,X29530,X29531,X29532,X29533,X29534,X29535] : hAPP(hAPP(c_Relation_Orel__comp(X29535,X29534,X29533),X29532),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29531,tc_fun(tc_prod(X29534,X29533),tc_HOL_Obool)),X29530),X29529)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29531,tc_fun(tc_prod(X29535,X29533),tc_HOL_Obool)),X29530),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29534,X29533),tc_HOL_Obool),tc_fun(tc_prod(X29535,X29533),tc_HOL_Obool),X29531),hAPP(c_Relation_Orel__comp(X29535,X29534,X29533),X29532)),X29529)),
inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib]) ).
fof(i_0_6889,plain,
! [X26636,X26637,X26638,X26639,X26640,X26641,X26642] : hAPP(c_Fun_Ocomp(X26642,X26641,X26640,X26639),hAPP(c_Fun_Ocomp(X26638,X26642,X26640,X26637),X26636)) = hAPP(c_Fun_Ocomp(X26638,X26641,X26640,hAPP(c_Fun_Ocomp(X26642,X26641,X26638,X26639),X26637)),X26636),
inference(variable_rename,[status(thm)],[fact_o__assoc]) ).
fof(i_0_6890,plain,
! [X24331,X24332,X24333,X24334] :
( hAPP(c_Set_Oimage(X24334,X24333,X24332),c_Orderings_Otop__class_Otop(tc_fun(X24334,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X24333,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24333,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24333,tc_HOL_Obool)),hAPP(c_Set_Oimage(X24334,X24333,X24332),X24331))),hAPP(c_Set_Oimage(X24334,X24333,X24332),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24334,tc_HOL_Obool)),X24331)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset])]) ).
fof(i_0_6891,plain,
! [X26396,X26397,X26398,X26399,X26400,X26401] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26401,X26401)),hAPP(hAPP(c_Product__Type_OPair(X26401,X26401),X26400),X26399)),hAPP(hAPP(c_Relation_Oinv__image(X26398,X26401),X26397),X26396)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26398,X26398)),hAPP(hAPP(c_Product__Type_OPair(X26398,X26398),hAPP(X26396,X26400)),hAPP(X26396,X26399))),X26397)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26398,X26398)),hAPP(hAPP(c_Product__Type_OPair(X26398,X26398),hAPP(X26396,X26400)),hAPP(X26396,X26399))),X26397))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26401,X26401)),hAPP(hAPP(c_Product__Type_OPair(X26401,X26401),X26400),X26399)),hAPP(hAPP(c_Relation_Oinv__image(X26398,X26401),X26397),X26396))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__image])]) ).
fof(i_0_6892,plain,
! [X26789,X26790,X26791,X26792,X26793,X26794] :
( ~ c_Finite__Set_Ofolding(X26794,X26793,X26792,X26791)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26794),X26790))
| ~ hBOOL(hAPP(hAPP(c_member(X26794),X26789),X26790))
| hAPP(X26791,X26790) = hAPP(c_Fun_Ocomp(X26793,X26793,X26793,hAPP(X26791,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26794,tc_HOL_Obool)),X26790),hAPP(hAPP(c_Set_Oinsert(X26794),X26789),c_Orderings_Obot__class_Obot(tc_fun(X26794,tc_HOL_Obool)))))),hAPP(X26792,X26789)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oremove])]) ).
fof(i_0_6893,plain,
! [X28761,X28762,X28763,X28764,X28765,X28766] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28766,X28765),tc_HOL_Obool)),X28764),hAPP(hAPP(c_Product__Type_OSigma(X28766,X28765),X28763),hAPP(c_COMBK(tc_fun(X28765,tc_HOL_Obool),X28766),X28762))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28765,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28766,X28765,X28764),X28761)),X28762)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset])]) ).
fof(i_0_6894,plain,
! [X33530,X33531,X33532] : hAPP(c_List_Otl(X33532),hAPP(hAPP(c_List_Oappend(X33532),X33531),X33530)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X33532),X33532,hAPP(c_List_Otl(X33532),X33530),hAPP(c_COMBK(tc_fun(tc_List_Olist(X33532),tc_List_Olist(X33532)),X33532),hAPP(hAPP(c_COMBC(tc_List_Olist(X33532),tc_List_Olist(X33532),tc_List_Olist(X33532)),c_List_Oappend(X33532)),X33530))),X33531),
inference(variable_rename,[status(thm)],[fact_tl__append]) ).
fof(i_0_6895,plain,
! [X29879,X29880,X29881,X29882] : c_New__Random__Sequence_Opos__map(X29882,X29881,X29880,X29879) = c_New__Random__Sequence_Opos__bind(X29882,X29881,X29879,hAPP(c_Fun_Ocomp(X29881,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X29881))))),X29882,c_New__Random__Sequence_Opos__single(X29881)),X29880)),
inference(variable_rename,[status(thm)],[fact_pos__map__def]) ).
fof(i_0_6896,plain,
! [X28134,X28135,X28136,X28137] :
( ~ c_Fun_Oinj__on(X28137,X28136,X28135,c_Orderings_Otop__class_Otop(tc_fun(X28137,tc_HOL_Obool)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28136,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28137,X28136,X28135),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28137,tc_HOL_Obool)),X28134))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28136,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28137,X28136,X28135),X28134)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset])]) ).
fof(i_0_6897,plain,
! [X26798,X26799,X26800,X26801,X26802,X26803] :
( ~ c_Finite__Set_Ofolding(X26803,X26802,X26801,X26800)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26803),X26799))
| hAPP(X26800,hAPP(hAPP(c_Set_Oinsert(X26803),X26798),X26799)) = hAPP(c_Fun_Ocomp(X26802,X26802,X26802,hAPP(X26800,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26803,tc_HOL_Obool)),X26799),hAPP(hAPP(c_Set_Oinsert(X26803),X26798),c_Orderings_Obot__class_Obot(tc_fun(X26803,tc_HOL_Obool)))))),hAPP(X26801,X26798)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oinsert__remove])]) ).
fof(i_0_6898,plain,
! [X32719,X32720,X32721,X32722] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32722),X32721))
| hBOOL(hAPP(hAPP(c_member(X32722),X32720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32722,tc_HOL_Obool)),hAPP(c_List_Oset(X32722),X32721)),hAPP(hAPP(c_Set_Oinsert(X32722),hAPP(hAPP(c_List_Onth(X32722),X32721),X32719)),c_Orderings_Obot__class_Obot(tc_fun(X32722,tc_HOL_Obool))))))
| hBOOL(hAPP(c_List_Odistinct(X32722),hAPP(hAPP(c_List_Olist__update(X32722,X32721),X32719),X32720))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5452])]) ).
fof(i_0_6899,plain,
! [X28088,X28089,X28090,X28091] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X28091),hAPP(c_Set_Oimage(X28090,X28091,X28089),X28088))),hAPP(c_Finite__Set_Ocard(X28090),X28088)))
| ~ c_Fun_Oinj__on(X28090,X28091,X28089,X28088) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5453])]) ).
cnf(i_0_6900,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5441]) ).
cnf(i_0_6901,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5454]) ).
fof(i_0_6902,plain,
! [X26849,X26850,X26851,X26852,X26853,X26854,X26855,X26856] :
( ~ c_Finite__Set_Ofolding(X26856,X26855,X26854,X26853)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26856),X26852))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26856),X26851))
| hAPP(c_Fun_Ocomp(X26855,X26855,X26850,hAPP(X26853,X26851)),hAPP(c_Fun_Ocomp(X26855,X26855,X26850,hAPP(X26853,X26852)),X26849)) = hAPP(c_Fun_Ocomp(X26855,X26855,X26850,hAPP(X26853,X26852)),hAPP(c_Fun_Ocomp(X26855,X26855,X26850,hAPP(X26853,X26851)),X26849)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H_H])]) ).
fof(i_0_6903,plain,
! [X31982,X31983,X31984,X31985,X31986] :
( ~ hBOOL(hAPP(c_List_Odistinct(X31986),hAPP(hAPP(c_List_Omap(tc_prod(X31986,X31985),X31986),c_Product__Type_Ofst(X31986,X31985)),X31984)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31986,X31985)),hAPP(hAPP(c_Product__Type_OPair(X31986,X31985),X31983),X31982)),hAPP(c_List_Oset(tc_prod(X31986,X31985)),X31984)))
| hAPP(c_Map_Omap__of(X31986,X31985,X31984),X31983) = hAPP(c_Option_Ooption_OSome(X31985),X31982) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeI])]) ).
fof(i_0_6904,plain,
! [X31987,X31988,X31989,X31990,X31991] :
( ( hAPP(c_Map_Omap__of(X31991,X31990,X31989),X31988) != hAPP(c_Option_Ooption_OSome(X31990),X31987)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X31991,X31990)),hAPP(hAPP(c_Product__Type_OPair(X31991,X31990),X31988),X31987)),hAPP(c_List_Oset(tc_prod(X31991,X31990)),X31989)))
| ~ hBOOL(hAPP(c_List_Odistinct(X31991),hAPP(hAPP(c_List_Omap(tc_prod(X31991,X31990),X31991),c_Product__Type_Ofst(X31991,X31990)),X31989))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31991,X31990)),hAPP(hAPP(c_Product__Type_OPair(X31991,X31990),X31988),X31987)),hAPP(c_List_Oset(tc_prod(X31991,X31990)),X31989)))
| hAPP(c_Map_Omap__of(X31991,X31990,X31989),X31988) = hAPP(c_Option_Ooption_OSome(X31990),X31987)
| ~ hBOOL(hAPP(c_List_Odistinct(X31991),hAPP(hAPP(c_List_Omap(tc_prod(X31991,X31990),X31991),c_Product__Type_Ofst(X31991,X31990)),X31989))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__eq__Some__iff])])]) ).
fof(i_0_6905,plain,
! [X31992,X31993,X31994,X31995,X31996] :
( ( hAPP(c_Option_Ooption_OSome(X31995),X31993) != hAPP(c_Map_Omap__of(X31996,X31995,X31994),X31992)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X31996,X31995)),hAPP(hAPP(c_Product__Type_OPair(X31996,X31995),X31992),X31993)),hAPP(c_List_Oset(tc_prod(X31996,X31995)),X31994)))
| ~ hBOOL(hAPP(c_List_Odistinct(X31996),hAPP(hAPP(c_List_Omap(tc_prod(X31996,X31995),X31996),c_Product__Type_Ofst(X31996,X31995)),X31994))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31996,X31995)),hAPP(hAPP(c_Product__Type_OPair(X31996,X31995),X31992),X31993)),hAPP(c_List_Oset(tc_prod(X31996,X31995)),X31994)))
| hAPP(c_Option_Ooption_OSome(X31995),X31993) = hAPP(c_Map_Omap__of(X31996,X31995,X31994),X31992)
| ~ hBOOL(hAPP(c_List_Odistinct(X31996),hAPP(hAPP(c_List_Omap(tc_prod(X31996,X31995),X31996),c_Product__Type_Ofst(X31996,X31995)),X31994))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Some__eq__map__of__iff])])]) ).
fof(i_0_6906,plain,
! [X28826,X28827,X28828,X28829] :
( ( hBOOL(hAPP(hAPP(c_member(X28829),esk285_4(X28826,X28827,X28828,X28829)),X28828))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28829,X28827)),hAPP(hAPP(c_Product__Type_OSigma(X28829,X28827),X28828),X28826)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28829),X28828)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28827),hAPP(X28826,esk285_4(X28826,X28827,X28828,X28829))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28829,X28827)),hAPP(hAPP(c_Product__Type_OSigma(X28829,X28827),X28828),X28826)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28829),X28828)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__SigmaI])])])]) ).
fof(i_0_6907,plain,
! [X19643,X19644,X19645,X19646,X19647,X19648] :
( ~ class_Rings_Olinordered__semiring__1(X19648)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19648),X19647),X19646))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19648),X19645),X19646))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19648),c_Groups_Ozero__class_Ozero(X19648)),X19644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19648),c_Groups_Ozero__class_Ozero(X19648)),X19643))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19648),X19644),X19643) != c_Groups_Oone__class_Oone(X19648)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19648),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19648),X19644),X19647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19648),X19643),X19645))),X19646)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).
fof(i_0_6908,plain,
! [X18984,X18985,X18986,X18987,X18988,X18989] :
( ~ class_Rings_Olinordered__semiring__1__strict(X18989)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18989),X18988),X18987))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18989),X18986),X18987))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18989),c_Groups_Ozero__class_Ozero(X18989)),X18985))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18989),c_Groups_Ozero__class_Ozero(X18989)),X18984))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18989),X18985),X18984) != c_Groups_Oone__class_Oone(X18989)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18989),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18989),X18985),X18988)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18989),X18984),X18986))),X18987)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).
fof(i_0_6909,plain,
! [X25434,X25435,X25436,X25437] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk170_4(X25434,X25435,X25436,X25437)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25436)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25437),X25435))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25437),X25436)),X25435))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25435),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25436)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk171_4(X25434,X25435,X25436,X25437)),X25434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25437),X25435))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25437),X25436)),X25435))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25435),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25436)) )
& ( X25437 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk171_4(X25434,X25435,X25436,X25437)),esk170_4(X25434,X25435,X25436,X25437))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25437),X25435))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25437),X25436)),X25435))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25435),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25436)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I6_J])])])])]) ).
fof(i_0_6910,plain,
! [X26835,X26836,X26837,X26838,X26839,X26840,X26841,X26842] :
( ~ c_Finite__Set_Ofolding(X26842,X26841,X26840,X26839)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26842),X26838))
| hAPP(c_Fun_Ocomp(X26841,X26841,X26837,hAPP(X26840,X26836)),hAPP(c_Fun_Ocomp(X26841,X26841,X26837,hAPP(X26839,X26838)),X26835)) = hAPP(c_Fun_Ocomp(X26841,X26841,X26837,hAPP(X26839,X26838)),hAPP(c_Fun_Ocomp(X26841,X26841,X26837,hAPP(X26840,X26836)),X26835)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H])]) ).
fof(i_0_6911,plain,
! [X33278,X33279,X33280,X33281,X33282,X33283,X33284,X33285] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33285,X33285)),hAPP(hAPP(c_Product__Type_OPair(X33285,X33285),X33284),X33283)),X33282))
| X33281 != hAPP(hAPP(c_List_Oappend(X33285),X33280),hAPP(hAPP(c_List_Olist_OCons(X33285),X33284),X33279))
| X33278 != hAPP(hAPP(c_List_Oappend(X33285),X33280),hAPP(hAPP(c_List_Olist_OCons(X33285),X33283),X33279))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33285),tc_List_Olist(X33285))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33285),tc_List_Olist(X33285)),X33281),X33278)),c_List_Olistrel1(X33285,X33282))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I])]) ).
cnf(i_0_6912,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_5455]) ).
fof(i_0_6913,plain,
! [X22806,X22807,X22808,X22809,X22810,X22811,X22812] :
( ( X22809 = X22807
| c_Sum__Type_Osum_Osum__case(X22812,X22811,X22810,X22809,X22808) != c_Sum__Type_Osum_Osum__case(X22812,X22811,X22810,X22807,X22806) )
& ( X22808 = X22806
| c_Sum__Type_Osum_Osum__case(X22812,X22811,X22810,X22809,X22808) != c_Sum__Type_Osum_Osum__case(X22812,X22811,X22810,X22807,X22806) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__case__inject])])]) ).
cnf(i_0_6914,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X3)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_5456]) ).
cnf(i_0_6915,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5456]) ).
fof(i_0_6916,plain,
! [X31501,X31502,X31503,X31504] :
( ( hBOOL(hAPP(hAPP(c_member(X31504),esk417_4(X31501,X31502,X31503,X31504)),X31503))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31504),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31504),X31502),X31501)),hAPP(hAPP(c_Finite__Set_Ofold(X31504,X31504,c_Lattices_Osemilattice__inf__class_Oinf(X31504)),X31501),X31503)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31504),X31503))
| ~ class_Lattices_Osemilattice__inf(X31504) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31504),X31502),esk417_4(X31501,X31502,X31503,X31504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31504),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31504),X31502),X31501)),hAPP(hAPP(c_Finite__Set_Ofold(X31504,X31504,c_Lattices_Osemilattice__inf__class_Oinf(X31504)),X31501),X31503)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31504),X31503))
| ~ class_Lattices_Osemilattice__inf(X31504) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le__fold__inf])])])]) ).
fof(i_0_6917,plain,
! [X31492,X31493,X31494,X31495] :
( ( hBOOL(hAPP(hAPP(c_member(X31495),esk415_4(X31492,X31493,X31494,X31495)),X31494))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31495),hAPP(hAPP(c_Orderings_Oord__class_Omin(X31495),X31493),X31492)),hAPP(hAPP(c_Finite__Set_Ofold(X31495,X31495,c_Orderings_Oord__class_Omin(X31495)),X31492),X31494)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31495),X31494))
| ~ class_Orderings_Olinorder(X31495) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31495),X31493),esk415_4(X31492,X31493,X31494,X31495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31495),hAPP(hAPP(c_Orderings_Oord__class_Omin(X31495),X31493),X31492)),hAPP(hAPP(c_Finite__Set_Ofold(X31495,X31495,c_Orderings_Oord__class_Omin(X31495)),X31492),X31494)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31495),X31494))
| ~ class_Orderings_Olinorder(X31495) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le__fold__inf])])])]) ).
fof(i_0_6918,plain,
! [X23581,X23582,X23583,X23584,X23585] :
( ~ class_Groups_Ocomm__monoid__add(X23585)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23585),X23584),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23583),X23582)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23581),X23582))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23585),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23585,tc_Nat_Onat),X23584),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X23582))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23583),X23581)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl])]) ).
fof(i_0_6919,plain,
! [X30211,X30212,X30213,X30214] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30214,X30214)),X30213),c_Transitive__Closure_Ortrancl(X30214,X30212)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30214,X30214)),X30213),c_Transitive__Closure_Ortrancl(X30214,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30214,X30214),tc_HOL_Obool)),X30212),X30211)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30214,X30214)),X30213),c_Transitive__Closure_Ortrancl(X30214,X30211)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30214,X30214)),X30213),c_Transitive__Closure_Ortrancl(X30214,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30214,X30214),tc_HOL_Obool)),X30212),X30211)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI])])]) ).
fof(i_0_6920,plain,
! [X26804,X26805,X26806,X26807,X26808,X26809,X26810,X26811] :
( ~ c_Finite__Set_Ofolding(X26811,X26810,X26809,X26808)
| hAPP(c_Fun_Ocomp(X26810,X26810,X26807,hAPP(X26809,X26806)),hAPP(c_Fun_Ocomp(X26810,X26810,X26807,hAPP(X26809,X26805)),X26804)) = hAPP(c_Fun_Ocomp(X26810,X26810,X26807,hAPP(X26809,X26805)),hAPP(c_Fun_Ocomp(X26810,X26810,X26807,hAPP(X26809,X26806)),X26804)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp])]) ).
fof(i_0_6921,plain,
! [X28009,X28010,X28011,X28012,X28014,X28015] :
( ( X28009 = hAPP(X28010,esk265_4(X28009,X28010,X28011,X28012))
| ~ hBOOL(hAPP(hAPP(c_member(X28011),X28009),hAPP(c_Set_Oimage(X28012,X28011,X28010),c_Orderings_Otop__class_Otop(tc_fun(X28012,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X28012,X28011,X28010,c_Orderings_Otop__class_Otop(tc_fun(X28012,tc_HOL_Obool))) )
& ( X28009 != hAPP(X28010,X28014)
| X28014 = esk265_4(X28009,X28010,X28011,X28012)
| ~ hBOOL(hAPP(hAPP(c_member(X28011),X28009),hAPP(c_Set_Oimage(X28012,X28011,X28010),c_Orderings_Otop__class_Otop(tc_fun(X28012,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X28012,X28011,X28010,c_Orderings_Otop__class_Otop(tc_fun(X28012,tc_HOL_Obool))) )
& ( X28009 = hAPP(X28010,esk266_5(X28009,X28010,X28011,X28012,X28015))
| X28009 != hAPP(X28010,X28015)
| hBOOL(hAPP(hAPP(c_member(X28011),X28009),hAPP(c_Set_Oimage(X28012,X28011,X28010),c_Orderings_Otop__class_Otop(tc_fun(X28012,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X28012,X28011,X28010,c_Orderings_Otop__class_Otop(tc_fun(X28012,tc_HOL_Obool))) )
& ( esk266_5(X28009,X28010,X28011,X28012,X28015) != X28015
| X28009 != hAPP(X28010,X28015)
| hBOOL(hAPP(hAPP(c_member(X28011),X28009),hAPP(c_Set_Oimage(X28012,X28011,X28010),c_Orderings_Otop__class_Otop(tc_fun(X28012,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X28012,X28011,X28010,c_Orderings_Otop__class_Otop(tc_fun(X28012,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__ex1__eq])])])])]) ).
fof(i_0_6922,plain,
! [X27584,X27585,X27586,X27587,X27588] :
( ~ class_Groups_Oab__group__add(X27588)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27587),X27586))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27587),X27585))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27587,X27588),X27584),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27587,tc_HOL_Obool)),X27586),X27585)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27588),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27588),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27587,X27588),X27584),X27586)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27587,X27588),X27584),X27585))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27587,X27588),X27584),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27587,tc_HOL_Obool)),X27586),X27585))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un])]) ).
fof(i_0_6923,plain,
! [X34343,X34344,X34345,X34346] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34346),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34345)),X34344)))
| hAPP(c_List_Orev(X34345),hAPP(hAPP(c_List_Olist__update(X34345,X34344),X34346),X34343)) = hAPP(hAPP(c_List_Olist__update(X34345,hAPP(c_List_Orev(X34345),X34344)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34345)),X34344)),X34346)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X34343) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__update])]) ).
fof(i_0_6924,plain,
! [X27765,X27766,X27767,X27768] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X27768,tc_HOL_Obool)),esk256_4(X27765,X27766,X27767,X27768)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27768),X27767),X27766)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27765),hAPP(c_Finite__Set_Ocard(X27768),X27767)))
| ~ c_Equiv__Relations_Oequiv(X27768,X27767,X27766)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27768),X27767)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27765),hAPP(c_Finite__Set_Ocard(X27768),esk256_4(X27765,X27766,X27767,X27768))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27765),hAPP(c_Finite__Set_Ocard(X27768),X27767)))
| ~ c_Equiv__Relations_Oequiv(X27768,X27767,X27766)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27768),X27767)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__imp__dvd__card])])])]) ).
cnf(i_0_6925,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
| c_Groups_Oone__class_Oone(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5417]) ).
cnf(i_0_6926,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5416]) ).
fof(i_0_6927,plain,
! [X29247,X29248,X29249] : hAPP(c_Set_OCollect(X29249),hAPP(hAPP(c_COMBS(X29249,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29249),c_fimplies),X29248)),X29247)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29249,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29249,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29249),X29248))),hAPP(c_Set_OCollect(X29249),X29247)),
inference(variable_rename,[status(thm)],[fact_Collect__imp__eq]) ).
fof(i_0_6928,plain,
! [X21782,X21783,X21784,X21785] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),c_Groups_Ozero__class_Ozero(X21785)),X21783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),X21784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)),X21783)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21783),c_Groups_Ozero__class_Ozero(X21785)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)),X21783)),X21784))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),c_Groups_Ozero__class_Ozero(X21785)),X21783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21783),c_Groups_Ozero__class_Ozero(X21785)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),c_Groups_Ozero__class_Ozero(X21785)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),c_Groups_Ozero__class_Ozero(X21785)),X21783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),c_Groups_Ozero__class_Ozero(X21785)),X21783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),c_Groups_Ozero__class_Ozero(X21785)),X21783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21783),c_Groups_Ozero__class_Ozero(X21785)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21783),c_Groups_Ozero__class_Ozero(X21785)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),c_Groups_Ozero__class_Ozero(X21785)),X21783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),c_Groups_Ozero__class_Ozero(X21785)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21783),c_Groups_Ozero__class_Ozero(X21785)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),c_Groups_Ozero__class_Ozero(X21785)),X21783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21783),c_Groups_Ozero__class_Ozero(X21785)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)),X21783)),X21784))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),c_Groups_Ozero__class_Ozero(X21785)),X21783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),c_Groups_Ozero__class_Ozero(X21785)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)),X21783)),X21784))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),c_Groups_Ozero__class_Ozero(X21785)),X21783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),c_Groups_Ozero__class_Ozero(X21785)),X21783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),X21784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)),X21783)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21783),c_Groups_Ozero__class_Ozero(X21785)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21783),c_Groups_Ozero__class_Ozero(X21785)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),X21784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)),X21783)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),c_Groups_Ozero__class_Ozero(X21785)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21783),c_Groups_Ozero__class_Ozero(X21785)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),X21784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)),X21783)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21783),c_Groups_Ozero__class_Ozero(X21785)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)),X21783)),X21784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),X21784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)),X21783)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),c_Groups_Ozero__class_Ozero(X21785)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)),X21783)),X21784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),X21784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)),X21783)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21784),X21783)),hAPP(c_Int_Onumber__class_Onumber__of(X21785),X21782)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21785)
| ~ class_Int_Onumber(X21785) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5457])])]) ).
fof(i_0_6929,plain,
! [X21764,X21765,X21766,X21767] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),X21765))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)),X21765)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21765),c_Groups_Ozero__class_Ozero(X21767)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)),X21765)),X21766))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),X21765))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21765),c_Groups_Ozero__class_Ozero(X21767)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),X21765))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),X21765))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),X21765))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21765),c_Groups_Ozero__class_Ozero(X21767)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21765),c_Groups_Ozero__class_Ozero(X21767)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),X21765))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21765),c_Groups_Ozero__class_Ozero(X21767)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),X21765))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21765),c_Groups_Ozero__class_Ozero(X21767)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)),X21765)),X21766))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),X21765))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)),X21765)),X21766))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),X21765))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),X21765))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)),X21765)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21765),c_Groups_Ozero__class_Ozero(X21767)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21765),c_Groups_Ozero__class_Ozero(X21767)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)),X21765)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21765),c_Groups_Ozero__class_Ozero(X21767)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)),X21765)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21765),c_Groups_Ozero__class_Ozero(X21767)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)),X21765)),X21766))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)),X21765)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),c_Groups_Ozero__class_Ozero(X21767)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)),X21765)),X21766))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),X21766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21767),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)),X21765)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21767),X21766),X21765)),hAPP(c_Int_Onumber__class_Onumber__of(X21767),X21764)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21767)
| ~ class_Int_Onumber(X21767) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5458])])]) ).
fof(i_0_6930,plain,
! [X30589,X30590,X30591,X30592,X30593,X30594,X30595,X30596,X30597] :
( ( ~ c_Relation_Osingle__valued(X30591,X30590,X30589)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30591,X30590)),hAPP(hAPP(c_Product__Type_OPair(X30591,X30590),X30592),X30593)),X30589))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30591,X30590)),hAPP(hAPP(c_Product__Type_OPair(X30591,X30590),X30592),X30594)),X30589))
| X30593 = X30594 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30597,X30596)),hAPP(hAPP(c_Product__Type_OPair(X30597,X30596),esk378_3(X30595,X30596,X30597)),esk379_3(X30595,X30596,X30597))),X30595))
| c_Relation_Osingle__valued(X30597,X30596,X30595) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30597,X30596)),hAPP(hAPP(c_Product__Type_OPair(X30597,X30596),esk378_3(X30595,X30596,X30597)),esk380_3(X30595,X30596,X30597))),X30595))
| c_Relation_Osingle__valued(X30597,X30596,X30595) )
& ( esk379_3(X30595,X30596,X30597) != esk380_3(X30595,X30596,X30597)
| c_Relation_Osingle__valued(X30597,X30596,X30595) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__def])])])])])]) ).
fof(i_0_6931,plain,
! [X21786,X21787,X21788,X21789] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),c_Groups_Ozero__class_Ozero(X21789)),X21786))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),X21786)),X21787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),X21786),c_Groups_Ozero__class_Ozero(X21789)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),X21787),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),X21786)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),c_Groups_Ozero__class_Ozero(X21789)),X21786))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),X21786),c_Groups_Ozero__class_Ozero(X21789)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),c_Groups_Ozero__class_Ozero(X21789)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),c_Groups_Ozero__class_Ozero(X21789)),X21786))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),c_Groups_Ozero__class_Ozero(X21789)),X21786))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),c_Groups_Ozero__class_Ozero(X21789)),X21786))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),X21786),c_Groups_Ozero__class_Ozero(X21789)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),X21786),c_Groups_Ozero__class_Ozero(X21789)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),c_Groups_Ozero__class_Ozero(X21789)),X21786))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),c_Groups_Ozero__class_Ozero(X21789)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),X21786),c_Groups_Ozero__class_Ozero(X21789)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),c_Groups_Ozero__class_Ozero(X21789)),X21786))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),X21786),c_Groups_Ozero__class_Ozero(X21789)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),X21787),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),X21786)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),c_Groups_Ozero__class_Ozero(X21789)),X21786))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),c_Groups_Ozero__class_Ozero(X21789)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),X21787),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),X21786)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),c_Groups_Ozero__class_Ozero(X21789)),X21786))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),c_Groups_Ozero__class_Ozero(X21789)),X21786))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),X21786)),X21787))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),X21786),c_Groups_Ozero__class_Ozero(X21789)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),X21786),c_Groups_Ozero__class_Ozero(X21789)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),X21786)),X21787))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),c_Groups_Ozero__class_Ozero(X21789)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),X21786),c_Groups_Ozero__class_Ozero(X21789)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),X21786)),X21787))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),X21786),c_Groups_Ozero__class_Ozero(X21789)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),X21787),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),X21786)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),X21786)),X21787))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),c_Groups_Ozero__class_Ozero(X21789)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),X21787),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),X21786)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),X21786)),X21787))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(c_Int_Onumber__class_Onumber__of(X21789),X21788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21787),X21786)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21789)
| ~ class_Int_Onumber(X21789) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5459])])]) ).
fof(i_0_6932,plain,
! [X21760,X21761,X21762,X21763] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),c_Groups_Ozero__class_Ozero(X21763)),X21760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),X21760)),X21761))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21760),c_Groups_Ozero__class_Ozero(X21763)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),X21760)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),c_Groups_Ozero__class_Ozero(X21763)),X21760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21760),c_Groups_Ozero__class_Ozero(X21763)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),c_Groups_Ozero__class_Ozero(X21763)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),c_Groups_Ozero__class_Ozero(X21763)),X21760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),c_Groups_Ozero__class_Ozero(X21763)),X21760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),c_Groups_Ozero__class_Ozero(X21763)),X21760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21760),c_Groups_Ozero__class_Ozero(X21763)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21760),c_Groups_Ozero__class_Ozero(X21763)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),c_Groups_Ozero__class_Ozero(X21763)),X21760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),c_Groups_Ozero__class_Ozero(X21763)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21760),c_Groups_Ozero__class_Ozero(X21763)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),c_Groups_Ozero__class_Ozero(X21763)),X21760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21760),c_Groups_Ozero__class_Ozero(X21763)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),X21760)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),c_Groups_Ozero__class_Ozero(X21763)),X21760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),c_Groups_Ozero__class_Ozero(X21763)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),X21760)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),c_Groups_Ozero__class_Ozero(X21763)),X21760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),c_Groups_Ozero__class_Ozero(X21763)),X21760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),X21760)),X21761))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21760),c_Groups_Ozero__class_Ozero(X21763)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21760),c_Groups_Ozero__class_Ozero(X21763)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),X21760)),X21761))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),c_Groups_Ozero__class_Ozero(X21763)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21760),c_Groups_Ozero__class_Ozero(X21763)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),X21760)),X21761))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21760),c_Groups_Ozero__class_Ozero(X21763)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),X21760)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),X21760)),X21761))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),c_Groups_Ozero__class_Ozero(X21763)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),X21761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),X21760)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),X21760)),X21761))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21763),hAPP(c_Int_Onumber__class_Onumber__of(X21763),X21762)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21763),X21761),X21760)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21763)
| ~ class_Int_Onumber(X21763) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5460])])]) ).
fof(i_0_6933,plain,
! [X22489,X22490,X22491,X22492,X22493] : c_Product__Type_Oprod_Oprod__size(X22493,X22492,X22491,X22490,X22489) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X22491,hAPP(c_Product__Type_Ofst(X22493,X22492),X22489))),hAPP(X22490,hAPP(c_Product__Type_Osnd(X22493,X22492),X22489)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_prod__size__simp]) ).
fof(i_0_6934,plain,
! [X23486,X23487,X23488,X23489,X23490] :
( ~ class_Groups_Ocomm__monoid__add(X23490)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23490),X23489),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23488),X23487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23486),X23487))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23490),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23490,tc_Nat_Onat),X23489),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X23487))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23488,X23486)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl])]) ).
fof(i_0_6935,plain,
! [X25440,X25441,X25442,X25443] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk172_4(X25440,X25441,X25442,X25443)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25442)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25441),X25443))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25443),X25442)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25441),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25440))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25442)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk173_4(X25440,X25441,X25442,X25443)),X25440))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25441),X25443))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25443),X25442)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25441),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25440))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25442)) )
& ( X25443 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk173_4(X25440,X25441,X25442,X25443)),esk172_4(X25440,X25441,X25442,X25443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25441),X25443))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25443),X25442)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25441),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25440))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25442)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I8_J])])])])]) ).
fof(i_0_6936,plain,
! [X28789,X28790,X28791,X28792] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28792),X28791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28792,X28792),tc_HOL_Obool)),X28790),hAPP(hAPP(c_Product__Type_OSigma(X28792,X28792),X28791),hAPP(c_COMBK(tc_fun(X28792,tc_HOL_Obool),X28792),X28791))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X28792,tc_HOL_Obool)),X28789),hAPP(hAPP(c_Equiv__Relations_Oquotient(X28792),X28791),X28790)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28792),X28789)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__equiv__class])]) ).
fof(i_0_6937,plain,
! [X26924,X26925,X26926,X26927,X26928,X26929,X26930] :
( ~ c_Equiv__Relations_Oequiv(X26930,X26929,X26928)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26930,tc_HOL_Obool)),X26927),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26930),X26929),X26928)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26930,tc_HOL_Obool)),X26926),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26930),X26929),X26928)))
| ~ hBOOL(hAPP(hAPP(c_member(X26930),X26925),X26927))
| ~ hBOOL(hAPP(hAPP(c_member(X26930),X26924),X26926))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26930,X26930)),hAPP(hAPP(c_Product__Type_OPair(X26930,X26930),X26925),X26924)),X26928))
| X26927 = X26926 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eqI])]) ).
fof(i_0_6938,plain,
! [X26917,X26918,X26919,X26920,X26921,X26922,X26923] :
( ( X26920 != X26919
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26923,X26923)),hAPP(hAPP(c_Product__Type_OPair(X26923,X26923),X26918),X26917)),X26921))
| ~ hBOOL(hAPP(hAPP(c_member(X26923),X26917),X26919))
| ~ hBOOL(hAPP(hAPP(c_member(X26923),X26918),X26920))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26923,tc_HOL_Obool)),X26919),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26923),X26922),X26921)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26923,tc_HOL_Obool)),X26920),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26923),X26922),X26921)))
| ~ c_Equiv__Relations_Oequiv(X26923,X26922,X26921) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26923,X26923)),hAPP(hAPP(c_Product__Type_OPair(X26923,X26923),X26918),X26917)),X26921))
| X26920 = X26919
| ~ hBOOL(hAPP(hAPP(c_member(X26923),X26917),X26919))
| ~ hBOOL(hAPP(hAPP(c_member(X26923),X26918),X26920))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26923,tc_HOL_Obool)),X26919),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26923),X26922),X26921)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26923,tc_HOL_Obool)),X26920),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26923),X26922),X26921)))
| ~ c_Equiv__Relations_Oequiv(X26923,X26922,X26921) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff])])]) ).
fof(i_0_6939,plain,
! [X20211,X20212,X20213] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20213),c_Groups_Ozero__class_Ozero(X20213)),esk66_3(X20211,X20212,X20213)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20213),X20212),X20211))
| ~ class_Fields_Olinordered__field__inverse__zero(X20213) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20213),esk66_3(X20211,X20212,X20213)),c_Groups_Oone__class_Oone(X20213)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20213),X20212),X20211))
| ~ class_Fields_Olinordered__field__inverse__zero(X20213) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20213),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20213),esk66_3(X20211,X20212,X20213)),X20212)),X20211))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20213),X20212),X20211))
| ~ class_Fields_Olinordered__field__inverse__zero(X20213) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__le__mult__one__interval])])])]) ).
fof(i_0_6940,plain,
! [X23012,X23013,X23014,X23015,X23016] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X23016,X23015,tc_HOL_Obool,X23014),X23013),X23012))
| hBOOL(hAPP(X23014,hAPP(hAPP(c_Product__Type_OPair(X23016,X23015),X23013),X23012))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryE])]) ).
fof(i_0_6941,plain,
! [X23007,X23008,X23009,X23010,X23011] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X23011,X23010,tc_HOL_Obool,X23009),X23008),X23007))
| hBOOL(hAPP(X23009,hAPP(hAPP(c_Product__Type_OPair(X23011,X23010),X23008),X23007))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryD])]) ).
fof(i_0_6942,plain,
! [X28386,X28387,X28388,X28389] : hAPP(c_Set_Ovimage(X28389,X28388,X28387),X28386) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28388,tc_fun(X28389,tc_HOL_Obool)),X28386),hAPP(hAPP(c_COMBB(tc_fun(X28388,tc_HOL_Obool),tc_fun(X28389,tc_HOL_Obool),X28388),c_Set_Ovimage(X28389,X28388,X28387)),hAPP(hAPP(c_COMBC(X28388,tc_fun(X28388,tc_HOL_Obool),tc_fun(X28388,tc_HOL_Obool)),c_Set_Oinsert(X28388)),c_Orderings_Obot__class_Obot(tc_fun(X28388,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_vimage__eq__UN]) ).
fof(i_0_6943,plain,
! [X26722,X26723,X26724,X26725] : hAPP(c_Relation_OImage(X26725,X26724,X26723),X26722) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26725,tc_fun(X26724,tc_HOL_Obool)),X26722),hAPP(hAPP(c_COMBB(tc_fun(X26725,tc_HOL_Obool),tc_fun(X26724,tc_HOL_Obool),X26725),c_Relation_OImage(X26725,X26724,X26723)),hAPP(hAPP(c_COMBC(X26725,tc_fun(X26725,tc_HOL_Obool),tc_fun(X26725,tc_HOL_Obool)),c_Set_Oinsert(X26725)),c_Orderings_Obot__class_Obot(tc_fun(X26725,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_Image__eq__UN]) ).
fof(i_0_6944,plain,
! [X27307,X27308,X27309,X27310] :
( ~ class_Lattices_Olattice(X27310)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27310),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27310),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27310),X27309),X27308)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27310),X27309),X27307))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27310),X27309),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27310),X27308),X27307)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__inf__le])]) ).
fof(i_0_6945,plain,
! [X22701,X22702,X22703,X22704] :
( ~ class_Orderings_Olinorder(X22704)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22704),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22704),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22704),X22703),X22702)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22704),X22703),X22701))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22704),X22703),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22704),X22702),X22701)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__inf__le])]) ).
fof(i_0_6946,plain,
! [X31978,X31979,X31980,X31981] :
( ( c_Map_Omap__of(X31981,X31980,X31979) != c_Map_Omap__of(X31981,X31980,X31978)
| hAPP(c_List_Oset(tc_prod(X31981,X31980)),X31979) = hAPP(c_List_Oset(tc_prod(X31981,X31980)),X31978)
| ~ hBOOL(hAPP(c_List_Odistinct(X31981),hAPP(hAPP(c_List_Omap(tc_prod(X31981,X31980),X31981),c_Product__Type_Ofst(X31981,X31980)),X31978)))
| ~ hBOOL(hAPP(c_List_Odistinct(X31981),hAPP(hAPP(c_List_Omap(tc_prod(X31981,X31980),X31981),c_Product__Type_Ofst(X31981,X31980)),X31979))) )
& ( hAPP(c_List_Oset(tc_prod(X31981,X31980)),X31979) != hAPP(c_List_Oset(tc_prod(X31981,X31980)),X31978)
| c_Map_Omap__of(X31981,X31980,X31979) = c_Map_Omap__of(X31981,X31980,X31978)
| ~ hBOOL(hAPP(c_List_Odistinct(X31981),hAPP(hAPP(c_List_Omap(tc_prod(X31981,X31980),X31981),c_Product__Type_Ofst(X31981,X31980)),X31978)))
| ~ hBOOL(hAPP(c_List_Odistinct(X31981),hAPP(hAPP(c_List_Omap(tc_prod(X31981,X31980),X31981),c_Product__Type_Ofst(X31981,X31980)),X31979))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__inject__set])])]) ).
fof(i_0_6947,plain,
! [X24933,X24934,X24935,X24936,X24937,X24938,X24939,X24940] :
( ~ hBOOL(hAPP(hAPP(c_member(X24940),X24939),X24938))
| ~ hBOOL(hAPP(hAPP(hAPP(X24937,X24939),X24936),X24935))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24940,tc_fun(X24934,tc_fun(X24933,tc_HOL_Obool))),X24938),X24937),X24936),X24935)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP2__I])]) ).
fof(i_0_6948,plain,
! [X22141,X22142,X22143,X22144,X22145,X22146,X22147] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22147,X22146,tc_fun(X22145,tc_HOL_Obool)),X22144),hAPP(hAPP(c_Product__Type_OPair(X22147,X22146),X22143),X22142)),X22141))
| hBOOL(hAPP(hAPP(hAPP(X22144,X22143),X22142),X22141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD_H])]) ).
fof(i_0_6949,plain,
! [X29515,X29516,X29517,X29518,X29519,X29520] : hAPP(hAPP(c_Relation_Orel__comp(X29520,X29519,X29518),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29520,X29519),tc_HOL_Obool)),X29517),X29516)),X29515) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29520,X29518),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29520,X29519,X29518),X29517),X29515)),hAPP(hAPP(c_Relation_Orel__comp(X29520,X29519,X29518),X29516),X29515)),
inference(variable_rename,[status(thm)],[fact_rel__comp__distrib2]) ).
fof(i_0_6950,plain,
! [X31194,X31195,X31196,X31197,X31198] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31198)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31197),X31196))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31198),X31195),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31197,X31198),X31196),X31194)) = hAPP(hAPP(c_Finite__Set_Ofold(X31197,X31198,hAPP(hAPP(c_COMBB(X31198,tc_fun(X31198,X31198),X31197),c_Lattices_Osemilattice__inf__class_Oinf(X31198)),X31194)),X31195),X31196) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf])]) ).
fof(i_0_6951,plain,
! [X30703,X30704,X30705,X30706,X30707] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X30707)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30706),X30705))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X30707),X30704),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30706,X30707),X30705),X30703)) = hAPP(hAPP(c_Finite__Set_Ofold(X30706,X30707,hAPP(hAPP(c_COMBB(X30707,tc_fun(X30707,X30707),X30706),c_Lattices_Osemilattice__sup__class_Osup(X30707)),X30703)),X30704),X30705) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup])]) ).
fof(i_0_6952,plain,
! [X26083,X26084,X26085,X26086,X26087,X26088,X26089] :
( X26089 = X26088
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26087,X26086),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26087,X26086),X26085),X26089),X26084)),X26088),X26083) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26087,X26086),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26087,X26086),X26085),X26088),X26083)),X26089),X26084) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__twist])]) ).
fof(i_0_6953,plain,
! [X27642,X27643,X27644,X27645] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27645),X27644))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27645),X27643))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27645,tc_Nat_Onat),X27642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27645,tc_HOL_Obool)),X27644),X27643)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27645,tc_Nat_Onat),X27642),X27644)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27645,tc_Nat_Onat),X27642),X27643))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27645,tc_Nat_Onat),X27642),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27645,tc_HOL_Obool)),X27644),X27643))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat])]) ).
fof(i_0_6954,plain,
! [X29236,X29237] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29237),hAPP(c_Set_OCollect(X29237),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29237),c_fNot),X29236))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29237),c_Orderings_Otop__class_Otop(tc_fun(X29237,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29237),hAPP(c_Set_OCollect(X29237),X29236))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29237),c_Orderings_Otop__class_Otop(tc_fun(X29237,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29237),hAPP(c_Set_OCollect(X29237),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29237),c_fNot),X29236))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29237),hAPP(c_Set_OCollect(X29237),X29236))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__not])])]) ).
fof(i_0_6955,plain,
! [X19752,X19753,X19754,X19755] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19754),X19753))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19753),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19754),X19755)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19754),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19752,X19755))),X19753))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1])]) ).
fof(i_0_6956,plain,
! [X20523,X20524,X20525,X20526,X20527] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20527),X20526))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20527),X20525)),X20524)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20526),X20525)),X20523)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20524),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20526),X20527)),X20525)),X20523)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).
fof(i_0_6957,plain,
! [X23287,X23288,X23289,X23290] :
( ~ class_Groups_Oordered__ab__group__add__abs(X23290)
| hAPP(c_Groups_Oabs__class_Oabs(X23290),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23289,X23290),hAPP(hAPP(c_COMBB(X23290,X23290,X23289),c_Groups_Oabs__class_Oabs(X23290)),X23288)),X23287)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23289,X23290),hAPP(hAPP(c_COMBB(X23290,X23290,X23289),c_Groups_Oabs__class_Oabs(X23290)),X23288)),X23287) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs])]) ).
fof(i_0_6958,plain,
! [X33168,X33169,X33170,X33171,X33172,X33173,X33174] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33174)),X33173)),X33172))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33172),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33171)),X33170)))
| c_Map_Omap__upds(X33174,X33171,X33169,X33173,hAPP(hAPP(c_List_Olist__update(X33171,X33170),X33172),X33168)) = c_Map_Omap__upds(X33174,X33171,X33169,X33173,X33170) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upds__list__update2__drop])]) ).
fof(i_0_6959,plain,
! [X28047,X28048,X28049,X28050,X28051] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28050,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28051,X28050,X28049),X28048)),hAPP(c_Set_Oimage(X28051,X28050,X28049),X28047)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28051,tc_HOL_Obool)),X28048),X28047))
| ~ c_Fun_Oinj__on(X28051,X28050,X28049,c_Orderings_Otop__class_Otop(tc_fun(X28051,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28051,tc_HOL_Obool)),X28048),X28047))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28050,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28051,X28050,X28049),X28048)),hAPP(c_Set_Oimage(X28051,X28050,X28049),X28047)))
| ~ c_Fun_Oinj__on(X28051,X28050,X28049,c_Orderings_Otop__class_Otop(tc_fun(X28051,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff])])]) ).
fof(i_0_6960,plain,
! [X21702,X21703,X21704] :
( ~ class_Fields_Olinordered__field(X21704)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21704),X21703),X21702))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21704),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21704),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21704),X21703),X21702)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21704),c_Groups_Oone__class_Oone(X21704)),c_Groups_Oone__class_Oone(X21704)))),X21702)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])]) ).
fof(i_0_6961,plain,
! [X19695,X19696,X19697] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19697),X19696)),X19695)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19697))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19696),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__neg__lemma])]) ).
fof(i_0_6962,plain,
! [X29157,X29158,X29159] :
( ( ~ hBOOL(hAPP(X29159,X29158))
| hAPP(c_Set_OCollect(X29157),hAPP(hAPP(c_COMBS(X29157,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29157),c_fconj),hAPP(c_fequal,X29158))),X29159)) = hAPP(hAPP(c_Set_Oinsert(X29157),X29158),c_Orderings_Obot__class_Obot(tc_fun(X29157,tc_HOL_Obool))) )
& ( hBOOL(hAPP(X29159,X29158))
| hAPP(c_Set_OCollect(X29157),hAPP(hAPP(c_COMBS(X29157,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29157),c_fconj),hAPP(c_fequal,X29158))),X29159)) = c_Orderings_Obot__class_Obot(tc_fun(X29157,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5461])]) ).
cnf(i_0_6963,plain,
hAPP(c_List_Orotate(X1,X2),X3) = hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),hAPP(hAPP(c_List_Otake(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),
inference(split_conjunct,[status(thm)],[i_0_5462]) ).
cnf(i_0_6964,plain,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5463]) ).
fof(i_0_6965,plain,
! [X32095,X32096,X32097,X32098] :
( ( hBOOL(hAPP(hAPP(c_member(X32098),X32097),hAPP(c_List_Oset(X32098),X32095)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32098,X32098)),hAPP(hAPP(c_Product__Type_OPair(X32098,X32098),X32097),X32096)),hAPP(c_List_Oset(tc_prod(X32098,X32098)),hAPP(hAPP(c_List_Ozip(X32098,X32098),X32095),X32095)))) )
& ( X32097 = X32096
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32098,X32098)),hAPP(hAPP(c_Product__Type_OPair(X32098,X32098),X32097),X32096)),hAPP(c_List_Oset(tc_prod(X32098,X32098)),hAPP(hAPP(c_List_Ozip(X32098,X32098),X32095),X32095)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X32098),X32097),hAPP(c_List_Oset(X32098),X32095)))
| X32097 != X32096
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32098,X32098)),hAPP(hAPP(c_Product__Type_OPair(X32098,X32098),X32097),X32096)),hAPP(c_List_Oset(tc_prod(X32098,X32098)),hAPP(hAPP(c_List_Ozip(X32098,X32098),X32095),X32095)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__same])])]) ).
fof(i_0_6966,plain,
! [X32077,X32078,X32079,X32080,X32081,X32082] :
( ( hBOOL(hAPP(hAPP(c_member(X32082),X32080),hAPP(c_List_Oset(X32082),X32078)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32082,X32081)),hAPP(hAPP(c_Product__Type_OPair(X32082,X32081),X32080),X32079)),hAPP(c_List_Oset(tc_prod(X32082,X32081)),hAPP(hAPP(c_List_Ozip(X32082,X32081),X32078),X32077)))) )
& ( hBOOL(hAPP(hAPP(c_member(X32081),X32079),hAPP(c_List_Oset(X32081),X32077)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32082,X32081)),hAPP(hAPP(c_Product__Type_OPair(X32082,X32081),X32080),X32079)),hAPP(c_List_Oset(tc_prod(X32082,X32081)),hAPP(hAPP(c_List_Ozip(X32082,X32081),X32078),X32077)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5464])])]) ).
fof(i_0_6967,plain,
! [X32089,X32090,X32091,X32092,X32093,X32094] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32094,X32093)),hAPP(hAPP(c_Product__Type_OPair(X32094,X32093),X32092),X32091)),hAPP(c_List_Oset(tc_prod(X32094,X32093)),hAPP(hAPP(c_List_Ozip(X32094,X32093),X32090),X32089))))
| hBOOL(hAPP(hAPP(c_member(X32094),X32092),hAPP(c_List_Oset(X32094),X32090))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__leftD])]) ).
fof(i_0_6968,plain,
! [X32083,X32084,X32085,X32086,X32087,X32088] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32088,X32087)),hAPP(hAPP(c_Product__Type_OPair(X32088,X32087),X32086),X32085)),hAPP(c_List_Oset(tc_prod(X32088,X32087)),hAPP(hAPP(c_List_Ozip(X32088,X32087),X32084),X32083))))
| hBOOL(hAPP(hAPP(c_member(X32087),X32085),hAPP(c_List_Oset(X32087),X32083))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__rightD])]) ).
fof(i_0_6969,plain,
! [X27548,X27549,X27550,X27551,X27552,X27553] :
( ~ c_Finite__Set_Ofolding(X27553,X27552,X27551,X27550)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27553),X27549))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27553),X27548))
| hAPP(c_Fun_Ocomp(X27552,X27552,X27552,hAPP(X27550,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27553,tc_HOL_Obool)),X27549),X27548))),hAPP(X27550,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27553,tc_HOL_Obool)),X27549),X27548))) = hAPP(c_Fun_Ocomp(X27552,X27552,X27552,hAPP(X27550,X27549)),hAPP(X27550,X27548)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion__inter])]) ).
fof(i_0_6970,plain,
! [X20686,X20687,X20688] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20688)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20688),hAPP(c_Groups_Oabs__class_Oabs(X20688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20688),hAPP(c_Groups_Oabs__class_Oabs(X20688),X20687)),hAPP(c_Groups_Oabs__class_Oabs(X20688),X20686)))),hAPP(c_Groups_Oabs__class_Oabs(X20688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20688),X20687),X20686)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])]) ).
fof(i_0_6971,plain,
! [X18626] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18626)),X18626)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18626),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18626),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18626)),X18626)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__less__0])]) ).
fof(i_0_6972,plain,
! [X31575,X31576,X31577,X31578,X31579,X31580] :
( hBOOL(hAPP(hAPP(c_member(X31580),X31579),c_Map_Odom(X31580,X31578,X31577)))
| c_Map_Omap__add(X31580,X31578,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31580,tc_Option_Ooption(X31578)),X31576),X31579),hAPP(c_Option_Ooption_OSome(X31578),X31575)),X31577) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31580,tc_Option_Ooption(X31578)),c_Map_Omap__add(X31580,X31578,X31576,X31577)),X31579),hAPP(c_Option_Ooption_OSome(X31578),X31575)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5465])]) ).
fof(i_0_6973,plain,
! [X30853,X30854,X30855,X30856] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X30856)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30855),X30854))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30855,X30856),X30854),X30853) = hAPP(hAPP(c_Finite__Set_Ofold(X30855,X30856,hAPP(hAPP(c_COMBB(X30856,tc_fun(X30856,X30856),X30855),c_Lattices_Osemilattice__inf__class_Oinf(X30856)),X30853)),c_Orderings_Otop__class_Otop(X30856)),X30854) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf])]) ).
fof(i_0_6974,plain,
! [X30758,X30759,X30760,X30761] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X30761)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30760),X30759))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30760,X30761),X30759),X30758) = hAPP(hAPP(c_Finite__Set_Ofold(X30760,X30761,hAPP(hAPP(c_COMBB(X30761,tc_fun(X30761,X30761),X30760),c_Lattices_Osemilattice__sup__class_Osup(X30761)),X30758)),c_Orderings_Obot__class_Obot(X30761)),X30759) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup])]) ).
fof(i_0_6975,plain,
! [X30316,X30317,X30318,X30319] :
( ( c_Wellfounded_Oacyclic(X30319,X30316)
| ~ c_Wellfounded_Oacyclic(X30319,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30319,X30319)),hAPP(hAPP(c_Product__Type_OPair(X30319,X30319),X30318),X30317)),X30316)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30319,X30319)),hAPP(hAPP(c_Product__Type_OPair(X30319,X30319),X30317),X30318)),c_Transitive__Closure_Ortrancl(X30319,X30316)))
| ~ c_Wellfounded_Oacyclic(X30319,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30319,X30319)),hAPP(hAPP(c_Product__Type_OPair(X30319,X30319),X30318),X30317)),X30316)) )
& ( ~ c_Wellfounded_Oacyclic(X30319,X30316)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30319,X30319)),hAPP(hAPP(c_Product__Type_OPair(X30319,X30319),X30317),X30318)),c_Transitive__Closure_Ortrancl(X30319,X30316)))
| c_Wellfounded_Oacyclic(X30319,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30319,X30319)),hAPP(hAPP(c_Product__Type_OPair(X30319,X30319),X30318),X30317)),X30316)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5466])])]) ).
fof(i_0_6976,plain,
! [X30312,X30313,X30314,X30315] :
( ( c_Wellfounded_Owf(X30315,X30312)
| ~ c_Wellfounded_Owf(X30315,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30315,X30315)),hAPP(hAPP(c_Product__Type_OPair(X30315,X30315),X30314),X30313)),X30312)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30315,X30315)),hAPP(hAPP(c_Product__Type_OPair(X30315,X30315),X30313),X30314)),c_Transitive__Closure_Ortrancl(X30315,X30312)))
| ~ c_Wellfounded_Owf(X30315,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30315,X30315)),hAPP(hAPP(c_Product__Type_OPair(X30315,X30315),X30314),X30313)),X30312)) )
& ( ~ c_Wellfounded_Owf(X30315,X30312)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30315,X30315)),hAPP(hAPP(c_Product__Type_OPair(X30315,X30315),X30313),X30314)),c_Transitive__Closure_Ortrancl(X30315,X30312)))
| c_Wellfounded_Owf(X30315,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30315,X30315)),hAPP(hAPP(c_Product__Type_OPair(X30315,X30315),X30314),X30313)),X30312)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5467])])]) ).
cnf(i_0_6977,plain,
c_Transitive__Closure_Otrancl(X1,X2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Otrancl(X1,X2)),X2)),
inference(split_conjunct,[status(thm)],[i_0_5468]) ).
fof(i_0_6978,plain,
! [X30601,X30602,X30603,X30604,X30605,X30606] :
( ~ c_Relation_Osingle__valued(X30606,X30605,X30604)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30606,X30605)),hAPP(hAPP(c_Product__Type_OPair(X30606,X30605),X30603),X30602)),X30604))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30606,X30605)),hAPP(hAPP(c_Product__Type_OPair(X30606,X30605),X30603),X30601)),X30604))
| X30602 = X30601 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])]) ).
fof(i_0_6979,plain,
! [X17678,X17679,X17680,X17681,X17682] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17682),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17681),c_Com_Ovname_OLoc(X17680)),hAPP(X17679,X17681))),X17678))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17680,X17679,X17682)),X17681),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17678),c_Com_Ovname_OLoc(X17680)),hAPP(hAPP(c_Natural_Ogetlocs,X17681),X17680)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OLocal])]) ).
fof(i_0_6980,plain,
! [X29194,X29195,X29196] : hAPP(c_Set_OCollect(X29196),hAPP(hAPP(c_COMBS(X29196,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29196),c_fdisj),X29195)),X29194)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29196,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29196),X29195)),hAPP(c_Set_OCollect(X29196),X29194)),
inference(variable_rename,[status(thm)],[fact_Collect__disj__eq]) ).
fof(i_0_6981,plain,
! [X29173,X29174,X29175] : hAPP(c_Set_OCollect(X29175),hAPP(hAPP(c_COMBS(X29175,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29175),c_fconj),X29174)),X29173)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29175,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29175),X29174)),hAPP(c_Set_OCollect(X29175),X29173)),
inference(variable_rename,[status(thm)],[fact_Collect__conj__eq]) ).
fof(i_0_6982,plain,
! [X31511,X31512,X31513,X31514,X31516,X31517,X31518,X31521] :
( ( hBOOL(hAPP(hAPP(c_member(X31512),esk419_3(X31511,X31512,X31513)),X31513))
| ~ hBOOL(hAPP(hAPP(c_member(X31512),X31514),X31513))
| ~ c_Wellfounded_Owf(X31512,X31511) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31512,X31512)),hAPP(hAPP(c_Product__Type_OPair(X31512,X31512),X31516),esk419_3(X31511,X31512,X31513))),X31511))
| ~ hBOOL(hAPP(hAPP(c_member(X31512),X31516),X31513))
| ~ hBOOL(hAPP(hAPP(c_member(X31512),X31514),X31513))
| ~ c_Wellfounded_Owf(X31512,X31511) )
& ( hBOOL(hAPP(hAPP(c_member(X31518),esk421_2(X31517,X31518)),esk420_2(X31517,X31518)))
| c_Wellfounded_Owf(X31518,X31517) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31518,X31518)),hAPP(hAPP(c_Product__Type_OPair(X31518,X31518),esk422_3(X31517,X31518,X31521)),X31521)),X31517))
| ~ hBOOL(hAPP(hAPP(c_member(X31518),X31521),esk420_2(X31517,X31518)))
| c_Wellfounded_Owf(X31518,X31517) )
& ( hBOOL(hAPP(hAPP(c_member(X31518),esk422_3(X31517,X31518,X31521)),esk420_2(X31517,X31518)))
| ~ hBOOL(hAPP(hAPP(c_member(X31518),X31521),esk420_2(X31517,X31518)))
| c_Wellfounded_Owf(X31518,X31517) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5469])])])])])]) ).
cnf(i_0_6983,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5470]) ).
cnf(i_0_6984,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5471]) ).
cnf(i_0_6985,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5472]) ).
cnf(i_0_6986,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5473]) ).
fof(i_0_6987,plain,
! [X26252,X26253,X26254,X26255,X26256] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X26256),X26255),X26254))
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26256,tc_Option_Ooption(X26253)),c_Map_Orestrict__map(X26256,X26253,X26252,X26254)),X26255),c_Option_Ooption_ONone(X26253)) = c_Map_Orestrict__map(X26256,X26253,X26252,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26256,tc_HOL_Obool)),X26254),hAPP(hAPP(c_Set_Oinsert(X26256),X26255),c_Orderings_Obot__class_Obot(tc_fun(X26256,tc_HOL_Obool))))) )
& ( hBOOL(hAPP(hAPP(c_member(X26256),X26255),X26254))
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26256,tc_Option_Ooption(X26253)),c_Map_Orestrict__map(X26256,X26253,X26252,X26254)),X26255),c_Option_Ooption_ONone(X26253)) = c_Map_Orestrict__map(X26256,X26253,X26252,X26254) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5474])]) ).
cnf(i_0_6988,plain,
c_Nitpick_Oint__lcm(X1,X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))),
inference(split_conjunct,[status(thm)],[i_0_5475]) ).
cnf(i_0_6989,plain,
c_Nitpick_Onat__lcm(X1,X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),c_Nitpick_Onat__gcd(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_5476]) ).
cnf(i_0_6990,plain,
c_List_Ofoldr(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),X6) = hAPP(hAPP(X3,X4),c_List_Ofoldr(X1,X2,X3,X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_5477]) ).
fof(i_0_6991,plain,
! [X32229,X32230,X32231,X32232,X32233,X32235] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32233),X32229),hAPP(c_List_Oset(X32233),X32232)))
| hAPP(c_Map_Omap__of(X32233,X32231,hAPP(hAPP(c_List_Ozip(X32233,X32231),X32232),X32230)),X32229) = hAPP(c_Option_Ooption_OSome(X32231),esk441_5(X32229,X32230,X32231,X32232,X32233))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32233)),X32232) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32231)),X32230) )
& ( hAPP(c_Map_Omap__of(X32233,X32231,hAPP(hAPP(c_List_Ozip(X32233,X32231),X32232),X32230)),X32229) != hAPP(c_Option_Ooption_OSome(X32231),X32235)
| hBOOL(hAPP(hAPP(c_member(X32233),X32229),hAPP(c_List_Oset(X32233),X32232)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32233)),X32232) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32231)),X32230) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__zip__is__Some])])])])]) ).
fof(i_0_6992,plain,
! [X30416,X30417,X30418,X30419] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30419,X30419)),hAPP(hAPP(c_Product__Type_OPair(X30419,X30419),X30418),X30417)),c_Transitive__Closure_Ortrancl(X30419,hAPP(c_Relation_Oconverse(X30419,X30419),X30416))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30419,X30419)),hAPP(hAPP(c_Product__Type_OPair(X30419,X30419),X30417),X30418)),c_Transitive__Closure_Ortrancl(X30419,X30416))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseD])]) ).
fof(i_0_6993,plain,
! [X29618,X29619,X29620,X29621] :
( ~ c_Wellfounded_Owf(X29621,X29620)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29621,X29621)),hAPP(hAPP(c_Product__Type_OPair(X29621,X29621),X29619),X29618)),X29620))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29621,X29621)),hAPP(hAPP(c_Product__Type_OPair(X29621,X29621),X29618),X29619)),X29620)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5478])]) ).
fof(i_0_6994,plain,
! [X29614,X29615,X29616,X29617] :
( ~ c_Wellfounded_Owf(X29617,X29616)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29617,X29617)),hAPP(hAPP(c_Product__Type_OPair(X29617,X29617),X29615),X29614)),X29616))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29617,X29617)),hAPP(hAPP(c_Product__Type_OPair(X29617,X29617),X29614),X29615)),X29616)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5479])]) ).
fof(i_0_6995,plain,
! [X32428,X32429,X32430,X32431,X32432] :
( ~ class_Rings_Osemiring__0(X32432)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32432),hAPP(hAPP(c_List_Omap(X32431,X32432),hAPP(hAPP(c_COMBB(X32432,X32432,X32431),hAPP(c_Groups_Otimes__class_Otimes(X32432),X32430)),X32429)),X32428)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32432),X32430),hAPP(c_List_Omonoid__add__class_Olistsum(X32432),hAPP(hAPP(c_List_Omap(X32431,X32432),X32429),X32428))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__const__mult])]) ).
fof(i_0_6996,plain,
! [X26693,X26694,X26695,X26696,X26697,X26698] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X26698,X26697),tc_HOL_Obool)),X26696),X26695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26698,tc_HOL_Obool)),X26694),X26693))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26697,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26698,X26697,X26696),X26694)),hAPP(c_Relation_OImage(X26698,X26697,X26695),X26693))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__mono])]) ).
fof(i_0_6997,plain,
! [X22526,X22527,X22528] :
( ( X22528 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( X22527 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| X22527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| X22527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22527),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| X22527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| X22527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( X22527 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| X22527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22527),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| X22527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527))
| X22527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22527),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527))
| X22527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( X22527 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22527),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22527),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22528 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22526)),X22527)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22526))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22528,X22527),X22526)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5480])])]) ).
fof(i_0_6998,plain,
! [X25604,X25605,X25606,X25607,X25608] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X25608,X25607)),hAPP(X25608,X25606)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25605,X25605)),hAPP(hAPP(c_Product__Type_OPair(X25605,X25605),X25607),X25606)),X25604))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X25605,X25605)),hAPP(hAPP(c_Product__Type_OPair(X25605,X25605),X25607),X25606)),c_Wellfounded_Omlex__prod(X25605,X25608,X25604))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
fof(i_0_6999,plain,
! [X21778,X21779,X21780,X21781] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),c_Groups_Ozero__class_Ozero(X21781)),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),X21780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21778),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)),c_Groups_Ozero__class_Ozero(X21781)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21778),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21780))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),c_Groups_Ozero__class_Ozero(X21781)),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)),c_Groups_Ozero__class_Ozero(X21781)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),c_Groups_Ozero__class_Ozero(X21781)),X21778))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),c_Groups_Ozero__class_Ozero(X21781)),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),c_Groups_Ozero__class_Ozero(X21781)),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),c_Groups_Ozero__class_Ozero(X21781)),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)),c_Groups_Ozero__class_Ozero(X21781)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)),c_Groups_Ozero__class_Ozero(X21781)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),c_Groups_Ozero__class_Ozero(X21781)),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),c_Groups_Ozero__class_Ozero(X21781)),X21778))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)),c_Groups_Ozero__class_Ozero(X21781)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),c_Groups_Ozero__class_Ozero(X21781)),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)),c_Groups_Ozero__class_Ozero(X21781)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21778),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21780))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),c_Groups_Ozero__class_Ozero(X21781)),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),c_Groups_Ozero__class_Ozero(X21781)),X21778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21778),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21780))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),c_Groups_Ozero__class_Ozero(X21781)),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),c_Groups_Ozero__class_Ozero(X21781)),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),X21780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21778),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)),c_Groups_Ozero__class_Ozero(X21781)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)),c_Groups_Ozero__class_Ozero(X21781)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),X21780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21778),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),c_Groups_Ozero__class_Ozero(X21781)),X21778))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)),c_Groups_Ozero__class_Ozero(X21781)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),X21780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21778),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779)),c_Groups_Ozero__class_Ozero(X21781)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21778),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21780))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),X21780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21778),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),c_Groups_Ozero__class_Ozero(X21781)),X21778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21778),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21780))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),X21780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21778),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21780),hAPP(c_Int_Onumber__class_Onumber__of(X21781),X21779))),X21778))
| ~ class_Fields_Olinordered__field__inverse__zero(X21781)
| ~ class_Int_Onumber(X21781) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5481])])]) ).
fof(i_0_7000,plain,
! [X21768,X21769,X21770,X21771] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),X21770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21771),X21768),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)),c_Groups_Ozero__class_Ozero(X21771)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21771),X21768),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21770))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)),c_Groups_Ozero__class_Ozero(X21771)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),X21768))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)),c_Groups_Ozero__class_Ozero(X21771)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)),c_Groups_Ozero__class_Ozero(X21771)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),X21768))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)),c_Groups_Ozero__class_Ozero(X21771)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)),c_Groups_Ozero__class_Ozero(X21771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21771),X21768),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21770))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),X21768))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21771),X21768),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21770))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),X21770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21771),X21768),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)),c_Groups_Ozero__class_Ozero(X21771)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)),c_Groups_Ozero__class_Ozero(X21771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),X21770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21771),X21768),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),X21768))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)),c_Groups_Ozero__class_Ozero(X21771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),X21770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21771),X21768),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769)),c_Groups_Ozero__class_Ozero(X21771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21771),X21768),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21770))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),X21770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21771),X21768),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),c_Groups_Ozero__class_Ozero(X21771)),X21768))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21771),X21768),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21770))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),X21770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21771),X21768),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21771),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21771),X21770),hAPP(c_Int_Onumber__class_Onumber__of(X21771),X21769))),X21768))
| ~ class_Fields_Olinordered__field__inverse__zero(X21771)
| ~ class_Int_Onumber(X21771) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5482])])]) ).
cnf(i_0_7001,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),c_Transitive__Closure_Otrancl(X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5450]) ).
fof(i_0_7002,plain,
! [X28697,X28698,X28699,X28700] : hAPP(c_Set_Oimage(tc_prod(X28700,X28699),tc_prod(X28699,X28700),hAPP(c_Product__Type_Oprod_Oprod__case(X28700,X28699,tc_prod(X28699,X28700)),hAPP(c_COMBC(X28699,X28700,tc_prod(X28699,X28700)),c_Product__Type_OPair(X28699,X28700)))),hAPP(hAPP(c_Product__Type_OSigma(X28700,X28699),X28698),hAPP(c_COMBK(tc_fun(X28699,tc_HOL_Obool),X28700),X28697))) = hAPP(hAPP(c_Product__Type_OSigma(X28699,X28700),X28697),hAPP(c_COMBK(tc_fun(X28700,tc_HOL_Obool),X28699),X28698)),
inference(variable_rename,[status(thm)],[fact_swap__product]) ).
cnf(i_0_7003,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X1)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),
inference(split_conjunct,[status(thm)],[i_0_5483]) ).
fof(i_0_7004,plain,
! [X26886,X26887,X26888,X26889] :
( ~ hBOOL(hAPP(hAPP(c_member(X26889),X26888),X26887))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26889,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26889,X26889,X26886),hAPP(hAPP(c_Set_Oinsert(X26889),X26888),c_Orderings_Obot__class_Obot(tc_fun(X26889,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26889),X26887),X26886))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotientI])]) ).
fof(i_0_7005,plain,
! [X17913,X17914,X17915,X17916,X17917,X17918] :
( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17918),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17917),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17916,X17917)),X17915,X17914)
| c_Natural_Oevaln(c_Com_Ocom_OCall(X17913,X17918,X17916),X17917,X17915,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17914),hAPP(c_Natural_Ogetlocs,X17917))),X17913),hAPP(hAPP(c_Natural_Ogetlocs,X17914),c_Com_ORes))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OCall])]) ).
fof(i_0_7006,plain,
! [X26726,X26727,X26728,X26729,X26730] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X26730),X26729),hAPP(c_Relation_OImage(X26728,X26730,X26727),hAPP(hAPP(c_Set_Oinsert(X26728),X26726),c_Orderings_Obot__class_Obot(tc_fun(X26728,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26728,X26730)),hAPP(hAPP(c_Product__Type_OPair(X26728,X26730),X26726),X26729)),X26727)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26728,X26730)),hAPP(hAPP(c_Product__Type_OPair(X26728,X26730),X26726),X26729)),X26727))
| hBOOL(hAPP(hAPP(c_member(X26730),X26729),hAPP(c_Relation_OImage(X26728,X26730,X26727),hAPP(hAPP(c_Set_Oinsert(X26728),X26726),c_Orderings_Obot__class_Obot(tc_fun(X26728,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff])]) ).
fof(i_0_7007,plain,
! [X22136,X22137,X22138] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk88_3(X22136,X22137,X22138)),esk89_3(X22136,X22137,X22138))))
| hBOOL(hAPP(hAPP(X22136,X22138),X22137))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22138),X22137))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk89_3(X22136,X22137,X22138)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X22136,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk88_3(X22136,X22137,X22138))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk89_3(X22136,X22137,X22138))))
| hBOOL(hAPP(hAPP(X22136,X22138),X22137))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22138),X22137))) )
& ( ~ hBOOL(hAPP(hAPP(X22136,esk88_3(X22136,X22137,X22138)),esk89_3(X22136,X22137,X22138)))
| hBOOL(hAPP(hAPP(X22136,X22138),X22137))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22138),X22137))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__frac_Opinduct])])])]) ).
fof(i_0_7008,plain,
! [X25521,X25522,X25523,X25524] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk180_4(X25521,X25522,X25523,X25524)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25523)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25524),X25522))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25524),X25523)),X25522))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25522),X25521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25523)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk181_4(X25521,X25522,X25523,X25524)),X25521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25524),X25522))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25524),X25523)),X25522))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25522),X25521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25523)) )
& ( X25524 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk181_4(X25521,X25522,X25523,X25524)),esk180_4(X25521,X25522,X25523,X25524))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25524),X25522))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25524),X25523)),X25522))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25522),X25521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25523)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I5_J])])])])]) ).
fof(i_0_7009,plain,
! [X20152,X20153,X20154,X20155] :
( ~ class_Divides_Osemiring__div(X20155)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20155),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20155),X20154),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20155),X20153),X20154))),c_Divides_Odiv__class_Omod(X20155,X20153,X20154))),X20152) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20155),X20153),X20152) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality2])]) ).
fof(i_0_7010,plain,
! [X33153,X33154,X33155,X33156,X33157,X33158,X33159] : c_Map_Omap__upds(X33159,X33158,X33157,hAPP(hAPP(c_List_Olist_OCons(X33159),X33156),X33155),hAPP(hAPP(c_List_Olist_OCons(X33158),X33154),X33153)) = c_Map_Omap__upds(X33159,X33158,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X33159,tc_Option_Ooption(X33158)),X33157),X33156),hAPP(c_Option_Ooption_OSome(X33158),X33154)),X33155,X33153),
inference(variable_rename,[status(thm)],[fact_map__upds__Cons]) ).
fof(i_0_7011,plain,
! [X33716,X33717,X33718,X33721,X33722,X33723,X33724,X33725] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33718),tc_List_Olist(X33718))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33718),tc_List_Olist(X33718)),c_List_Olist_ONil(X33718)),X33717)),c_List_Olexord(X33718,X33716)))
| X33717 = hAPP(hAPP(c_List_Olist_OCons(X33718),esk469_3(X33716,X33717,X33718)),esk470_3(X33716,X33717,X33718)) )
& ( X33722 != hAPP(hAPP(c_List_Olist_OCons(X33723),X33724),X33725)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33723),tc_List_Olist(X33723))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33723),tc_List_Olist(X33723)),c_List_Olist_ONil(X33723)),X33722)),c_List_Olexord(X33723,X33721))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__Nil__left])])])])]) ).
fof(i_0_7012,plain,
! [X28284,X28285,X28286,X28287] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28287,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28286,X28287,X28285),hAPP(c_Set_Ovimage(X28286,X28287,X28285),X28284))),X28284)),
inference(variable_rename,[status(thm)],[fact_image__vimage__subset]) ).
fof(i_0_7013,plain,
! [X34193,X34194,X34195,X34196,X34197] :
( ~ class_Orderings_Olinorder(X34197)
| ~ c_Fun_Oinj__on(X34196,X34197,X34195,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X34196,tc_HOL_Obool)),hAPP(c_List_Oset(X34196),X34194)),hAPP(c_List_Oset(X34196),X34193)))
| ~ c_List_Olinorder__class_Osorted(X34197,hAPP(hAPP(c_List_Omap(X34196,X34197),X34195),X34194))
| ~ hBOOL(hAPP(c_List_Odistinct(X34197),hAPP(hAPP(c_List_Omap(X34196,X34197),X34195),X34194)))
| ~ c_List_Olinorder__class_Osorted(X34197,hAPP(hAPP(c_List_Omap(X34196,X34197),X34195),X34193))
| ~ hBOOL(hAPP(c_List_Odistinct(X34197),hAPP(hAPP(c_List_Omap(X34196,X34197),X34195),X34193)))
| hAPP(c_List_Oset(X34196),X34194) != hAPP(c_List_Oset(X34196),X34193)
| X34194 = X34193 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__sorted__distinct__set__unique])]) ).
fof(i_0_7014,plain,
! [X18182,X18183,X18184,X18185,X18186] :
( ( hBOOL(hAPP(X18186,X18184))
| X18182 = X18184
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18186,X18185),X18184,X18183,X18182) )
& ( c_Natural_Oevaln(X18185,X18184,X18183,esk26_5(X18182,X18183,X18184,X18185,X18186))
| X18182 = X18184
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18186,X18185),X18184,X18183,X18182) )
& ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X18186,X18185),esk26_5(X18182,X18183,X18184,X18185,X18186),X18183,X18182)
| X18182 = X18184
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18186,X18185),X18184,X18183,X18182) )
& ( hBOOL(hAPP(X18186,X18184))
| ~ hBOOL(hAPP(X18186,X18184))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18186,X18185),X18184,X18183,X18182) )
& ( c_Natural_Oevaln(X18185,X18184,X18183,esk26_5(X18182,X18183,X18184,X18185,X18186))
| ~ hBOOL(hAPP(X18186,X18184))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18186,X18185),X18184,X18183,X18182) )
& ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X18186,X18185),esk26_5(X18182,X18183,X18184,X18185,X18186),X18183,X18182)
| ~ hBOOL(hAPP(X18186,X18184))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18186,X18185),X18184,X18183,X18182) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5484])])])]) ).
fof(i_0_7015,plain,
! [X17747,X17748,X17749,X17750,X17751,X17753,X17754,X17755,X17756,X17757,X17758] :
( ( hBOOL(hAPP(X17751,X17749))
| X17747 = X17749
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17751,X17750),X17749,X17748,X17747) )
& ( c_Natural_Oevaln(X17750,X17749,X17748,esk10_5(X17747,X17748,X17749,X17750,X17751))
| X17747 = X17749
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17751,X17750),X17749,X17748,X17747) )
& ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X17751,X17750),esk10_5(X17747,X17748,X17749,X17750,X17751),X17748,X17747)
| X17747 = X17749
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17751,X17750),X17749,X17748,X17747) )
& ( hBOOL(hAPP(X17751,X17749))
| ~ hBOOL(hAPP(X17751,X17749))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17751,X17750),X17749,X17748,X17747) )
& ( c_Natural_Oevaln(X17750,X17749,X17748,esk10_5(X17747,X17748,X17749,X17750,X17751))
| ~ hBOOL(hAPP(X17751,X17749))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17751,X17750),X17749,X17748,X17747) )
& ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X17751,X17750),esk10_5(X17747,X17748,X17749,X17750,X17751),X17748,X17747)
| ~ hBOOL(hAPP(X17751,X17749))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17751,X17750),X17749,X17748,X17747) )
& ( X17753 != X17755
| hBOOL(hAPP(X17757,X17755))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17757,X17756),X17755,X17754,X17753) )
& ( ~ hBOOL(hAPP(X17757,X17755))
| ~ c_Natural_Oevaln(X17756,X17755,X17754,X17758)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17757,X17756),X17758,X17754,X17753)
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17757,X17756),X17755,X17754,X17753) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5485])])])])])]) ).
fof(i_0_7016,plain,
! [X19744,X19745,X19746,X19747] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19747))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19746))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19746),X19745))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19745),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19744,X19747))),X19746))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3])]) ).
fof(i_0_7017,plain,
! [X28805,X28806,X28807] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28807),X28806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28807,X28807),tc_HOL_Obool)),X28805),hAPP(hAPP(c_Product__Type_OSigma(X28807,X28807),X28806),hAPP(c_COMBK(tc_fun(X28807,tc_HOL_Obool),X28807),X28806))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X28807,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X28807),X28806),X28805))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__quotient])]) ).
fof(i_0_7018,plain,
! [X33595,X33596,X33597,X33598,X33599,X33600] : hAPP(c_List_Ofoldl(X33600,X33599,X33598,X33597),hAPP(hAPP(c_List_Oappend(X33599),X33596),X33595)) = hAPP(c_List_Ofoldl(X33600,X33599,X33598,hAPP(c_List_Ofoldl(X33600,X33599,X33598,X33597),X33596)),X33595),
inference(variable_rename,[status(thm)],[fact_foldl__append]) ).
fof(i_0_7019,plain,
! [X30412,X30413,X30414,X30415] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30415,X30415)),hAPP(hAPP(c_Product__Type_OPair(X30415,X30415),X30414),X30413)),c_Transitive__Closure_Ortrancl(X30415,X30412)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30415,X30415)),hAPP(hAPP(c_Product__Type_OPair(X30415,X30415),X30413),X30414)),c_Transitive__Closure_Ortrancl(X30415,hAPP(c_Relation_Oconverse(X30415,X30415),X30412)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseI])]) ).
fof(i_0_7020,plain,
! [X33437,X33438,X33439,X33440,X33441] : hAPP(hAPP(c_List_Ozip(X33441,X33440),hAPP(hAPP(c_List_Oappend(X33441),X33439),X33438)),X33437) = hAPP(hAPP(c_List_Oappend(tc_prod(X33441,X33440)),hAPP(hAPP(c_List_Ozip(X33441,X33440),X33439),hAPP(hAPP(c_List_Otake(X33440),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33441)),X33439)),X33437))),hAPP(hAPP(c_List_Ozip(X33441,X33440),X33438),hAPP(hAPP(c_List_Odrop(X33440),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33441)),X33439)),X33437))),
inference(variable_rename,[status(thm)],[fact_zip__append1]) ).
fof(i_0_7021,plain,
! [X24073,X24074,X24075,X24076] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24076,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24076,tc_HOL_Obool)),X24075),X24074)),X24073))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24076,tc_HOL_Obool)),X24075),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24076,tc_HOL_Obool)),X24074),X24073))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24076,tc_HOL_Obool)),X24075),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24076,tc_HOL_Obool)),X24074),X24073)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24076,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24076,tc_HOL_Obool)),X24075),X24074)),X24073)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv])]) ).
fof(i_0_7022,plain,
! [X17668,X17669,X17670,X17671,X17672] :
( ( c_Natural_Oevaln(X17672,X17670,X17669,esk6_5(X17668,X17669,X17670,X17671,X17672))
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17672,X17671),X17670,X17669,X17668) )
& ( c_Natural_Oevaln(X17671,esk6_5(X17668,X17669,X17670,X17671,X17672),X17669,X17668)
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17672,X17671),X17670,X17669,X17668) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5486])])])]) ).
fof(i_0_7023,plain,
! [X17516,X17517,X17518,X17519,X17520,X17522,X17523,X17524,X17525,X17526,X17527] :
( ( c_Natural_Oevaln(X17520,X17518,X17517,esk4_5(X17516,X17517,X17518,X17519,X17520))
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17520,X17519),X17518,X17517,X17516) )
& ( c_Natural_Oevaln(X17519,esk4_5(X17516,X17517,X17518,X17519,X17520),X17517,X17516)
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17520,X17519),X17518,X17517,X17516) )
& ( ~ c_Natural_Oevaln(X17526,X17524,X17523,X17527)
| ~ c_Natural_Oevaln(X17525,X17527,X17523,X17522)
| c_Natural_Oevaln(c_Com_Ocom_OSemi(X17526,X17525),X17524,X17523,X17522) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I4_J])])])])])]) ).
cnf(i_0_7024,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
inference(split_conjunct,[status(thm)],[i_0_5487]) ).
fof(i_0_7025,plain,
! [X26898,X26899,X26900,X26901] :
( ( X26900 = hAPP(c_Relation_OImage(X26901,X26901,X26898),hAPP(hAPP(c_Set_Oinsert(X26901),esk242_4(X26898,X26899,X26900,X26901)),c_Orderings_Obot__class_Obot(tc_fun(X26901,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26901,tc_HOL_Obool)),X26900),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26901),X26899),X26898))) )
& ( hBOOL(hAPP(hAPP(c_member(X26901),esk242_4(X26898,X26899,X26900,X26901)),X26899))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26901,tc_HOL_Obool)),X26900),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26901),X26899),X26898))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5488])])])]) ).
cnf(i_0_7026,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| c_Divides_Odivmod__nat(X2,X1) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5489]) ).
cnf(i_0_7027,plain,
c_Divides_Odivmod__nat(X1,X2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_5490]) ).
cnf(i_0_7028,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_5491]) ).
fof(i_0_7029,plain,
! [X31645,X31646,X31647,X31648,X31649,X31650] : c_Map_Omap__add(X31650,X31649,X31648,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31650,tc_Option_Ooption(X31649)),X31647),X31646),hAPP(c_Option_Ooption_OSome(X31649),X31645))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31650,tc_Option_Ooption(X31649)),c_Map_Omap__add(X31650,X31649,X31648,X31647)),X31646),hAPP(c_Option_Ooption_OSome(X31649),X31645)),
inference(variable_rename,[status(thm)],[fact_map__add__upd]) ).
fof(i_0_7030,plain,
! [X23617,X23618,X23619,X23620] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk107_4(X23617,X23618,X23619,X23620)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23619)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23620),X23617))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23620),X23619)),X23617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23619)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk108_4(X23617,X23618,X23619,X23620)),X23618))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23620),X23617))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23620),X23619)),X23617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23619)) )
& ( X23620 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk108_4(X23617,X23618,X23619,X23620)),esk107_4(X23617,X23618,X23619,X23620))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23620),X23617))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23620),X23619)),X23617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23619)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I6_J])])])])]) ).
fof(i_0_7031,plain,
! [X23631,X23632,X23633,X23634] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk113_4(X23631,X23632,X23633,X23634)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23633)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23634),X23631))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23634),X23633)),X23631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23633)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk114_4(X23631,X23632,X23633,X23634)),X23632))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23634),X23631))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23634),X23633)),X23631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23633)) )
& ( X23634 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk114_4(X23631,X23632,X23633,X23634)),esk113_4(X23631,X23632,X23633,X23634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23634),X23631))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23634),X23633)),X23631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23633)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I5_J])])])])]) ).
fof(i_0_7032,plain,
! [X33410,X33411,X33412,X33413,X33414] :
( ( X33413 = hAPP(hAPP(c_List_Otake(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),X33411)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)))
| hAPP(hAPP(c_List_Oappend(X33414),X33413),X33412) != hAPP(hAPP(c_List_Oappend(X33414),X33411),X33410) )
& ( X33412 = hAPP(hAPP(c_List_Oappend(X33414),hAPP(hAPP(c_List_Odrop(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),X33411)),X33410)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)))
| hAPP(hAPP(c_List_Oappend(X33414),X33413),X33412) != hAPP(hAPP(c_List_Oappend(X33414),X33411),X33410) )
& ( hAPP(hAPP(c_List_Otake(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)),X33413) = X33411
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)))
| hAPP(hAPP(c_List_Oappend(X33414),X33413),X33412) != hAPP(hAPP(c_List_Oappend(X33414),X33411),X33410) )
& ( hAPP(hAPP(c_List_Oappend(X33414),hAPP(hAPP(c_List_Odrop(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)),X33413)),X33412) = X33410
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)))
| hAPP(hAPP(c_List_Oappend(X33414),X33413),X33412) != hAPP(hAPP(c_List_Oappend(X33414),X33411),X33410) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)))
| hAPP(hAPP(c_List_Oappend(X33414),X33413),X33412) = hAPP(hAPP(c_List_Oappend(X33414),X33411),X33410) )
& ( hAPP(hAPP(c_List_Otake(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)),X33413) != X33411
| hAPP(hAPP(c_List_Oappend(X33414),hAPP(hAPP(c_List_Odrop(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)),X33413)),X33412) != X33410
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)))
| hAPP(hAPP(c_List_Oappend(X33414),X33413),X33412) = hAPP(hAPP(c_List_Oappend(X33414),X33411),X33410) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)))
| X33413 != hAPP(hAPP(c_List_Otake(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),X33411)
| X33412 != hAPP(hAPP(c_List_Oappend(X33414),hAPP(hAPP(c_List_Odrop(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),X33411)),X33410)
| hAPP(hAPP(c_List_Oappend(X33414),X33413),X33412) = hAPP(hAPP(c_List_Oappend(X33414),X33411),X33410) )
& ( hAPP(hAPP(c_List_Otake(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)),X33413) != X33411
| hAPP(hAPP(c_List_Oappend(X33414),hAPP(hAPP(c_List_Odrop(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33411)),X33413)),X33412) != X33410
| X33413 != hAPP(hAPP(c_List_Otake(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),X33411)
| X33412 != hAPP(hAPP(c_List_Oappend(X33414),hAPP(hAPP(c_List_Odrop(X33414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33414)),X33413)),X33411)),X33410)
| hAPP(hAPP(c_List_Oappend(X33414),X33413),X33412) = hAPP(hAPP(c_List_Oappend(X33414),X33411),X33410) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5492])])]) ).
fof(i_0_7033,plain,
! [X27529,X27530,X27531,X27532,X27533] :
( ~ class_Groups_Ocomm__monoid__mult(X27533)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27532),X27531))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27532),X27530))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27533),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27532,X27533),X27529),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27532,tc_HOL_Obool)),X27531),X27530))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27532,X27533),X27529),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27532,tc_HOL_Obool)),X27531),X27530))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27533),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27532,X27533),X27529),X27531)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27532,X27533),X27529),X27530)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int])]) ).
fof(i_0_7034,plain,
! [X27524,X27525,X27526,X27527,X27528] :
( ~ class_Groups_Ocomm__monoid__mult(X27528)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27527),X27526))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27527),X27525))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27528),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27527,X27528),X27524),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27527,tc_HOL_Obool)),X27526),X27525))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27527,X27528),X27524),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27527,tc_HOL_Obool)),X27526),X27525))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27528),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27527,X27528),X27524),X27526)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27527,X27528),X27524),X27525)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter])]) ).
fof(i_0_7035,plain,
! [X27519,X27520,X27521,X27522,X27523] :
( ~ class_Groups_Ocomm__monoid__add(X27523)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27522),X27521))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27522),X27520))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27523),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27522,X27523),X27519),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27522,tc_HOL_Obool)),X27521),X27520))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27522,X27523),X27519),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27522,tc_HOL_Obool)),X27521),X27520))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27523),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27522,X27523),X27519),X27521)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27522,X27523),X27519),X27520)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int])]) ).
cnf(i_0_7036,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin)) ),
inference(split_conjunct,[status(thm)],[i_0_5493]) ).
cnf(i_0_7037,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_5494]) ).
cnf(i_0_7038,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_5495]) ).
cnf(i_0_7039,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin)) ),
inference(split_conjunct,[status(thm)],[i_0_5496]) ).
cnf(i_0_7040,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_5497]) ).
fof(i_0_7041,plain,
! [X27719,X27720,X27721,X27722,X27723,X27724] :
( ~ hBOOL(hAPP(hAPP(X27724,X27723),X27722))
| ~ hBOOL(hAPP(hAPP(X27721,X27723),X27722))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27720,tc_fun(X27719,tc_HOL_Obool))),X27724),X27721),X27723),X27722)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2I])]) ).
fof(i_0_7042,plain,
! [X28365,X28366,X28367,X28368,X28369] :
( hAPP(c_Set_Oimage(X28369,X28368,X28367),c_Orderings_Otop__class_Otop(tc_fun(X28369,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28368,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28369,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28369,X28368,X28367),X28366)),X28365))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28368,tc_HOL_Obool)),X28366),hAPP(c_Set_Oimage(X28369,X28368,X28367),X28365))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetD])]) ).
fof(i_0_7043,plain,
! [X25539,X25540,X25541,X25542] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk186_4(X25539,X25540,X25541,X25542)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25541)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25540),X25542))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25540),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25542),X25541)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25540),X25539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25541)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk187_4(X25539,X25540,X25541,X25542)),X25539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25540),X25542))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25540),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25542),X25541)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25540),X25539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25541)) )
& ( X25542 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk187_4(X25539,X25540,X25541,X25542)),esk186_4(X25539,X25540,X25541,X25542))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25540),X25542))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25540),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25542),X25541)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25540),X25539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25541)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I7_J])])])])]) ).
fof(i_0_7044,plain,
! [X19684,X19685,X19686,X19687,X19688,X19689] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19689),X19688)),X19687) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19686),X19685)),X19684)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19686),X19685)),X19684)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19684),X19686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19686),X19689))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19688),X19685)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).
fof(i_0_7045,plain,
! [X31102,X31103,X31104,X31105,X31106] : hAPP(c_Relation_Oconverse(X31106,X31105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31104,tc_fun(tc_prod(X31106,X31105),tc_HOL_Obool)),X31103),X31102)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31104,tc_fun(tc_prod(X31105,X31106),tc_HOL_Obool)),X31103),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X31106,X31105),tc_HOL_Obool),tc_fun(tc_prod(X31105,X31106),tc_HOL_Obool),X31104),c_Relation_Oconverse(X31106,X31105)),X31102)),
inference(variable_rename,[status(thm)],[fact_converse__INTER]) ).
fof(i_0_7046,plain,
! [X30391,X30392,X30393,X30394,X30395] : hAPP(c_Relation_Oconverse(X30395,X30394),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30393,tc_fun(tc_prod(X30395,X30394),tc_HOL_Obool)),X30392),X30391)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30393,tc_fun(tc_prod(X30394,X30395),tc_HOL_Obool)),X30392),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X30395,X30394),tc_HOL_Obool),tc_fun(tc_prod(X30394,X30395),tc_HOL_Obool),X30393),c_Relation_Oconverse(X30395,X30394)),X30391)),
inference(variable_rename,[status(thm)],[fact_converse__UNION]) ).
fof(i_0_7047,plain,
! [X26795] : X26795 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk238_1(X26795)),esk239_1(X26795))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Abs__Integ])])]) ).
fof(i_0_7048,plain,
! [X25050,X25051,X25052,X25053,X25054,X25056,X25057,X25058,X25059,X25060,X25061] :
( ( hBOOL(hAPP(hAPP(c_member(X25052),esk167_4(X25050,X25051,X25052,X25053)),X25050))
| ~ hBOOL(hAPP(hAPP(c_member(X25054),X25053),hAPP(c_Set_Oimage(X25052,X25054,X25051),X25050))) )
& ( X25053 = hAPP(X25051,esk167_4(X25050,X25051,X25052,X25053))
| ~ hBOOL(hAPP(hAPP(c_member(X25054),X25053),hAPP(c_Set_Oimage(X25052,X25054,X25051),X25050))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25058),X25060),X25056))
| X25059 != hAPP(X25057,X25060)
| hBOOL(hAPP(hAPP(c_member(X25061),X25059),hAPP(c_Set_Oimage(X25058,X25061,X25057),X25056))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__iff])])])])])]) ).
fof(i_0_7049,plain,
! [X26903,X26904,X26905,X26906,X26907] :
( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X26907),hAPP(hAPP(c_Set_Oinsert(X26907),X26904),c_Orderings_Obot__class_Obot(tc_fun(X26907,tc_HOL_Obool)))),X26905) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X26907),hAPP(hAPP(c_Set_Oinsert(X26907),X26903),c_Orderings_Obot__class_Obot(tc_fun(X26907,tc_HOL_Obool)))),X26905)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26907,X26907)),hAPP(hAPP(c_Product__Type_OPair(X26907,X26907),X26904),X26903)),X26905))
| ~ hBOOL(hAPP(hAPP(c_member(X26907),X26903),X26906))
| ~ hBOOL(hAPP(hAPP(c_member(X26907),X26904),X26906))
| ~ c_Equiv__Relations_Oequiv(X26907,X26906,X26905) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26907,X26907)),hAPP(hAPP(c_Product__Type_OPair(X26907,X26907),X26904),X26903)),X26905))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X26907),hAPP(hAPP(c_Set_Oinsert(X26907),X26904),c_Orderings_Obot__class_Obot(tc_fun(X26907,tc_HOL_Obool)))),X26905) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X26907),hAPP(hAPP(c_Set_Oinsert(X26907),X26903),c_Orderings_Obot__class_Obot(tc_fun(X26907,tc_HOL_Obool)))),X26905)
| ~ hBOOL(hAPP(hAPP(c_member(X26907),X26903),X26906))
| ~ hBOOL(hAPP(hAPP(c_member(X26907),X26904),X26906))
| ~ c_Equiv__Relations_Oequiv(X26907,X26906,X26905) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2])])]) ).
fof(i_0_7050,plain,
! [X26745,X26746,X26747,X26748,X26749,X26750,X26751] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X26751,X26750,X26749),hAPP(c_Fun_Ocomp(X26748,tc_fun(X26750,X26749),X26751,X26747),X26746)),X26745) = hAPP(hAPP(X26747,hAPP(X26746,hAPP(c_Product__Type_Ofst(X26751,X26750),X26745))),hAPP(c_Product__Type_Osnd(X26751,X26750),X26745)),
inference(variable_rename,[status(thm)],[fact_split__comp]) ).
cnf(i_0_7051,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X1))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5498]) ).
cnf(i_0_7052,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X1))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5499]) ).
fof(i_0_7053,plain,
! [X23696,X23697] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23697),X23696))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23697)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23696))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23697)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23696)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23697),X23696)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J])]) ).
fof(i_0_7054,plain,
! [X23694,X23695] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23695),X23694))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23695)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23694))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23695)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23694)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23695),X23694)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J])]) ).
fof(i_0_7055,plain,
! [X26389,X26390,X26391] :
( ~ class_Orderings_Olinorder(X26391)
| hAPP(X26390,hAPP(hAPP(c_Orderings_Oord__class_Omin(X26391),esk217_3(X26389,X26390,X26391)),esk218_3(X26389,X26390,X26391))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X26391),hAPP(X26390,esk217_3(X26389,X26390,X26391))),hAPP(X26390,esk218_3(X26389,X26390,X26391)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26391),X26389))
| X26389 = c_Orderings_Obot__class_Obot(tc_fun(X26391,tc_HOL_Obool))
| hAPP(X26390,c_Big__Operators_Olattice_OInf__fin(X26391,c_Orderings_Oord__class_Omin(X26391),X26389)) = c_Big__Operators_Olattice_OInf__fin(X26391,c_Orderings_Oord__class_Omin(X26391),hAPP(c_Set_Oimage(X26391,X26391,X26390),X26389)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute])])]) ).
fof(i_0_7056,plain,
! [X26329,X26330,X26331] :
( ~ class_Orderings_Olinorder(X26331)
| hAPP(X26330,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26331),esk215_3(X26329,X26330,X26331)),esk216_3(X26329,X26330,X26331))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X26331),hAPP(X26330,esk215_3(X26329,X26330,X26331))),hAPP(X26330,esk216_3(X26329,X26330,X26331)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26331),X26329))
| X26329 = c_Orderings_Obot__class_Obot(tc_fun(X26331,tc_HOL_Obool))
| hAPP(X26330,c_Big__Operators_Olattice_OSup__fin(X26331,c_Orderings_Oord__class_Omax(X26331),X26329)) = c_Big__Operators_Olattice_OSup__fin(X26331,c_Orderings_Oord__class_Omax(X26331),hAPP(c_Set_Oimage(X26331,X26331,X26330),X26329)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute])])]) ).
fof(i_0_7057,plain,
! [X28413,X28414,X28415,X28416,X28417] :
( ~ c_Fun_Oinj__on(X28417,X28416,X28415,c_Orderings_Otop__class_Otop(tc_fun(X28417,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28416,tc_HOL_Obool)),X28414),hAPP(c_Set_Oimage(X28417,X28416,X28415),X28413)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28417,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28417,X28416,X28415),X28414)),X28413)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetI])]) ).
cnf(i_0_7058,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5444]) ).
cnf(i_0_7059,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5445]) ).
cnf(i_0_7060,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5446]) ).
cnf(i_0_7061,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5447]) ).
fof(i_0_7062,plain,
! [X21790,X21791,X21792,X21793] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),c_Groups_Ozero__class_Ozero(X21793)),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))),X21791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)),c_Groups_Ozero__class_Ozero(X21793)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),c_Groups_Ozero__class_Ozero(X21793)),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)),c_Groups_Ozero__class_Ozero(X21793)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),c_Groups_Ozero__class_Ozero(X21793)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),c_Groups_Ozero__class_Ozero(X21793)),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),c_Groups_Ozero__class_Ozero(X21793)),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),c_Groups_Ozero__class_Ozero(X21793)),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)),c_Groups_Ozero__class_Ozero(X21793)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)),c_Groups_Ozero__class_Ozero(X21793)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),c_Groups_Ozero__class_Ozero(X21793)),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),c_Groups_Ozero__class_Ozero(X21793)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)),c_Groups_Ozero__class_Ozero(X21793)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),c_Groups_Ozero__class_Ozero(X21793)),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)),c_Groups_Ozero__class_Ozero(X21793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),c_Groups_Ozero__class_Ozero(X21793)),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),c_Groups_Ozero__class_Ozero(X21793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),c_Groups_Ozero__class_Ozero(X21793)),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),c_Groups_Ozero__class_Ozero(X21793)),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))),X21791))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)),c_Groups_Ozero__class_Ozero(X21793)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)),c_Groups_Ozero__class_Ozero(X21793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))),X21791))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),c_Groups_Ozero__class_Ozero(X21793)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)),c_Groups_Ozero__class_Ozero(X21793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))),X21791))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790)),c_Groups_Ozero__class_Ozero(X21793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))),X21791))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),c_Groups_Ozero__class_Ozero(X21793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))),X21791))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21791),hAPP(c_Int_Onumber__class_Onumber__of(X21793),X21790))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ class_Int_Onumber(X21793) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5500])])]) ).
fof(i_0_7063,plain,
! [X21756,X21757,X21758,X21759] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),c_Groups_Ozero__class_Ozero(X21759)),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21759),X21758),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))),X21757))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)),c_Groups_Ozero__class_Ozero(X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21759),X21758),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),c_Groups_Ozero__class_Ozero(X21759)),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)),c_Groups_Ozero__class_Ozero(X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),c_Groups_Ozero__class_Ozero(X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),c_Groups_Ozero__class_Ozero(X21759)),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),c_Groups_Ozero__class_Ozero(X21759)),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),c_Groups_Ozero__class_Ozero(X21759)),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)),c_Groups_Ozero__class_Ozero(X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)),c_Groups_Ozero__class_Ozero(X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),c_Groups_Ozero__class_Ozero(X21759)),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),c_Groups_Ozero__class_Ozero(X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)),c_Groups_Ozero__class_Ozero(X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),c_Groups_Ozero__class_Ozero(X21759)),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)),c_Groups_Ozero__class_Ozero(X21759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21759),X21758),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),c_Groups_Ozero__class_Ozero(X21759)),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),c_Groups_Ozero__class_Ozero(X21759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21759),X21758),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),c_Groups_Ozero__class_Ozero(X21759)),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),c_Groups_Ozero__class_Ozero(X21759)),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21759),X21758),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))),X21757))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)),c_Groups_Ozero__class_Ozero(X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)),c_Groups_Ozero__class_Ozero(X21759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21759),X21758),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))),X21757))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),c_Groups_Ozero__class_Ozero(X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)),c_Groups_Ozero__class_Ozero(X21759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21759),X21758),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))),X21757))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756)),c_Groups_Ozero__class_Ozero(X21759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21759),X21758),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21759),X21758),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))),X21757))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),c_Groups_Ozero__class_Ozero(X21759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21759),X21758),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21759),X21758),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))),X21757))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21759),X21758),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21759),X21757),hAPP(c_Int_Onumber__class_Onumber__of(X21759),X21756))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21759)
| ~ class_Int_Onumber(X21759) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5501])])]) ).
fof(i_0_7064,plain,
! [X30383,X30384,X30385,X30386,X30387] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30387,X30386)),hAPP(hAPP(c_Product__Type_OPair(X30387,X30386),X30385),X30384)),hAPP(c_Relation_Oconverse(X30386,X30387),X30383)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30386,X30387)),hAPP(hAPP(c_Product__Type_OPair(X30386,X30387),X30384),X30385)),X30383)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30386,X30387)),hAPP(hAPP(c_Product__Type_OPair(X30386,X30387),X30384),X30385)),X30383))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30387,X30386)),hAPP(hAPP(c_Product__Type_OPair(X30387,X30386),X30385),X30384)),hAPP(c_Relation_Oconverse(X30386,X30387),X30383))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__iff])]) ).
fof(i_0_7065,plain,
! [X30373,X30374,X30375,X30376,X30377] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30377,X30376)),hAPP(hAPP(c_Product__Type_OPair(X30377,X30376),X30375),X30374)),hAPP(c_Relation_Oconverse(X30376,X30377),X30373)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30376,X30377)),hAPP(hAPP(c_Product__Type_OPair(X30376,X30377),X30374),X30375)),X30373)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseD])]) ).
fof(i_0_7066,plain,
! [X25487,X25488,X25489,X25490,X25491,X25492] :
( ~ hBOOL(hAPP(hAPP(X25492,X25491),X25490))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25489,tc_fun(X25488,tc_HOL_Obool))),X25492),X25487),X25491),X25490)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I1])]) ).
fof(i_0_7067,plain,
! [X25446,X25447,X25448,X25449,X25450,X25451] :
( ( ~ hBOOL(hAPP(hAPP(X25451,X25450),X25449))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25447,tc_fun(X25446,tc_HOL_Obool))),X25448),X25451),X25450),X25449)) )
& ( ~ hBOOL(hAPP(hAPP(X25448,X25450),X25449))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25447,tc_fun(X25446,tc_HOL_Obool))),X25448),X25451),X25450),X25449)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5502])])]) ).
fof(i_0_7068,plain,
! [X25481,X25482,X25483,X25484,X25485,X25486] :
( ~ hBOOL(hAPP(hAPP(X25486,X25485),X25484))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25483,tc_fun(X25482,tc_HOL_Obool))),X25481),X25486),X25485),X25484)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I2])]) ).
fof(i_0_7069,plain,
! [X27042,X27043,X27044,X27045,X27046] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27046,tc_HOL_Obool)),X27045),X27044))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27046,tc_HOL_Obool)),X27043),X27042))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27046,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27046,tc_HOL_Obool)),X27045),X27043)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27046,tc_HOL_Obool)),X27044),X27042))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])]) ).
fof(i_0_7070,plain,
! [X24007,X24008,X24009,X24010,X24011] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24011,tc_HOL_Obool)),X24010),X24009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24011,tc_HOL_Obool)),X24008),X24007))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24011,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24011,tc_HOL_Obool)),X24010),X24008)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24011,tc_HOL_Obool)),X24009),X24007))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__mono])]) ).
fof(i_0_7071,plain,
! [X22426,X22427,X22428,X22429,X22430] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22430,tc_HOL_Obool)),X22429),X22428))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22430,tc_HOL_Obool)),X22427),X22426))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22430,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22430,tc_HOL_Obool)),X22429),X22426)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22430,tc_HOL_Obool)),X22428),X22427))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__mono])]) ).
fof(i_0_7072,plain,
! [X29093,X29094,X29095] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X29095)
| hAPP(X29094,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29095),esk302_3(X29093,X29094,X29095)),esk303_3(X29093,X29094,X29095))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29095),hAPP(X29094,esk302_3(X29093,X29094,X29095))),hAPP(X29094,esk303_3(X29093,X29094,X29095)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29095),X29093))
| X29093 = c_Orderings_Obot__class_Obot(tc_fun(X29095,tc_HOL_Obool))
| hAPP(X29094,hAPP(c_Finite__Set_Ofold1(X29095,c_Groups_Otimes__class_Otimes(X29095)),X29093)) = hAPP(c_Finite__Set_Ofold1(X29095,c_Groups_Otimes__class_Otimes(X29095)),hAPP(c_Set_Oimage(X29095,X29095,X29094),X29093)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute])])]) ).
fof(i_0_7073,plain,
! [X28124,X28125,X28126,X28127,X28128] :
( ~ class_Groups_Ocomm__monoid__mult(X28128)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28127),X28126))
| ~ c_Fun_Oinj__on(X28127,X28127,X28125,X28126)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28127,X28128),X28124),hAPP(c_Set_Oimage(X28127,X28127,X28125),X28126)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28127,X28128),hAPP(c_Fun_Ocomp(X28127,X28128,X28127,X28124),X28125)),X28126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oreindex])]) ).
fof(i_0_7074,plain,
! [X28113,X28114,X28115,X28116,X28117] :
( ~ class_Groups_Ocomm__monoid__add(X28117)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28116),X28115))
| ~ c_Fun_Oinj__on(X28116,X28116,X28114,X28115)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28116,X28117),X28113),hAPP(c_Set_Oimage(X28116,X28116,X28114),X28115)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28116,X28117),hAPP(c_Fun_Ocomp(X28116,X28117,X28116,X28113),X28114)),X28115) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oreindex])]) ).
fof(i_0_7075,plain,
! [X30048,X30049,X30050] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30050,X30050)),hAPP(hAPP(c_Product__Type_OPair(X30050,X30050),esk354_3(X30048,X30049,X30050)),X30049)),X30048))
| hBOOL(hAPP(hAPP(c_member(X30050),X30049),c_Wellfounded_Oacc(X30050,X30048))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X30050),esk354_3(X30048,X30049,X30050)),c_Wellfounded_Oacc(X30050,X30048)))
| hBOOL(hAPP(hAPP(c_member(X30050),X30049),c_Wellfounded_Oacc(X30050,X30048))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_OaccI])])])]) ).
fof(i_0_7076,plain,
! [X30044,X30045,X30046] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30046,X30046)),hAPP(hAPP(c_Product__Type_OPair(X30046,X30046),esk353_3(X30044,X30045,X30046)),X30045)),X30044))
| hBOOL(hAPP(hAPP(c_member(X30046),X30045),c_Wellfounded_Oacc(X30046,X30044))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X30046),esk353_3(X30044,X30045,X30046)),c_Wellfounded_Oacc(X30046,X30044)))
| hBOOL(hAPP(hAPP(c_member(X30046),X30045),c_Wellfounded_Oacc(X30046,X30044))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5503])])])]) ).
fof(i_0_7077,plain,
! [X28547,X28548,X28549,X28550,X28551,X28552,X28553] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28549),X28548),c_Wellfounded_Oacc(X28549,X28547)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28549,X28549)),hAPP(hAPP(c_Product__Type_OPair(X28549,X28549),X28550),X28548)),X28547))
| hBOOL(hAPP(hAPP(c_member(X28549),X28550),c_Wellfounded_Oacc(X28549,X28547))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28553,X28553)),hAPP(hAPP(c_Product__Type_OPair(X28553,X28553),esk275_3(X28551,X28552,X28553)),X28552)),X28551))
| hBOOL(hAPP(hAPP(c_member(X28553),X28552),c_Wellfounded_Oacc(X28553,X28551))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28553),esk275_3(X28551,X28552,X28553)),c_Wellfounded_Oacc(X28553,X28551)))
| hBOOL(hAPP(hAPP(c_member(X28553),X28552),c_Wellfounded_Oacc(X28553,X28551))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_Osimps])])])])])]) ).
fof(i_0_7078,plain,
! [X33236,X33237,X33238,X33239] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33239),tc_List_Olist(X33239))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33239),tc_List_Olist(X33239)),X33238),X33237)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33239),c_List_Olistrel1(X33239,X33236))))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33239)),X33238) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33239)),X33237) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len])]) ).
fof(i_0_7079,plain,
! [X32793,X32794,X32795,X32796,X32797] : hAPP(hAPP(c_List_Olist__update(X32797,hAPP(hAPP(c_List_Olist_OCons(X32797),X32796),X32795)),X32794),X32793) = c_Nat_Onat_Onat__case(tc_List_Olist(X32797),hAPP(hAPP(c_List_Olist_OCons(X32797),X32793),X32795),hAPP(hAPP(c_COMBB(tc_List_Olist(X32797),tc_List_Olist(X32797),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X32797),X32796)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X32797,tc_List_Olist(X32797)),c_List_Olist__update(X32797,X32795)),X32793)),X32794),
inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I2_J]) ).
fof(i_0_7080,plain,
! [X22108,X22109,X22110,X22111] : hAPP(c_Product__Type_Oprod_Oprod__case(X22111,X22110,X22109),hAPP(hAPP(c_COMBB(tc_fun(X22110,tc_prod(X22111,X22110)),tc_fun(X22110,X22109),X22111),hAPP(c_COMBB(tc_prod(X22111,X22110),X22109,X22110),X22108)),c_Product__Type_OPair(X22111,X22110))) = X22108,
inference(variable_rename,[status(thm)],[fact_split__eta]) ).
fof(i_0_7081,plain,
! [X23611,X23612,X23613,X23614] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk105_4(X23611,X23612,X23613,X23614)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23613)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23611),X23614))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23611),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23614),X23613)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23613)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk106_4(X23611,X23612,X23613,X23614)),X23612))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23611),X23614))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23611),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23614),X23613)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23613)) )
& ( X23614 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk106_4(X23611,X23612,X23613,X23614)),esk105_4(X23611,X23612,X23613,X23614))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23611),X23614))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23611),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23614),X23613)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23613)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I8_J])])])])]) ).
fof(i_0_7082,plain,
! [X23639,X23640,X23641,X23642] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk115_4(X23639,X23640,X23641,X23642)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23641)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23639),X23642))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23639),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23642),X23641)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23641)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk116_4(X23639,X23640,X23641,X23642)),X23640))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23639),X23642))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23639),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23642),X23641)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23641)) )
& ( X23642 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk116_4(X23639,X23640,X23641,X23642)),esk115_4(X23639,X23640,X23641,X23642))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23639),X23642))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23639),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23642),X23641)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23641)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I7_J])])])])]) ).
fof(i_0_7083,plain,
! [X25601,X25602,X25603] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25603,tc_HOL_Obool)),X25602),hAPP(hAPP(c_Set_Oinsert(X25603),X25601),c_Orderings_Obot__class_Obot(tc_fun(X25603,tc_HOL_Obool)))))
| c_Partial__Function_Oflat__lub(X25603,X25601,X25602) = X25601 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25603,tc_HOL_Obool)),X25602),hAPP(hAPP(c_Set_Oinsert(X25603),X25601),c_Orderings_Obot__class_Obot(tc_fun(X25603,tc_HOL_Obool)))))
| c_Partial__Function_Oflat__lub(X25603,X25601,X25602) = c_HOL_OThe(X25603,hAPP(hAPP(c_COMBC(X25603,tc_fun(X25603,tc_HOL_Obool),tc_HOL_Obool),c_member(X25603)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25603,tc_HOL_Obool)),X25602),hAPP(hAPP(c_Set_Oinsert(X25603),X25601),c_Orderings_Obot__class_Obot(tc_fun(X25603,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5504])]) ).
fof(i_0_7084,plain,
! [X33796,X33797,X33798,X33799] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk478_4(X33796,X33797,X33798,X33799)),X33799))
| hAPP(hAPP(c_List_Otake(X33798),X33799),X33797) = hAPP(hAPP(c_List_Otake(X33798),X33799),X33796)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33799),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33798)),X33796)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33799),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33798)),X33797))) )
& ( hAPP(hAPP(c_List_Onth(X33798),X33797),esk478_4(X33796,X33797,X33798,X33799)) != hAPP(hAPP(c_List_Onth(X33798),X33796),esk478_4(X33796,X33797,X33798,X33799))
| hAPP(hAPP(c_List_Otake(X33798),X33799),X33797) = hAPP(hAPP(c_List_Otake(X33798),X33799),X33796)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33799),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33798)),X33796)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33799),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33798)),X33797))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take__lemma])])])]) ).
fof(i_0_7085,plain,
! [X30496,X30497,X30498,X30499] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30499,X30499)),hAPP(hAPP(c_Product__Type_OPair(X30499,X30499),X30498),X30497)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30499,X30499),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30496)))
| X30498 = X30497 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__0__E])]) ).
fof(i_0_7086,plain,
! [X22494,X22495,X22496,X22497,X22498] :
( ~ hBOOL(hAPP(hAPP(X22498,X22497),X22496))
| hBOOL(hAPP(hAPP(X22498,hAPP(c_Product__Type_Osnd(X22495,X22494),hAPP(hAPP(c_Product__Type_OPair(X22495,X22494),X22496),X22497))),hAPP(c_Product__Type_Ofst(X22495,X22494),hAPP(hAPP(c_Product__Type_OPair(X22495,X22494),X22496),X22497)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exI__realizer])]) ).
fof(i_0_7087,plain,
! [X27911,X27912,X27913,X27914,X27915,X27916] :
( ( ~ c_Fun_Oinj__on(X27915,X27912,X27911,hAPP(c_Set_Oimage(X27916,X27915,X27914),X27913))
| c_Fun_Oinj__on(X27916,X27912,hAPP(c_Fun_Ocomp(X27915,X27912,X27916,X27911),X27914),X27913)
| ~ c_Fun_Oinj__on(X27916,X27915,X27914,X27913) )
& ( ~ c_Fun_Oinj__on(X27916,X27912,hAPP(c_Fun_Ocomp(X27915,X27912,X27916,X27911),X27914),X27913)
| c_Fun_Oinj__on(X27915,X27912,X27911,hAPP(c_Set_Oimage(X27916,X27915,X27914),X27913))
| ~ c_Fun_Oinj__on(X27916,X27915,X27914,X27913) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on__iff])])]) ).
fof(i_0_7088,plain,
! [X26688,X26689,X26690,X26691,X26692] :
( hAPP(c_Set_Oimage(X26692,X26691,X26690),c_Orderings_Otop__class_Otop(tc_fun(X26692,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26691,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X26691,X26689,X26688),c_Orderings_Otop__class_Otop(tc_fun(X26691,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26689,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X26692,X26689,hAPP(c_Fun_Ocomp(X26691,X26689,X26692,X26688),X26690)),c_Orderings_Otop__class_Otop(tc_fun(X26692,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X26689,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__surj])]) ).
fof(i_0_7089,plain,
! [X20123,X20124,X20125] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20125),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20124),X20125))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20124,X20125))),X20123) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20124),X20123),
inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality]) ).
fof(i_0_7090,plain,
! [X28106,X28107,X28108,X28109,X28110,X28111] :
( ~ class_Groups_Ocomm__monoid__mult(X28111)
| ~ c_Fun_Oinj__on(X28110,X28109,X28108,X28107)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28109,X28111),X28106),hAPP(c_Set_Oimage(X28110,X28109,X28108),X28107)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28110,X28111),hAPP(c_Fun_Ocomp(X28109,X28111,X28110,X28106),X28108)),X28107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex])]) ).
fof(i_0_7091,plain,
! [X28082,X28083,X28084,X28085,X28086,X28087] :
( ~ class_Groups_Ocomm__monoid__add(X28087)
| ~ c_Fun_Oinj__on(X28086,X28085,X28084,X28083)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28085,X28087),X28082),hAPP(c_Set_Oimage(X28086,X28085,X28084),X28083)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28086,X28087),hAPP(c_Fun_Ocomp(X28085,X28087,X28086,X28082),X28084)),X28083) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex])]) ).
fof(i_0_7092,plain,
! [X27629,X27630,X27631] :
( ~ class_Orderings_Olinorder(X27631)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27631),X27630))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27631),X27629))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27631,tc_HOL_Obool)),X27630),X27629) = c_Orderings_Obot__class_Obot(tc_fun(X27631,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X27631),c_Big__Operators_Olattice_OSup__fin(X27631,c_Orderings_Oord__class_Omax(X27631),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27631,tc_HOL_Obool)),X27630),X27629))),c_Big__Operators_Olattice_OSup__fin(X27631,c_Orderings_Oord__class_Omax(X27631),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27631,tc_HOL_Obool)),X27630),X27629))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27631),c_Big__Operators_Olattice_OSup__fin(X27631,c_Orderings_Oord__class_Omax(X27631),X27630)),c_Big__Operators_Olattice_OSup__fin(X27631,c_Orderings_Oord__class_Omax(X27631),X27629)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter])]) ).
fof(i_0_7093,plain,
! [X27620,X27621,X27622] :
( ~ class_Orderings_Olinorder(X27622)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27622),X27621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27622),X27620))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27622,tc_HOL_Obool)),X27621),X27620) = c_Orderings_Obot__class_Obot(tc_fun(X27622,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X27622),c_Big__Operators_Olattice_OInf__fin(X27622,c_Orderings_Oord__class_Omin(X27622),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27622,tc_HOL_Obool)),X27621),X27620))),c_Big__Operators_Olattice_OInf__fin(X27622,c_Orderings_Oord__class_Omin(X27622),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27622,tc_HOL_Obool)),X27621),X27620))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27622),c_Big__Operators_Olattice_OInf__fin(X27622,c_Orderings_Oord__class_Omin(X27622),X27621)),c_Big__Operators_Olattice_OInf__fin(X27622,c_Orderings_Oord__class_Omin(X27622),X27620)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter])]) ).
fof(i_0_7094,plain,
! [X32158,X32159,X32160,X32161,X32162] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32162)),X32161) = X32158
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32162),tc_List_Olist(X32162))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32162),tc_List_Olist(X32162)),X32161),X32160)),hAPP(c_List_Olexn(X32162,X32159),X32158))) )
& ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32162)),X32160) = X32158
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32162),tc_List_Olist(X32162))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32162),tc_List_Olist(X32162)),X32161),X32160)),hAPP(c_List_Olexn(X32162,X32159),X32158))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexn__length])])]) ).
fof(i_0_7095,plain,
! [X30378,X30379,X30380,X30381,X30382] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30382,X30381)),hAPP(hAPP(c_Product__Type_OPair(X30382,X30381),X30380),X30379)),X30378))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30381,X30382)),hAPP(hAPP(c_Product__Type_OPair(X30381,X30382),X30379),X30380)),hAPP(c_Relation_Oconverse(X30382,X30381),X30378))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseI])]) ).
fof(i_0_7096,plain,
! [X18177,X18178,X18179,X18180] :
( ( hBOOL(hAPP(X18180,X18178))
| X18177 = X18178
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18180,X18179)),X18178),X18177)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X18179),X18178),esk25_4(X18177,X18178,X18179,X18180)))
| X18177 = X18178
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18180,X18179)),X18178),X18177)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18180,X18179)),esk25_4(X18177,X18178,X18179,X18180)),X18177))
| X18177 = X18178
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18180,X18179)),X18178),X18177)) )
& ( hBOOL(hAPP(X18180,X18178))
| ~ hBOOL(hAPP(X18180,X18178))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18180,X18179)),X18178),X18177)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X18179),X18178),esk25_4(X18177,X18178,X18179,X18180)))
| ~ hBOOL(hAPP(X18180,X18178))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18180,X18179)),X18178),X18177)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18180,X18179)),esk25_4(X18177,X18178,X18179,X18180)),X18177))
| ~ hBOOL(hAPP(X18180,X18178))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18180,X18179)),X18178),X18177)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5505])])])]) ).
fof(i_0_7097,plain,
! [X17769,X17770,X17771,X17772,X17774,X17775,X17776,X17777,X17778] :
( ( hBOOL(hAPP(X17772,X17770))
| X17769 = X17770
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17772,X17771)),X17770),X17769)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17771),X17770),esk12_4(X17769,X17770,X17771,X17772)))
| X17769 = X17770
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17772,X17771)),X17770),X17769)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17772,X17771)),esk12_4(X17769,X17770,X17771,X17772)),X17769))
| X17769 = X17770
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17772,X17771)),X17770),X17769)) )
& ( hBOOL(hAPP(X17772,X17770))
| ~ hBOOL(hAPP(X17772,X17770))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17772,X17771)),X17770),X17769)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17771),X17770),esk12_4(X17769,X17770,X17771,X17772)))
| ~ hBOOL(hAPP(X17772,X17770))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17772,X17771)),X17770),X17769)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17772,X17771)),esk12_4(X17769,X17770,X17771,X17772)),X17769))
| ~ hBOOL(hAPP(X17772,X17770))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17772,X17771)),X17770),X17769)) )
& ( X17774 != X17775
| hBOOL(hAPP(X17777,X17775))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17777,X17776)),X17775),X17774)) )
& ( ~ hBOOL(hAPP(X17777,X17775))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17776),X17775),X17778))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17777,X17776)),X17778),X17774))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17777,X17776)),X17775),X17774)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5506])])])])])]) ).
fof(i_0_7098,plain,
! [X29509,X29510,X29511,X29512,X29513,X29514] : hAPP(hAPP(c_Relation_Orel__comp(X29514,X29513,X29512),X29511),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29513,X29512),tc_HOL_Obool)),X29510),X29509)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29514,X29512),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29514,X29513,X29512),X29511),X29510)),hAPP(hAPP(c_Relation_Orel__comp(X29514,X29513,X29512),X29511),X29509)),
inference(variable_rename,[status(thm)],[fact_rel__comp__distrib]) ).
cnf(i_0_7099,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5507]) ).
fof(i_0_7100,plain,
! [X25018,X25019,X25020,X25021] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X25021,tc_fun(X25020,tc_HOL_Obool))),X25019),X25018))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X25021,X25020)),hAPP(hAPP(c_Product__Type_OPair(X25021,X25020),X25019),X25018)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X25021,X25020),tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25021,X25020)),hAPP(hAPP(c_Product__Type_OPair(X25021,X25020),X25019),X25018)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X25021,X25020),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X25021,tc_fun(X25020,tc_HOL_Obool))),X25019),X25018)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2])]) ).
fof(i_0_7101,plain,
! [X34373,X34374] :
( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34374),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34374))),X34373)))
| c_List_Otranspose(X34374,c_List_Otranspose(X34374,X34373)) = c_List_OtakeWhile(tc_List_Olist(X34374),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X34374)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X34374),tc_List_Olist(X34374),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X34374))),X34373) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__transpose])]) ).
fof(i_0_7102,plain,
! [X27874,X27875,X27876] :
( ~ class_Lattices_Olattice(X27876)
| hAPP(X27875,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27876),esk261_3(X27874,X27875,X27876)),esk262_3(X27874,X27875,X27876))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27876),hAPP(X27875,esk261_3(X27874,X27875,X27876))),hAPP(X27875,esk262_3(X27874,X27875,X27876)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27876),X27874))
| X27874 = c_Orderings_Obot__class_Obot(tc_fun(X27876,tc_HOL_Obool))
| hAPP(X27875,c_Big__Operators_Olattice__class_OInf__fin(X27876,X27874)) = c_Big__Operators_Olattice__class_OInf__fin(X27876,hAPP(c_Set_Oimage(X27876,X27876,X27875),X27874)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute])])]) ).
fof(i_0_7103,plain,
! [X26407,X26408,X26409] :
( ~ class_Orderings_Olinorder(X26409)
| hAPP(X26408,hAPP(hAPP(c_Orderings_Oord__class_Omin(X26409),esk221_3(X26407,X26408,X26409)),esk222_3(X26407,X26408,X26409))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X26409),hAPP(X26408,esk221_3(X26407,X26408,X26409))),hAPP(X26408,esk222_3(X26407,X26408,X26409)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26409),X26407))
| X26407 = c_Orderings_Obot__class_Obot(tc_fun(X26409,tc_HOL_Obool))
| hAPP(X26408,c_Big__Operators_Olinorder__class_OMin(X26409,X26407)) = c_Big__Operators_Olinorder__class_OMin(X26409,hAPP(c_Set_Oimage(X26409,X26409,X26408),X26407)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute])])]) ).
fof(i_0_7104,plain,
! [X26402,X26403,X26404] :
( ~ class_Orderings_Olinorder(X26404)
| hAPP(X26403,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26404),esk219_3(X26402,X26403,X26404)),esk220_3(X26402,X26403,X26404))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X26404),hAPP(X26403,esk219_3(X26402,X26403,X26404))),hAPP(X26403,esk220_3(X26402,X26403,X26404)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26404),X26402))
| X26402 = c_Orderings_Obot__class_Obot(tc_fun(X26404,tc_HOL_Obool))
| hAPP(X26403,c_Big__Operators_Olinorder__class_OMax(X26404,X26402)) = c_Big__Operators_Olinorder__class_OMax(X26404,hAPP(c_Set_Oimage(X26404,X26404,X26403),X26402)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute])])]) ).
fof(i_0_7105,plain,
! [X26449,X26450,X26451] :
( ~ class_Lattices_Olattice(X26451)
| hAPP(X26450,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26451),esk225_3(X26449,X26450,X26451)),esk226_3(X26449,X26450,X26451))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26451),hAPP(X26450,esk225_3(X26449,X26450,X26451))),hAPP(X26450,esk226_3(X26449,X26450,X26451)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26451),X26449))
| X26449 = c_Orderings_Obot__class_Obot(tc_fun(X26451,tc_HOL_Obool))
| hAPP(X26450,c_Big__Operators_Olattice__class_OSup__fin(X26451,X26449)) = c_Big__Operators_Olattice__class_OSup__fin(X26451,hAPP(c_Set_Oimage(X26451,X26451,X26450),X26449)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute])])]) ).
fof(i_0_7106,plain,
! [X23623,X23624,X23627,X23629] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk111_2(X23623,X23624)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23624)))
| ~ hBOOL(hAPP(X23623,X23627))
| ~ hBOOL(hAPP(X23623,esk109_2(X23623,X23624)))
| ~ hBOOL(hAPP(X23623,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X23623,X23624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X23623,X23624)),X23624))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23624)) )
& ( hBOOL(hAPP(X23623,esk111_2(X23623,X23624)))
| ~ hBOOL(hAPP(X23623,X23627))
| ~ hBOOL(hAPP(X23623,esk109_2(X23623,X23624)))
| ~ hBOOL(hAPP(X23623,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X23623,X23624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X23623,X23624)),X23624))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23624)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X23629),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23624)))
| ~ hBOOL(hAPP(X23623,X23629))
| hBOOL(hAPP(X23623,esk112_2(X23623,X23624)))
| ~ hBOOL(hAPP(X23623,esk109_2(X23623,X23624)))
| ~ hBOOL(hAPP(X23623,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X23623,X23624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X23623,X23624)),X23624))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23624)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk111_2(X23623,X23624)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23624)))
| ~ hBOOL(hAPP(X23623,X23627))
| hBOOL(hAPP(X23623,esk109_2(X23623,X23624)))
| hBOOL(hAPP(X23623,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X23623,X23624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X23623,X23624)),X23624))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23624)) )
& ( hBOOL(hAPP(X23623,esk111_2(X23623,X23624)))
| ~ hBOOL(hAPP(X23623,X23627))
| hBOOL(hAPP(X23623,esk109_2(X23623,X23624)))
| hBOOL(hAPP(X23623,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X23623,X23624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X23623,X23624)),X23624))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23624)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X23629),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X23624)))
| ~ hBOOL(hAPP(X23623,X23629))
| hBOOL(hAPP(X23623,esk112_2(X23623,X23624)))
| hBOOL(hAPP(X23623,esk109_2(X23623,X23624)))
| hBOOL(hAPP(X23623,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X23623,X23624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X23623,X23624)),X23624))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23624)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_periodic__finite__ex])])])])]) ).
fof(i_0_7107,plain,
! [X32489,X32490,X32491] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32491),tc_List_Olist(X32491))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32491),tc_List_Olist(X32491)),c_List_Olist_ONil(X32491)),X32490)),c_List_Olistrel(X32491,X32489)))
| X32490 = c_List_Olist_ONil(X32491) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil1])]) ).
fof(i_0_7108,plain,
! [X24901,X24902] : c_Set_Othe__elem(X24902,X24901) = c_HOL_OThe(X24902,hAPP(hAPP(c_COMBB(tc_fun(X24902,tc_HOL_Obool),tc_HOL_Obool,X24902),hAPP(c_fequal,X24901)),hAPP(hAPP(c_COMBC(X24902,tc_fun(X24902,tc_HOL_Obool),tc_fun(X24902,tc_HOL_Obool)),c_Set_Oinsert(X24902)),c_Orderings_Obot__class_Obot(tc_fun(X24902,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_the__elem__def]) ).
cnf(i_0_7109,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk375_2(X2,X1)),esk375_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_5508]) ).
cnf(i_0_7110,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk365_2(X2,X1)),esk365_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_5463]) ).
fof(i_0_7111,plain,
! [X33240,X33241,X33242] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33242),tc_List_Olist(X33242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33242),tc_List_Olist(X33242)),c_List_Olist_ONil(X33242)),X33241)),c_List_Olistrel1(X33242,X33240))),
inference(variable_rename,[status(thm)],[i_0_5509]) ).
fof(i_0_7112,plain,
! [X32559,X32560,X32561] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32561),tc_List_Olist(X32561))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32561),tc_List_Olist(X32561)),c_List_Olist_ONil(X32561)),X32560)),c_List_Olex(X32561,X32559))),
inference(variable_rename,[status(thm)],[i_0_5510]) ).
fof(i_0_7113,plain,
! [X23793,X23794] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23794),X23793))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23794)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23793)))
| ~ c_Nat__Transfer_Onat__set(X23793)
| ~ c_Nat__Transfer_Onat__set(X23794) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23794)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23793)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23794),X23793))
| ~ c_Nat__Transfer_Onat__set(X23793)
| ~ c_Nat__Transfer_Onat__set(X23794) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I5_J])])]) ).
fof(i_0_7114,plain,
! [X23791,X23792] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23792),X23791))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23792)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23791)))
| ~ c_Nat__Transfer_Onat__set(X23791)
| ~ c_Nat__Transfer_Onat__set(X23792) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23792)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23791)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23792),X23791))
| ~ c_Nat__Transfer_Onat__set(X23791)
| ~ c_Nat__Transfer_Onat__set(X23792) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I4_J])])]) ).
fof(i_0_7115,plain,
! [X29547,X29548,X29549,X29550] :
( hAPP(hAPP(c_Relation_Orel__comp(X29550,X29550,X29550),X29549),X29548) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29550,X29550),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X29550,X29550,X29550),X29547),X29548) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29550,X29550),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X29550,X29550,X29550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29550,X29550),tc_HOL_Obool)),X29549),X29547)),X29548) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29550,X29550),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__comp__emptyL])]) ).
fof(i_0_7116,plain,
! [X26754] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26754) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26754),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_int__def]) ).
fof(i_0_7117,plain,
! [X27303,X27304,X27305,X27306] :
( ~ class_Lattices_Olattice(X27306)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27306),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27306),X27305),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27306),X27304),X27303))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27306),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27306),X27305),X27304)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27306),X27305),X27303)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__sup__le])]) ).
fof(i_0_7118,plain,
! [X22697,X22698,X22699,X22700] :
( ~ class_Orderings_Olinorder(X22700)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22700),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22700),X22699),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22700),X22698),X22697))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22700),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22700),X22699),X22698)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22700),X22699),X22697)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__sup__le])]) ).
fof(i_0_7119,plain,
! [X30717,X30718,X30719,X30720] :
( ~ class_Lattices_Osemilattice__inf(X30720)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30720),X30719))
| ~ hBOOL(hAPP(hAPP(c_member(X30720),X30718),X30719))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30720),hAPP(hAPP(c_Finite__Set_Ofold(X30720,X30720,c_Lattices_Osemilattice__inf__class_Oinf(X30720)),X30717),X30719)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X30720),X30718),X30717))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf])]) ).
fof(i_0_7120,plain,
! [X30721,X30722,X30723,X30724] :
( ~ class_Orderings_Olinorder(X30724)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30724),X30723))
| ~ hBOOL(hAPP(hAPP(c_member(X30724),X30722),X30723))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30724),hAPP(hAPP(c_Finite__Set_Ofold(X30724,X30724,c_Orderings_Oord__class_Omin(X30724)),X30721),X30723)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X30724),X30722),X30721))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf])]) ).
fof(i_0_7121,plain,
! [X32798,X32799,X32800,X32801,X32802] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32802,tc_HOL_Obool)),hAPP(c_List_Oset(X32802),X32801)),X32800))
| ~ hBOOL(hAPP(hAPP(c_member(X32802),X32799),X32800))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32802,tc_HOL_Obool)),hAPP(c_List_Oset(X32802),hAPP(hAPP(c_List_Olist__update(X32802,X32801),X32798),X32799))),X32800)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__subsetI])]) ).
fof(i_0_7122,plain,
! [X23510,X23511,X23512,X23513,X23514] :
( ~ class_Groups_Ocomm__monoid__add(X23514)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23512),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23514),X23511),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23513,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23512),X23510))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23514),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23514),X23511),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23513,X23512))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23514),X23511),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23512),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23512),X23510)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat])]) ).
fof(i_0_7123,plain,
! [X26009,X26010,X26011,X26012,X26013,X26014] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X26014),X26013),X26012))
| hAPP(c_Set_Oimage(X26014,X26011,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26014,X26011),X26010),X26013),X26009)),X26012) = hAPP(hAPP(c_Set_Oinsert(X26011),X26009),hAPP(c_Set_Oimage(X26014,X26011,X26010),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26014,tc_HOL_Obool)),X26012),hAPP(hAPP(c_Set_Oinsert(X26014),X26013),c_Orderings_Obot__class_Obot(tc_fun(X26014,tc_HOL_Obool)))))) )
& ( hBOOL(hAPP(hAPP(c_member(X26014),X26013),X26012))
| hAPP(c_Set_Oimage(X26014,X26011,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26014,X26011),X26010),X26013),X26009)),X26012) = hAPP(c_Set_Oimage(X26014,X26011,X26010),X26012) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5511])]) ).
fof(i_0_7124,plain,
! [X28713,X28714,X28715,X28716,X28717] : hAPP(hAPP(c_Product__Type_OSigma(X28717,X28716),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28717,tc_HOL_Obool)),X28715),X28714)),hAPP(c_COMBK(tc_fun(X28716,tc_HOL_Obool),X28717),X28713)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28717,X28716),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28717,X28716),X28715),hAPP(c_COMBK(tc_fun(X28716,tc_HOL_Obool),X28717),X28713))),hAPP(hAPP(c_Product__Type_OSigma(X28717,X28716),X28714),hAPP(c_COMBK(tc_fun(X28716,tc_HOL_Obool),X28717),X28713))),
inference(variable_rename,[status(thm)],[fact_Times__Int__distrib1]) ).
fof(i_0_7125,plain,
! [X28687,X28688,X28689,X28690,X28691] : hAPP(hAPP(c_Product__Type_OSigma(X28691,X28690),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28691,tc_HOL_Obool)),X28689),X28688)),hAPP(c_COMBK(tc_fun(X28690,tc_HOL_Obool),X28691),X28687)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28691,X28690),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28691,X28690),X28689),hAPP(c_COMBK(tc_fun(X28690,tc_HOL_Obool),X28691),X28687))),hAPP(hAPP(c_Product__Type_OSigma(X28691,X28690),X28688),hAPP(c_COMBK(tc_fun(X28690,tc_HOL_Obool),X28691),X28687))),
inference(variable_rename,[status(thm)],[fact_Times__Un__distrib1]) ).
fof(i_0_7126,plain,
! [X28634,X28635,X28636,X28637,X28638] : hAPP(hAPP(c_Product__Type_OSigma(X28638,X28637),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28638,tc_HOL_Obool)),X28636),X28635)),hAPP(c_COMBK(tc_fun(X28637,tc_HOL_Obool),X28638),X28634)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28638,X28637),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28638,X28637),X28636),hAPP(c_COMBK(tc_fun(X28637,tc_HOL_Obool),X28638),X28634))),hAPP(hAPP(c_Product__Type_OSigma(X28638,X28637),X28635),hAPP(c_COMBK(tc_fun(X28637,tc_HOL_Obool),X28638),X28634))),
inference(variable_rename,[status(thm)],[fact_Times__Diff__distrib1]) ).
fof(i_0_7127,plain,
! [X28170,X28171,X28172,X28173,X28174] :
( ~ c_Fun_Oinj__on(X28174,X28173,X28172,X28171)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28173,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28174,X28173,X28172),X28171)),X28170))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28173),X28170))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X28174),X28171)),hAPP(c_Finite__Set_Ocard(X28173),X28170))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).
fof(i_0_7128,plain,
! [X30052,X30053,X30054,X30055] :
( ( hBOOL(hAPP(hAPP(c_member(X30054),esk355_4(X30052,X30053,X30054,X30055)),X30053))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30055,X30054,c_Groups_Otimes__class_Otimes(X30055)),X30052),c_Groups_Oone__class_Oone(X30055)),X30053) = c_Groups_Oone__class_Oone(X30055)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30054),X30053))
| ~ class_Groups_Ocomm__monoid__mult(X30055) )
& ( hAPP(X30052,esk355_4(X30052,X30053,X30054,X30055)) != c_Groups_Oone__class_Oone(X30055)
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30055,X30054,c_Groups_Otimes__class_Otimes(X30055)),X30052),c_Groups_Oone__class_Oone(X30055)),X30053) = c_Groups_Oone__class_Oone(X30055)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30054),X30053))
| ~ class_Groups_Ocomm__monoid__mult(X30055) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__1])])])]) ).
fof(i_0_7129,plain,
! [X22776,X22777,X22778,X22779] : c_Sum__Type_Osum_Osum__case(X22779,X22778,X22777,hAPP(hAPP(c_COMBB(tc_sum(X22779,X22777),X22778,X22779),X22776),c_Sum__Type_OInl(X22779,X22777)),hAPP(hAPP(c_COMBB(tc_sum(X22779,X22777),X22778,X22777),X22776),c_Sum__Type_OInr(X22777,X22779))) = X22776,
inference(variable_rename,[status(thm)],[fact_surjective__sum]) ).
fof(i_0_7130,plain,
! [X22794,X22795,X22796,X22797,X22798] : hAPP(c_Sum__Type_Osum_Osum__case(X22798,X22797,X22796,hAPP(c_COMBK(X22797,X22798),X22795),hAPP(c_COMBK(X22797,X22796),X22795)),X22794) = X22795,
inference(variable_rename,[status(thm)],[fact_sum__case__KK]) ).
fof(i_0_7131,plain,
! [X33966,X33967,X33968,X33969,X33970,X33971] :
( hAPP(c_Map_Omap__of(X33971,X33970,X33969),X33968) != hAPP(c_Option_Ooption_OSome(X33970),X33967)
| ~ hBOOL(hAPP(hAPP(X33966,X33968),X33967))
| hAPP(c_Map_Omap__of(X33971,X33970,hAPP(c_List_Ofilter(tc_prod(X33971,X33970),hAPP(c_Product__Type_Oprod_Oprod__case(X33971,X33970,tc_HOL_Obool),X33966)),X33969)),X33968) = hAPP(c_Option_Ooption_OSome(X33970),X33967) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__filter__in])]) ).
fof(i_0_7132,plain,
! [X32486,X32487,X32488] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32488),tc_List_Olist(X32488))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32488),tc_List_Olist(X32488)),X32487),c_List_Olist_ONil(X32488))),c_List_Olistrel(X32488,X32486)))
| X32487 = c_List_Olist_ONil(X32488) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil2])]) ).
fof(i_0_7133,plain,
! [X31030,X31031,X31032,X31033,X31034,X31035] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31035)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31034,X31035),X31033),hAPP(hAPP(c_COMBB(tc_fun(X31032,X31035),X31035,X31034),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31032,X31035),X31031)),X31030)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31032,X31035),X31031),hAPP(hAPP(c_COMBB(tc_fun(X31034,X31035),X31035,X31032),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31034,X31035),X31033)),hAPP(c_COMBC(X31034,X31032,X31035),X31030))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__commute])]) ).
fof(i_0_7134,plain,
! [X24220,X24221,X24222,X24223,X24224,X24225] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X24225)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24224,X24225),X24223),hAPP(hAPP(c_COMBB(tc_fun(X24222,X24225),X24225,X24224),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24222,X24225),X24221)),X24220)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24222,X24225),X24221),hAPP(hAPP(c_COMBB(tc_fun(X24224,X24225),X24225,X24222),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24224,X24225),X24223)),hAPP(c_COMBC(X24224,X24222,X24225),X24220))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__commute])]) ).
fof(i_0_7135,plain,
! [X33243,X33244,X33245] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33245),tc_List_Olist(X33245))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33245),tc_List_Olist(X33245)),X33244),c_List_Olist_ONil(X33245))),c_List_Olistrel1(X33245,X33243))),
inference(variable_rename,[status(thm)],[i_0_5512]) ).
fof(i_0_7136,plain,
! [X33023,X33024,X33025] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33025),tc_List_Olist(X33025))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33025),tc_List_Olist(X33025)),X33024),c_List_Olist_ONil(X33025))),c_List_Olexord(X33025,X33023))),
inference(variable_rename,[status(thm)],[i_0_5513]) ).
fof(i_0_7137,plain,
! [X32562,X32563,X32564] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32564),tc_List_Olist(X32564))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32564),tc_List_Olist(X32564)),X32563),c_List_Olist_ONil(X32564))),c_List_Olex(X32564,X32562))),
inference(variable_rename,[status(thm)],[i_0_5514]) ).
fof(i_0_7138,plain,
! [X26936,X26937,X26938,X26939,X26940] :
( ( hAPP(c_Relation_OImage(X26940,X26940,X26938),hAPP(hAPP(c_Set_Oinsert(X26940),X26937),c_Orderings_Obot__class_Obot(tc_fun(X26940,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X26940,X26940,X26938),hAPP(hAPP(c_Set_Oinsert(X26940),X26936),c_Orderings_Obot__class_Obot(tc_fun(X26940,tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26940,X26940)),hAPP(hAPP(c_Product__Type_OPair(X26940,X26940),X26937),X26936)),X26938))
| ~ hBOOL(hAPP(hAPP(c_member(X26940),X26936),X26939))
| ~ hBOOL(hAPP(hAPP(c_member(X26940),X26937),X26939))
| ~ c_Equiv__Relations_Oequiv(X26940,X26939,X26938) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26940,X26940)),hAPP(hAPP(c_Product__Type_OPair(X26940,X26940),X26937),X26936)),X26938))
| hAPP(c_Relation_OImage(X26940,X26940,X26938),hAPP(hAPP(c_Set_Oinsert(X26940),X26937),c_Orderings_Obot__class_Obot(tc_fun(X26940,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X26940,X26940,X26938),hAPP(hAPP(c_Set_Oinsert(X26940),X26936),c_Orderings_Obot__class_Obot(tc_fun(X26940,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(X26940),X26936),X26939))
| ~ hBOOL(hAPP(hAPP(c_member(X26940),X26937),X26939))
| ~ c_Equiv__Relations_Oequiv(X26940,X26939,X26938) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff])])]) ).
fof(i_0_7139,plain,
! [X26243,X26244,X26245] :
( ( hBOOL(hAPP(hAPP(c_member(X26245),esk213_3(X26243,X26244,X26245)),X26244))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26245,tc_Int_Oint),X26243),X26244) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26245,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X26245),c_Int_Onat),X26243)),X26244)) )
& ( ~ c_Nat__Transfer_Ois__nat(hAPP(X26243,esk213_3(X26243,X26244,X26245)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26245,tc_Int_Oint),X26243),X26244) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26245,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X26245),c_Int_Onat),X26243)),X26244)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I2_J])])])]) ).
fof(i_0_7140,plain,
! [X25430,X25431,X25432] :
( ( hBOOL(hAPP(hAPP(c_member(X25432),esk169_3(X25430,X25431,X25432)),X25431))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25432,tc_Int_Oint),X25430),X25431) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25432,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X25432),c_Int_Onat),X25430)),X25431)) )
& ( ~ c_Nat__Transfer_Ois__nat(hAPP(X25430,esk169_3(X25430,X25431,X25432)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25432,tc_Int_Oint),X25430),X25431) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25432,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X25432),c_Int_Onat),X25430)),X25431)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I1_J])])])]) ).
fof(i_0_7141,plain,
! [X33232,X33233,X33234,X33235] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33235),tc_List_Olist(X33235))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33235),tc_List_Olist(X33235)),X33234),X33233)),c_List_Olistrel1(X33235,X33232)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33235)),X33234) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33235)),X33233) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len])]) ).
fof(i_0_7142,plain,
! [X32261,X32262,X32263,X32264] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32264),tc_List_Olist(X32264))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32264),tc_List_Olist(X32264)),X32263),X32262)),c_List_Olistrel(X32264,X32261)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32264)),X32263) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32264)),X32262) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__eq__len])]) ).
cnf(i_0_7143,plain,
( hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3,c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5515]) ).
cnf(i_0_7144,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Relation_OId(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5516]) ).
fof(i_0_7145,plain,
! [X31333,X31334,X31335,X31336] : hAPP(hAPP(c_Product__Type_OSigma(X31336,X31335),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31336,tc_HOL_Obool),X31334)),X31333) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31336,tc_HOL_Obool),tc_fun(tc_prod(X31336,X31335),tc_HOL_Obool)),X31334),hAPP(hAPP(c_COMBC(tc_fun(X31336,tc_HOL_Obool),tc_fun(X31336,tc_fun(X31335,tc_HOL_Obool)),tc_fun(tc_prod(X31336,X31335),tc_HOL_Obool)),c_Product__Type_OSigma(X31336,X31335)),X31333)),
inference(variable_rename,[status(thm)],[fact_Sigma__Union]) ).
fof(i_0_7146,plain,
! [X25533,X25534,X25535,X25536] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk184_4(X25533,X25534,X25535,X25536)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25535)))
| X25536 = X25534
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25536),X25535) != X25534
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25534),X25533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25535)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk185_4(X25533,X25534,X25535,X25536)),X25533))
| X25536 = X25534
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25536),X25535) != X25534
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25534),X25533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25535)) )
& ( X25536 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk185_4(X25533,X25534,X25535,X25536)),esk184_4(X25533,X25534,X25535,X25536))
| X25536 = X25534
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25536),X25535) != X25534
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25534),X25533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25535)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I4_J])])])])]) ).
fof(i_0_7147,plain,
! [X25527,X25528,X25529,X25530] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk182_4(X25527,X25528,X25529,X25530)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25529)))
| X25530 = X25528
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25530),X25529) != X25528
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25528),X25527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25529)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk183_4(X25527,X25528,X25529,X25530)),X25527))
| X25530 = X25528
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25530),X25529) != X25528
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25528),X25527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25529)) )
& ( X25530 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk183_4(X25527,X25528,X25529,X25530)),esk182_4(X25527,X25528,X25529,X25530))
| X25530 = X25528
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25530),X25529) != X25528
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25528),X25527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25529)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I4_J])])])])]) ).
fof(i_0_7148,plain,
! [X30667,X30668,X30669,X30670,X30671] : hAPP(hAPP(c_Finite__Set_Ofold(X30671,X30670,X30669),X30668),X30667) = c_HOL_OThe(X30670,c_Finite__Set_Ofold__graph(X30671,X30670,X30669,X30668,X30667)),
inference(variable_rename,[status(thm)],[fact_fold__def]) ).
fof(i_0_7149,plain,
! [X22073,X22074,X22075,X22077,X22078,X22079,X22080,X22081,X22084] :
( ( ~ hBOOL(hAPP(X22075,esk85_3(X22073,X22074,X22075)))
| hBOOL(hAPP(X22075,hAPP(hAPP(c_Product__Type_OPair(X22074,X22073),X22077),X22078))) )
& ( ~ hBOOL(hAPP(X22081,hAPP(hAPP(c_Product__Type_OPair(X22080,X22079),esk86_3(X22079,X22080,X22081)),esk87_3(X22079,X22080,X22081))))
| hBOOL(hAPP(X22081,X22084)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__paired__All])])])])]) ).
fof(i_0_7150,plain,
! [X31955,X31956,X31957,X31958] :
( ( hAPP(c_Map_Omap__of(X31958,X31957,X31956),X31955) != c_Option_Ooption_ONone(X31957)
| ~ hBOOL(hAPP(hAPP(c_member(X31958),X31955),hAPP(c_Set_Oimage(tc_prod(X31958,X31957),X31958,c_Product__Type_Ofst(X31958,X31957)),hAPP(c_List_Oset(tc_prod(X31958,X31957)),X31956)))) )
& ( hBOOL(hAPP(hAPP(c_member(X31958),X31955),hAPP(c_Set_Oimage(tc_prod(X31958,X31957),X31958,c_Product__Type_Ofst(X31958,X31957)),hAPP(c_List_Oset(tc_prod(X31958,X31957)),X31956))))
| hAPP(c_Map_Omap__of(X31958,X31957,X31956),X31955) = c_Option_Ooption_ONone(X31957) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5517])]) ).
fof(i_0_7151,plain,
! [X23002,X23003,X23004,X23005,X23006] :
( ~ hBOOL(hAPP(X23006,hAPP(hAPP(c_Product__Type_OPair(X23005,X23004),X23003),X23002)))
| hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X23005,X23004,tc_HOL_Obool,X23006),X23003),X23002)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryI])]) ).
fof(i_0_7152,plain,
! [X24506,X24507,X24508] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24508),X24507))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24508),X24506)),hAPP(c_Finite__Set_Ocard(X24508),X24507))),hAPP(c_Finite__Set_Ocard(X24508),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24508,tc_HOL_Obool)),X24506),X24507)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff])]) ).
fof(i_0_7153,plain,
! [X31463,X31464,X31465,X31466] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31465,tc_HOL_Obool)),esk410_4(X31463,X31464,X31465,X31466)),X31466))
| c_Fun_Oinj__on(X31465,X31464,X31463,c_Complete__Lattice_OInf__class_OInf(tc_fun(X31465,tc_HOL_Obool),X31466))
| X31466 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31465,tc_HOL_Obool),tc_HOL_Obool)) )
& ( ~ c_Fun_Oinj__on(X31465,X31464,X31463,esk410_4(X31463,X31464,X31465,X31466))
| c_Fun_Oinj__on(X31465,X31464,X31463,c_Complete__Lattice_OInf__class_OInf(tc_fun(X31465,tc_HOL_Obool),X31466))
| X31466 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31465,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Inter])])])]) ).
cnf(i_0_7154,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5518]) ).
cnf(i_0_7155,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_card__UNIV__bool]) ).
fof(i_0_7156,plain,
! [X25493,X25494,X25495,X25496,X25497] :
( ( ~ c_Nitpick_Orefl_H(X25494,X25493)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X25494,X25494)),hAPP(hAPP(c_Product__Type_OPair(X25494,X25494),X25495),X25495)),X25493)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25497,X25497)),hAPP(hAPP(c_Product__Type_OPair(X25497,X25497),esk175_2(X25496,X25497)),esk175_2(X25496,X25497))),X25496))
| c_Nitpick_Orefl_H(X25497,X25496) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def])])])])]) ).
fof(i_0_7157,plain,
! [X20580,X20581,X20582,X20584] :
( ( hBOOL(hAPP(X20581,esk69_3(X20580,X20581,X20582)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20580))
| ~ hBOOL(hAPP(X20581,X20584))
| hBOOL(hAPP(X20581,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20584),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20580),X20582))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20582)) )
& ( ~ hBOOL(hAPP(X20581,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk69_3(X20580,X20581,X20582)),X20582)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20580))
| ~ hBOOL(hAPP(X20581,X20584))
| hBOOL(hAPP(X20581,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20584),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20580),X20582))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20582)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__mult__lemma])])])])]) ).
fof(i_0_7158,plain,
! [X20206,X20207,X20208,X20210] :
( ( hBOOL(hAPP(X20207,esk65_3(X20206,X20207,X20208)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20206))
| ~ hBOOL(hAPP(X20207,X20210))
| hBOOL(hAPP(X20207,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20210),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20206),X20208))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20208)) )
& ( ~ hBOOL(hAPP(X20207,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk65_3(X20206,X20207,X20208)),X20208)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20206))
| ~ hBOOL(hAPP(X20207,X20210))
| hBOOL(hAPP(X20207,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20210),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20206),X20208))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20208)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma])])])])]) ).
cnf(i_0_7159,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_nat__1__add__1]) ).
fof(i_0_7160,plain,
! [X27841,X27842,X27843,X27844,X27845,X27846,X27847] :
( ~ c_Finite__Set_Ofolding__idem(X27847,X27846,X27845,X27844)
| hAPP(c_Fun_Ocomp(X27846,X27846,X27843,hAPP(X27845,X27842)),hAPP(c_Fun_Ocomp(X27846,X27846,X27843,hAPP(X27845,X27842)),X27841)) = hAPP(c_Fun_Ocomp(X27846,X27846,X27843,hAPP(X27845,X27842)),X27841) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp])]) ).
fof(i_0_7161,plain,
! [X24994,X24995,X24996,X24997,X24998,X24999,X25000] :
( ~ hBOOL(hAPP(hAPP(c_member(X25000),X24999),hAPP(hAPP(X24998,X24997),X24996)))
| hBOOL(hAPP(hAPP(c_member(X25000),X24999),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X24995,X24994,tc_fun(X25000,tc_HOL_Obool)),X24998),hAPP(hAPP(c_Product__Type_OPair(X24995,X24994),X24997),X24996)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI])]) ).
fof(i_0_7162,plain,
! [X33113,X33114,X33115,X33116,X33117,X33118] :
( hBOOL(hAPP(hAPP(c_member(X33118),X33117),hAPP(c_List_Oset(X33118),X33116)))
| hAPP(c_Map_Omap__upds(X33118,X33115,X33114,X33116,X33113),X33117) = hAPP(X33114,X33117) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5519])]) ).
fof(i_0_7163,plain,
! [X32372,X32373,X32374,X32375] : hAPP(c_Relation_OImage(tc_List_Olist(X32375),tc_List_Olist(X32375),c_List_Olistrel(X32375,X32374)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32375)),hAPP(hAPP(c_List_Olist_OCons(X32375),X32373),X32372)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32375),tc_HOL_Obool)))) = c_List_Oset__Cons(X32375,hAPP(c_Relation_OImage(X32375,X32375,X32374),hAPP(hAPP(c_Set_Oinsert(X32375),X32373),c_Orderings_Obot__class_Obot(tc_fun(X32375,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X32375),tc_List_Olist(X32375),c_List_Olistrel(X32375,X32374)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32375)),X32372),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32375),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_listrel__Cons]) ).
fof(i_0_7164,plain,
! [X24168,X24169,X24170,X24171] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24171,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24170)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X24171,tc_HOL_Obool),tc_Nat_Onat),X24169),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X24168))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24171,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24168,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24170),X24168))),X24169),
inference(variable_rename,[status(thm)],[fact_UN__le__add__shift]) ).
cnf(i_0_7165,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[fact_numeral__2__eq__2]) ).
cnf(i_0_7166,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).
fof(i_0_7167,plain,
! [X33060,X33061,X33062,X33063,X33064,X33065] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33065)),X33064) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33063)),X33062)
| c_Map_Omap__upds(X33065,X33063,X33061,hAPP(hAPP(c_List_Oappend(X33065),X33064),X33060),X33062) = c_Map_Omap__upds(X33065,X33063,X33061,X33064,X33062) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upds__append__drop])]) ).
fof(i_0_7168,plain,
! [X33054,X33055,X33056,X33057,X33058,X33059] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33059)),X33058) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33057)),X33056)
| c_Map_Omap__upds(X33059,X33057,X33055,X33058,hAPP(hAPP(c_List_Oappend(X33057),X33056),X33054)) = c_Map_Omap__upds(X33059,X33057,X33055,X33058,X33056) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upds__append2__drop])]) ).
fof(i_0_7169,plain,
! [X31883,X31884,X31885,X31886,X31887,X31889,X31890,X31891,X31892,X31893,X31894] :
( ( X31884 = hAPP(c_Option_Ooption_OSome(X31887),esk437_5(X31883,X31884,X31885,X31886,X31887))
| hAPP(hAPP(c_Option_Omap(X31887,X31886),X31885),X31884) != hAPP(c_Option_Ooption_OSome(X31886),X31883) )
& ( hAPP(X31885,esk437_5(X31883,X31884,X31885,X31886,X31887)) = X31883
| hAPP(hAPP(c_Option_Omap(X31887,X31886),X31885),X31884) != hAPP(c_Option_Ooption_OSome(X31886),X31883) )
& ( X31890 != hAPP(c_Option_Ooption_OSome(X31893),X31894)
| hAPP(X31891,X31894) != X31889
| hAPP(hAPP(c_Option_Omap(X31893,X31892),X31891),X31890) = hAPP(c_Option_Ooption_OSome(X31892),X31889) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option__map__eq__Some])])])])])]) ).
fof(i_0_7170,plain,
! [X29337,X29338,X29339,X29340,X29341,X29342] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X29342),X29341),X29340))
| hAPP(c_Fun_Ooverride__on(X29342,X29339,X29338,X29337,X29340),X29341) = hAPP(X29337,X29341) )
& ( hBOOL(hAPP(hAPP(c_member(X29342),X29341),X29340))
| hAPP(c_Fun_Ooverride__on(X29342,X29339,X29338,X29337,X29340),X29341) = hAPP(X29338,X29341) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5520])]) ).
fof(i_0_7171,plain,
! [X29318,X29319,X29320,X29321,X29322,X29323] :
( ~ hBOOL(hAPP(hAPP(c_member(X29323),X29322),X29321))
| hAPP(c_Fun_Ooverride__on(X29323,X29320,X29319,X29318,X29321),X29322) = hAPP(X29318,X29322) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_override__on__apply__in])]) ).
fof(i_0_7172,plain,
! [X26271,X26272,X26273,X26274,X26275] : c_Map_Orestrict__map(X26275,X26274,X26273,hAPP(hAPP(c_Set_Oinsert(X26275),X26272),X26271)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26275,tc_Option_Ooption(X26274)),c_Map_Orestrict__map(X26275,X26274,X26273,X26271)),X26272),hAPP(X26273,X26272)),
inference(variable_rename,[status(thm)],[fact_restrict__map__insert]) ).
cnf(i_0_7173,plain,
( c_Divides_Odivmod__nat(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5521]) ).
fof(i_0_7174,plain,
! [X33710,X33711,X33712,X33713,X33714,X33715] :
( X33713 != hAPP(hAPP(c_List_Olist_OCons(X33712),X33714),X33715)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33712),tc_List_Olist(X33712))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33712),tc_List_Olist(X33712)),X33711),hAPP(hAPP(c_List_Oappend(X33712),X33711),X33713))),c_List_Olexord(X33712,X33710))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI])])]) ).
fof(i_0_7175,plain,
! [X32216,X32217,X32218,X32219,X32220,X32221,X32222] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32216)),X32218) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32216)),X32217)
| X32218 != X32217 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32216,X32216)),X32219),hAPP(c_List_Oset(tc_prod(X32216,X32216)),hAPP(hAPP(c_List_Ozip(X32216,X32216),X32218),X32217))))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32216,X32216,tc_HOL_Obool),c_fequal),X32219))
| X32218 != X32217 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32220,X32220)),esk440_3(X32220,X32221,X32222)),hAPP(c_List_Oset(tc_prod(X32220,X32220)),hAPP(hAPP(c_List_Ozip(X32220,X32220),X32222),X32221))))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32220)),X32222) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32220)),X32221)
| X32222 = X32221 )
& ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32220,X32220,tc_HOL_Obool),c_fequal),esk440_3(X32220,X32221,X32222)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32220)),X32222) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32220)),X32221)
| X32222 = X32221 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__eq__iff__zip__eq])])])])])]) ).
fof(i_0_7176,plain,
! [X22246,X22247,X22248] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk90_3(X22246,X22247,X22248)),esk91_3(X22246,X22247,X22248))))
| hBOOL(hAPP(hAPP(X22246,X22248),X22247))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22248),X22247))) )
& ( esk91_3(X22246,X22247,X22248) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(X22246,esk91_3(X22246,X22247,X22248)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk90_3(X22246,X22247,X22248),esk91_3(X22246,X22247,X22248))))
| hBOOL(hAPP(hAPP(X22246,X22248),X22247))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22248),X22247))) )
& ( ~ hBOOL(hAPP(hAPP(X22246,esk90_3(X22246,X22247,X22248)),esk91_3(X22246,X22247,X22248)))
| hBOOL(hAPP(hAPP(X22246,X22248),X22247))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22248),X22247))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opinduct])])])]) ).
fof(i_0_7177,plain,
! [X27999,X28000,X28001,X28002,X28003] :
( ~ c_Fun_Oinj__on(X28003,X28002,X28001,X28000)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X28003,tc_HOL_Obool)),X27999),X28000))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X28002,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28003,X28002,X28001),X27999)),hAPP(c_Set_Oimage(X28003,X28002,X28001),X28000))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).
fof(i_0_7178,plain,
! [X17663,X17664,X17665,X17666] :
( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17666),X17664),esk5_4(X17663,X17664,X17665,X17666)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17666,X17665)),X17664),X17663)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17665),esk5_4(X17663,X17664,X17665,X17666)),X17663))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17666,X17665)),X17664),X17663)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5522])])])]) ).
fof(i_0_7179,plain,
! [X17391,X17392,X17393,X17394,X17396,X17397,X17398,X17399,X17400] :
( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17394),X17392),esk2_4(X17391,X17392,X17393,X17394)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17394,X17393)),X17392),X17391)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17393),esk2_4(X17391,X17392,X17393,X17394)),X17391))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17394,X17393)),X17392),X17391)) )
& ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17399),X17397),X17400))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17398),X17400),X17396))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17399,X17398)),X17397),X17396)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I4_J])])])])])]) ).
fof(i_0_7180,plain,
! [X28052,X28053,X28054,X28055,X28056,X28057] :
( ~ c_Fun_Oinj__on(X28057,X28056,X28055,X28054)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28057,tc_HOL_Obool)),X28053),X28054))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28057,tc_HOL_Obool)),X28052),X28054))
| hAPP(c_Set_Oimage(X28057,X28056,X28055),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28057,tc_HOL_Obool)),X28053),X28052)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28056,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28057,X28056,X28055),X28053)),hAPP(c_Set_Oimage(X28057,X28056,X28055),X28052)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int])]) ).
fof(i_0_7181,plain,
! [X28071,X28072,X28073,X28074,X28075,X28076] :
( ~ c_Fun_Oinj__on(X28076,X28075,X28074,X28073)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28076,tc_HOL_Obool)),X28072),X28073))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28076,tc_HOL_Obool)),X28071),X28073))
| hAPP(c_Set_Oimage(X28076,X28075,X28074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28076,tc_HOL_Obool)),X28072),X28071)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28075,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28076,X28075,X28074),X28072)),hAPP(c_Set_Oimage(X28076,X28075,X28074),X28071)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff])]) ).
fof(i_0_7182,plain,
! [X33950,X33951,X33952] :
( ~ hBOOL(hAPP(c_List_Odistinct(X33952),X33951))
| hAPP(c_List_Ofilter(X33952,hAPP(hAPP(c_COMBC(X33952,tc_fun(X33952,tc_HOL_Obool),tc_HOL_Obool),c_member(X33952)),hAPP(c_List_Oset(X33952),c_List_Osublist(X33952,X33951,X33950)))),X33951) = c_List_Osublist(X33952,X33951,X33950) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__in__sublist])]) ).
cnf(i_0_7183,plain,
hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5) = c_List_Ofoldr(X2,X1,hAPP(c_COMBC(X1,X2,X1),X3),hAPP(c_List_Orev(X2),X5),X4),
inference(split_conjunct,[status(thm)],[i_0_5523]) ).
cnf(i_0_7184,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk368_3(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),X2),c_Transitive__Closure_Otrancl(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5450]) ).
fof(i_0_7185,plain,
! [X28037,X28038,X28039] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28039),X28038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28039,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28039,X28039,X28037),X28038)),X28038))
| ~ c_Fun_Oinj__on(X28039,X28039,X28037,X28038)
| hAPP(c_Set_Oimage(X28039,X28039,X28037),X28038) = X28038 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).
fof(i_0_7186,plain,
! [X29324,X29325,X29326,X29327,X29328,X29329] :
( hBOOL(hAPP(hAPP(c_member(X29329),X29328),X29327))
| hAPP(c_Fun_Ooverride__on(X29329,X29326,X29325,X29324,X29327),X29328) = hAPP(X29325,X29328) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5524])]) ).
fof(i_0_7187,plain,
! [X32833,X32834,X32835,X32836,X32837] :
( ~ class_Orderings_Olinorder(X32837)
| ~ hBOOL(hAPP(hAPP(c_member(X32837),hAPP(X32836,X32835)),hAPP(c_Set_Oimage(X32834,X32837,X32836),hAPP(c_List_Oset(X32834),X32833))))
| c_List_Olinorder__class_Oinsort__insert__key(X32834,X32837,X32836,X32835,X32833) = X32833 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__key__triv])]) ).
fof(i_0_7188,plain,
! [X32827,X32828,X32829] :
( ~ class_Orderings_Olinorder(X32829)
| hAPP(c_List_Oset(X32829),c_List_Olinorder__class_Oinsort__insert__key(X32829,X32829,c_COMBI(X32829),X32828,X32827)) = hAPP(hAPP(c_Set_Oinsert(X32829),X32828),hAPP(c_List_Oset(X32829),X32827)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort__insert])]) ).
fof(i_0_7189,plain,
! [X33275,X33276,X33277] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33277,X33277),tc_HOL_Obool)),X33276),X33275))
| ~ c_Relation_Orefl__on(X33277,c_Orderings_Otop__class_Otop(tc_fun(X33277,tc_HOL_Obool)),X33275)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X33277),tc_List_Olist(X33277)),tc_HOL_Obool)),c_List_Olistrel1(X33277,X33276)),c_List_Olistrel(X33277,X33275))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__subset__listrel])]) ).
cnf(i_0_7190,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5507]) ).
fof(i_0_7191,plain,
! [X28198,X28199,X28200,X28201,X28202,X28203,X28204] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28203),X28199))
| hAPP(hAPP(X28200,X28198),X28199) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28204,X28203,X28202),X28198),X28201),X28199)
| ~ c_Big__Operators_Ocomm__monoid__big(X28204,X28203,X28202,X28201,X28200) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28203),X28199))
| hAPP(hAPP(X28200,X28198),X28199) = X28201
| ~ c_Big__Operators_Ocomm__monoid__big(X28204,X28203,X28202,X28201,X28200) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5525])])]) ).
fof(i_0_7192,plain,
! [X28242,X28243,X28244,X28245,X28246,X28247,X28248] :
( ~ c_Finite__Set_Ofolding__image(X28248,X28247,X28246,X28245,X28244)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28247),X28243))
| hAPP(hAPP(X28244,X28242),X28243) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28248,X28247,X28246),X28242),X28245),X28243) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold])]) ).
fof(i_0_7193,plain,
! [X30780,X30781,X30782,X30783,X30784,X30785] :
( ~ c_Finite__Set_Ofun__left__comm(X30785,X30784,X30783)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30785),X30782))
| ~ hBOOL(hAPP(hAPP(c_member(X30785),X30781),X30782))
| hAPP(hAPP(c_Finite__Set_Ofold(X30785,X30784,X30783),X30780),X30782) = hAPP(hAPP(X30783,X30781),hAPP(hAPP(c_Finite__Set_Ofold(X30785,X30784,X30783),X30780),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30785,tc_HOL_Obool)),X30782),hAPP(hAPP(c_Set_Oinsert(X30785),X30781),c_Orderings_Obot__class_Obot(tc_fun(X30785,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec])]) ).
fof(i_0_7194,plain,
! [X29955,X29956,X29957,X29958,X29960,X29961,X29962,X29963,X29965] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29957)),esk337_4(X29955,X29956,X29957,X29958)),X29956))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29957)),X29960),X29955))
| c_Hoare__Mirabelle_Otriple__valid(X29957,X29958,X29960)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X29957,X29956,X29955) )
& ( ~ c_Hoare__Mirabelle_Otriple__valid(X29957,X29958,esk337_4(X29955,X29956,X29957,X29958))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29957)),X29960),X29955))
| c_Hoare__Mirabelle_Otriple__valid(X29957,X29958,X29960)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X29957,X29956,X29955) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29963)),X29965),X29962))
| c_Hoare__Mirabelle_Otriple__valid(X29963,esk338_3(X29961,X29962,X29963),X29965)
| c_Hoare__Mirabelle_Ohoare__valids(X29963,X29962,X29961) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29963)),esk339_3(X29961,X29962,X29963)),X29961))
| c_Hoare__Mirabelle_Ohoare__valids(X29963,X29962,X29961) )
& ( ~ c_Hoare__Mirabelle_Otriple__valid(X29963,esk338_3(X29961,X29962,X29963),esk339_3(X29961,X29962,X29963))
| c_Hoare__Mirabelle_Ohoare__valids(X29963,X29962,X29961) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__valids__def])])])])])]) ).
fof(i_0_7195,plain,
! [X22835,X22836,X22837,X22838,X22839,X22840] : hAPP(c_Sum__Type_Osum_Osum__case(X22840,X22839,X22838,X22837,X22836),hAPP(c_Sum__Type_OInl(X22840,X22838),X22835)) = hAPP(X22837,X22835),
inference(variable_rename,[status(thm)],[fact_sum_Osimps_I5_J]) ).
fof(i_0_7196,plain,
! [X22829,X22830,X22831,X22832,X22833,X22834] : hAPP(c_Sum__Type_Osum_Osum__case(X22834,X22833,X22832,X22831,X22830),hAPP(c_Sum__Type_OInr(X22832,X22834),X22829)) = hAPP(X22830,X22829),
inference(variable_rename,[status(thm)],[fact_sum_Osimps_I6_J]) ).
fof(i_0_7197,plain,
! [X28337,X28338,X28339,X28340,X28341,X28342] : hAPP(c_Set_Ovimage(X28342,X28341,hAPP(c_Fun_Ocomp(X28340,X28341,X28342,X28339),X28338)),X28337) = hAPP(c_Set_Ovimage(X28342,X28340,X28338),hAPP(c_Set_Ovimage(X28340,X28341,X28339),X28337)),
inference(variable_rename,[status(thm)],[fact_vimage__compose]) ).
fof(i_0_7198,plain,
! [X26600,X26601,X26602,X26603,X26604,X26605] : hAPP(c_Set_Oimage(X26605,X26604,hAPP(c_Fun_Ocomp(X26603,X26604,X26605,X26602),X26601)),X26600) = hAPP(c_Set_Oimage(X26603,X26604,X26602),hAPP(c_Set_Oimage(X26605,X26603,X26601),X26600)),
inference(variable_rename,[status(thm)],[fact_image__compose]) ).
fof(i_0_7199,plain,
! [X30452,X30453,X30454,X30456,X30457,X30458,X30459] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30454,X30454)),X30453),c_Transitive__Closure_Ortrancl(X30454,X30452)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30454,X30454)),X30453),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30454,X30454),tc_HOL_Obool),esk367_3(X30452,X30453,X30454)),X30452))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30458,X30458)),X30457),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30458,X30458),tc_HOL_Obool),X30459),X30456)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30458,X30458)),X30457),c_Transitive__Closure_Ortrancl(X30458,X30456))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__power])])])])]) ).
fof(i_0_7200,plain,
! [X22848,X22849,X22850,X22851,X22852,X22853,X22854] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X22854,X22853,X22852,X22851),X22850),X22849),X22848) = hAPP(hAPP(X22849,hAPP(c_Product__Type_Ofst(X22853,X22852),hAPP(X22850,X22848))),hAPP(c_Product__Type_Osnd(X22853,X22852),hAPP(X22850,X22848))),
inference(variable_rename,[status(thm)],[fact_scomp__unfold]) ).
fof(i_0_7201,plain,
! [X26941,X26942,X26943,X26944,X26945] :
( ( hAPP(c_Relation_OImage(X26945,X26945,X26943),hAPP(hAPP(c_Set_Oinsert(X26945),X26942),c_Orderings_Obot__class_Obot(tc_fun(X26945,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X26945,X26945,X26943),hAPP(hAPP(c_Set_Oinsert(X26945),X26941),c_Orderings_Obot__class_Obot(tc_fun(X26945,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26945,X26945)),hAPP(hAPP(c_Product__Type_OPair(X26945,X26945),X26942),X26941)),X26943))
| ~ c_Equiv__Relations_Oequiv(X26945,X26944,X26943) )
& ( hBOOL(hAPP(hAPP(c_member(X26945),X26942),X26944))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26945,X26945)),hAPP(hAPP(c_Product__Type_OPair(X26945,X26945),X26942),X26941)),X26943))
| ~ c_Equiv__Relations_Oequiv(X26945,X26944,X26943) )
& ( hBOOL(hAPP(hAPP(c_member(X26945),X26941),X26944))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26945,X26945)),hAPP(hAPP(c_Product__Type_OPair(X26945,X26945),X26942),X26941)),X26943))
| ~ c_Equiv__Relations_Oequiv(X26945,X26944,X26943) )
& ( hAPP(c_Relation_OImage(X26945,X26945,X26943),hAPP(hAPP(c_Set_Oinsert(X26945),X26942),c_Orderings_Obot__class_Obot(tc_fun(X26945,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X26945,X26945,X26943),hAPP(hAPP(c_Set_Oinsert(X26945),X26941),c_Orderings_Obot__class_Obot(tc_fun(X26945,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(X26945),X26942),X26944))
| ~ hBOOL(hAPP(hAPP(c_member(X26945),X26941),X26944))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26945,X26945)),hAPP(hAPP(c_Product__Type_OPair(X26945,X26945),X26942),X26941)),X26943))
| ~ c_Equiv__Relations_Oequiv(X26945,X26944,X26943) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff])])]) ).
fof(i_0_7202,plain,
! [X18961,X18962,X18963] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18963),c_Groups_Ozero__class_Ozero(X18963)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18963),X18962),X18962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18963),X18961),X18961))))
| X18962 != c_Groups_Ozero__class_Ozero(X18963)
| X18961 != c_Groups_Ozero__class_Ozero(X18963)
| ~ class_Rings_Olinordered__ring__strict(X18963) )
& ( X18962 = c_Groups_Ozero__class_Ozero(X18963)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18963),c_Groups_Ozero__class_Ozero(X18963)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18963),X18962),X18962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18963),X18961),X18961))))
| ~ class_Rings_Olinordered__ring__strict(X18963) )
& ( X18961 = c_Groups_Ozero__class_Ozero(X18963)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18963),c_Groups_Ozero__class_Ozero(X18963)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18963),X18962),X18962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18963),X18961),X18961))))
| ~ class_Rings_Olinordered__ring__strict(X18963) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).
fof(i_0_7203,plain,
! [X30542,X30543] : c_Transitive__Closure_Ortrancl(X30543,X30542) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X30543,X30543),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X30543,X30543),tc_HOL_Obool),tc_fun(tc_prod(X30543,X30543),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X30543,X30543),tc_HOL_Obool)),X30542)),
inference(variable_rename,[status(thm)],[fact_rtrancl__is__UN__rel__pow]) ).
fof(i_0_7204,plain,
! [X27923,X27924,X27925,X27926,X27927,X27928] :
( ~ c_Fun_Oinj__on(X27928,X27927,hAPP(c_Fun_Ocomp(X27926,X27927,X27928,X27925),X27924),X27923)
| c_Fun_Oinj__on(X27926,X27927,X27925,hAPP(c_Set_Oimage(X27928,X27926,X27924),X27923)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI])]) ).
fof(i_0_7205,plain,
! [X24471,X24472,X24473,X24475,X24476] :
( ( hBOOL(hAPP(hAPP(c_member(X24473),esk157_3(X24471,X24472,X24473)),X24472))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24473,tc_Nat_Onat),X24471),X24472) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24473),X24472)) )
& ( hAPP(X24471,esk157_3(X24471,X24472,X24473)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24473,tc_Nat_Onat),X24471),X24472) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24473),X24472)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24473),X24475),X24472))
| esk157_3(X24471,X24472,X24473) = X24475
| hAPP(X24471,X24475) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24473,tc_Nat_Onat),X24471),X24472) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24473),X24472)) )
& ( hBOOL(hAPP(hAPP(c_member(X24473),esk158_4(X24471,X24472,X24473,X24476)),X24472))
| ~ hBOOL(hAPP(hAPP(c_member(X24473),X24476),X24472))
| hAPP(X24471,X24476) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24473,tc_Nat_Onat),X24471),X24472) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24473),X24472)) )
& ( X24476 != esk158_4(X24471,X24472,X24473,X24476)
| ~ hBOOL(hAPP(hAPP(c_member(X24473),X24476),X24472))
| hAPP(X24471,X24476) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24473,tc_Nat_Onat),X24471),X24472) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24473),X24472)) )
& ( hAPP(X24471,esk158_4(X24471,X24472,X24473,X24476)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X24473),X24476),X24472))
| hAPP(X24471,X24476) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24473,tc_Nat_Onat),X24471),X24472) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24473),X24472)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__eq__Suc0__iff])])])])]) ).
fof(i_0_7206,plain,
! [X34085,X34086,X34087] :
( ~ class_Orderings_Olinorder(X34087)
| ~ c_List_Olinorder__class_Osorted(X34087,X34086)
| c_List_Olinorder__class_Osorted(X34087,c_List_Olinorder__class_Oinsort__insert__key(X34087,X34087,c_COMBI(X34087),X34085,X34086)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert])]) ).
fof(i_0_7207,plain,
! [X20681,X20682,X20683,X20684,X20685] :
( ~ class_Rings_Olinordered__idom(X20685)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20685),hAPP(c_Groups_Oabs__class_Oabs(X20685),X20684)),X20683))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20685),hAPP(c_Groups_Oabs__class_Oabs(X20685),X20682)),X20681))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20685),hAPP(c_Groups_Oabs__class_Oabs(X20685),X20684)),hAPP(c_Groups_Oabs__class_Oabs(X20685),X20682))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20685),X20683),X20681))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).
fof(i_0_7208,plain,
! [X30786,X30787,X30788,X30789,X30790,X30791] :
( ~ c_Finite__Set_Ofun__left__comm(X30791,X30790,X30789)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30791),X30788))
| hAPP(hAPP(c_Finite__Set_Ofold(X30791,X30790,X30789),X30787),hAPP(hAPP(c_Set_Oinsert(X30791),X30786),X30788)) = hAPP(hAPP(X30789,X30786),hAPP(hAPP(c_Finite__Set_Ofold(X30791,X30790,X30789),X30787),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30791,tc_HOL_Obool)),X30788),hAPP(hAPP(c_Set_Oinsert(X30791),X30786),c_Orderings_Obot__class_Obot(tc_fun(X30791,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove])]) ).
fof(i_0_7209,plain,
! [X34375,X34376,X34377,X34378,X34379] : c_List_OtakeWhile(X34379,X34378,hAPP(hAPP(c_List_Omap(X34377,X34379),X34376),X34375)) = hAPP(hAPP(c_List_Omap(X34377,X34379),X34376),c_List_OtakeWhile(X34377,hAPP(c_Fun_Ocomp(X34379,tc_HOL_Obool,X34377,X34378),X34376),X34375)),
inference(variable_rename,[status(thm)],[fact_takeWhile__map]) ).
fof(i_0_7210,plain,
! [X24478,X24479,X24480,X24482,X24483] :
( ( hBOOL(hAPP(hAPP(c_member(X24480),esk159_3(X24478,X24479,X24480)),X24479))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24480,tc_Nat_Onat),X24478),X24479) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24480),X24479)) )
& ( hAPP(X24478,esk159_3(X24478,X24479,X24480)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24480,tc_Nat_Onat),X24478),X24479) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24480),X24479)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24480),X24482),X24479))
| esk159_3(X24478,X24479,X24480) = X24482
| hAPP(X24478,X24482) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24480,tc_Nat_Onat),X24478),X24479) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24480),X24479)) )
& ( hBOOL(hAPP(hAPP(c_member(X24480),esk160_4(X24478,X24479,X24480,X24483)),X24479))
| ~ hBOOL(hAPP(hAPP(c_member(X24480),X24483),X24479))
| hAPP(X24478,X24483) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24480,tc_Nat_Onat),X24478),X24479) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24480),X24479)) )
& ( X24483 != esk160_4(X24478,X24479,X24480,X24483)
| ~ hBOOL(hAPP(hAPP(c_member(X24480),X24483),X24479))
| hAPP(X24478,X24483) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24480,tc_Nat_Onat),X24478),X24479) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24480),X24479)) )
& ( hAPP(X24478,esk160_4(X24478,X24479,X24480,X24483)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X24480),X24483),X24479))
| hAPP(X24478,X24483) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24480,tc_Nat_Onat),X24478),X24479) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24480),X24479)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__eq__1__iff])])])])]) ).
fof(i_0_7211,plain,
! [X30433,X30434,X30435] :
( ~ c_Relation_Orefl__on(X30435,X30434,X30433)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30435,X30435),tc_HOL_Obool)),X30433),hAPP(hAPP(c_Relation_Orel__comp(X30435,X30435,X30435),hAPP(c_Relation_Oconverse(X30435,X30435),X30433)),X30433))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset])]) ).
fof(i_0_7212,plain,
! [X27917,X27918,X27919,X27920,X27921,X27922] :
( ~ c_Fun_Oinj__on(X27922,X27921,X27920,X27919)
| ~ c_Fun_Oinj__on(X27921,X27918,X27917,hAPP(c_Set_Oimage(X27922,X27921,X27920),X27919))
| c_Fun_Oinj__on(X27922,X27918,hAPP(c_Fun_Ocomp(X27921,X27918,X27922,X27917),X27920),X27919) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on])]) ).
cnf(i_0_7213,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(c_Wellfounded_Omeasure(X1),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5526]) ).
cnf(i_0_7214,plain,
c_Wellfounded_Omeasure(X1) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),
inference(split_conjunct,[status(thm)],[i_0_5527]) ).
fof(i_0_7215,plain,
! [X33665,X33666] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33666),hAPP(c_List_Oset(tc_Nat_Onat),X33665)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33666),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33665))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__sum])]) ).
fof(i_0_7216,plain,
! [X26704,X26705,X26706,X26707,X26708,X26709] :
( ~ hBOOL(hAPP(hAPP(c_member(X26709),X26708),X26707))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26709,X26706)),hAPP(hAPP(c_Product__Type_OPair(X26709,X26706),X26708),X26705)),X26704))
| hBOOL(hAPP(hAPP(c_member(X26706),X26705),hAPP(c_Relation_OImage(X26709,X26706,X26704),X26707))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__ImageI])]) ).
fof(i_0_7217,plain,
! [X31857,X31858,X31859,X31860,X31861,X31862] : hAPP(hAPP(c_Option_Omap(X31862,X31861),X31860),hAPP(hAPP(c_Option_Omap(X31859,X31862),X31858),X31857)) = hAPP(hAPP(c_Option_Omap(X31859,X31861),hAPP(c_Fun_Ocomp(X31862,X31861,X31859,X31860),X31858)),X31857),
inference(variable_rename,[status(thm)],[fact_Option_Omap_Ocompositionality]) ).
fof(i_0_7218,plain,
! [X31851,X31852,X31853,X31854,X31855,X31856] : hAPP(hAPP(c_Option_Omap(X31856,X31855),X31854),hAPP(hAPP(c_Option_Omap(X31853,X31856),X31852),X31851)) = hAPP(hAPP(c_Option_Omap(X31853,X31855),hAPP(c_Fun_Ocomp(X31856,X31855,X31853,X31854),X31852)),X31851),
inference(variable_rename,[status(thm)],[fact_option__map__comp]) ).
fof(i_0_7219,plain,
! [X31787,X31788,X31789,X31790,X31791,X31792] : hAPP(hAPP(c_List_Omap(X31792,X31791),X31790),hAPP(hAPP(c_List_Omap(X31789,X31792),X31788),X31787)) = hAPP(hAPP(c_List_Omap(X31789,X31791),hAPP(c_Fun_Ocomp(X31792,X31791,X31789,X31790),X31788)),X31787),
inference(variable_rename,[status(thm)],[fact_map__map]) ).
fof(i_0_7220,plain,
! [X31781,X31782,X31783,X31784,X31785,X31786] : hAPP(hAPP(c_List_Omap(X31786,X31785),X31784),hAPP(hAPP(c_List_Omap(X31783,X31786),X31782),X31781)) = hAPP(hAPP(c_List_Omap(X31783,X31785),hAPP(c_Fun_Ocomp(X31786,X31785,X31783,X31784),X31782)),X31781),
inference(variable_rename,[status(thm)],[fact_List_Omap_Ocompositionality]) ).
fof(i_0_7221,plain,
! [X33160,X33161,X33162,X33163] : hAPP(hAPP(c_List_Otake(X33163),X33162),hAPP(hAPP(c_List_Olist_OCons(X33163),X33161),X33160)) = c_Nat_Onat_Onat__case(tc_List_Olist(X33163),c_List_Olist_ONil(X33163),hAPP(hAPP(c_COMBB(tc_List_Olist(X33163),tc_List_Olist(X33163),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X33163),X33161)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X33163),tc_List_Olist(X33163)),c_List_Otake(X33163)),X33160)),X33162),
inference(variable_rename,[status(thm)],[fact_take__Cons]) ).
fof(i_0_7222,plain,
! [X26699,X26700,X26701,X26702,X26703] : hAPP(c_Relation_OImage(X26703,X26702,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X26703,X26702),tc_HOL_Obool)),X26701),X26700)),X26699) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26702,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26703,X26702,X26701),X26699)),hAPP(c_Relation_OImage(X26703,X26702,X26700),X26699)),
inference(variable_rename,[status(thm)],[fact_Un__Image]) ).
fof(i_0_7223,plain,
! [X22780,X22781,X22782,X22783,X22784] :
( ( X22784 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Random_Oiterate(X22783,X22782,X22784,X22781),X22780) = hAPP(c_Product__Type_OPair(X22783,X22782),X22780) )
& ( X22784 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Random_Oiterate(X22783,X22782,X22784,X22781),X22780) = hAPP(hAPP(c_Product__Type_Oscomp(X22782,X22783,X22782,tc_prod(X22783,X22782)),hAPP(X22781,X22780)),c_Random_Oiterate(X22783,X22782,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X22784),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X22781)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iterate_Osimps])]) ).
fof(i_0_7224,plain,
! [X26912,X26913,X26914,X26915,X26916] :
( ~ c_Equiv__Relations_Oequiv(X26916,X26915,X26914)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26916,X26916)),hAPP(hAPP(c_Product__Type_OPair(X26916,X26916),X26913),X26912)),X26914))
| hAPP(c_Relation_OImage(X26916,X26916,X26914),hAPP(hAPP(c_Set_Oinsert(X26916),X26913),c_Orderings_Obot__class_Obot(tc_fun(X26916,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X26916,X26916,X26914),hAPP(hAPP(c_Set_Oinsert(X26916),X26912),c_Orderings_Obot__class_Obot(tc_fun(X26916,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq])]) ).
fof(i_0_7225,plain,
! [X28745,X28746,X28747,X28748,X28749,X28750] :
( ( hBOOL(hAPP(hAPP(c_member(X28750),X28748),X28746))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28750,X28749)),hAPP(hAPP(c_Product__Type_OPair(X28750,X28749),X28748),X28747)),hAPP(hAPP(c_Product__Type_OSigma(X28750,X28749),X28746),X28745))) )
& ( hBOOL(hAPP(hAPP(c_member(X28749),X28747),hAPP(X28745,X28748)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28750,X28749)),hAPP(hAPP(c_Product__Type_OPair(X28750,X28749),X28748),X28747)),hAPP(hAPP(c_Product__Type_OSigma(X28750,X28749),X28746),X28745))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5528])])]) ).
fof(i_0_7226,plain,
! [X28727,X28728,X28729,X28730,X28731,X28732] :
( ( hBOOL(hAPP(hAPP(c_member(X28732),X28730),X28728))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28732,X28731)),hAPP(hAPP(c_Product__Type_OPair(X28732,X28731),X28730),X28729)),hAPP(hAPP(c_Product__Type_OSigma(X28732,X28731),X28728),X28727))) )
& ( hBOOL(hAPP(hAPP(c_member(X28731),X28729),hAPP(X28727,X28730)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28732,X28731)),hAPP(hAPP(c_Product__Type_OPair(X28732,X28731),X28730),X28729)),hAPP(hAPP(c_Product__Type_OSigma(X28732,X28731),X28728),X28727))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28732),X28730),X28728))
| ~ hBOOL(hAPP(hAPP(c_member(X28731),X28729),hAPP(X28727,X28730)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X28732,X28731)),hAPP(hAPP(c_Product__Type_OPair(X28732,X28731),X28730),X28729)),hAPP(hAPP(c_Product__Type_OSigma(X28732,X28731),X28728),X28727))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff])])]) ).
fof(i_0_7227,plain,
! [X28739,X28740,X28741,X28742,X28743,X28744] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28744,X28743)),hAPP(hAPP(c_Product__Type_OPair(X28744,X28743),X28742),X28741)),hAPP(hAPP(c_Product__Type_OSigma(X28744,X28743),X28740),X28739)))
| hBOOL(hAPP(hAPP(c_member(X28743),X28741),hAPP(X28739,X28742))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD2])]) ).
fof(i_0_7228,plain,
! [X33213,X33214,X33215] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33215,X33215),tc_HOL_Obool)),X33214),X33213))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X33215),tc_List_Olist(X33215)),tc_HOL_Obool)),c_List_Olistrel1(X33215,X33214)),c_List_Olistrel1(X33215,X33213))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__mono])]) ).
fof(i_0_7229,plain,
! [X32270,X32271,X32272] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32272,X32272),tc_HOL_Obool)),X32271),X32270))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X32272),tc_List_Olist(X32272)),tc_HOL_Obool)),c_List_Olistrel(X32272,X32271)),c_List_Olistrel(X32272,X32270))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__mono])]) ).
cnf(i_0_7230,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Oconcat(X1,X4)) = c_List_Oconcat(X2,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X2)),hAPP(c_List_Omap(X1,X2),X3)),X4)),
inference(split_conjunct,[status(thm)],[i_0_5529]) ).
fof(i_0_7231,plain,
! [X22841,X22842,X22843,X22844,X22845,X22846,X22847] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X22847,X22846,X22845,X22844),X22843),X22842),X22841) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22846,X22845,X22844),X22842),hAPP(X22843,X22841)),
inference(variable_rename,[status(thm)],[fact_scomp__def]) ).
fof(i_0_7232,plain,
! [X22822,X22823,X22824,X22825,X22826,X22827,X22828] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X22828,X22827,X22826,X22825),X22824),X22823),X22822) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22827,X22826,X22825),X22823),hAPP(X22824,X22822)),
inference(variable_rename,[status(thm)],[fact_scomp__apply]) ).
fof(i_0_7233,plain,
! [X24003,X24004,X24005,X24006] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24006,tc_HOL_Obool)),X24005),X24004))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24006,tc_HOL_Obool)),X24003),X24004))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24006,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24006,tc_HOL_Obool)),X24005),X24003)),X24004)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__least])]) ).
fof(i_0_7234,plain,
! [X27574,X27575,X27576,X27577,X27578] :
( ~ c_Finite__Set_Ofolding__one(X27578,X27577,X27576)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27578),X27575))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27578),X27574))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27578,tc_HOL_Obool)),X27575),X27574) = c_Orderings_Obot__class_Obot(tc_fun(X27578,tc_HOL_Obool))
| hAPP(hAPP(X27577,hAPP(X27576,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27578,tc_HOL_Obool)),X27575),X27574))),hAPP(X27576,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27578,tc_HOL_Obool)),X27575),X27574))) = hAPP(hAPP(X27577,hAPP(X27576,X27575)),hAPP(X27576,X27574)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter])]) ).
fof(i_0_7235,plain,
! [X28429,X28430,X28431,X28432,X28433] :
( ~ c_Fun_Oinj__on(X28433,X28432,X28431,X28430)
| ~ hBOOL(hAPP(hAPP(c_member(X28432),X28429),hAPP(c_Set_Oimage(X28433,X28432,X28431),X28430)))
| hAPP(X28431,hAPP(c_Fun_Othe__inv__into(X28433,X28432,X28430,X28431),X28429)) = X28429 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f])]) ).
cnf(i_0_7236,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_5530]) ).
cnf(i_0_7237,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_5531]) ).
fof(i_0_7238,plain,
! [X31226,X31227,X31228,X31229] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X31229,tc_HOL_Obool),tc_fun(X31228,tc_HOL_Obool)),X31227),hAPP(hAPP(c_COMBC(tc_fun(X31229,tc_HOL_Obool),tc_fun(X31229,tc_fun(X31228,tc_HOL_Obool)),tc_fun(X31228,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31229,tc_fun(X31228,tc_HOL_Obool))),X31226)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31229,tc_fun(X31228,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31229,tc_HOL_Obool),X31227)),X31226),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I8_J]) ).
fof(i_0_7239,plain,
! [X31351,X31352,X31353,X31354] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31354,tc_HOL_Obool),tc_fun(X31353,tc_HOL_Obool)),X31352),hAPP(hAPP(c_COMBC(tc_fun(X31354,tc_HOL_Obool),tc_fun(X31354,tc_fun(X31353,tc_HOL_Obool)),tc_fun(X31353,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31354,tc_fun(X31353,tc_HOL_Obool))),X31351)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31354,tc_fun(X31353,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31354,tc_HOL_Obool),X31352)),X31351),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I8_J]) ).
fof(i_0_7240,plain,
! [X31230,X31231,X31232,X31233] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31233,tc_fun(X31232,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31233,tc_HOL_Obool),X31231)),X31230) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X31233,tc_HOL_Obool),tc_fun(X31232,tc_HOL_Obool)),X31231),hAPP(hAPP(c_COMBC(tc_fun(X31233,tc_HOL_Obool),tc_fun(X31233,tc_fun(X31232,tc_HOL_Obool)),tc_fun(X31232,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31233,tc_fun(X31232,tc_HOL_Obool))),X31230)),
inference(variable_rename,[status(thm)],[fact_INT__simps_I8_J]) ).
fof(i_0_7241,plain,
! [X31347,X31348,X31349,X31350] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31350,tc_fun(X31349,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31350,tc_HOL_Obool),X31348)),X31347) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31350,tc_HOL_Obool),tc_fun(X31349,tc_HOL_Obool)),X31348),hAPP(hAPP(c_COMBC(tc_fun(X31350,tc_HOL_Obool),tc_fun(X31350,tc_fun(X31349,tc_HOL_Obool)),tc_fun(X31349,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31350,tc_fun(X31349,tc_HOL_Obool))),X31347)),
inference(variable_rename,[status(thm)],[fact_UN__simps_I8_J]) ).
fof(i_0_7242,plain,
! [X27945,X27946,X27947,X27948,X27949,X27950,X27951,X27952,X27953,X27954] :
( ( ~ c_Fun_Oinj__on(X27948,X27947,X27946,X27945)
| ~ hBOOL(hAPP(hAPP(c_member(X27948),X27949),X27945))
| ~ hBOOL(hAPP(hAPP(c_member(X27948),X27950),X27945))
| hAPP(X27946,X27949) != hAPP(X27946,X27950)
| X27949 = X27950 )
& ( hBOOL(hAPP(hAPP(c_member(X27954),esk263_4(X27951,X27952,X27953,X27954)),X27951))
| c_Fun_Oinj__on(X27954,X27953,X27952,X27951) )
& ( hBOOL(hAPP(hAPP(c_member(X27954),esk264_4(X27951,X27952,X27953,X27954)),X27951))
| c_Fun_Oinj__on(X27954,X27953,X27952,X27951) )
& ( hAPP(X27952,esk263_4(X27951,X27952,X27953,X27954)) = hAPP(X27952,esk264_4(X27951,X27952,X27953,X27954))
| c_Fun_Oinj__on(X27954,X27953,X27952,X27951) )
& ( esk263_4(X27951,X27952,X27953,X27954) != esk264_4(X27951,X27952,X27953,X27954)
| c_Fun_Oinj__on(X27954,X27953,X27952,X27951) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__def])])])])])]) ).
fof(i_0_7243,plain,
! [X30221,X30222,X30223] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30223,X30223),tc_HOL_Obool)),X30222),X30221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30223,X30223),tc_HOL_Obool)),X30221),c_Transitive__Closure_Ortrancl(X30223,X30222)))
| c_Transitive__Closure_Ortrancl(X30223,X30221) = c_Transitive__Closure_Ortrancl(X30223,X30222) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])]) ).
fof(i_0_7244,plain,
! [X26931,X26932,X26933,X26934,X26935] :
( hAPP(c_Relation_OImage(X26935,X26935,X26934),hAPP(hAPP(c_Set_Oinsert(X26935),X26933),c_Orderings_Obot__class_Obot(tc_fun(X26935,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X26935,X26935,X26934),hAPP(hAPP(c_Set_Oinsert(X26935),X26932),c_Orderings_Obot__class_Obot(tc_fun(X26935,tc_HOL_Obool))))
| ~ c_Equiv__Relations_Oequiv(X26935,X26931,X26934)
| ~ hBOOL(hAPP(hAPP(c_member(X26935),X26932),X26931))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26935,X26935)),hAPP(hAPP(c_Product__Type_OPair(X26935,X26935),X26933),X26932)),X26934)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class])]) ).
fof(i_0_7245,plain,
! [X32347,X32348,X32349,X32350,X32351,X32352] :
( ( X32352 != X32351
| hAPP(c_Map_Omap__of(X32350,X32349,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X32350,X32349)),hAPP(hAPP(c_Product__Type_OPair(X32350,X32349),X32352),X32348)),X32347)),X32351) = hAPP(c_Option_Ooption_OSome(X32349),X32348) )
& ( X32352 = X32351
| hAPP(c_Map_Omap__of(X32350,X32349,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X32350,X32349)),hAPP(hAPP(c_Product__Type_OPair(X32350,X32349),X32352),X32348)),X32347)),X32351) = hAPP(c_Map_Omap__of(X32350,X32349,X32347),X32351) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__Cons__code_I2_J])]) ).
fof(i_0_7246,plain,
! [X28733,X28734,X28735,X28736,X28737,X28738] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28738,X28737)),hAPP(hAPP(c_Product__Type_OPair(X28738,X28737),X28736),X28735)),hAPP(hAPP(c_Product__Type_OSigma(X28738,X28737),X28734),X28733)))
| hBOOL(hAPP(hAPP(c_member(X28738),X28736),X28734)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD1])]) ).
fof(i_0_7247,plain,
! [X26112,X26113,X26114,X26115,X26117] :
( ( hBOOL(hAPP(hAPP(c_member(X26114),esk210_4(X26112,X26113,X26114,X26115)),X26113))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26114,X26115),X26112),X26113) != c_Groups_Ozero__class_Ozero(X26115)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26114),X26113))
| ~ class_Rings_Ocomm__semiring__1(X26115)
| ~ class_Rings_Ono__zero__divisors(X26115) )
& ( hAPP(X26112,esk210_4(X26112,X26113,X26114,X26115)) = c_Groups_Ozero__class_Ozero(X26115)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26114,X26115),X26112),X26113) != c_Groups_Ozero__class_Ozero(X26115)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26114),X26113))
| ~ class_Rings_Ocomm__semiring__1(X26115)
| ~ class_Rings_Ono__zero__divisors(X26115) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X26114),X26117),X26113))
| hAPP(X26112,X26117) != c_Groups_Ozero__class_Ozero(X26115)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26114,X26115),X26112),X26113) = c_Groups_Ozero__class_Ozero(X26115)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26114),X26113))
| ~ class_Rings_Ocomm__semiring__1(X26115)
| ~ class_Rings_Ono__zero__divisors(X26115) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__zero__iff])])])])]) ).
fof(i_0_7248,plain,
! [X24590,X24591,X24592,X24593] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24593),X24592))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24591),hAPP(c_Set_Oimage(X24593,X24591,X24590),X24592))),hAPP(c_Finite__Set_Ocard(X24593),X24592))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).
fof(i_0_7249,plain,
! [X32714,X32715,X32716,X32717,X32718] :
( ~ class_Orderings_Olinorder(X32718)
| hBOOL(hAPP(hAPP(c_member(X32718),hAPP(X32717,X32716)),hAPP(c_Set_Oimage(X32715,X32718,X32717),hAPP(c_List_Oset(X32715),X32714))))
| c_List_Olinorder__class_Oinsort__insert__key(X32715,X32718,X32717,X32716,X32714) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32715,X32718,X32717),X32716),X32714) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5532])]) ).
cnf(i_0_7250,plain,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Relation_OId(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5533]) ).
fof(i_0_7251,plain,
! [X31076,X31077,X31078,X31079,X31080,X31081,X31082,X31083,X31084] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31079,tc_fun(X31078,tc_HOL_Obool)),X31077),X31076) != c_Orderings_Otop__class_Otop(tc_fun(X31078,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X31079),X31080),X31077))
| hAPP(X31076,X31080) = c_Orderings_Otop__class_Otop(tc_fun(X31078,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X31084),esk394_4(X31081,X31082,X31083,X31084)),X31082))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31084,tc_fun(X31083,tc_HOL_Obool)),X31082),X31081) = c_Orderings_Otop__class_Otop(tc_fun(X31083,tc_HOL_Obool)) )
& ( hAPP(X31081,esk394_4(X31081,X31082,X31083,X31084)) != c_Orderings_Otop__class_Otop(tc_fun(X31083,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31084,tc_fun(X31083,tc_HOL_Obool)),X31082),X31081) = c_Orderings_Otop__class_Otop(tc_fun(X31083,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I2_J])])])])])]) ).
fof(i_0_7252,plain,
! [X24693,X24694,X24695,X24696,X24697,X24698,X24699,X24700,X24701] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24696,tc_fun(X24695,tc_HOL_Obool)),X24694),X24693) != c_Orderings_Obot__class_Obot(tc_fun(X24695,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X24696),X24697),X24694))
| hAPP(X24693,X24697) = c_Orderings_Obot__class_Obot(tc_fun(X24695,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X24701),esk164_4(X24698,X24699,X24700,X24701)),X24699))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24701,tc_fun(X24700,tc_HOL_Obool)),X24699),X24698) = c_Orderings_Obot__class_Obot(tc_fun(X24700,tc_HOL_Obool)) )
& ( hAPP(X24698,esk164_4(X24698,X24699,X24700,X24701)) != c_Orderings_Obot__class_Obot(tc_fun(X24700,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24701,tc_fun(X24700,tc_HOL_Obool)),X24699),X24698) = c_Orderings_Obot__class_Obot(tc_fun(X24700,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I2_J])])])])])]) ).
fof(i_0_7253,plain,
! [X24676,X24677,X24678,X24679,X24680,X24681,X24682,X24683,X24684] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X24679,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24678,tc_fun(X24679,tc_HOL_Obool)),X24677),X24676)
| ~ hBOOL(hAPP(hAPP(c_member(X24678),X24680),X24677))
| hAPP(X24676,X24680) = c_Orderings_Obot__class_Obot(tc_fun(X24679,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X24683),esk163_4(X24681,X24682,X24683,X24684)),X24682))
| c_Orderings_Obot__class_Obot(tc_fun(X24684,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24683,tc_fun(X24684,tc_HOL_Obool)),X24682),X24681) )
& ( hAPP(X24681,esk163_4(X24681,X24682,X24683,X24684)) != c_Orderings_Obot__class_Obot(tc_fun(X24684,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X24684,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24683,tc_fun(X24684,tc_HOL_Obool)),X24682),X24681) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I1_J])])])])])]) ).
fof(i_0_7254,plain,
! [X31086,X31087,X31088,X31089,X31090,X31091,X31092,X31093,X31094] :
( ( c_Orderings_Otop__class_Otop(tc_fun(X31089,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31088,tc_fun(X31089,tc_HOL_Obool)),X31087),X31086)
| ~ hBOOL(hAPP(hAPP(c_member(X31088),X31090),X31087))
| hAPP(X31086,X31090) = c_Orderings_Otop__class_Otop(tc_fun(X31089,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X31093),esk395_4(X31091,X31092,X31093,X31094)),X31092))
| c_Orderings_Otop__class_Otop(tc_fun(X31094,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31093,tc_fun(X31094,tc_HOL_Obool)),X31092),X31091) )
& ( hAPP(X31091,esk395_4(X31091,X31092,X31093,X31094)) != c_Orderings_Otop__class_Otop(tc_fun(X31094,tc_HOL_Obool))
| c_Orderings_Otop__class_Otop(tc_fun(X31094,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31093,tc_fun(X31094,tc_HOL_Obool)),X31092),X31091) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I1_J])])])])])]) ).
fof(i_0_7255,plain,
! [X23732,X23733,X23734,X23735] :
( ( hBOOL(hAPP(hAPP(c_member(X23735),esk128_4(X23732,X23733,X23734,X23735)),X23733))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23735,tc_Nat_Onat),X23734),X23733) != hAPP(c_Nat_OSuc,X23732) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X23734,esk128_4(X23732,X23733,X23734,X23735))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23735,tc_Nat_Onat),X23734),X23733) != hAPP(c_Nat_OSuc,X23732) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__SucD])])])]) ).
fof(i_0_7256,plain,
! [X27798,X27799,X27800] :
( ~ class_Lattices_Olattice(X27800)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27800),X27799))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27800),X27798))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27800,tc_HOL_Obool)),X27799),X27798) = c_Orderings_Obot__class_Obot(tc_fun(X27800,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27800),c_Big__Operators_Olattice__class_OInf__fin(X27800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27800,tc_HOL_Obool)),X27799),X27798))),c_Big__Operators_Olattice__class_OInf__fin(X27800,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27800,tc_HOL_Obool)),X27799),X27798))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27800),c_Big__Operators_Olattice__class_OInf__fin(X27800,X27799)),c_Big__Operators_Olattice__class_OInf__fin(X27800,X27798)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter])]) ).
fof(i_0_7257,plain,
! [X27602,X27603,X27604] :
( ~ class_Lattices_Olattice(X27604)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27604),X27603))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27604),X27602))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27604,tc_HOL_Obool)),X27603),X27602) = c_Orderings_Obot__class_Obot(tc_fun(X27604,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27604),c_Big__Operators_Olattice__class_OSup__fin(X27604,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27604,tc_HOL_Obool)),X27603),X27602))),c_Big__Operators_Olattice__class_OSup__fin(X27604,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27604,tc_HOL_Obool)),X27603),X27602))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27604),c_Big__Operators_Olattice__class_OSup__fin(X27604,X27603)),c_Big__Operators_Olattice__class_OSup__fin(X27604,X27602)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter])]) ).
fof(i_0_7258,plain,
! [X27617,X27618,X27619] :
( ~ class_Orderings_Olinorder(X27619)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27619),X27618))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27619),X27617))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27619,tc_HOL_Obool)),X27618),X27617) = c_Orderings_Obot__class_Obot(tc_fun(X27619,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X27619),c_Big__Operators_Olinorder__class_OMax(X27619,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27619,tc_HOL_Obool)),X27618),X27617))),c_Big__Operators_Olinorder__class_OMax(X27619,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27619,tc_HOL_Obool)),X27618),X27617))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27619),c_Big__Operators_Olinorder__class_OMax(X27619,X27618)),c_Big__Operators_Olinorder__class_OMax(X27619,X27617)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter])]) ).
fof(i_0_7259,plain,
! [X27608,X27609,X27610] :
( ~ class_Orderings_Olinorder(X27610)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27610),X27609))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27610),X27608))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27610,tc_HOL_Obool)),X27609),X27608) = c_Orderings_Obot__class_Obot(tc_fun(X27610,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X27610),c_Big__Operators_Olinorder__class_OMin(X27610,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27610,tc_HOL_Obool)),X27609),X27608))),c_Big__Operators_Olinorder__class_OMin(X27610,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27610,tc_HOL_Obool)),X27609),X27608))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27610),c_Big__Operators_Olinorder__class_OMin(X27610,X27609)),c_Big__Operators_Olinorder__class_OMin(X27610,X27608)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter])]) ).
fof(i_0_7260,plain,
! [X25160,X25161,X25162,X25163,X25164,X25165,X25166] :
( ( hAPP(X25163,X25161) != hAPP(X25163,X25160)
| X25161 = X25160
| ~ hBOOL(hAPP(hAPP(c_member(X25165),X25160),X25162))
| ~ hBOOL(hAPP(hAPP(c_member(X25165),X25161),X25162))
| ~ c_Typedef_Otype__definition(X25166,X25165,X25164,X25163,X25162) )
& ( X25161 != X25160
| hAPP(X25163,X25161) = hAPP(X25163,X25160)
| ~ hBOOL(hAPP(hAPP(c_member(X25165),X25160),X25162))
| ~ hBOOL(hAPP(hAPP(c_member(X25165),X25161),X25162))
| ~ c_Typedef_Otype__definition(X25166,X25165,X25164,X25163,X25162) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inject])])]) ).
fof(i_0_7261,plain,
! [X26419,X26420,X26421,X26422] : hAPP(c_Relation_OField(X26422),hAPP(hAPP(c_Set_Oinsert(tc_prod(X26422,X26422)),hAPP(hAPP(c_Product__Type_OPair(X26422,X26422),X26421),X26420)),X26419)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26422,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26422),X26421),hAPP(hAPP(c_Set_Oinsert(X26422),X26420),c_Orderings_Obot__class_Obot(tc_fun(X26422,tc_HOL_Obool))))),hAPP(c_Relation_OField(X26422),X26419)),
inference(variable_rename,[status(thm)],[fact_Field__insert]) ).
fof(i_0_7262,plain,
! [X33574,X33575,X33576] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33576),X33575))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33576),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33575),X33574))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_start__le__sum])]) ).
cnf(i_0_7263,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5534]) ).
fof(i_0_7264,plain,
! [X18188,X18189,X18190,X18191,X18192,X18193] : c_Nitpick_Opair__box_Opair__box__size(X18193,X18192,X18191,X18190,c_Nitpick_Opair__box_OPairBox(X18193,X18192,X18189,X18188)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X18191,X18189)),hAPP(X18190,X18188))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I1_J]) ).
fof(i_0_7265,plain,
! [X31445,X31446,X31447] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31447,tc_HOL_Obool)),esk405_3(X31445,X31446,X31447)),X31446))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31445),hAPP(c_Finite__Set_Ocard(tc_fun(X31447,tc_HOL_Obool)),X31446)) = hAPP(c_Finite__Set_Ocard(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31447,tc_HOL_Obool)),esk404_3(X31445,X31446,X31447)),X31446))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31447,tc_HOL_Obool)),X31446)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31447,tc_HOL_Obool)),esk406_3(X31445,X31446,X31447)),X31446))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31445),hAPP(c_Finite__Set_Ocard(tc_fun(X31447,tc_HOL_Obool)),X31446)) = hAPP(c_Finite__Set_Ocard(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31447,tc_HOL_Obool)),esk404_3(X31445,X31446,X31447)),X31446))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31447,tc_HOL_Obool)),X31446)) )
& ( esk405_3(X31445,X31446,X31447) != esk406_3(X31445,X31446,X31447)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31445),hAPP(c_Finite__Set_Ocard(tc_fun(X31447,tc_HOL_Obool)),X31446)) = hAPP(c_Finite__Set_Ocard(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31447,tc_HOL_Obool)),esk404_3(X31445,X31446,X31447)),X31446))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31447,tc_HOL_Obool)),X31446)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31447,tc_HOL_Obool)),esk405_3(X31445,X31446,X31447)),esk406_3(X31445,X31446,X31447)) != c_Orderings_Obot__class_Obot(tc_fun(X31447,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31445),hAPP(c_Finite__Set_Ocard(tc_fun(X31447,tc_HOL_Obool)),X31446)) = hAPP(c_Finite__Set_Ocard(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31447,tc_HOL_Obool)),esk404_3(X31445,X31446,X31447)),X31446))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31447,tc_HOL_Obool)),X31446)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31447,tc_HOL_Obool)),esk405_3(X31445,X31446,X31447)),X31446))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31445),hAPP(c_Finite__Set_Ocard(tc_fun(X31447,tc_HOL_Obool)),X31446)) = hAPP(c_Finite__Set_Ocard(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446))
| hAPP(c_Finite__Set_Ocard(X31447),esk404_3(X31445,X31446,X31447)) != X31445
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31447,tc_HOL_Obool)),X31446)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31447,tc_HOL_Obool)),esk406_3(X31445,X31446,X31447)),X31446))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31445),hAPP(c_Finite__Set_Ocard(tc_fun(X31447,tc_HOL_Obool)),X31446)) = hAPP(c_Finite__Set_Ocard(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446))
| hAPP(c_Finite__Set_Ocard(X31447),esk404_3(X31445,X31446,X31447)) != X31445
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31447,tc_HOL_Obool)),X31446)) )
& ( esk405_3(X31445,X31446,X31447) != esk406_3(X31445,X31446,X31447)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31445),hAPP(c_Finite__Set_Ocard(tc_fun(X31447,tc_HOL_Obool)),X31446)) = hAPP(c_Finite__Set_Ocard(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446))
| hAPP(c_Finite__Set_Ocard(X31447),esk404_3(X31445,X31446,X31447)) != X31445
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31447,tc_HOL_Obool)),X31446)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31447,tc_HOL_Obool)),esk405_3(X31445,X31446,X31447)),esk406_3(X31445,X31446,X31447)) != c_Orderings_Obot__class_Obot(tc_fun(X31447,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31445),hAPP(c_Finite__Set_Ocard(tc_fun(X31447,tc_HOL_Obool)),X31446)) = hAPP(c_Finite__Set_Ocard(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446))
| hAPP(c_Finite__Set_Ocard(X31447),esk404_3(X31445,X31446,X31447)) != X31445
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31447,tc_HOL_Obool),X31446)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31447,tc_HOL_Obool)),X31446)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__partition])])])]) ).
fof(i_0_7266,plain,
! [X34022,X34023,X34024] :
( ~ class_Orderings_Olinorder(X34024)
| c_List_Olinorder__class_Osorted(X34024,hAPP(c_List_Ofilter(X34024,hAPP(hAPP(c_COMBC(X34024,X34024,tc_HOL_Obool),c_fequal),hAPP(X34023,X34022))),X34022)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__same])]) ).
fof(i_0_7267,plain,
! [X27994,X27995,X27996,X27997,X27998] :
( ~ c_Fun_Oinj__on(X27998,X27997,X27996,c_Orderings_Otop__class_Otop(tc_fun(X27998,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X27995,X27998,X27994,c_Orderings_Otop__class_Otop(tc_fun(X27995,tc_HOL_Obool)))
| c_Fun_Oinj__on(X27995,X27997,hAPP(c_Fun_Ocomp(X27998,X27997,X27995,X27996),X27994),c_Orderings_Otop__class_Otop(tc_fun(X27995,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__comp])]) ).
fof(i_0_7268,plain,
! [X32803,X32804,X32805,X32806] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32806,tc_HOL_Obool)),hAPP(c_List_Oset(X32806),hAPP(hAPP(c_List_Olist__update(X32806,X32805),X32804),X32803))),hAPP(hAPP(c_Set_Oinsert(X32806),X32803),hAPP(c_List_Oset(X32806),X32805)))),
inference(variable_rename,[status(thm)],[fact_set__update__subset__insert]) ).
cnf(i_0_7269,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X2),
inference(split_conjunct,[status(thm)],[i_0_5535]) ).
fof(i_0_7270,plain,
! [X25944,X25945,X25946] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25946,tc_HOL_Obool)),X25945),hAPP(hAPP(c_Set_Oinsert(X25946),X25944),c_Orderings_Obot__class_Obot(tc_fun(X25946,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25946,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25946,c_Orderings_Oord__class_Omin(X25946),X25945) = X25944
| ~ hBOOL(hAPP(hAPP(c_member(X25946),X25944),X25945))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25946),X25945))
| ~ class_Orderings_Olinorder(X25946) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25946,tc_HOL_Obool)),X25945),hAPP(hAPP(c_Set_Oinsert(X25946),X25944),c_Orderings_Obot__class_Obot(tc_fun(X25946,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25946,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25946,c_Orderings_Oord__class_Omin(X25946),X25945) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25946),X25944),c_Big__Operators_Olattice_OInf__fin(X25946,c_Orderings_Oord__class_Omin(X25946),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25946,tc_HOL_Obool)),X25945),hAPP(hAPP(c_Set_Oinsert(X25946),X25944),c_Orderings_Obot__class_Obot(tc_fun(X25946,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X25946),X25944),X25945))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25946),X25945))
| ~ class_Orderings_Olinorder(X25946) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oremove])])]) ).
fof(i_0_7271,plain,
! [X25941,X25942,X25943] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25943,tc_HOL_Obool)),X25942),hAPP(hAPP(c_Set_Oinsert(X25943),X25941),c_Orderings_Obot__class_Obot(tc_fun(X25943,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25943,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25943,c_Orderings_Oord__class_Omax(X25943),X25942) = X25941
| ~ hBOOL(hAPP(hAPP(c_member(X25943),X25941),X25942))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25943),X25942))
| ~ class_Orderings_Olinorder(X25943) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25943,tc_HOL_Obool)),X25942),hAPP(hAPP(c_Set_Oinsert(X25943),X25941),c_Orderings_Obot__class_Obot(tc_fun(X25943,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25943,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25943,c_Orderings_Oord__class_Omax(X25943),X25942) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25943),X25941),c_Big__Operators_Olattice_OSup__fin(X25943,c_Orderings_Oord__class_Omax(X25943),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25943,tc_HOL_Obool)),X25942),hAPP(hAPP(c_Set_Oinsert(X25943),X25941),c_Orderings_Obot__class_Obot(tc_fun(X25943,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X25943),X25941),X25942))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25943),X25942))
| ~ class_Orderings_Olinorder(X25943) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oremove])])]) ).
fof(i_0_7272,plain,
! [X26043,X26044,X26045] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26045,tc_Nat_Onat),X26044),X26043) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26045,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X26045),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X26044)),X26043)),
inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I2_J]) ).
fof(i_0_7273,plain,
! [X23494,X23495,X23496] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23496,tc_Nat_Onat),X23495),X23494) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23496,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X23496),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23495)),X23494)),
inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I1_J]) ).
fof(i_0_7274,plain,
! [X28351,X28352,X28353,X28354,X28355] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28355),X28354),hAPP(c_Set_Ovimage(X28355,X28353,X28352),hAPP(hAPP(c_Set_Oinsert(X28353),X28351),c_Orderings_Obot__class_Obot(tc_fun(X28353,tc_HOL_Obool))))))
| hAPP(X28352,X28354) = X28351 )
& ( hAPP(X28352,X28354) != X28351
| hBOOL(hAPP(hAPP(c_member(X28355),X28354),hAPP(c_Set_Ovimage(X28355,X28353,X28352),hAPP(hAPP(c_Set_Oinsert(X28353),X28351),c_Orderings_Obot__class_Obot(tc_fun(X28353,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq])]) ).
cnf(i_0_7275,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5536]) ).
fof(i_0_7276,plain,
! [X27962,X27963,X27964,X27965,X27966,X27967] :
( ~ c_Fun_Oinj__on(X27967,X27966,hAPP(c_Fun_Ocomp(X27965,X27966,X27967,X27964),X27963),X27962)
| c_Fun_Oinj__on(X27967,X27965,X27963,X27962) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI2])]) ).
cnf(i_0_7277,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_Osucc(X2))),
inference(split_conjunct,[status(thm)],[i_0_5537]) ).
fof(i_0_7278,plain,
! [X24564,X24565,X24566,X24567] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24567),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24567,tc_HOL_Obool)),X24566),hAPP(hAPP(c_Set_Oinsert(X24567),X24565),X24564))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24567),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24567,tc_HOL_Obool)),X24566),X24564))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24567),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24567,tc_HOL_Obool)),X24566),X24564)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24567),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24567,tc_HOL_Obool)),X24566),hAPP(hAPP(c_Set_Oinsert(X24567),X24565),X24564)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert])]) ).
fof(i_0_7279,plain,
! [X29238,X29239,X29240] : hAPP(hAPP(c_Set_Oinsert(X29240),X29239),X29238) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29240,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29240),hAPP(hAPP(c_COMBC(X29240,X29240,tc_HOL_Obool),c_fequal),X29239))),X29238),
inference(variable_rename,[status(thm)],[fact_insert__def]) ).
cnf(i_0_7280,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5538]) ).
cnf(i_0_7281,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5539]) ).
cnf(i_0_7282,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5540]) ).
cnf(i_0_7283,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5541]) ).
cnf(i_0_7284,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5470]) ).
cnf(i_0_7285,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5471]) ).
cnf(i_0_7286,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5472]) ).
cnf(i_0_7287,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5473]) ).
fof(i_0_7288,plain,
! [X20372,X20373,X20374,X20375,X20376,X20377] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20377),X20376),X20375)),X20374) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20377),X20373),X20375)),X20372)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20377),X20376),X20373)),X20375)),X20374) = X20372
| ~ class_Rings_Oring(X20377) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20377),X20376),X20373)),X20375)),X20374) != X20372
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20377),X20376),X20375)),X20374) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20377),X20373),X20375)),X20372)
| ~ class_Rings_Oring(X20377) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).
fof(i_0_7289,plain,
! [X20366,X20367,X20368,X20369,X20370,X20371] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20371),X20370),X20369)),X20368) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20371),X20367),X20369)),X20366)
| X20368 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20371),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20371),X20367),X20370)),X20369)),X20366)
| ~ class_Rings_Oring(X20371) )
& ( X20368 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20371),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20371),X20367),X20370)),X20369)),X20366)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20371),X20370),X20369)),X20368) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20371),X20367),X20369)),X20366)
| ~ class_Rings_Oring(X20371) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).
fof(i_0_7290,plain,
! [X31188,X31189,X31190,X31191,X31192,X31193] :
( ~ c_Relation_Osingle__valued(X31193,X31192,hAPP(c_Relation_Oconverse(X31192,X31193),X31191))
| X31190 = c_Orderings_Obot__class_Obot(tc_fun(X31189,tc_HOL_Obool))
| hAPP(c_Relation_OImage(X31192,X31193,X31191),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31189,tc_fun(X31192,tc_HOL_Obool)),X31190),X31188)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31189,tc_fun(X31193,tc_HOL_Obool)),X31190),hAPP(hAPP(c_COMBB(tc_fun(X31192,tc_HOL_Obool),tc_fun(X31193,tc_HOL_Obool),X31189),c_Relation_OImage(X31192,X31193,X31191)),X31188)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__INT__eq])]) ).
fof(i_0_7291,plain,
! [X33926,X33927,X33928] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X33928),tc_List_Olist(X33928)),c_List_Opartition(X33928,X33927,X33926)) = hAPP(c_List_Ofilter(X33928,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X33928,c_fNot),X33927)),X33926),
inference(variable_rename,[status(thm)],[fact_partition__filter2]) ).
fof(i_0_7292,plain,
! [X28307,X28308,X28309,X28310,X28311] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28311,tc_HOL_Obool)),X28310),X28309))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28308,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28308,X28311,X28307),X28310)),hAPP(c_Set_Ovimage(X28308,X28311,X28307),X28309))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__mono])]) ).
fof(i_0_7293,plain,
! [X23712,X23713,X23714,X23715,X23716] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23716,tc_HOL_Obool)),X23715),X23714))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23713,tc_HOL_Obool)),hAPP(c_Set_Oimage(X23716,X23713,X23712),X23715)),hAPP(c_Set_Oimage(X23716,X23713,X23712),X23714))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_7294,plain,
! [X26951,X26952,X26953,X26954,X26955,X26956] :
( ~ c_Equiv__Relations_Oequiv(X26956,X26955,X26954)
| ~ c_Equiv__Relations_Ocongruent(X26956,tc_fun(X26953,tc_HOL_Obool),X26954,X26952)
| ~ hBOOL(hAPP(hAPP(c_member(X26956),X26951),X26955))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26956,tc_fun(X26953,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26956,X26956,X26954),hAPP(hAPP(c_Set_Oinsert(X26956),X26951),c_Orderings_Obot__class_Obot(tc_fun(X26956,tc_HOL_Obool))))),X26952) = hAPP(X26952,X26951) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class])]) ).
fof(i_0_7295,plain,
! [X25989,X25990,X25991] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25991,tc_HOL_Obool)),X25990),hAPP(hAPP(c_Set_Oinsert(X25991),X25989),c_Orderings_Obot__class_Obot(tc_fun(X25991,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25991,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25991,c_Orderings_Oord__class_Omin(X25991),hAPP(hAPP(c_Set_Oinsert(X25991),X25989),X25990)) = X25989
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25991),X25990))
| ~ class_Orderings_Olinorder(X25991) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25991,tc_HOL_Obool)),X25990),hAPP(hAPP(c_Set_Oinsert(X25991),X25989),c_Orderings_Obot__class_Obot(tc_fun(X25991,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25991,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25991,c_Orderings_Oord__class_Omin(X25991),hAPP(hAPP(c_Set_Oinsert(X25991),X25989),X25990)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25991),X25989),c_Big__Operators_Olattice_OInf__fin(X25991,c_Orderings_Oord__class_Omin(X25991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25991,tc_HOL_Obool)),X25990),hAPP(hAPP(c_Set_Oinsert(X25991),X25989),c_Orderings_Obot__class_Obot(tc_fun(X25991,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25991),X25990))
| ~ class_Orderings_Olinorder(X25991) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove])])]) ).
fof(i_0_7296,plain,
! [X25992,X25993,X25994] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25994,tc_HOL_Obool)),X25993),hAPP(hAPP(c_Set_Oinsert(X25994),X25992),c_Orderings_Obot__class_Obot(tc_fun(X25994,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25994,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25994,c_Orderings_Oord__class_Omax(X25994),hAPP(hAPP(c_Set_Oinsert(X25994),X25992),X25993)) = X25992
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25994),X25993))
| ~ class_Orderings_Olinorder(X25994) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25994,tc_HOL_Obool)),X25993),hAPP(hAPP(c_Set_Oinsert(X25994),X25992),c_Orderings_Obot__class_Obot(tc_fun(X25994,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25994,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25994,c_Orderings_Oord__class_Omax(X25994),hAPP(hAPP(c_Set_Oinsert(X25994),X25992),X25993)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25994),X25992),c_Big__Operators_Olattice_OSup__fin(X25994,c_Orderings_Oord__class_Omax(X25994),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25994,tc_HOL_Obool)),X25993),hAPP(hAPP(c_Set_Oinsert(X25994),X25992),c_Orderings_Obot__class_Obot(tc_fun(X25994,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25994),X25993))
| ~ class_Orderings_Olinorder(X25994) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove])])]) ).
fof(i_0_7297,plain,
! [X26657,X26658,X26659,X26660,X26661,X26662,X26663,X26664,X26665,X26666,X26667] :
( hAPP(X26667,hAPP(X26666,X26665)) != hAPP(X26664,hAPP(X26663,X26662))
| hAPP(hAPP(c_Fun_Ocomp(X26661,X26660,X26659,X26667),X26666),X26665) = hAPP(hAPP(c_Fun_Ocomp(X26658,X26660,X26657,X26664),X26663),X26662) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__cong])]) ).
fof(i_0_7298,plain,
! [X25561,X25562,X25563,X25564,X25565] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25565,tc_HOL_Obool)),X25562),hAPP(hAPP(c_Set_Oinsert(X25565),X25561),c_Orderings_Obot__class_Obot(tc_fun(X25565,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25565,tc_HOL_Obool))
| hAPP(X25563,X25562) = X25561
| ~ hBOOL(hAPP(hAPP(c_member(X25565),X25561),X25562))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25565),X25562))
| ~ c_Finite__Set_Ofolding__one(X25565,X25564,X25563) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25565,tc_HOL_Obool)),X25562),hAPP(hAPP(c_Set_Oinsert(X25565),X25561),c_Orderings_Obot__class_Obot(tc_fun(X25565,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25565,tc_HOL_Obool))
| hAPP(X25563,X25562) = hAPP(hAPP(X25564,X25561),hAPP(X25563,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25565,tc_HOL_Obool)),X25562),hAPP(hAPP(c_Set_Oinsert(X25565),X25561),c_Orderings_Obot__class_Obot(tc_fun(X25565,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X25565),X25561),X25562))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25565),X25562))
| ~ c_Finite__Set_Ofolding__one(X25565,X25564,X25563) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove])])]) ).
fof(i_0_7299,plain,
! [X27534,X27535,X27536] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27536),X27535))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27536),X27534))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27536),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27536,tc_HOL_Obool)),X27535),X27534))),hAPP(c_Finite__Set_Ocard(X27536),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27536,tc_HOL_Obool)),X27535),X27534))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27536),X27535)),hAPP(c_Finite__Set_Ocard(X27536),X27534)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter])]) ).
fof(i_0_7300,plain,
! [X27537,X27538,X27539] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27539),X27538))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27539),X27537))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27539),X27538)),hAPP(c_Finite__Set_Ocard(X27539),X27537)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27539),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27539,tc_HOL_Obool)),X27538),X27537))),hAPP(c_Finite__Set_Ocard(X27539),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27539,tc_HOL_Obool)),X27538),X27537))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__Int])]) ).
fof(i_0_7301,plain,
! [X29700,X29701,X29702,X29703] :
( ( hBOOL(hAPP(X29703,esk322_4(X29700,X29701,X29702,X29703)))
| c_Wellfounded_Owf(tc_prod(X29700,X29702),c_Recdef_Osame__fst(X29700,X29702,X29703,X29701)) )
& ( ~ c_Wellfounded_Owf(X29702,hAPP(X29701,esk322_4(X29700,X29701,X29702,X29703)))
| c_Wellfounded_Owf(tc_prod(X29700,X29702),c_Recdef_Osame__fst(X29700,X29702,X29703,X29701)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__same__fst])])])]) ).
fof(i_0_7302,plain,
! [X25425,X25426,X25427,X25428,X25429] :
( ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X25429,X25428,X25427),X25426),X25425))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X25429,X25428)),hAPP(hAPP(c_Product__Type_OPair(X25429,X25428),X25426),X25425)),X25427)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25429,X25428)),hAPP(hAPP(c_Product__Type_OPair(X25429,X25428),X25426),X25425)),X25427))
| hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X25429,X25428,X25427),X25426),X25425)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_7303,plain,
! [X31968,X31969,X31970] :
( ~ hBOOL(hAPP(c_List_Odistinct(X31970),hAPP(hAPP(c_List_Omap(tc_prod(X31970,X31969),X31970),c_Product__Type_Ofst(X31970,X31969)),X31968)))
| c_Map_Oran(X31970,X31969,c_Map_Omap__of(X31970,X31969,X31968)) = hAPP(c_Set_Oimage(tc_prod(X31970,X31969),X31969,c_Product__Type_Osnd(X31970,X31969)),hAPP(c_List_Oset(tc_prod(X31970,X31969)),X31968)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__distinct])]) ).
fof(i_0_7304,plain,
! [X26314,X26315,X26316,X26317,X26318] : c_Map_Orestrict__map(X26318,X26317,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26318,tc_Option_Ooption(X26317)),X26316),X26315),hAPP(c_Option_Ooption_OSome(X26317),X26314)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26318,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26318),X26315),c_Orderings_Obot__class_Obot(tc_fun(X26318,tc_HOL_Obool))))) = c_Map_Orestrict__map(X26318,X26317,X26316,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26318,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26318),X26315),c_Orderings_Obot__class_Obot(tc_fun(X26318,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_restrict__upd__same]) ).
cnf(i_0_7305,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_5542]) ).
fof(i_0_7306,plain,
! [X30215,X30216,X30217] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30217,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30217,X30217,X30216),X30215)),X30215))
| hAPP(c_Relation_OImage(X30217,X30217,c_Transitive__Closure_Ortrancl(X30217,X30216)),X30215) = X30215 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl])]) ).
cnf(i_0_7307,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5543]) ).
fof(i_0_7308,plain,
! [X30304,X30305,X30306,X30307] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30307,X30307)),hAPP(hAPP(c_Product__Type_OPair(X30307,X30307),X30306),X30305)),c_Transitive__Closure_Ortrancl(X30307,X30304)))
| ~ hBOOL(hAPP(hAPP(c_member(X30307),X30305),c_Wellfounded_Oacc(X30307,X30304)))
| hBOOL(hAPP(hAPP(c_member(X30307),X30306),c_Wellfounded_Oacc(X30307,X30304))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux])]) ).
fof(i_0_7309,plain,
! [X30308,X30309,X30310,X30311] :
( ~ hBOOL(hAPP(hAPP(c_member(X30311),X30310),c_Wellfounded_Oacc(X30311,X30309)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30311,X30311)),hAPP(hAPP(c_Product__Type_OPair(X30311,X30311),X30308),X30310)),c_Transitive__Closure_Ortrancl(X30311,X30309)))
| hBOOL(hAPP(hAPP(c_member(X30311),X30308),c_Wellfounded_Oacc(X30311,X30309))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards])]) ).
fof(i_0_7310,plain,
! [X25418,X25419,X25420,X25421] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25421),X25420))
| ~ hBOOL(hAPP(hAPP(c_member(X25421),X25419),X25420))
| hBOOL(hAPP(hAPP(c_member(X25421),X25419),X25418))
| hAPP(c_Finite__Set_Ocard(X25421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25421,tc_HOL_Obool)),X25420),hAPP(hAPP(c_Set_Oinsert(X25421),X25419),X25418))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25421,tc_HOL_Obool)),X25420),X25418))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5544])]) ).
cnf(i_0_7311,plain,
hAPP(c_List_Orev(X1),c_List_Oconcat(X1,X2)) = c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Orev(X1)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2))),
inference(split_conjunct,[status(thm)],[i_0_5545]) ).
fof(i_0_7312,plain,
! [X31158,X31159,X31160,X31161,X31162] :
( ( X31162 != c_Orderings_Obot__class_Obot(tc_fun(X31161,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31161,tc_fun(X31160,tc_HOL_Obool)),X31162),hAPP(hAPP(c_COMBB(tc_fun(X31160,tc_HOL_Obool),tc_fun(X31160,tc_HOL_Obool),X31161),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31160,tc_HOL_Obool)),X31159)),X31158)) = c_Orderings_Otop__class_Otop(tc_fun(X31160,tc_HOL_Obool)) )
& ( X31162 = c_Orderings_Obot__class_Obot(tc_fun(X31161,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31161,tc_fun(X31160,tc_HOL_Obool)),X31162),hAPP(hAPP(c_COMBB(tc_fun(X31160,tc_HOL_Obool),tc_fun(X31160,tc_HOL_Obool),X31161),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31160,tc_HOL_Obool)),X31159)),X31158)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31160,tc_HOL_Obool)),X31159),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31161,tc_fun(X31160,tc_HOL_Obool)),X31162),X31158)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J])]) ).
fof(i_0_7313,plain,
! [X31183,X31184,X31185,X31186,X31187] :
( ( X31187 != c_Orderings_Obot__class_Obot(tc_fun(X31186,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31186,tc_fun(X31185,tc_HOL_Obool)),X31187),hAPP(hAPP(c_COMBB(tc_fun(X31185,tc_HOL_Obool),tc_fun(X31185,tc_HOL_Obool),X31186),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31185,tc_HOL_Obool)),X31184)),X31183)) = c_Orderings_Otop__class_Otop(tc_fun(X31185,tc_HOL_Obool)) )
& ( X31187 = c_Orderings_Obot__class_Obot(tc_fun(X31186,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31186,tc_fun(X31185,tc_HOL_Obool)),X31187),hAPP(hAPP(c_COMBB(tc_fun(X31185,tc_HOL_Obool),tc_fun(X31185,tc_HOL_Obool),X31186),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31185,tc_HOL_Obool)),X31184)),X31183)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31185,tc_HOL_Obool)),X31184),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31186,tc_fun(X31185,tc_HOL_Obool)),X31187),X31183)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J])]) ).
fof(i_0_7314,plain,
! [X24820,X24821,X24822,X24823,X24824] :
( ( X24824 != c_Orderings_Obot__class_Obot(tc_fun(X24823,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24823,tc_fun(X24822,tc_HOL_Obool)),X24824),hAPP(hAPP(c_COMBB(tc_fun(X24822,tc_HOL_Obool),tc_fun(X24822,tc_HOL_Obool),X24823),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24822,tc_HOL_Obool)),X24821)),X24820)) = c_Orderings_Obot__class_Obot(tc_fun(X24822,tc_HOL_Obool)) )
& ( X24824 = c_Orderings_Obot__class_Obot(tc_fun(X24823,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24823,tc_fun(X24822,tc_HOL_Obool)),X24824),hAPP(hAPP(c_COMBB(tc_fun(X24822,tc_HOL_Obool),tc_fun(X24822,tc_HOL_Obool),X24823),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24822,tc_HOL_Obool)),X24821)),X24820)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24822,tc_HOL_Obool)),X24821),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24823,tc_fun(X24822,tc_HOL_Obool)),X24824),X24820)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J])]) ).
fof(i_0_7315,plain,
! [X30942,X30943,X30944,X30945,X30946] :
( ( X30946 != c_Orderings_Obot__class_Obot(tc_fun(X30945,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30944,tc_HOL_Obool)),X30943),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30945,tc_fun(X30944,tc_HOL_Obool)),X30946),X30942)) = X30943 )
& ( X30946 = c_Orderings_Obot__class_Obot(tc_fun(X30945,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30944,tc_HOL_Obool)),X30943),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30945,tc_fun(X30944,tc_HOL_Obool)),X30946),X30942)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30945,tc_fun(X30944,tc_HOL_Obool)),X30946),hAPP(hAPP(c_COMBB(tc_fun(X30944,tc_HOL_Obool),tc_fun(X30944,tc_HOL_Obool),X30945),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30944,tc_HOL_Obool)),X30943)),X30942)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J])]) ).
fof(i_0_7316,plain,
! [X24830,X24831,X24832,X24833,X24834] :
( ( X24834 != c_Orderings_Obot__class_Obot(tc_fun(X24833,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24832,tc_HOL_Obool)),X24831),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24833,tc_fun(X24832,tc_HOL_Obool)),X24834),X24830)) = X24831 )
& ( X24834 = c_Orderings_Obot__class_Obot(tc_fun(X24833,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24832,tc_HOL_Obool)),X24831),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24833,tc_fun(X24832,tc_HOL_Obool)),X24834),X24830)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24833,tc_fun(X24832,tc_HOL_Obool)),X24834),hAPP(hAPP(c_COMBB(tc_fun(X24832,tc_HOL_Obool),tc_fun(X24832,tc_HOL_Obool),X24833),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24832,tc_HOL_Obool)),X24831)),X24830)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J])]) ).
fof(i_0_7317,plain,
! [X31173,X31174,X31175,X31176,X31177] :
( ( X31177 != c_Orderings_Obot__class_Obot(tc_fun(X31176,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31175,tc_HOL_Obool)),X31174),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31176,tc_fun(X31175,tc_HOL_Obool)),X31177),X31173)) = X31174 )
& ( X31177 = c_Orderings_Obot__class_Obot(tc_fun(X31176,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31175,tc_HOL_Obool)),X31174),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31176,tc_fun(X31175,tc_HOL_Obool)),X31177),X31173)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31176,tc_fun(X31175,tc_HOL_Obool)),X31177),hAPP(hAPP(c_COMBB(tc_fun(X31175,tc_HOL_Obool),tc_fun(X31175,tc_HOL_Obool),X31176),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31175,tc_HOL_Obool)),X31174)),X31173)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J])]) ).
fof(i_0_7318,plain,
! [X25596,X25597,X25598,X25599,X25600] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25600,tc_HOL_Obool)),X25597),hAPP(hAPP(c_Set_Oinsert(X25600),X25596),c_Orderings_Obot__class_Obot(tc_fun(X25600,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25600,tc_HOL_Obool))
| hAPP(X25598,hAPP(hAPP(c_Set_Oinsert(X25600),X25596),X25597)) = X25596
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25600),X25597))
| ~ c_Finite__Set_Ofolding__one(X25600,X25599,X25598) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25600,tc_HOL_Obool)),X25597),hAPP(hAPP(c_Set_Oinsert(X25600),X25596),c_Orderings_Obot__class_Obot(tc_fun(X25600,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25600,tc_HOL_Obool))
| hAPP(X25598,hAPP(hAPP(c_Set_Oinsert(X25600),X25596),X25597)) = hAPP(hAPP(X25599,X25596),hAPP(X25598,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25600,tc_HOL_Obool)),X25597),hAPP(hAPP(c_Set_Oinsert(X25600),X25596),c_Orderings_Obot__class_Obot(tc_fun(X25600,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25600),X25597))
| ~ c_Finite__Set_Ofolding__one(X25600,X25599,X25598) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove])])]) ).
fof(i_0_7319,plain,
! [X27762,X27763,X27764] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27764,tc_HOL_Obool)),X27763),hAPP(hAPP(c_Set_Oinsert(X27764),X27762),c_Orderings_Obot__class_Obot(tc_fun(X27764,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X27764,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X27764,X27763) = X27762
| ~ hBOOL(hAPP(hAPP(c_member(X27764),X27762),X27763))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27764),X27763))
| ~ class_Lattices_Olattice(X27764) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27764,tc_HOL_Obool)),X27763),hAPP(hAPP(c_Set_Oinsert(X27764),X27762),c_Orderings_Obot__class_Obot(tc_fun(X27764,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X27764,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X27764,X27763) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27764),X27762),c_Big__Operators_Olattice__class_OInf__fin(X27764,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27764,tc_HOL_Obool)),X27763),hAPP(hAPP(c_Set_Oinsert(X27764),X27762),c_Orderings_Obot__class_Obot(tc_fun(X27764,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X27764),X27762),X27763))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27764),X27763))
| ~ class_Lattices_Olattice(X27764) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove])])]) ).
fof(i_0_7320,plain,
! [X25816,X25817,X25818] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25818,tc_HOL_Obool)),X25817),hAPP(hAPP(c_Set_Oinsert(X25818),X25816),c_Orderings_Obot__class_Obot(tc_fun(X25818,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25818,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25818,X25817) = X25816
| ~ hBOOL(hAPP(hAPP(c_member(X25818),X25816),X25817))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25818),X25817))
| ~ class_Orderings_Olinorder(X25818) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25818,tc_HOL_Obool)),X25817),hAPP(hAPP(c_Set_Oinsert(X25818),X25816),c_Orderings_Obot__class_Obot(tc_fun(X25818,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25818,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25818,X25817) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25818),X25816),c_Big__Operators_Olinorder__class_OMin(X25818,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25818,tc_HOL_Obool)),X25817),hAPP(hAPP(c_Set_Oinsert(X25818),X25816),c_Orderings_Obot__class_Obot(tc_fun(X25818,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X25818),X25816),X25817))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25818),X25817))
| ~ class_Orderings_Olinorder(X25818) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oremove])])]) ).
fof(i_0_7321,plain,
! [X25813,X25814,X25815] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25815,tc_HOL_Obool)),X25814),hAPP(hAPP(c_Set_Oinsert(X25815),X25813),c_Orderings_Obot__class_Obot(tc_fun(X25815,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25815,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25815,X25814) = X25813
| ~ hBOOL(hAPP(hAPP(c_member(X25815),X25813),X25814))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25815),X25814))
| ~ class_Orderings_Olinorder(X25815) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25815,tc_HOL_Obool)),X25814),hAPP(hAPP(c_Set_Oinsert(X25815),X25813),c_Orderings_Obot__class_Obot(tc_fun(X25815,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25815,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25815,X25814) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25815),X25813),c_Big__Operators_Olinorder__class_OMax(X25815,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25815,tc_HOL_Obool)),X25814),hAPP(hAPP(c_Set_Oinsert(X25815),X25813),c_Orderings_Obot__class_Obot(tc_fun(X25815,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X25815),X25813),X25814))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25815),X25814))
| ~ class_Orderings_Olinorder(X25815) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oremove])])]) ).
fof(i_0_7322,plain,
! [X25676,X25677,X25678] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25678,tc_HOL_Obool)),X25677),hAPP(hAPP(c_Set_Oinsert(X25678),X25676),c_Orderings_Obot__class_Obot(tc_fun(X25678,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25678,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25678,X25677) = X25676
| ~ hBOOL(hAPP(hAPP(c_member(X25678),X25676),X25677))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25678),X25677))
| ~ class_Lattices_Olattice(X25678) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25678,tc_HOL_Obool)),X25677),hAPP(hAPP(c_Set_Oinsert(X25678),X25676),c_Orderings_Obot__class_Obot(tc_fun(X25678,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25678,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25678,X25677) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25678),X25676),c_Big__Operators_Olattice__class_OSup__fin(X25678,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25678,tc_HOL_Obool)),X25677),hAPP(hAPP(c_Set_Oinsert(X25678),X25676),c_Orderings_Obot__class_Obot(tc_fun(X25678,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X25678),X25676),X25677))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25678),X25677))
| ~ class_Lattices_Olattice(X25678) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove])])]) ).
fof(i_0_7323,plain,
! [X25173,X25174,X25175,X25176,X25177,X25178] :
( ~ c_Typedef_Otype__definition(X25178,X25177,X25176,X25175,X25174)
| hBOOL(hAPP(hAPP(c_member(X25177),hAPP(X25176,X25173)),X25174)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep])]) ).
fof(i_0_7324,plain,
! [X25167,X25168,X25169,X25170,X25171,X25172] :
( ~ c_Typedef_Otype__definition(X25172,X25171,X25170,X25169,X25168)
| ~ hBOOL(hAPP(hAPP(c_member(X25171),X25167),X25168))
| hAPP(X25170,hAPP(X25169,X25167)) = X25167 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inverse])]) ).
fof(i_0_7325,plain,
! [X34122,X34123,X34124,X34125,X34126] :
( ( ~ c_List_Olinorder__class_Osorted(X34126,hAPP(hAPP(c_List_Omap(X34125,X34126),X34124),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34125,X34126,X34124),X34123),X34122)))
| c_List_Olinorder__class_Osorted(X34126,hAPP(hAPP(c_List_Omap(X34125,X34126),X34124),X34122))
| ~ class_Orderings_Olinorder(X34126) )
& ( ~ c_List_Olinorder__class_Osorted(X34126,hAPP(hAPP(c_List_Omap(X34125,X34126),X34124),X34122))
| c_List_Olinorder__class_Osorted(X34126,hAPP(hAPP(c_List_Omap(X34125,X34126),X34124),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34125,X34126,X34124),X34123),X34122)))
| ~ class_Orderings_Olinorder(X34126) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__key])])]) ).
fof(i_0_7326,plain,
! [X20595,X20596,X20597] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk71_3(X20595,X20596,X20597)),X20597))
| ~ hBOOL(hAPP(X20596,X20595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20595),X20597))
| hBOOL(hAPP(X20596,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X20596,esk71_3(X20595,X20596,X20597)))
| ~ hBOOL(hAPP(X20596,X20595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20595),X20597))
| hBOOL(hAPP(X20596,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(X20596,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk71_3(X20595,X20596,X20597)),X20597)))
| ~ hBOOL(hAPP(X20596,X20595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20595),X20597))
| hBOOL(hAPP(X20596,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__induct__0])])])]) ).
fof(i_0_7327,plain,
! [X20120,X20121,X20122] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20122),X20121)),X20120) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20122),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20121),X20120))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20122),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20121,X20120))),X20120)),
inference(variable_rename,[status(thm)],[fact_zdiv__zmult1__eq]) ).
fof(i_0_7328,plain,
! [X19963,X19964,X19965] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19965),X19964)),X19963) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19965),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19964),X19963))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19965),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19964,X19963))),X19963)),
inference(variable_rename,[status(thm)],[fact_div__mult1__eq]) ).
fof(i_0_7329,plain,
! [X20533,X20534,X20535,X20536,X20537] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20536),X20535)),X20534) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20537),X20535)),X20533)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20536),X20537)),X20535)),X20534) = X20533
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20537),X20536)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20536),X20537)),X20535)),X20534) != X20533
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20536),X20535)),X20534) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20537),X20535)),X20533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20537),X20536)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).
fof(i_0_7330,plain,
! [X20518,X20519,X20520,X20521,X20522] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20522),X20520)),X20519) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20521),X20520)),X20518)
| X20519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20521),X20522)),X20520)),X20518)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20522),X20521)) )
& ( X20519 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20521),X20522)),X20520)),X20518)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20522),X20520)),X20519) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20521),X20520)),X20518)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20522),X20521)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).
fof(i_0_7331,plain,
! [X28138,X28139,X28140,X28141,X28142,X28143] :
( ~ class_Groups_Oab__semigroup__mult(X28143)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28142),X28141))
| hBOOL(hAPP(hAPP(c_member(X28142),X28140),X28141))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28143,X28142,c_Groups_Otimes__class_Otimes(X28143)),X28139),X28138),hAPP(hAPP(c_Set_Oinsert(X28142),X28140),X28141)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28143),hAPP(X28139,X28140)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28143,X28142,c_Groups_Otimes__class_Otimes(X28143)),X28139),X28138),X28141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5546])]) ).
cnf(i_0_7332,plain,
hAPP(c_List_Ofilter(X1,X2),c_List_Oconcat(X1,X3)) = c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Ofilter(X1,X2)),X3)),
inference(split_conjunct,[status(thm)],[i_0_5547]) ).
fof(i_0_7333,plain,
! [X27359,X27360,X27361,X27362] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27362,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27362,tc_HOL_Obool)),X27361),X27360)),X27359) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27362,tc_HOL_Obool)),X27361),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27362,tc_HOL_Obool)),X27360),X27359))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27362,tc_HOL_Obool)),X27359),X27361)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27362,tc_HOL_Obool)),X27359),X27361))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27362,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27362,tc_HOL_Obool)),X27361),X27360)),X27359) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27362,tc_HOL_Obool)),X27361),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27362,tc_HOL_Obool)),X27360),X27359)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq])]) ).
fof(i_0_7334,plain,
! [X31134,X31135,X31136,X31137,X31138] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31138,tc_fun(X31137,tc_HOL_Obool)),X31136),hAPP(hAPP(c_COMBB(tc_fun(X31137,tc_HOL_Obool),tc_fun(X31137,tc_HOL_Obool),X31138),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31137,tc_HOL_Obool)),X31135)),X31134)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31137,tc_HOL_Obool)),X31135),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31138,tc_fun(X31137,tc_HOL_Obool)),X31136),X31134)),
inference(variable_rename,[status(thm)],[fact_INT__simps_I7_J]) ).
fof(i_0_7335,plain,
! [X27271,X27272,X27273,X27274,X27275] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27275,tc_fun(X27274,tc_HOL_Obool)),X27273),hAPP(hAPP(c_COMBB(tc_fun(X27274,tc_HOL_Obool),tc_fun(X27274,tc_HOL_Obool),X27275),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27274,tc_HOL_Obool)),X27272)),X27271)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27274,tc_HOL_Obool)),X27272),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27275,tc_fun(X27274,tc_HOL_Obool)),X27273),X27271)),
inference(variable_rename,[status(thm)],[fact_UN__simps_I5_J]) ).
fof(i_0_7336,plain,
! [X30927,X30928,X30929,X30930,X30931] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30931,tc_fun(X30930,tc_HOL_Obool)),X30929),hAPP(hAPP(c_COMBB(tc_fun(X30930,tc_HOL_Obool),tc_fun(X30930,tc_HOL_Obool),X30931),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30930,tc_HOL_Obool)),X30928)),X30927)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30930,tc_HOL_Obool)),X30928),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30931,tc_fun(X30930,tc_HOL_Obool)),X30929),X30927)),
inference(variable_rename,[status(thm)],[fact_UN__simps_I7_J]) ).
fof(i_0_7337,plain,
! [X27286,X27287,X27288,X27289,X27290] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27290,tc_HOL_Obool)),X27289),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27288,tc_fun(X27290,tc_HOL_Obool)),X27287),X27286)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27288,tc_fun(X27290,tc_HOL_Obool)),X27287),hAPP(hAPP(c_COMBB(tc_fun(X27290,tc_HOL_Obool),tc_fun(X27290,tc_HOL_Obool),X27288),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27290,tc_HOL_Obool)),X27289)),X27286)),
inference(variable_rename,[status(thm)],[fact_Int__UN__distrib]) ).
fof(i_0_7338,plain,
! [X27281,X27282,X27283,X27284,X27285] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27285,tc_HOL_Obool)),X27284),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27283,tc_fun(X27285,tc_HOL_Obool)),X27282),X27281)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27283,tc_fun(X27285,tc_HOL_Obool)),X27282),hAPP(hAPP(c_COMBB(tc_fun(X27285,tc_HOL_Obool),tc_fun(X27285,tc_HOL_Obool),X27283),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27285,tc_HOL_Obool)),X27284)),X27281)),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I5_J]) ).
fof(i_0_7339,plain,
! [X31124,X31125,X31126,X31127,X31128] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31128,tc_HOL_Obool)),X31127),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31126,tc_fun(X31128,tc_HOL_Obool)),X31125),X31124)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31126,tc_fun(X31128,tc_HOL_Obool)),X31125),hAPP(hAPP(c_COMBB(tc_fun(X31128,tc_HOL_Obool),tc_fun(X31128,tc_HOL_Obool),X31126),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31128,tc_HOL_Obool)),X31127)),X31124)),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I7_J]) ).
fof(i_0_7340,plain,
! [X31119,X31120,X31121,X31122,X31123] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31123,tc_HOL_Obool)),X31122),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31121,tc_fun(X31123,tc_HOL_Obool)),X31120),X31119)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31121,tc_fun(X31123,tc_HOL_Obool)),X31120),hAPP(hAPP(c_COMBB(tc_fun(X31123,tc_HOL_Obool),tc_fun(X31123,tc_HOL_Obool),X31121),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31123,tc_HOL_Obool)),X31122)),X31119)),
inference(variable_rename,[status(thm)],[fact_Un__INT__distrib]) ).
fof(i_0_7341,plain,
! [X30922,X30923,X30924,X30925,X30926] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30926,tc_HOL_Obool)),X30925),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30924,tc_fun(X30926,tc_HOL_Obool)),X30923),X30922)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30924,tc_fun(X30926,tc_HOL_Obool)),X30923),hAPP(hAPP(c_COMBB(tc_fun(X30926,tc_HOL_Obool),tc_fun(X30926,tc_HOL_Obool),X30924),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30926,tc_HOL_Obool)),X30925)),X30922)),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I7_J]) ).
fof(i_0_7342,plain,
! [X29543,X29544,X29545,X29546] :
( hAPP(hAPP(c_Relation_Orel__comp(X29546,X29546,X29546),X29545),X29544) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29546,X29546),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X29546,X29546,X29546),X29545),X29543) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29546,X29546),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X29546,X29546,X29546),X29545),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29546,X29546),tc_HOL_Obool)),X29544),X29543)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29546,X29546),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__comp__emptyR])]) ).
cnf(i_0_7343,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5498]) ).
cnf(i_0_7344,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5499]) ).
fof(i_0_7345,plain,
! [X24366,X24367,X24368,X24369,X24370] :
( ~ c_Typedef_Otype__definition(X24370,X24369,X24368,X24367,X24366)
| hAPP(c_Set_Oimage(X24370,X24369,X24368),c_Orderings_Otop__class_Otop(tc_fun(X24370,tc_HOL_Obool))) = X24366 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range])]) ).
fof(i_0_7346,plain,
! [X26890,X26891,X26892] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X26892),hAPP(hAPP(c_Set_Oinsert(X26892),X26891),c_Orderings_Obot__class_Obot(tc_fun(X26892,tc_HOL_Obool)))),X26890) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X26892,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26892,X26892,X26890),hAPP(hAPP(c_Set_Oinsert(X26892),X26891),c_Orderings_Obot__class_Obot(tc_fun(X26892,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26892,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__quotient]) ).
fof(i_0_7347,plain,
! [X27652,X27653,X27654,X27655,X27656,X27657] :
( ~ c_Equiv__Relations_Ocongruent(X27657,X27656,X27655,X27654)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27657,X27657)),hAPP(hAPP(c_Product__Type_OPair(X27657,X27657),X27653),X27652)),X27655))
| hAPP(X27654,X27653) = hAPP(X27654,X27652) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruentD])]) ).
fof(i_0_7348,plain,
! [X30224,X30225,X30226] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30226,X30226),tc_HOL_Obool)),X30225),c_Transitive__Closure_Ortrancl(X30226,X30224)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30226,X30226),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30226,X30225)),c_Transitive__Closure_Ortrancl(X30226,X30224))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl])]) ).
cnf(i_0_7349,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_5491]) ).
cnf(i_0_7350,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5487]) ).
fof(i_0_7351,plain,
! [X30460,X30461,X30462,X30463] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30463,X30463)),X30462),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30463,X30463),tc_HOL_Obool),X30461),X30460)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30463,X30463)),X30462),c_Transitive__Closure_Ortrancl(X30463,X30460))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__imp__rtrancl])]) ).
fof(i_0_7352,plain,
! [X28543,X28544,X28545,X28546] :
( ~ hBOOL(hAPP(hAPP(c_member(X28546),X28545),c_Wellfounded_Oacc(X28546,X28544)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28546,X28546)),hAPP(hAPP(c_Product__Type_OPair(X28546,X28546),X28543),X28545)),X28544))
| hBOOL(hAPP(hAPP(c_member(X28546),X28543),c_Wellfounded_Oacc(X28546,X28544))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])]) ).
fof(i_0_7353,plain,
! [X27792,X27793,X27794] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27794,tc_HOL_Obool)),X27793),hAPP(hAPP(c_Set_Oinsert(X27794),X27792),c_Orderings_Obot__class_Obot(tc_fun(X27794,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X27794,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X27794,hAPP(hAPP(c_Set_Oinsert(X27794),X27792),X27793)) = X27792
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27794),X27793))
| ~ class_Lattices_Olattice(X27794) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27794,tc_HOL_Obool)),X27793),hAPP(hAPP(c_Set_Oinsert(X27794),X27792),c_Orderings_Obot__class_Obot(tc_fun(X27794,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X27794,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X27794,hAPP(hAPP(c_Set_Oinsert(X27794),X27792),X27793)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27794),X27792),c_Big__Operators_Olattice__class_OInf__fin(X27794,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27794,tc_HOL_Obool)),X27793),hAPP(hAPP(c_Set_Oinsert(X27794),X27792),c_Orderings_Obot__class_Obot(tc_fun(X27794,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27794),X27793))
| ~ class_Lattices_Olattice(X27794) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove])])]) ).
fof(i_0_7354,plain,
! [X25875,X25876,X25877] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25877,tc_HOL_Obool)),X25876),hAPP(hAPP(c_Set_Oinsert(X25877),X25875),c_Orderings_Obot__class_Obot(tc_fun(X25877,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25877,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25877,hAPP(hAPP(c_Set_Oinsert(X25877),X25875),X25876)) = X25875
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25877),X25876))
| ~ class_Orderings_Olinorder(X25877) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25877,tc_HOL_Obool)),X25876),hAPP(hAPP(c_Set_Oinsert(X25877),X25875),c_Orderings_Obot__class_Obot(tc_fun(X25877,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25877,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25877,hAPP(hAPP(c_Set_Oinsert(X25877),X25875),X25876)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25877),X25875),c_Big__Operators_Olinorder__class_OMin(X25877,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25877,tc_HOL_Obool)),X25876),hAPP(hAPP(c_Set_Oinsert(X25877),X25875),c_Orderings_Obot__class_Obot(tc_fun(X25877,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25877),X25876))
| ~ class_Orderings_Olinorder(X25877) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove])])]) ).
fof(i_0_7355,plain,
! [X25878,X25879,X25880] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25880,tc_HOL_Obool)),X25879),hAPP(hAPP(c_Set_Oinsert(X25880),X25878),c_Orderings_Obot__class_Obot(tc_fun(X25880,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25880,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25880,hAPP(hAPP(c_Set_Oinsert(X25880),X25878),X25879)) = X25878
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25880),X25879))
| ~ class_Orderings_Olinorder(X25880) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25880,tc_HOL_Obool)),X25879),hAPP(hAPP(c_Set_Oinsert(X25880),X25878),c_Orderings_Obot__class_Obot(tc_fun(X25880,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25880,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25880,hAPP(hAPP(c_Set_Oinsert(X25880),X25878),X25879)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25880),X25878),c_Big__Operators_Olinorder__class_OMax(X25880,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25880,tc_HOL_Obool)),X25879),hAPP(hAPP(c_Set_Oinsert(X25880),X25878),c_Orderings_Obot__class_Obot(tc_fun(X25880,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25880),X25879))
| ~ class_Orderings_Olinorder(X25880) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove])])]) ).
fof(i_0_7356,plain,
! [X25784,X25785,X25786] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25786,tc_HOL_Obool)),X25785),hAPP(hAPP(c_Set_Oinsert(X25786),X25784),c_Orderings_Obot__class_Obot(tc_fun(X25786,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25786,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25786,hAPP(hAPP(c_Set_Oinsert(X25786),X25784),X25785)) = X25784
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25786),X25785))
| ~ class_Lattices_Olattice(X25786) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25786,tc_HOL_Obool)),X25785),hAPP(hAPP(c_Set_Oinsert(X25786),X25784),c_Orderings_Obot__class_Obot(tc_fun(X25786,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25786,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25786,hAPP(hAPP(c_Set_Oinsert(X25786),X25784),X25785)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25786),X25784),c_Big__Operators_Olattice__class_OSup__fin(X25786,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25786,tc_HOL_Obool)),X25785),hAPP(hAPP(c_Set_Oinsert(X25786),X25784),c_Orderings_Obot__class_Obot(tc_fun(X25786,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25786),X25785))
| ~ class_Lattices_Olattice(X25786) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove])])]) ).
fof(i_0_7357,plain,
! [X24361,X24362,X24363,X24364,X24365] :
( ~ c_Typedef_Otype__definition(X24365,X24364,X24363,X24362,X24361)
| hAPP(c_Set_Oimage(X24364,X24365,X24362),X24361) = c_Orderings_Otop__class_Otop(tc_fun(X24365,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__image])]) ).
fof(i_0_7358,plain,
! [X31934,X31935,X31936,X31937] :
( ~ c_Fun_Oinj__on(X31937,X31936,X31935,c_Complete__Lattice_OSup__class_OSup(tc_fun(X31937,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X31937),tc_fun(X31937,tc_HOL_Obool),c_List_Oset(X31937)),X31934)))
| c_Fun_Oinj__on(tc_List_Olist(X31937),tc_List_Olist(X31936),hAPP(c_List_Omap(X31937,X31936),X31935),X31934) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__mapI])]) ).
fof(i_0_7359,plain,
! [X21720,X21721,X21722,X21723] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21721))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),X21722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21723),X21720),X21721)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),X21721),c_Groups_Ozero__class_Ozero(X21723)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21723),X21720),X21721)),X21722))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),X21721),c_Groups_Ozero__class_Ozero(X21723)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21720))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21721))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21721))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),X21721),c_Groups_Ozero__class_Ozero(X21723)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),X21721),c_Groups_Ozero__class_Ozero(X21723)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21721))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21720))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),X21721),c_Groups_Ozero__class_Ozero(X21723)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21721))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),X21721),c_Groups_Ozero__class_Ozero(X21723)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21723),X21720),X21721)),X21722))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21721))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21720))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21723),X21720),X21721)),X21722))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21721))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),X21722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21723),X21720),X21721)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),X21721),c_Groups_Ozero__class_Ozero(X21723)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),X21721),c_Groups_Ozero__class_Ozero(X21723)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),X21722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21723),X21720),X21721)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21720))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),X21721),c_Groups_Ozero__class_Ozero(X21723)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),X21722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21723),X21720),X21721)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21723),X21721),c_Groups_Ozero__class_Ozero(X21723)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21723),X21720),X21721)),X21722))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),X21722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21723),X21720),X21721)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),c_Groups_Ozero__class_Ozero(X21723)),X21720))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21723),X21720),X21721)),X21722))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),X21722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21723),X21720),X21721)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21723),X21722),X21721)),X21720))
| ~ class_Fields_Olinordered__field__inverse__zero(X21723) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5548])])]) ).
fof(i_0_7360,plain,
! [X21640,X21641,X21642,X21643] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21641))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21643),X21640),X21641)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21641),c_Groups_Ozero__class_Ozero(X21643)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21643),X21640),X21641)),X21642))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21641),c_Groups_Ozero__class_Ozero(X21643)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21640))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21641))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21641))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21641),c_Groups_Ozero__class_Ozero(X21643)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21641),c_Groups_Ozero__class_Ozero(X21643)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21641))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21640))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21641),c_Groups_Ozero__class_Ozero(X21643)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21641))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21641),c_Groups_Ozero__class_Ozero(X21643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21643),X21640),X21641)),X21642))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21641))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21640))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21643),X21640),X21641)),X21642))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21641))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21643),X21640),X21641)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21641),c_Groups_Ozero__class_Ozero(X21643)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21641),c_Groups_Ozero__class_Ozero(X21643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21643),X21640),X21641)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21640))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21641),c_Groups_Ozero__class_Ozero(X21643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21643),X21640),X21641)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21641),c_Groups_Ozero__class_Ozero(X21643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21643),X21640),X21641)),X21642))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21643),X21640),X21641)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),c_Groups_Ozero__class_Ozero(X21643)),X21640))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21643),X21640),X21641)),X21642))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),X21642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21643),X21640),X21641)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21643),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21643),X21642),X21641)),X21640))
| ~ class_Fields_Olinordered__field__inverse__zero(X21643) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5549])])]) ).
fof(i_0_7361,plain,
! [X32748,X32749,X32750,X32751,X32752,X32753] : hAPP(hAPP(c_List_Olist__update(tc_prod(X32753,X32752),hAPP(hAPP(c_List_Ozip(X32753,X32752),X32751),X32750)),X32749),X32748) = hAPP(hAPP(c_List_Ozip(X32753,X32752),hAPP(hAPP(c_List_Olist__update(X32753,X32751),X32749),hAPP(c_Product__Type_Ofst(X32753,X32752),X32748))),hAPP(hAPP(c_List_Olist__update(X32752,X32750),X32749),hAPP(c_Product__Type_Osnd(X32753,X32752),X32748))),
inference(variable_rename,[status(thm)],[fact_update__zip]) ).
cnf(i_0_7362,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_5494]) ).
cnf(i_0_7363,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
inference(split_conjunct,[status(thm)],[i_0_5493]) ).
cnf(i_0_7364,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_5495]) ).
cnf(i_0_7365,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin)) ),
inference(split_conjunct,[status(thm)],[i_0_5496]) ).
cnf(i_0_7366,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X1))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5497]) ).
cnf(i_0_7367,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),X3))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate(X1,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_5550]) ).
fof(i_0_7368,plain,
! [X29153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X29153)))),
inference(variable_rename,[status(thm)],[fact_finite__Collect__le__nat]) ).
fof(i_0_7369,plain,
! [X29152] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X29152)))),
inference(variable_rename,[status(thm)],[fact_finite__Collect__less__nat]) ).
fof(i_0_7370,plain,
! [X29495,X29496,X29497,X29498,X29499,X29500,X29501] : hAPP(hAPP(c_Relation_Orel__comp(X29501,X29500,X29499),hAPP(hAPP(c_Relation_Orel__comp(X29501,X29498,X29500),X29497),X29496)),X29495) = hAPP(hAPP(c_Relation_Orel__comp(X29501,X29498,X29499),X29497),hAPP(hAPP(c_Relation_Orel__comp(X29498,X29500,X29499),X29496),X29495)),
inference(variable_rename,[status(thm)],[fact_O__assoc]) ).
fof(i_0_7371,plain,
! [X26194,X26195,X26196,X26197,X26198] :
( ~ class_Groups_Ocomm__monoid__mult(X26198)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26197),X26196))
| ~ hBOOL(hAPP(hAPP(c_member(X26197),X26195),X26196))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26197,X26198),X26194),X26196) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26198),hAPP(X26194,X26195)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26197,X26198),X26194),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26197,tc_HOL_Obool)),X26196),hAPP(hAPP(c_Set_Oinsert(X26197),X26195),c_Orderings_Obot__class_Obot(tc_fun(X26197,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oremove])]) ).
fof(i_0_7372,plain,
! [X25393,X25394,X25395,X25396,X25397] :
( ~ class_Groups_Ocomm__monoid__add(X25397)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25396),X25395))
| ~ hBOOL(hAPP(hAPP(c_member(X25396),X25394),X25395))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25396,X25397),X25393),X25395) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25397),hAPP(X25393,X25394)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25396,X25397),X25393),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25396,tc_HOL_Obool)),X25395),hAPP(hAPP(c_Set_Oinsert(X25396),X25394),c_Orderings_Obot__class_Obot(tc_fun(X25396,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oremove])]) ).
fof(i_0_7373,plain,
! [X25388,X25389,X25390,X25391,X25392] :
( ~ class_Groups_Ocomm__monoid__add(X25392)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25391),X25390))
| ~ hBOOL(hAPP(hAPP(c_member(X25391),X25389),X25390))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25391,X25392),X25388),X25390) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25392),hAPP(X25388,X25389)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25391,X25392),X25388),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25391,tc_HOL_Obool)),X25390),hAPP(hAPP(c_Set_Oinsert(X25391),X25389),c_Orderings_Obot__class_Obot(tc_fun(X25391,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H])]) ).
fof(i_0_7374,plain,
! [X31026,X31027,X31028,X31029] : hAPP(c_Set_OPow(X31029),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31028,tc_fun(X31029,tc_HOL_Obool)),X31027),X31026)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31028,tc_fun(tc_fun(X31029,tc_HOL_Obool),tc_HOL_Obool)),X31027),hAPP(hAPP(c_COMBB(tc_fun(X31029,tc_HOL_Obool),tc_fun(tc_fun(X31029,tc_HOL_Obool),tc_HOL_Obool),X31028),c_Set_OPow(X31029)),X31026)),
inference(variable_rename,[status(thm)],[fact_Pow__INT__eq]) ).
fof(i_0_7375,plain,
! [X19698,X19699,X19700] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19700),X19699)),X19698)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19698),X19700))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19700))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19699)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).
fof(i_0_7376,plain,
! [X24138,X24139,X24140] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24140,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24139)),X24138) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24140,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X24140,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X24139)),X24138)),hAPP(X24138,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_UN__le__eq__Un0]) ).
fof(i_0_7377,plain,
! [X27540,X27541,X27542] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27542),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27542,tc_HOL_Obool)),X27541),X27540)))
| hAPP(c_Finite__Set_Ocard(X27542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27542,tc_HOL_Obool)),X27541),X27540)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27542),X27541)),hAPP(c_Finite__Set_Ocard(X27542),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27542,tc_HOL_Obool)),X27541),X27540))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int])]) ).
cnf(i_0_7378,plain,
c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[fact_pair__leq__def]) ).
fof(i_0_7379,plain,
! [X31139,X31140,X31141,X31142,X31143] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31143,tc_fun(X31142,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31143,tc_HOL_Obool)),X31141),X31140)),X31139) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31142,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31143,tc_fun(X31142,tc_HOL_Obool)),X31141),X31139)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31143,tc_fun(X31142,tc_HOL_Obool)),X31140),X31139)),
inference(variable_rename,[status(thm)],[fact_INT__Un]) ).
fof(i_0_7380,plain,
! [X24288,X24289,X24290,X24291,X24292] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24292,tc_fun(X24291,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24292,tc_HOL_Obool)),X24290),X24289)),X24288) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24291,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24292,tc_fun(X24291,tc_HOL_Obool)),X24290),X24288)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24292,tc_fun(X24291,tc_HOL_Obool)),X24289),X24288)),
inference(variable_rename,[status(thm)],[fact_UN__Un]) ).
fof(i_0_7381,plain,
! [X30300,X30301,X30302,X30303] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30303,X30303)),hAPP(hAPP(c_Product__Type_OPair(X30303,X30303),X30302),X30300)),c_Transitive__Closure_Ortrancl(X30303,X30301)))
| X30302 = X30300
| hBOOL(hAPP(hAPP(c_member(X30303),X30302),hAPP(c_Relation_ODomain(X30303,X30303),X30301))) )
& ( X30302 != X30300
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30303,X30303)),hAPP(hAPP(c_Product__Type_OPair(X30303,X30303),X30302),X30300)),c_Transitive__Closure_Ortrancl(X30303,X30301)))
| hBOOL(hAPP(hAPP(c_member(X30303),X30302),hAPP(c_Relation_ODomain(X30303,X30303),X30301))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5551])])]) ).
cnf(i_0_7382,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_5552]) ).
fof(i_0_7383,plain,
! [X28449,X28450,X28451,X28452,X28454,X28455,X28456,X28457,X28458] :
( ( c_Map_Odom(X28452,X28451,X28450) != hAPP(hAPP(c_Set_Oinsert(X28452),X28449),c_Orderings_Obot__class_Obot(tc_fun(X28452,tc_HOL_Obool)))
| X28450 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X28452,tc_Option_Ooption(X28451)),hAPP(c_COMBK(tc_Option_Ooption(X28451),X28452),c_Option_Ooption_ONone(X28451))),X28449),hAPP(c_Option_Ooption_OSome(X28451),esk273_4(X28449,X28450,X28451,X28452))) )
& ( X28455 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X28457,tc_Option_Ooption(X28456)),hAPP(c_COMBK(tc_Option_Ooption(X28456),X28457),c_Option_Ooption_ONone(X28456))),X28454),hAPP(c_Option_Ooption_OSome(X28456),X28458))
| c_Map_Odom(X28457,X28456,X28455) = hAPP(hAPP(c_Set_Oinsert(X28457),X28454),c_Orderings_Obot__class_Obot(tc_fun(X28457,tc_HOL_Obool))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__eq__singleton__conv])])])])]) ).
fof(i_0_7384,plain,
! [X28249,X28250,X28251,X28252,X28253,X28254,X28255] :
( ~ c_Big__Operators_Ocomm__monoid__big(X28255,X28254,X28253,X28252,X28251)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28254),X28250))
| hAPP(hAPP(X28251,X28249),X28250) = X28252 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5553])]) ).
fof(i_0_7385,plain,
! [X22435,X22436,X22437] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22437,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22437,tc_HOL_Obool)),X22436)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22437,tc_HOL_Obool)),X22435)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22437,tc_HOL_Obool)),X22435),X22436)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22437,tc_HOL_Obool)),X22435),X22436))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22437,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22437,tc_HOL_Obool)),X22436)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22437,tc_HOL_Obool)),X22435))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff])]) ).
fof(i_0_7386,plain,
! [X30998,X30999,X31000,X31001,X31002] :
( ~ hBOOL(hAPP(hAPP(c_member(X31002),X31001),X31000))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30999,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31002,tc_fun(X30999,tc_HOL_Obool)),X31000),X30998)),hAPP(X30998,X31001))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__lower])]) ).
fof(i_0_7387,plain,
! [X30218,X30219,X30220] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30220,X30220),tc_HOL_Obool)),X30219),X30218))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30220,X30220),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30220,X30219)),c_Transitive__Closure_Ortrancl(X30220,X30218))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])]) ).
fof(i_0_7388,plain,
! [X31096,X31097,X31098,X31099,X31100,X31101] : hAPP(c_Set_Ovimage(X31101,X31100,X31099),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31098,tc_fun(X31100,tc_HOL_Obool)),X31097),X31096)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31098,tc_fun(X31101,tc_HOL_Obool)),X31097),hAPP(hAPP(c_COMBB(tc_fun(X31100,tc_HOL_Obool),tc_fun(X31101,tc_HOL_Obool),X31098),c_Set_Ovimage(X31101,X31100,X31099)),X31096)),
inference(variable_rename,[status(thm)],[fact_vimage__INT]) ).
fof(i_0_7389,plain,
! [X28331,X28332,X28333,X28334,X28335,X28336] : hAPP(c_Set_Ovimage(X28336,X28335,X28334),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28333,tc_fun(X28335,tc_HOL_Obool)),X28332),X28331)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28333,tc_fun(X28336,tc_HOL_Obool)),X28332),hAPP(hAPP(c_COMBB(tc_fun(X28335,tc_HOL_Obool),tc_fun(X28336,tc_HOL_Obool),X28333),c_Set_Ovimage(X28336,X28335,X28334)),X28331)),
inference(variable_rename,[status(thm)],[fact_vimage__UN]) ).
fof(i_0_7390,plain,
! [X26594,X26595,X26596,X26597,X26598,X26599] : hAPP(c_Relation_OImage(X26599,X26598,X26597),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26596,tc_fun(X26599,tc_HOL_Obool)),X26595),X26594)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26596,tc_fun(X26598,tc_HOL_Obool)),X26595),hAPP(hAPP(c_COMBB(tc_fun(X26599,tc_HOL_Obool),tc_fun(X26598,tc_HOL_Obool),X26596),c_Relation_OImage(X26599,X26598,X26597)),X26594)),
inference(variable_rename,[status(thm)],[fact_Image__UN]) ).
fof(i_0_7391,plain,
! [X24276,X24277,X24278,X24279,X24280,X24281] : hAPP(c_Set_Oimage(X24281,X24280,X24279),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24278,tc_fun(X24281,tc_HOL_Obool)),X24277),X24276)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24278,tc_fun(X24280,tc_HOL_Obool)),X24277),hAPP(hAPP(c_COMBB(tc_fun(X24281,tc_HOL_Obool),tc_fun(X24280,tc_HOL_Obool),X24278),c_Set_Oimage(X24281,X24280,X24279)),X24276)),
inference(variable_rename,[status(thm)],[fact_image__UN]) ).
fof(i_0_7392,plain,
! [X21670,X21671,X21672,X21673,X21674] :
( ~ class_Fields_Ofield(X21674)
| X21673 = c_Groups_Ozero__class_Ozero(X21674)
| X21672 = c_Groups_Ozero__class_Ozero(X21674)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21674),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21674),X21671),X21673)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21674),X21670),X21672)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21674),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21674),X21671),X21672)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21674),X21670),X21673))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21674),X21673),X21672)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__frac__eq])]) ).
fof(i_0_7393,plain,
! [X21649,X21650,X21651,X21652,X21653] :
( ~ class_Fields_Ofield(X21653)
| X21652 = c_Groups_Ozero__class_Ozero(X21653)
| X21651 = c_Groups_Ozero__class_Ozero(X21653)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21653),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21653),X21650),X21652)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21653),X21649),X21651)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21653),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21653),X21650),X21651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21653),X21649),X21652))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21653),X21652),X21651)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__eq])]) ).
fof(i_0_7394,plain,
! [X29241,X29242] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29242,tc_HOL_Obool)),X29241) = hAPP(c_Set_OCollect(X29242),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29242),c_fNot),hAPP(hAPP(c_COMBC(X29242,tc_fun(X29242,tc_HOL_Obool),tc_HOL_Obool),c_member(X29242)),X29241))),
inference(variable_rename,[status(thm)],[fact_Compl__eq]) ).
cnf(i_0_7395,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5554]) ).
fof(i_0_7396,plain,
! [X18999,X19000,X19001] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19001)),X19000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19001)),X18999)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19000),X18999)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19000),X18999))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19001)),X19000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19001)),X18999))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])]) ).
fof(i_0_7397,plain,
! [X19459,X19460,X19461] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19461)),X19460)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19461)),X19459)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19460),X19459)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19460),X19459))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19461)),X19460)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19461)),X19459))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).
fof(i_0_7398,plain,
! [X19922,X19923,X19924,X19925,X19926] :
( ( ~ hBOOL(hAPP(hAPP(X19923,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19922),X19924)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19922,X19924)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19926),X19924))
| X19922 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19924),X19925)),X19926)
| hBOOL(hAPP(hAPP(X19923,X19925),X19926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19924)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk56_3(X19922,X19923,X19924)))
| hBOOL(hAPP(hAPP(X19923,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19922),X19924)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19922,X19924)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19924)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk56_3(X19922,X19923,X19924)),X19924))
| hBOOL(hAPP(hAPP(X19923,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19922),X19924)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19922,X19924)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19924)) )
& ( X19922 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19924),esk55_3(X19922,X19923,X19924))),esk56_3(X19922,X19923,X19924))
| hBOOL(hAPP(hAPP(X19923,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19922),X19924)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19922,X19924)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19924)) )
& ( ~ hBOOL(hAPP(hAPP(X19923,esk55_3(X19922,X19923,X19924)),esk56_3(X19922,X19923,X19924)))
| hBOOL(hAPP(hAPP(X19923,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19922),X19924)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19922,X19924)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19924)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__pos__lemma])])])])]) ).
fof(i_0_7399,plain,
! [X32196,X32197,X32198,X32199,X32200] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32199),X32197),hAPP(c_List_Oset(X32199),X32196)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32199),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32199,X32200,X32198),X32197),X32196)))
| ~ class_Orderings_Olinorder(X32200) )
& ( hBOOL(hAPP(c_List_Odistinct(X32199),X32196))
| ~ hBOOL(hAPP(c_List_Odistinct(X32199),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32199,X32200,X32198),X32197),X32196)))
| ~ class_Orderings_Olinorder(X32200) )
& ( hBOOL(hAPP(hAPP(c_member(X32199),X32197),hAPP(c_List_Oset(X32199),X32196)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32199),X32196))
| hBOOL(hAPP(c_List_Odistinct(X32199),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32199,X32200,X32198),X32197),X32196)))
| ~ class_Orderings_Olinorder(X32200) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5555])])]) ).
fof(i_0_7400,plain,
! [X26738,X26739,X26740,X26741,X26742,X26743] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26743,tc_fun(X26742,tc_HOL_Obool)),X26741),hAPP(c_Fun_Ocomp(X26740,tc_fun(X26742,tc_HOL_Obool),X26743,X26739),X26738)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26740,tc_fun(X26742,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26743,X26740,X26738),X26741)),X26739),
inference(variable_rename,[status(thm)],[fact_UN__o]) ).
fof(i_0_7401,plain,
! [X26189,X26190,X26191,X26192,X26193] :
( ~ class_Groups_Ocomm__monoid__mult(X26193)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26192),X26191))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26192,X26193),X26190),hAPP(hAPP(c_Set_Oinsert(X26192),X26189),X26191)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26193),hAPP(X26190,X26189)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26192,X26193),X26190),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26192,tc_HOL_Obool)),X26191),hAPP(hAPP(c_Set_Oinsert(X26192),X26189),c_Orderings_Obot__class_Obot(tc_fun(X26192,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove])]) ).
fof(i_0_7402,plain,
! [X24875,X24876,X24877,X24878,X24879] :
( ~ class_Groups_Ocomm__monoid__add(X24879)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24878),X24877))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24878,X24879),X24876),hAPP(hAPP(c_Set_Oinsert(X24878),X24875),X24877)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24879),hAPP(X24876,X24875)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24878,X24879),X24876),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24878,tc_HOL_Obool)),X24877),hAPP(hAPP(c_Set_Oinsert(X24878),X24875),c_Orderings_Obot__class_Obot(tc_fun(X24878,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove])]) ).
fof(i_0_7403,plain,
! [X26066,X26067,X26068,X26069,X26070,X26071] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26071,X26070),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26071,X26070),X26069),X26068),X26067)),X26068),X26066) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26071,X26070),X26069),X26068),X26066),
inference(variable_rename,[status(thm)],[fact_fun__upd__upd]) ).
fof(i_0_7404,plain,
! [X19929,X19930,X19931,X19932,X19933] :
( ( ~ hBOOL(hAPP(hAPP(X19930,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19929),X19931)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19929,X19931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19931),X19933))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19933),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X19929 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19931),X19932)),X19933)
| hBOOL(hAPP(hAPP(X19930,X19932),X19933))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19931),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19931),esk58_3(X19929,X19930,X19931)))
| hBOOL(hAPP(hAPP(X19930,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19929),X19931)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19929,X19931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19931),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk58_3(X19929,X19930,X19931)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X19930,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19929),X19931)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19929,X19931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19931),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( X19929 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19931),esk57_3(X19929,X19930,X19931))),esk58_3(X19929,X19930,X19931))
| hBOOL(hAPP(hAPP(X19930,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19929),X19931)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19929,X19931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19931),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(X19930,esk57_3(X19929,X19930,X19931)),esk58_3(X19929,X19930,X19931)))
| hBOOL(hAPP(hAPP(X19930,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19929),X19931)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19929,X19931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19931),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__neg__lemma])])])])]) ).
fof(i_0_7405,plain,
! [X32056,X32057] : hAPP(hAPP(c_List_Ozip(X32057,X32057),X32056),X32056) = hAPP(hAPP(c_List_Omap(X32057,tc_prod(X32057,X32057)),hAPP(hAPP(c_COMBS(X32057,X32057,tc_prod(X32057,X32057)),c_Product__Type_OPair(X32057,X32057)),c_COMBI(X32057))),X32056),
inference(variable_rename,[status(thm)],[fact_zip__same__conv__map]) ).
fof(i_0_7406,plain,
! [X27378,X27379] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X27379),X27378) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X27379)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X27378))),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J]) ).
fof(i_0_7407,plain,
! [X24080,X24081] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X24081),X24080) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24081)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24080))),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J]) ).
fof(i_0_7408,plain,
! [X24857,X24858,X24859,X24860] : c_Sum__Type_OPlus(X24860,X24859,X24858,X24857) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(X24860,X24859),tc_HOL_Obool)),hAPP(c_Set_Oimage(X24860,tc_sum(X24860,X24859),c_Sum__Type_OInl(X24860,X24859)),X24858)),hAPP(c_Set_Oimage(X24859,tc_sum(X24860,X24859),c_Sum__Type_OInr(X24859,X24860)),X24857)),
inference(variable_rename,[status(thm)],[fact_Plus__def]) ).
fof(i_0_7409,plain,
! [X20999,X21000,X21001] :
( ~ class_Rings_Olinordered__semidom(X21001)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21001),c_Groups_Ozero__class_Ozero(X21001)),X21000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21001),X21000),c_Groups_Oone__class_Oone(X21001)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21001),X21000),hAPP(hAPP(c_Power_Opower__class_Opower(X21001),X21000),X20999))),hAPP(hAPP(c_Power_Opower__class_Opower(X21001),X21000),X20999))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).
fof(i_0_7410,plain,
! [X24485,X24486,X24487,X24488,X24489,X24490,X24491] :
( ( hAPP(X24489,X24486) != hAPP(X24489,X24485)
| X24486 = X24485
| ~ c_Typedef_Otype__definition(X24491,X24490,X24489,X24488,X24487) )
& ( X24486 != X24485
| hAPP(X24489,X24486) = hAPP(X24489,X24485)
| ~ c_Typedef_Otype__definition(X24491,X24490,X24489,X24488,X24487) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject])])]) ).
fof(i_0_7411,plain,
! [X28767,X28768,X28769,X28770] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28770,X28769)),hAPP(hAPP(c_Product__Type_OSigma(X28770,X28769),X28768),hAPP(c_COMBK(tc_fun(X28769,tc_HOL_Obool),X28770),X28767))))
| X28768 = c_Orderings_Obot__class_Obot(tc_fun(X28770,tc_HOL_Obool))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28769),X28767)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD2])]) ).
fof(i_0_7412,plain,
! [X28771,X28772,X28773,X28774] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28774,X28773)),hAPP(hAPP(c_Product__Type_OSigma(X28774,X28773),X28772),hAPP(c_COMBK(tc_fun(X28773,tc_HOL_Obool),X28774),X28771))))
| X28771 = c_Orderings_Obot__class_Obot(tc_fun(X28773,tc_HOL_Obool))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28774),X28772)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD1])]) ).
fof(i_0_7413,plain,
! [X24492,X24493,X24494,X24495,X24496,X24497] :
( ~ c_Typedef_Otype__definition(X24497,X24496,X24495,X24494,X24493)
| hAPP(X24494,hAPP(X24495,X24492)) = X24492 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse])]) ).
cnf(i_0_7414,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5556]) ).
fof(i_0_7415,plain,
! [X20689,X20690,X20691] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20691)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20691),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20691),hAPP(c_Groups_Oabs__class_Oabs(X20691),X20690)),hAPP(c_Groups_Oabs__class_Oabs(X20691),X20689))),hAPP(c_Groups_Oabs__class_Oabs(X20691),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20691),X20690),X20689)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])]) ).
fof(i_0_7416,plain,
! [X20692,X20693,X20694] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20694)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20694),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20694),hAPP(c_Groups_Oabs__class_Oabs(X20694),X20693)),hAPP(c_Groups_Oabs__class_Oabs(X20694),X20692))),hAPP(c_Groups_Oabs__class_Oabs(X20694),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20694),X20692),X20693)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])]) ).
cnf(i_0_7417,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_5557]) ).
fof(i_0_7418,plain,
! [X28356,X28357,X28358,X28359,X28360] : hAPP(c_Set_Ovimage(X28360,X28359,X28358),hAPP(hAPP(c_Set_Oinsert(X28359),X28357),X28356)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28360,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28360,X28359,X28358),hAPP(hAPP(c_Set_Oinsert(X28359),X28357),c_Orderings_Obot__class_Obot(tc_fun(X28359,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X28360,X28359,X28358),X28356)),
inference(variable_rename,[status(thm)],[fact_vimage__insert]) ).
fof(i_0_7419,plain,
! [X29783,X29784,X29785,X29786,X29787] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29787,X29786)),hAPP(hAPP(c_Product__Type_OPair(X29787,X29786),X29785),X29784)),X29783))
| hBOOL(hAPP(hAPP(c_member(X29787),X29785),hAPP(c_Relation_ODomain(X29787,X29786),X29783))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainI])]) ).
fof(i_0_7420,plain,
! [X29708,X29709,X29710,X29711,X29712] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29712,X29711)),hAPP(hAPP(c_Product__Type_OPair(X29712,X29711),X29710),X29709)),X29708))
| hBOOL(hAPP(hAPP(c_member(X29711),X29709),hAPP(c_Relation_ORange(X29712,X29711),X29708))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeI])]) ).
fof(i_0_7421,plain,
! [X33383,X33384,X33385,X33386] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33386),X33385))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33384,tc_HOL_Obool)),hAPP(c_List_Oset(X33384),hAPP(hAPP(c_List_Odrop(X33384),X33385),X33383))),hAPP(c_List_Oset(X33384),hAPP(hAPP(c_List_Odrop(X33384),X33386),X33383)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__drop__subset__set__drop])]) ).
fof(i_0_7422,plain,
! [X33105,X33106,X33107,X33108] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33108),X33107))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33106,tc_HOL_Obool)),hAPP(c_List_Oset(X33106),hAPP(hAPP(c_List_Otake(X33106),X33108),X33105))),hAPP(c_List_Oset(X33106),hAPP(hAPP(c_List_Otake(X33106),X33107),X33105)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__take__subset__set__take])]) ).
fof(i_0_7423,plain,
! [X32119,X32120,X32121] :
( ~ class_Orderings_Olinorder(X32121)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32121),X32120))
| c_List_Olinorder__class_Osorted__list__of__set(X32121,hAPP(hAPP(c_Set_Oinsert(X32121),X32119),X32120)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32121,X32121,c_COMBI(X32121)),X32119),c_List_Olinorder__class_Osorted__list__of__set(X32121,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32121,tc_HOL_Obool)),X32120),hAPP(hAPP(c_Set_Oinsert(X32121),X32119),c_Orderings_Obot__class_Obot(tc_fun(X32121,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__insert])]) ).
fof(i_0_7424,plain,
! [X20962,X20963,X20964,X20965] :
( ~ class_Rings_Olinordered__semidom(X20965)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20965),hAPP(hAPP(c_Power_Opower__class_Opower(X20965),X20964),hAPP(c_Nat_OSuc,X20963))),hAPP(hAPP(c_Power_Opower__class_Opower(X20965),X20962),hAPP(c_Nat_OSuc,X20963))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20965),c_Groups_Ozero__class_Ozero(X20965)),X20962))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20965),X20964),X20962)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base])]) ).
cnf(i_0_7425,plain,
c_List_Oconcat(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Oconcat(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_5558]) ).
fof(i_0_7426,plain,
! [X30713,X30714,X30715,X30716] :
( ~ class_Lattices_Osemilattice__sup(X30716)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30716),X30715))
| ~ hBOOL(hAPP(hAPP(c_member(X30716),X30714),X30715))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30716),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X30716),X30714),X30713)),hAPP(hAPP(c_Finite__Set_Ofold(X30716,X30716,c_Lattices_Osemilattice__sup__class_Osup(X30716)),X30713),X30715))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup])]) ).
fof(i_0_7427,plain,
! [X30725,X30726,X30727,X30728] :
( ~ class_Orderings_Olinorder(X30728)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30728),X30727))
| ~ hBOOL(hAPP(hAPP(c_member(X30728),X30726),X30727))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30728),hAPP(hAPP(c_Orderings_Oord__class_Omax(X30728),X30726),X30725)),hAPP(hAPP(c_Finite__Set_Ofold(X30728,X30728,c_Orderings_Oord__class_Omax(X30728)),X30725),X30727))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup])]) ).
fof(i_0_7428,plain,
! [X29807,X29808,X29809,X29810] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29810,X29809),tc_HOL_Obool)),X29808),X29807))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29810,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29810,X29809),X29808)),hAPP(c_Relation_ODomain(X29810,X29809),X29807))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])]) ).
cnf(i_0_7429,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5559]) ).
fof(i_0_7430,plain,
! [X21699,X21700,X21701] :
( ~ class_Fields_Olinordered__field(X21701)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21701),X21700),X21699))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21701),X21700),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21701),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21701),X21700),X21699)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21701),c_Groups_Oone__class_Oone(X21701)),c_Groups_Oone__class_Oone(X21701))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])]) ).
fof(i_0_7431,plain,
! [X27408,X27409] :
( ~ c_Nat__Transfer_Onat__set(X27409)
| ~ c_Nat__Transfer_Onat__set(X27408)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X27409),X27408) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X27409)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X27408))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J])]) ).
fof(i_0_7432,plain,
! [X24089,X24090] :
( ~ c_Nat__Transfer_Onat__set(X24090)
| ~ c_Nat__Transfer_Onat__set(X24089)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X24090),X24089) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24090)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24089))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J])]) ).
fof(i_0_7433,plain,
! [X23497,X23498,X23499,X23500,X23501] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23498),X23500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23500),X23499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23501,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23500,X23499)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23498,X23497)))
| ~ class_Orderings_Oorder(X23501) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23499),X23497))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23500),X23499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23501,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23500,X23499)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23498,X23497)))
| ~ class_Orderings_Oorder(X23501) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23501),X23498),X23500))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23501),X23499),X23497))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23500),X23499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23501,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23500,X23499)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23498,X23497)))
| ~ class_Orderings_Oorder(X23501) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23498),X23497))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23501,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23500,X23499)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23498,X23497)))
| ~ class_Orderings_Oorder(X23501) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23500),X23499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23498),X23497))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23501,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23500,X23499)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23498,X23497)))
| ~ class_Orderings_Oorder(X23501) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23501),X23498),X23500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23498),X23500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23499),X23497))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23498),X23497))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23501,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23500,X23499)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23498,X23497)))
| ~ class_Orderings_Oorder(X23501) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23501),X23499),X23497))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23498),X23500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23499),X23497))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23498),X23497))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23501,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23500,X23499)),c_SetInterval_Oord__class_OatLeastAtMost(X23501,X23498,X23497)))
| ~ class_Orderings_Oorder(X23501) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5560])])]) ).
fof(i_0_7434,plain,
! [X18820,X18821,X18822,X18823,X18824] :
( ~ class_Rings_Osemiring(X18824)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18824),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18824),X18823),X18822)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18824),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18824),X18821),X18822)),X18820)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18824),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18824),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18824),X18823),X18821)),X18822)),X18820) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).
fof(i_0_7435,plain,
! [X28723,X28724] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28724,X28724),tc_HOL_Obool)),c_Relation_OId__on(X28724,X28723)),hAPP(hAPP(c_Product__Type_OSigma(X28724,X28724),X28723),hAPP(c_COMBK(tc_fun(X28724,tc_HOL_Obool),X28724),X28723)))),
inference(variable_rename,[status(thm)],[fact_Id__on__subset__Times]) ).
fof(i_0_7436,plain,
! [X31962] :
( ( ~ c_Com_OWT__bodies
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X31962),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X31962)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),esk438_0),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
| c_Com_OWT__bodies )
& ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),esk438_0))
| c_Com_OWT__bodies ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT__bodies__def])])])])]) ).
fof(i_0_7437,plain,
! [X29705,X29706,X29707] : hAPP(c_Relation_ORange(X29707,X29706),hAPP(c_Set_OCollect(tc_prod(X29707,X29706)),hAPP(c_Product__Type_Oprod_Oprod__case(X29707,X29706,tc_HOL_Obool),X29705))) = hAPP(c_Set_OCollect(X29706),hAPP(hAPP(c_COMBB(tc_fun(X29707,tc_HOL_Obool),tc_HOL_Obool,X29706),c_HOL_OEx(X29707)),hAPP(c_COMBC(X29707,X29706,tc_HOL_Obool),X29705))),
inference(variable_rename,[status(thm)],[fact_Range__Collect__split]) ).
fof(i_0_7438,plain,
! [X28705,X28706,X28707] :
( ~ c_Equiv__Relations_Oequiv(X28707,X28706,X28705)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28707,X28707),tc_HOL_Obool)),X28705),hAPP(hAPP(c_Product__Type_OSigma(X28707,X28707),X28706),hAPP(c_COMBK(tc_fun(X28707,tc_HOL_Obool),X28707),X28706)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__type])]) ).
fof(i_0_7439,plain,
! [X31776,X31777,X31778,X31779,X31780] : hAPP(c_Fun_Ocomp(tc_List_Olist(X31780),tc_List_Olist(X31779),tc_List_Olist(X31778),hAPP(c_List_Omap(X31780,X31779),X31777)),hAPP(c_List_Omap(X31778,X31780),X31776)) = hAPP(c_List_Omap(X31778,X31779),hAPP(c_Fun_Ocomp(X31780,X31779,X31778,X31777),X31776)),
inference(variable_rename,[status(thm)],[fact_map__comp__map]) ).
fof(i_0_7440,plain,
! [X31771,X31772,X31773,X31774,X31775] : hAPP(c_Fun_Ocomp(tc_List_Olist(X31775),tc_List_Olist(X31774),tc_List_Olist(X31773),hAPP(c_List_Omap(X31775,X31774),X31772)),hAPP(c_List_Omap(X31773,X31775),X31771)) = hAPP(c_List_Omap(X31773,X31774),hAPP(c_Fun_Ocomp(X31775,X31774,X31773,X31772),X31771)),
inference(variable_rename,[status(thm)],[fact_List_Omap_Ocomp]) ).
fof(i_0_7441,plain,
! [X31863,X31864,X31865,X31866,X31867] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31867),tc_Option_Ooption(X31866),tc_Option_Ooption(X31865),hAPP(c_Option_Omap(X31867,X31866),X31864)),hAPP(c_Option_Omap(X31865,X31867),X31863)) = hAPP(c_Option_Omap(X31865,X31866),hAPP(c_Fun_Ocomp(X31867,X31866,X31865,X31864),X31863)),
inference(variable_rename,[status(thm)],[fact_Option_Omap_Ocomp]) ).
fof(i_0_7442,plain,
! [X28999,X29000,X29001,X29002,X29003] :
( ~ c_Relation_Orefl__on(X29003,X29002,X29001)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29003,X29003)),hAPP(hAPP(c_Product__Type_OPair(X29003,X29003),X29000),X28999)),X29001))
| hBOOL(hAPP(hAPP(c_member(X29003),X29000),X29002)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD1])]) ).
fof(i_0_7443,plain,
! [X29004,X29005,X29006,X29007,X29008] :
( ~ c_Relation_Orefl__on(X29008,X29007,X29006)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29008,X29008)),hAPP(hAPP(c_Product__Type_OPair(X29008,X29008),X29005),X29004)),X29006))
| hBOOL(hAPP(hAPP(c_member(X29008),X29004),X29007)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD2])]) ).
cnf(i_0_7444,plain,
( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5561]) ).
fof(i_0_7445,plain,
! [X32557,X32558] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32558),tc_List_Olist(X32558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32558),tc_List_Olist(X32558)),c_List_Olist_ONil(X32558)),c_List_Olist_ONil(X32558))),c_List_Olistrel(X32558,X32557))),
inference(variable_rename,[status(thm)],[fact_listrel_ONil]) ).
fof(i_0_7446,plain,
! [X31341,X31342,X31343] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31343,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31343,tc_HOL_Obool),X31342)),X31341) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31343,tc_HOL_Obool),tc_fun(X31343,tc_HOL_Obool)),X31342),hAPP(hAPP(c_COMBC(tc_fun(X31343,tc_HOL_Obool),tc_fun(X31343,tc_HOL_Obool),tc_fun(X31343,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31343,tc_HOL_Obool))),X31341)),
inference(variable_rename,[status(thm)],[fact_Int__Union2]) ).
fof(i_0_7447,plain,
! [X26441,X26442,X26443,X26444] :
( ( X26443 = X26442
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26444,X26444)),hAPP(hAPP(c_Product__Type_OPair(X26444,X26444),X26443),X26442)),c_Relation_OId__on(X26444,X26441))) )
& ( hBOOL(hAPP(hAPP(c_member(X26444),X26443),X26441))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26444,X26444)),hAPP(hAPP(c_Product__Type_OPair(X26444,X26444),X26443),X26442)),c_Relation_OId__on(X26444,X26441))) )
& ( X26443 != X26442
| ~ hBOOL(hAPP(hAPP(c_member(X26444),X26443),X26441))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26444,X26444)),hAPP(hAPP(c_Product__Type_OPair(X26444,X26444),X26443),X26442)),c_Relation_OId__on(X26444,X26441))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])]) ).
fof(i_0_7448,plain,
! [X24710,X24711,X24712,X24713] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24713),X24711))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24713,X24712)),c_Sum__Type_OPlus(X24713,X24712,X24711,X24710))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24712),X24710))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24713,X24712)),c_Sum__Type_OPlus(X24713,X24712,X24711,X24710))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24713),X24711))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24712),X24710))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24713,X24712)),c_Sum__Type_OPlus(X24713,X24712,X24711,X24710))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).
fof(i_0_7449,plain,
! [X24718,X24719,X24720,X24721] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24721,X24720)),c_Sum__Type_OPlus(X24721,X24720,X24719,X24718)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24721),X24719)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).
fof(i_0_7450,plain,
! [X24722,X24723,X24724,X24725] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24725,X24724)),c_Sum__Type_OPlus(X24725,X24724,X24723,X24722)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24724),X24722)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).
fof(i_0_7451,plain,
! [X28623,X28624,X28625,X28626,X28627,X28628] :
( ~ hBOOL(hAPP(hAPP(c_member(X28628),X28627),X28626))
| ~ hBOOL(hAPP(hAPP(c_member(X28625),X28624),hAPP(X28623,X28627)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X28628,X28625)),hAPP(hAPP(c_Product__Type_OPair(X28628,X28625),X28627),X28624)),hAPP(hAPP(c_Product__Type_OSigma(X28628,X28625),X28626),X28623))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaI])]) ).
fof(i_0_7452,plain,
! [X31458,X31459,X31460] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31460,tc_HOL_Obool)),esk408_3(X31458,X31459,X31460)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31460,tc_HOL_Obool)),X31459),X31458)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31460,tc_HOL_Obool)),X31459),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31460,tc_HOL_Obool),X31458)) = c_Orderings_Obot__class_Obot(tc_fun(X31460,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31460,tc_HOL_Obool)),X31459),X31458)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31460,tc_HOL_Obool)),esk409_3(X31458,X31459,X31460)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31460,tc_HOL_Obool)),X31459),X31458)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31460,tc_HOL_Obool)),X31459),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31460,tc_HOL_Obool),X31458)) = c_Orderings_Obot__class_Obot(tc_fun(X31460,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31460,tc_HOL_Obool)),X31459),X31458)) )
& ( esk408_3(X31458,X31459,X31460) != esk409_3(X31458,X31459,X31460)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31460,tc_HOL_Obool)),X31459),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31460,tc_HOL_Obool),X31458)) = c_Orderings_Obot__class_Obot(tc_fun(X31460,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31460,tc_HOL_Obool)),X31459),X31458)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31460,tc_HOL_Obool)),esk408_3(X31458,X31459,X31460)),esk409_3(X31458,X31459,X31460)) != c_Orderings_Obot__class_Obot(tc_fun(X31460,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31460,tc_HOL_Obool)),X31459),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31460,tc_HOL_Obool),X31458)) = c_Orderings_Obot__class_Obot(tc_fun(X31460,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31460,tc_HOL_Obool)),X31459),X31458)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5562])])])]) ).
fof(i_0_7453,plain,
! [X33570,X33571,X33572,X33573] :
( ~ class_Groups_Osemigroup__add(X33573)
| hAPP(c_List_Ofoldl(X33573,X33573,c_Groups_Oplus__class_Oplus(X33573),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33573),X33572),X33571)),X33570) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33573),X33572),hAPP(c_List_Ofoldl(X33573,X33573,c_Groups_Oplus__class_Oplus(X33573),X33571),X33570)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__assoc])]) ).
fof(i_0_7454,plain,
! [X30500,X30501,X30502] : hBOOL(hAPP(hAPP(c_member(tc_prod(X30502,X30502)),hAPP(hAPP(c_Product__Type_OPair(X30502,X30502),X30501),X30501)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30502,X30502),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30500))),
inference(variable_rename,[status(thm)],[fact_rel__pow__0__I]) ).
cnf(i_0_7455,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),c_Relation_OId(X1)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_5563]) ).
fof(i_0_7456,plain,
! [X33018,X33019,X33020,X33021,X33022] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33022),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33021)),X33020)))
| hAPP(hAPP(c_List_Olist__update(X33021,hAPP(hAPP(c_List_Oappend(X33021),X33020),X33019)),X33022),X33018) = hAPP(hAPP(c_List_Oappend(X33021),hAPP(hAPP(c_List_Olist__update(X33021,X33020),X33022),X33018)),X33019) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33022),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33021)),X33020)))
| hAPP(hAPP(c_List_Olist__update(X33021,hAPP(hAPP(c_List_Oappend(X33021),X33020),X33019)),X33022),X33018) = hAPP(hAPP(c_List_Oappend(X33021),X33020),hAPP(hAPP(c_List_Olist__update(X33021,X33019),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33022),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33021)),X33020))),X33018)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5564])]) ).
fof(i_0_7457,plain,
! [X27554,X27555,X27556,X27557,X27558] :
( ~ c_Equiv__Relations_Oequiv(X27558,X27557,X27556)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27558,tc_HOL_Obool)),X27555),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27558),X27557),X27556)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27558,tc_HOL_Obool)),X27554),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27558),X27557),X27556)))
| X27555 = X27554
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27558,tc_HOL_Obool)),X27555),X27554) = c_Orderings_Obot__class_Obot(tc_fun(X27558,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__disj])]) ).
fof(i_0_7458,plain,
! [X32618,X32619,X32620] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32620),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32619)),X32618)))
| hAPP(c_Random_Opick(X32619,hAPP(hAPP(c_List_Omap(X32619,tc_prod(tc_Code__Numeral_Ocode__numeral,X32619)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X32619),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X32618)),hAPP(c_Code__Numeral_Oof__nat,X32620)) = hAPP(hAPP(c_List_Onth(X32619),X32618),X32620) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__same])]) ).
fof(i_0_7459,plain,
! [X21716,X21717,X21718,X21719] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),c_Groups_Ozero__class_Ozero(X21719)),X21716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21719),X21718),X21716)),X21717))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),X21716),c_Groups_Ozero__class_Ozero(X21719)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21719),X21718),X21716)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),c_Groups_Ozero__class_Ozero(X21719)),X21716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),X21716),c_Groups_Ozero__class_Ozero(X21719)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),c_Groups_Ozero__class_Ozero(X21719)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),c_Groups_Ozero__class_Ozero(X21719)),X21716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),c_Groups_Ozero__class_Ozero(X21719)),X21716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),c_Groups_Ozero__class_Ozero(X21719)),X21716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),X21716),c_Groups_Ozero__class_Ozero(X21719)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),X21716),c_Groups_Ozero__class_Ozero(X21719)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),c_Groups_Ozero__class_Ozero(X21719)),X21716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),c_Groups_Ozero__class_Ozero(X21719)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),X21716),c_Groups_Ozero__class_Ozero(X21719)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),c_Groups_Ozero__class_Ozero(X21719)),X21716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),X21716),c_Groups_Ozero__class_Ozero(X21719)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21719),X21718),X21716)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),c_Groups_Ozero__class_Ozero(X21719)),X21716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),c_Groups_Ozero__class_Ozero(X21719)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21719),X21718),X21716)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),c_Groups_Ozero__class_Ozero(X21719)),X21716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),c_Groups_Ozero__class_Ozero(X21719)),X21716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21719),X21718),X21716)),X21717))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),X21716),c_Groups_Ozero__class_Ozero(X21719)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),X21716),c_Groups_Ozero__class_Ozero(X21719)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21719),X21718),X21716)),X21717))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),c_Groups_Ozero__class_Ozero(X21719)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),X21716),c_Groups_Ozero__class_Ozero(X21719)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21719),X21718),X21716)),X21717))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21719),X21716),c_Groups_Ozero__class_Ozero(X21719)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21719),X21718),X21716)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21719),X21718),X21716)),X21717))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),c_Groups_Ozero__class_Ozero(X21719)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21719),X21718),X21716)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21719),X21718),X21716)),X21717))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21719),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21719),X21717),X21716)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21719) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5565])])]) ).
fof(i_0_7460,plain,
! [X21644,X21645,X21646,X21647] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),c_Groups_Ozero__class_Ozero(X21647)),X21644))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21647),X21646),X21644)),X21645))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21644),c_Groups_Ozero__class_Ozero(X21647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21647),X21646),X21644)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),c_Groups_Ozero__class_Ozero(X21647)),X21644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21644),c_Groups_Ozero__class_Ozero(X21647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),c_Groups_Ozero__class_Ozero(X21647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),c_Groups_Ozero__class_Ozero(X21647)),X21644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),c_Groups_Ozero__class_Ozero(X21647)),X21644))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),c_Groups_Ozero__class_Ozero(X21647)),X21644))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21644),c_Groups_Ozero__class_Ozero(X21647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21644),c_Groups_Ozero__class_Ozero(X21647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),c_Groups_Ozero__class_Ozero(X21647)),X21644))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),c_Groups_Ozero__class_Ozero(X21647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21644),c_Groups_Ozero__class_Ozero(X21647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),c_Groups_Ozero__class_Ozero(X21647)),X21644))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21644),c_Groups_Ozero__class_Ozero(X21647)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21647),X21646),X21644)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),c_Groups_Ozero__class_Ozero(X21647)),X21644))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),c_Groups_Ozero__class_Ozero(X21647)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21647),X21646),X21644)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),c_Groups_Ozero__class_Ozero(X21647)),X21644))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),c_Groups_Ozero__class_Ozero(X21647)),X21644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21647),X21646),X21644)),X21645))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21644),c_Groups_Ozero__class_Ozero(X21647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21644),c_Groups_Ozero__class_Ozero(X21647)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21647),X21646),X21644)),X21645))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),c_Groups_Ozero__class_Ozero(X21647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21644),c_Groups_Ozero__class_Ozero(X21647)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21647),X21646),X21644)),X21645))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21644),c_Groups_Ozero__class_Ozero(X21647)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21647),X21646),X21644)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21647),X21646),X21644)),X21645))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),c_Groups_Ozero__class_Ozero(X21647)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21647),X21646),X21644)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21647),X21646),X21644)),X21645))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21647),X21646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21647),X21645),X21644)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21647) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5566])])]) ).
fof(i_0_7461,plain,
! [X23816,X23817] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23817),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23816),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23816),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X23817)))))
| X23817 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23816),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23816),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X23817))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).
fof(i_0_7462,plain,
! [X25262,X25263,X25264,X25265,X25266] :
( ( hBOOL(hAPP(hAPP(X25264,X25263),X25265))
| ~ hBOOL(hAPP(hAPP(c_member(X25266),X25265),c_SetInterval_Oord_OgreaterThanLessThan(X25266,X25264,X25263,X25262))) )
& ( hBOOL(hAPP(hAPP(X25264,X25265),X25262))
| ~ hBOOL(hAPP(hAPP(c_member(X25266),X25265),c_SetInterval_Oord_OgreaterThanLessThan(X25266,X25264,X25263,X25262))) )
& ( ~ hBOOL(hAPP(hAPP(X25264,X25263),X25265))
| ~ hBOOL(hAPP(hAPP(X25264,X25265),X25262))
| hBOOL(hAPP(hAPP(c_member(X25266),X25265),c_SetInterval_Oord_OgreaterThanLessThan(X25266,X25264,X25263,X25262))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff])])]) ).
fof(i_0_7463,plain,
! [X25090,X25091,X25092,X25093,X25094] :
( ( hBOOL(hAPP(hAPP(X25092,X25091),X25093))
| ~ hBOOL(hAPP(hAPP(c_member(X25094),X25093),c_SetInterval_Oord_OatLeastAtMost(X25094,X25092,X25091,X25090))) )
& ( hBOOL(hAPP(hAPP(X25092,X25093),X25090))
| ~ hBOOL(hAPP(hAPP(c_member(X25094),X25093),c_SetInterval_Oord_OatLeastAtMost(X25094,X25092,X25091,X25090))) )
& ( ~ hBOOL(hAPP(hAPP(X25092,X25091),X25093))
| ~ hBOOL(hAPP(hAPP(X25092,X25093),X25090))
| hBOOL(hAPP(hAPP(c_member(X25094),X25093),c_SetInterval_Oord_OatLeastAtMost(X25094,X25092,X25091,X25090))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff])])]) ).
fof(i_0_7464,plain,
! [X32574,X32575] : c_List_Oset__Cons(X32575,X32574,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32575)),c_List_Olist_ONil(X32575)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32575),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X32575,tc_List_Olist(X32575),hAPP(hAPP(c_COMBC(X32575,tc_List_Olist(X32575),tc_List_Olist(X32575)),c_List_Olist_OCons(X32575)),c_List_Olist_ONil(X32575))),X32574),
inference(variable_rename,[status(thm)],[fact_set__Cons__sing__Nil]) ).
fof(i_0_7465,plain,
! [X31003,X31004,X31005,X31006,X31007,X31008] :
( ~ hBOOL(hAPP(hAPP(c_member(X31008),X31007),X31006))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31008,tc_fun(X31005,tc_HOL_Obool)),X31006),hAPP(hAPP(c_COMBB(tc_fun(X31005,tc_HOL_Obool),tc_fun(X31005,tc_HOL_Obool),X31008),hAPP(c_Set_Oinsert(X31005),X31004)),X31003)) = hAPP(hAPP(c_Set_Oinsert(X31005),X31004),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31008,tc_fun(X31005,tc_HOL_Obool)),X31006),X31003)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib])]) ).
fof(i_0_7466,plain,
! [X25302,X25303,X25304,X25305,X25306,X25307] :
( ~ hBOOL(hAPP(hAPP(c_member(X25307),X25306),X25305))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25307,tc_fun(X25304,tc_HOL_Obool)),X25305),hAPP(hAPP(c_COMBB(tc_fun(X25304,tc_HOL_Obool),tc_fun(X25304,tc_HOL_Obool),X25307),hAPP(c_Set_Oinsert(X25304),X25303)),X25302)) = hAPP(hAPP(c_Set_Oinsert(X25304),X25303),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25307,tc_fun(X25304,tc_HOL_Obool)),X25305),X25302)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib])]) ).
fof(i_0_7467,plain,
! [X29474,X29475,X29478,X29479,X29480,X29481] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29475),X29474))
| X29474 = hAPP(c_Set_Oimage(tc_Nat_Onat,X29475,esk316_2(X29474,X29475)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk315_2(X29474,X29475)))) )
& ( X29478 != hAPP(c_Set_Oimage(tc_Nat_Onat,X29479,X29481),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X29480)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29479),X29478)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__conv__nat__seg__image])])])])]) ).
fof(i_0_7468,plain,
! [X29273,X29274,X29275,X29276] :
( X29276 != hAPP(c_Set_Oimage(tc_Nat_Onat,X29275,X29274),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X29273)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29275),X29276)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__seg__image__imp__finite])]) ).
fof(i_0_7469,plain,
! [X33445,X33446,X33447] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33447),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33446)),X33445)))
| hAPP(hAPP(c_List_Oappend(X33446),hAPP(hAPP(c_List_Otake(X33446),X33447),X33445)),hAPP(hAPP(c_List_Olist_OCons(X33446),hAPP(c_List_Ohd(X33446),hAPP(hAPP(c_List_Odrop(X33446),X33447),X33445))),c_List_Olist_ONil(X33446))) = hAPP(hAPP(c_List_Otake(X33446),hAPP(c_Nat_OSuc,X33447)),X33445) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__hd__drop])]) ).
fof(i_0_7470,plain,
! [X24753,X24754,X24755,X24756] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24756,tc_HOL_Obool)),X24755),hAPP(hAPP(c_Set_Oinsert(X24756),X24754),X24753)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24756,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24756,tc_HOL_Obool)),X24755),hAPP(hAPP(c_Set_Oinsert(X24756),X24754),c_Orderings_Obot__class_Obot(tc_fun(X24756,tc_HOL_Obool))))),X24753),
inference(variable_rename,[status(thm)],[fact_Diff__insert2]) ).
fof(i_0_7471,plain,
! [X32258,X32259,X32260] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32260),tc_List_Olist(X32260))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32260),tc_List_Olist(X32260)),X32259),X32259)),c_List_Olistrel(X32260,c_Transitive__Closure_Ortrancl(X32260,X32258)))),
inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__refl]) ).
fof(i_0_7472,plain,
! [X25013,X25014,X25015,X25016,X25017] :
( ~ hBOOL(hAPP(hAPP(c_member(X25017),X25016),X25015))
| hBOOL(hAPP(hAPP(c_member(tc_sum(X25017,X25014)),hAPP(c_Sum__Type_OInl(X25017,X25014),X25016)),c_Sum__Type_OPlus(X25017,X25014,X25015,X25013))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InlI])]) ).
fof(i_0_7473,plain,
! [X25008,X25009,X25010,X25011,X25012] :
( ~ hBOOL(hAPP(hAPP(c_member(X25012),X25011),X25010))
| hBOOL(hAPP(hAPP(c_member(tc_sum(X25009,X25012)),hAPP(c_Sum__Type_OInr(X25012,X25009),X25011)),c_Sum__Type_OPlus(X25009,X25012,X25008,X25010))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InrI])]) ).
cnf(i_0_7474,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))),X2) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5567]) ).
fof(i_0_7475,plain,
! [X31468,X31469,X31470] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31470,tc_HOL_Obool)),esk411_3(X31468,X31469,X31470)),X31469))
| X31469 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31470,tc_HOL_Obool),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31470,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31470,tc_HOL_Obool),X31469)),X31468)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31470,tc_HOL_Obool)),esk411_3(X31468,X31469,X31470)),X31468))
| X31469 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31470,tc_HOL_Obool),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31470,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31470,tc_HOL_Obool),X31469)),X31468)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__subset])])])]) ).
fof(i_0_7476,plain,
! [X19936,X19937,X19938] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19938))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19937,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19936),X19938)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19936),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19937),X19936),X19938))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19937,X19936)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq])]) ).
fof(i_0_7477,plain,
! [X27047,X27048,X27049,X27050] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27050,tc_HOL_Obool)),X27049),X27048))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27050,tc_HOL_Obool)),X27049),X27047))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27050,tc_HOL_Obool)),X27049),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27050,tc_HOL_Obool)),X27048),X27047))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greatest])]) ).
fof(i_0_7478,plain,
! [X22720,X22721] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22721),hAPP(c_Nat_OSuc,X22720)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22720),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),X22720)),X22721),
inference(variable_rename,[status(thm)],[fact_max__Suc2]) ).
cnf(i_0_7479,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),hAPP(c_Wellfounded_Omeasure(X4),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_5526]) ).
fof(i_0_7480,plain,
! [X30470,X30471,X30472,X30473] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30473,X30473),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30472),X30471)),X30470) = hAPP(hAPP(c_Relation_Orel__comp(X30473,X30473,X30473),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30473,X30473),tc_HOL_Obool),X30472),X30470)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30473,X30473),tc_HOL_Obool),X30471),X30470)),
inference(variable_rename,[status(thm)],[fact_rel__pow__add]) ).
fof(i_0_7481,plain,
! [X31304,X31305,X31306] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X31306,tc_HOL_Obool),tc_HOL_Obool)),X31305),X31304))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31306,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31306,tc_HOL_Obool),X31305)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31306,tc_HOL_Obool),X31304))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__mono])]) ).
fof(i_0_7482,plain,
! [X31324,X31325,X31326] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X31326,tc_HOL_Obool),tc_HOL_Obool)),X31325),X31324))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31326,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31326,tc_HOL_Obool),X31324)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31326,tc_HOL_Obool),X31325))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono])]) ).
fof(i_0_7483,plain,
! [X20798,X20799,X20800] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20800)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20800),hAPP(c_Groups_Oabs__class_Oabs(X20800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20800),X20799),X20798))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20800),hAPP(c_Groups_Oabs__class_Oabs(X20800),X20799)),hAPP(c_Groups_Oabs__class_Oabs(X20800),X20798)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])]) ).
fof(i_0_7484,plain,
! [X20678,X20679,X20680] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20680)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20680),hAPP(c_Groups_Oabs__class_Oabs(X20680),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20680),X20679),X20678))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20680),hAPP(c_Groups_Oabs__class_Oabs(X20680),X20679)),hAPP(c_Groups_Oabs__class_Oabs(X20680),X20678)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])]) ).
cnf(i_0_7485,plain,
c_List_Orotate(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orotate(X1,X2)),c_List_Orotate(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_5568]) ).
fof(i_0_7486,plain,
! [X23477,X23478,X23479,X23480,X23481] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23481),X23478),X23480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23481),X23480),X23479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23481,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23481,X23480,X23479)),c_SetInterval_Oord__class_OatLeastAtMost(X23481,X23478,X23477)))
| ~ class_Orderings_Oorder(X23481) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23481),X23479),X23477))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23481),X23480),X23479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23481,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23481,X23480,X23479)),c_SetInterval_Oord__class_OatLeastAtMost(X23481,X23478,X23477)))
| ~ class_Orderings_Oorder(X23481) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23481),X23480),X23479))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23481,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23481,X23480,X23479)),c_SetInterval_Oord__class_OatLeastAtMost(X23481,X23478,X23477)))
| ~ class_Orderings_Oorder(X23481) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23481),X23478),X23480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23481),X23479),X23477))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23481,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23481,X23480,X23479)),c_SetInterval_Oord__class_OatLeastAtMost(X23481,X23478,X23477)))
| ~ class_Orderings_Oorder(X23481) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5569])])]) ).
fof(i_0_7487,plain,
! [X22476,X22477] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22477),hAPP(c_Nat_OSuc,X22476)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),X22476)),X22477),
inference(variable_rename,[status(thm)],[fact_min__Suc2]) ).
fof(i_0_7488,plain,
! [X25422,X25423,X25424] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25424),X25423))
| ~ hBOOL(hAPP(hAPP(c_member(X25424),X25422),X25423))
| hAPP(c_Finite__Set_Ocard(X25424),X25423) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X25424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25424,tc_HOL_Obool)),X25423),hAPP(hAPP(c_Set_Oinsert(X25424),X25422),c_Orderings_Obot__class_Obot(tc_fun(X25424,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oremove])]) ).
fof(i_0_7489,plain,
! [X32741,X32742,X32743,X32744,X32745,X32746,X32747] : hAPP(hAPP(c_List_Ozip(X32747,X32746),hAPP(hAPP(c_List_Olist__update(X32747,X32745),X32744),X32743)),hAPP(hAPP(c_List_Olist__update(X32746,X32742),X32744),X32741)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X32747,X32746),hAPP(hAPP(c_List_Ozip(X32747,X32746),X32745),X32742)),X32744),hAPP(hAPP(c_Product__Type_OPair(X32747,X32746),X32743),X32741)),
inference(variable_rename,[status(thm)],[fact_zip__update]) ).
fof(i_0_7490,plain,
! [X28058,X28059,X28060,X28061,X28062] :
( ~ c_Fun_Oinj__on(X28062,X28061,X28060,c_Orderings_Otop__class_Otop(tc_fun(X28062,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(X28062,X28061,X28060),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28062,tc_HOL_Obool)),X28059),X28058)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28061,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28062,X28061,X28060),X28059)),hAPP(c_Set_Oimage(X28062,X28061,X28060),X28058)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Int])]) ).
fof(i_0_7491,plain,
! [X28077,X28078,X28079,X28080,X28081] :
( ~ c_Fun_Oinj__on(X28081,X28080,X28079,c_Orderings_Otop__class_Otop(tc_fun(X28081,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(X28081,X28080,X28079),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28081,tc_HOL_Obool)),X28078),X28077)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28080,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28081,X28080,X28079),X28078)),hAPP(c_Set_Oimage(X28081,X28080,X28079),X28077)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__set__diff])]) ).
fof(i_0_7492,plain,
! [X28405,X28406,X28407,X28408] :
( ~ c_Fun_Oinj__on(X28408,X28407,X28406,X28405)
| hAPP(c_Set_Oimage(X28407,X28408,c_Fun_Othe__inv__into(X28408,X28407,X28405,X28406)),hAPP(c_Set_Oimage(X28408,X28407,X28406),X28405)) = X28405 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto])]) ).
fof(i_0_7493,plain,
! [X18366,X18367,X18368,X18369,X18370,X18371] : c_Nitpick_Opair__box_Opair__box__rec(X18371,X18370,X18369,X18368,c_Nitpick_Opair__box_OPairBox(X18371,X18370,X18367,X18366)) = hAPP(hAPP(X18368,X18367),X18366),
inference(variable_rename,[status(thm)],[fact_pair__box_Orecs]) ).
fof(i_0_7494,plain,
! [X18360,X18361,X18362,X18363,X18364,X18365] : c_Nitpick_Opair__box_Opair__box__case(X18365,X18364,X18363,X18362,c_Nitpick_Opair__box_OPairBox(X18365,X18364,X18361,X18360)) = hAPP(hAPP(X18362,X18361),X18360),
inference(variable_rename,[status(thm)],[fact_pair__box_Osimps_I2_J]) ).
fof(i_0_7495,plain,
! [X26160,X26161,X26162,X26163,X26164] :
( ~ class_Groups_Ocomm__monoid__mult(X26164)
| ~ class_Rings_Odvd(X26164)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26163),X26162))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26163,tc_HOL_Obool)),X26161),X26162))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X26164),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26163,X26164),X26160),X26161)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26163,X26164),X26160),X26162))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__dvd__setprod__subset])]) ).
cnf(i_0_7496,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5570]) ).
cnf(i_0_7497,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5571]) ).
cnf(i_0_7498,plain,
( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk388_2(X2,X1)),esk388_2(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Relation_OId(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5572]) ).
fof(i_0_7499,plain,
! [X17406,X17407,X17408,X17409,X17410] :
( ( ~ hBOOL(hAPP(X17410,X17407))
| hBOOL(hAPP(X17410,X17407))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17410,X17409,X17408)),X17407),X17406)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17408),X17407),X17406))
| hBOOL(hAPP(X17410,X17407))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17410,X17409,X17408)),X17407),X17406)) )
& ( ~ hBOOL(hAPP(X17410,X17407))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17409),X17407),X17406))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17410,X17409,X17408)),X17407),X17406)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17408),X17407),X17406))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17409),X17407),X17406))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17410,X17409,X17408)),X17407),X17406)) )
& ( ~ hBOOL(hAPP(X17410,X17407))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17409),X17407),X17406))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17410,X17409,X17408)),X17407),X17406)) )
& ( hBOOL(hAPP(X17410,X17407))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17408),X17407),X17406))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17410,X17409,X17408)),X17407),X17406)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5573])])]) ).
fof(i_0_7500,plain,
! [X17401,X17402,X17403,X17404,X17405] :
( ( ~ hBOOL(hAPP(X17405,X17402))
| hBOOL(hAPP(X17405,X17402))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17405,X17404,X17403)),X17402),X17401)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17403),X17402),X17401))
| hBOOL(hAPP(X17405,X17402))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17405,X17404,X17403)),X17402),X17401)) )
& ( ~ hBOOL(hAPP(X17405,X17402))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17404),X17402),X17401))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17405,X17404,X17403)),X17402),X17401)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17403),X17402),X17401))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17404),X17402),X17401))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17405,X17404,X17403)),X17402),X17401)) )
& ( ~ hBOOL(hAPP(X17405,X17402))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17404),X17402),X17401))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17405,X17404,X17403)),X17402),X17401)) )
& ( hBOOL(hAPP(X17405,X17402))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17403),X17402),X17401))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17405,X17404,X17403)),X17402),X17401)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5574])])]) ).
fof(i_0_7501,plain,
! [X17378,X17379,X17380,X17381,X17382] :
( ( ~ hBOOL(hAPP(X17382,X17379))
| hBOOL(hAPP(X17382,X17379))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17382,X17381,X17380)),X17379),X17378)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17380),X17379),X17378))
| hBOOL(hAPP(X17382,X17379))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17382,X17381,X17380)),X17379),X17378)) )
& ( ~ hBOOL(hAPP(X17382,X17379))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17381),X17379),X17378))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17382,X17381,X17380)),X17379),X17378)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17380),X17379),X17378))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17381),X17379),X17378))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17382,X17381,X17380)),X17379),X17378)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5575])])]) ).
cnf(i_0_7502,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),
inference(split_conjunct,[status(thm)],[i_0_5576]) ).
fof(i_0_7503,plain,
! [X18612,X18613,X18614] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18614),X18613))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18612))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18612)),X18614)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18612)),X18613))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma])]) ).
cnf(i_0_7504,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId(X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_5516]) ).
cnf(i_0_7505,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Relation_OId(X1))),
inference(split_conjunct,[status(thm)],[i_0_5577]) ).
fof(i_0_7506,plain,
! [X27264,X27265,X27266,X27267] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27267,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27267,tc_HOL_Obool)),X27266),X27265)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27267,tc_HOL_Obool)),X27264),X27265)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27267,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27267,tc_HOL_Obool)),X27266),X27265)),X27264),
inference(variable_rename,[status(thm)],[fact_Diff__Int2]) ).
fof(i_0_7507,plain,
! [X27098,X27099,X27100,X27101] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27101,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27101,tc_HOL_Obool)),X27100),X27099)),X27098) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27101,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27101,tc_HOL_Obool)),X27100),X27098)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27101,tc_HOL_Obool)),X27099),X27098)),
inference(variable_rename,[status(thm)],[fact_Int__Un__distrib2]) ).
fof(i_0_7508,plain,
! [X27260,X27261,X27262,X27263] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27263,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27263,tc_HOL_Obool)),X27262),X27261)),X27260) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27263,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27263,tc_HOL_Obool)),X27262),X27260)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27263,tc_HOL_Obool)),X27261),X27260)),
inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib2]) ).
fof(i_0_7509,plain,
! [X27094,X27095,X27096,X27097] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27097,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27097,tc_HOL_Obool)),X27096),X27095)),X27094) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27097,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27097,tc_HOL_Obool)),X27096),X27094)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27097,tc_HOL_Obool)),X27095),X27094)),
inference(variable_rename,[status(thm)],[fact_Un__Int__distrib2]) ).
fof(i_0_7510,plain,
! [X23964,X23965,X23966,X23967] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23967,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23967,tc_HOL_Obool)),X23966),X23965)),X23964) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23967,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23967,tc_HOL_Obool)),X23966),X23964)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23967,tc_HOL_Obool)),X23965),X23964)),
inference(variable_rename,[status(thm)],[fact_Un__Diff]) ).
fof(i_0_7511,plain,
! [X25511,X25512,X25513] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk176_3(X25511,X25512,X25513)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25513)))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25512),X25513) = X25512
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25512),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25513)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk177_3(X25511,X25512,X25513)),X25511))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25512),X25513) = X25512
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25512),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25513)) )
& ( X25512 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk177_3(X25511,X25512,X25513)),esk176_3(X25511,X25512,X25513))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25512),X25513) = X25512
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25512),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25513)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I3_J])])])]) ).
fof(i_0_7512,plain,
! [X25516,X25517,X25518] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk178_3(X25516,X25517,X25518)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25518)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25517),X25518) = X25517
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25517),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25518)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk179_3(X25516,X25517,X25518)),X25516))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25517),X25518) = X25517
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25517),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25518)) )
& ( X25517 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk179_3(X25516,X25517,X25518)),esk178_3(X25516,X25517,X25518))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25517),X25518) = X25517
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25517),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25518)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_aset_I3_J])])])]) ).
fof(i_0_7513,plain,
! [X33426,X33427,X33428,X33429] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33429),X33428)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33427)),X33426)))
| hAPP(hAPP(c_List_Otake(X33427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33429),X33428)),X33426) = hAPP(hAPP(c_List_Oappend(X33427),hAPP(hAPP(c_List_Otake(X33427),X33429),X33426)),hAPP(hAPP(c_List_Otake(X33427),X33428),hAPP(hAPP(c_List_Odrop(X33427),X33429),X33426))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__add])]) ).
fof(i_0_7514,plain,
! [X27703,X27704,X27705] :
( ( hBOOL(hAPP(hAPP(c_member(X27705),esk250_3(X27703,X27704,X27705)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27705,tc_HOL_Obool)),X27704),X27703)))
| hAPP(c_Finite__Set_Ocard(X27705),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27705,tc_HOL_Obool)),X27704),X27703)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27705),X27704)),hAPP(c_Finite__Set_Ocard(X27705),X27703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27705),X27703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27705),X27704)) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(X27705),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27705,tc_HOL_Obool)),X27704),X27703)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27705),X27704)),hAPP(c_Finite__Set_Ocard(X27705),X27703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27705),X27703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27705),X27704)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter__neutral])])])]) ).
cnf(i_0_7515,plain,
hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),X2),X3) = hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Oconcat(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_5578]) ).
cnf(i_0_7516,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_5579]) ).
fof(i_0_7517,plain,
! [X31651,X31652,X31653,X31654] :
( ( ~ c_Fun_Oinj__on(X31654,tc_Option_Ooption(X31653),c_Map_Omap__add(X31654,X31653,X31652,X31651),c_Map_Odom(X31654,X31653,X31651))
| c_Fun_Oinj__on(X31654,tc_Option_Ooption(X31653),X31651,c_Map_Odom(X31654,X31653,X31651)) )
& ( ~ c_Fun_Oinj__on(X31654,tc_Option_Ooption(X31653),X31651,c_Map_Odom(X31654,X31653,X31651))
| c_Fun_Oinj__on(X31654,tc_Option_Ooption(X31653),c_Map_Omap__add(X31654,X31653,X31652,X31651),c_Map_Odom(X31654,X31653,X31651)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__add__dom])]) ).
fof(i_0_7518,plain,
! [X25408,X25409,X25410] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25410),X25409))
| ~ hBOOL(hAPP(hAPP(c_member(X25410),X25408),X25409))
| hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X25410),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25410,tc_HOL_Obool)),X25409),hAPP(hAPP(c_Set_Oinsert(X25410),X25408),c_Orderings_Obot__class_Obot(tc_fun(X25410,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X25410),X25409) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1])]) ).
fof(i_0_7519,plain,
! [X26843,X26844,X26845,X26846,X26847,X26848] :
( ~ c_Finite__Set_Ofolding(X26848,X26847,X26846,X26845)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26848),X26844))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26848),X26843))
| hAPP(c_Fun_Ocomp(X26847,X26847,X26847,hAPP(X26845,X26843)),hAPP(X26845,X26844)) = hAPP(c_Fun_Ocomp(X26847,X26847,X26847,hAPP(X26845,X26844)),hAPP(X26845,X26843)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H_H])]) ).
fof(i_0_7520,plain,
! [X30906,X30907,X30908,X30909] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30909,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30908,tc_fun(X30909,tc_HOL_Obool)),X30907),X30906)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30908,tc_fun(X30909,tc_HOL_Obool)),X30907),hAPP(hAPP(c_COMBB(tc_fun(X30909,tc_HOL_Obool),tc_fun(X30909,tc_HOL_Obool),X30908),c_Groups_Ouminus__class_Ouminus(tc_fun(X30909,tc_HOL_Obool))),X30906)),
inference(variable_rename,[status(thm)],[fact_Compl__INT]) ).
fof(i_0_7521,plain,
! [X30902,X30903,X30904,X30905] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30905,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30904,tc_fun(X30905,tc_HOL_Obool)),X30903),X30902)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30904,tc_fun(X30905,tc_HOL_Obool)),X30903),hAPP(hAPP(c_COMBB(tc_fun(X30905,tc_HOL_Obool),tc_fun(X30905,tc_HOL_Obool),X30904),c_Groups_Ouminus__class_Ouminus(tc_fun(X30905,tc_HOL_Obool))),X30902)),
inference(variable_rename,[status(thm)],[fact_Compl__UN]) ).
fof(i_0_7522,plain,
! [X28592,X28593,X28594,X28595] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28595,X28594,hAPP(hAPP(c_Set_Oinsert(X28595),X28593),c_Orderings_Obot__class_Obot(tc_fun(X28595,tc_HOL_Obool)))),X28592))
| X28593 = X28592 )
& ( X28593 != X28592
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28595,X28594,hAPP(hAPP(c_Set_Oinsert(X28595),X28593),c_Orderings_Obot__class_Obot(tc_fun(X28595,tc_HOL_Obool)))),X28592)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__sing])]) ).
fof(i_0_7523,plain,
! [X32838,X32839,X32840] :
( ~ class_Orderings_Olinorder(X32840)
| hBOOL(hAPP(hAPP(c_member(X32840),X32839),hAPP(c_List_Oset(X32840),X32838)))
| c_List_Olinorder__class_Oinsort__insert__key(X32840,X32840,c_COMBI(X32840),X32839,X32838) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32840,X32840,c_COMBI(X32840)),X32839),X32838) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5580])]) ).
fof(i_0_7524,plain,
! [X26413,X26414,X26415,X26416,X26417] :
( ( ~ c_Relation_Oirrefl(X26414,X26413)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26414,X26414)),hAPP(hAPP(c_Product__Type_OPair(X26414,X26414),X26415),X26415)),X26413)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X26417,X26417)),hAPP(hAPP(c_Product__Type_OPair(X26417,X26417),esk223_2(X26416,X26417)),esk223_2(X26416,X26417))),X26416))
| c_Relation_Oirrefl(X26417,X26416) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5581])])])])]) ).
fof(i_0_7525,plain,
! [X27646,X27647,X27648,X27649,X27650,X27651] :
( ~ c_Finite__Set_Ofolding(X27651,X27650,X27649,X27648)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27651),X27647))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27651),X27646))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27651,tc_HOL_Obool)),X27647),X27646) != c_Orderings_Obot__class_Obot(tc_fun(X27651,tc_HOL_Obool))
| hAPP(X27648,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27651,tc_HOL_Obool)),X27647),X27646)) = hAPP(c_Fun_Ocomp(X27650,X27650,X27650,hAPP(X27648,X27647)),hAPP(X27648,X27646)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion])]) ).
fof(i_0_7526,plain,
! [X19948,X19949,X19950,X19952,X19953,X19954,X19955] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19948),esk59_3(X19948,X19949,X19950))),X19949))
| X19948 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X19950,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19949),X19948))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19948),hAPP(c_Nat_OSuc,esk59_3(X19948,X19949,X19950)))))
| X19948 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X19950,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19949),X19948))) )
& ( hBOOL(hAPP(X19950,esk59_3(X19948,X19949,X19950)))
| X19948 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X19950,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19949),X19948))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19948),esk59_3(X19948,X19949,X19950))),X19949))
| hBOOL(hAPP(X19950,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X19950,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19949),X19948))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19948),hAPP(c_Nat_OSuc,esk59_3(X19948,X19949,X19950)))))
| hBOOL(hAPP(X19950,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X19950,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19949),X19948))) )
& ( hBOOL(hAPP(X19950,esk59_3(X19948,X19949,X19950)))
| hBOOL(hAPP(X19950,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X19950,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19949),X19948))) )
& ( X19952 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X19954,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X19954,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19953),X19952))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19952),X19955)),X19953))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19952),hAPP(c_Nat_OSuc,X19955))))
| ~ hBOOL(hAPP(X19954,X19955))
| hBOOL(hAPP(X19954,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19953),X19952))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div_H])])])])])]) ).
fof(i_0_7527,plain,
! [X24898,X24899,X24900] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24900),X24899))
| hAPP(c_Finite__Set_Ocard(X24900),hAPP(hAPP(c_Set_Oinsert(X24900),X24898),X24899)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24900),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24900,tc_HOL_Obool)),X24899),hAPP(hAPP(c_Set_Oinsert(X24900),X24898),c_Orderings_Obot__class_Obot(tc_fun(X24900,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove])]) ).
fof(i_0_7528,plain,
! [X26621,X26622,X26623,X26624,X26625,X26626,X26627,X26628,X26629] :
( hAPP(c_Fun_Ocomp(X26629,X26628,X26627,X26626),X26625) != hAPP(c_Fun_Ocomp(X26624,X26628,X26627,X26623),X26622)
| hAPP(X26626,hAPP(X26625,X26621)) = hAPP(X26623,hAPP(X26622,X26621)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest])]) ).
fof(i_0_7529,plain,
! [X26612,X26613,X26614,X26615,X26616,X26617,X26618,X26619,X26620] :
( hAPP(c_Fun_Ocomp(X26619,X26618,X26617,X26616),X26615) != hAPP(c_Fun_Ocomp(X26614,X26618,X26617,X26613),X26612)
| hAPP(X26616,hAPP(X26615,X26620)) = hAPP(X26613,hAPP(X26612,X26620)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__elim])])]) ).
fof(i_0_7530,plain,
! [X32139,X32140,X32141,X32142] :
( ~ class_Orderings_Olinorder(X32142)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32142,X32142,c_COMBI(X32142)),X32141),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32142,X32142,c_COMBI(X32142)),X32140),X32139)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32142,X32142,c_COMBI(X32142)),X32140),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32142,X32142,c_COMBI(X32142)),X32141),X32139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__left__comm])]) ).
fof(i_0_7531,plain,
! [X29428,X29429,X29430,X29431,X29432,X29433,X29434] :
( hAPP(c_Fun_Ocomp(X29434,X29433,X29432,X29431),X29430) != hAPP(c_Fun_Ocomp(X29433,X29433,X29432,c_Fun_Oid(X29433)),X29429)
| hAPP(X29431,hAPP(X29430,X29428)) = hAPP(X29429,X29428) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest])]) ).
fof(i_0_7532,plain,
! [X26908,X26909,X26910,X26911] :
( ~ c_Equiv__Relations_Oequiv(X26911,X26910,X26909)
| ~ hBOOL(hAPP(hAPP(c_member(X26911),X26908),X26910))
| hBOOL(hAPP(hAPP(c_member(X26911),X26908),hAPP(c_Relation_OImage(X26911,X26911,X26909),hAPP(hAPP(c_Set_Oinsert(X26911),X26908),c_Orderings_Obot__class_Obot(tc_fun(X26911,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__self])]) ).
fof(i_0_7533,plain,
! [X28017,X28018,X28019,X28020,X28021] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28020),hAPP(X28019,X28018)),hAPP(c_Set_Oimage(X28021,X28020,X28019),X28017)))
| hBOOL(hAPP(hAPP(c_member(X28021),X28018),X28017))
| ~ c_Fun_Oinj__on(X28021,X28020,X28019,c_Orderings_Otop__class_Otop(tc_fun(X28021,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28021),X28018),X28017))
| hBOOL(hAPP(hAPP(c_member(X28020),hAPP(X28019,X28018)),hAPP(c_Set_Oimage(X28021,X28020,X28019),X28017)))
| ~ c_Fun_Oinj__on(X28021,X28020,X28019,c_Orderings_Otop__class_Otop(tc_fun(X28021,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__mem__iff])])]) ).
fof(i_0_7534,plain,
! [X31144,X31145,X31146,X31147,X31148] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31148)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31147,tc_HOL_Obool)),X31146),X31145))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31148),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31147,X31148),X31145),X31144)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31147,X31148),X31146),X31144))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__subset])]) ).
fof(i_0_7535,plain,
! [X24183,X24184,X24185,X24186,X24187] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X24187)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24186,tc_HOL_Obool)),X24185),X24184))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24187),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24186,X24187),X24185),X24183)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24186,X24187),X24184),X24183))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__subset])]) ).
fof(i_0_7536,plain,
! [X29622,X29623,X29624] :
( ~ c_Wellfounded_Owf(X29624,X29623)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29624,X29624)),hAPP(hAPP(c_Product__Type_OPair(X29624,X29624),X29622),X29622)),X29623)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5582])]) ).
fof(i_0_7537,plain,
! [X29611,X29612,X29613] :
( ~ c_Wellfounded_Owf(X29613,X29612)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29613,X29613)),hAPP(hAPP(c_Product__Type_OPair(X29613,X29613),X29611),X29611)),X29612)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5583])]) ).
fof(i_0_7538,plain,
! [X31675,X31676,X31677] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X31677)),hAPP(c_Set_Oimage(X31676,tc_Option_Ooption(X31677),c_Map_Omap__of(X31676,X31677,X31675)),c_Orderings_Otop__class_Otop(tc_fun(X31676,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_finite__range__map__of]) ).
fof(i_0_7539,plain,
! [X24802,X24803,X24804,X24805,X24806] :
( ( X24806 != c_Orderings_Obot__class_Obot(tc_fun(X24805,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24805,tc_fun(X24804,tc_HOL_Obool)),X24806),hAPP(hAPP(c_COMBB(tc_fun(X24804,tc_HOL_Obool),tc_fun(X24804,tc_HOL_Obool),X24805),hAPP(c_Set_Oinsert(X24804),X24803)),X24802)) = c_Orderings_Obot__class_Obot(tc_fun(X24804,tc_HOL_Obool)) )
& ( X24806 = c_Orderings_Obot__class_Obot(tc_fun(X24805,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24805,tc_fun(X24804,tc_HOL_Obool)),X24806),hAPP(hAPP(c_COMBB(tc_fun(X24804,tc_HOL_Obool),tc_fun(X24804,tc_HOL_Obool),X24805),hAPP(c_Set_Oinsert(X24804),X24803)),X24802)) = hAPP(hAPP(c_Set_Oinsert(X24804),X24803),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24805,tc_fun(X24804,tc_HOL_Obool)),X24806),X24802)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J])]) ).
fof(i_0_7540,plain,
! [X24809,X24810,X24811,X24812,X24813] :
( ( X24813 != c_Orderings_Obot__class_Obot(tc_fun(X24812,tc_HOL_Obool))
| hAPP(hAPP(c_Set_Oinsert(X24811),X24810),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24812,tc_fun(X24811,tc_HOL_Obool)),X24813),X24809)) = hAPP(hAPP(c_Set_Oinsert(X24811),X24810),c_Orderings_Obot__class_Obot(tc_fun(X24811,tc_HOL_Obool))) )
& ( X24813 = c_Orderings_Obot__class_Obot(tc_fun(X24812,tc_HOL_Obool))
| hAPP(hAPP(c_Set_Oinsert(X24811),X24810),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24812,tc_fun(X24811,tc_HOL_Obool)),X24813),X24809)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24812,tc_fun(X24811,tc_HOL_Obool)),X24813),hAPP(hAPP(c_COMBB(tc_fun(X24811,tc_HOL_Obool),tc_fun(X24811,tc_HOL_Obool),X24812),hAPP(c_Set_Oinsert(X24811),X24810)),X24809)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J])]) ).
cnf(i_0_7541,plain,
c_Transitive__Closure_Ortrancl(X1,X2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Relation_OId(X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)),
inference(split_conjunct,[status(thm)],[i_0_5584]) ).
fof(i_0_7542,plain,
! [X23268,X23269,X23270,X23271,X23272] :
( ~ class_Rings_Osemiring__0(X23272)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23272),X23271),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23270,X23272),X23269),X23268)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23270,X23272),hAPP(hAPP(c_COMBB(X23272,X23272,X23270),hAPP(c_Groups_Otimes__class_Otimes(X23272),X23271)),X23269)),X23268) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib])]) ).
fof(i_0_7543,plain,
! [X25609,X25610,X25611,X25612,X25613] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X25613,X25612)),hAPP(X25613,X25611)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X25610,X25610)),hAPP(hAPP(c_Product__Type_OPair(X25610,X25610),X25612),X25611)),c_Wellfounded_Omlex__prod(X25610,X25613,X25609))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).
fof(i_0_7544,plain,
! [X24320,X24321,X24322,X24323,X24324] : hAPP(c_Set_Oimage(X24324,X24323,hAPP(hAPP(c_COMBB(X24322,X24323,X24324),X24321),X24320)),c_Orderings_Otop__class_Otop(tc_fun(X24324,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X24322,X24323,X24321),hAPP(c_Set_Oimage(X24324,X24322,X24320),c_Orderings_Otop__class_Otop(tc_fun(X24324,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_range__composition]) ).
fof(i_0_7545,plain,
! [X34183,X34184,X34185,X34186] :
( ( ~ c_List_Olinorder__class_Osorted(X34184,X34183)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34185),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34184)),X34183)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34186),X34185))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34184),hAPP(hAPP(c_List_Onth(X34184),X34183),X34186)),hAPP(hAPP(c_List_Onth(X34184),X34183),X34185)))
| ~ class_Orderings_Olinorder(X34184) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk486_2(X34183,X34184)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34184)),X34183)))
| c_List_Olinorder__class_Osorted(X34184,X34183)
| ~ class_Orderings_Olinorder(X34184) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk487_2(X34183,X34184)),esk486_2(X34183,X34184)))
| c_List_Olinorder__class_Osorted(X34184,X34183)
| ~ class_Orderings_Olinorder(X34184) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34184),hAPP(hAPP(c_List_Onth(X34184),X34183),esk487_2(X34183,X34184))),hAPP(hAPP(c_List_Onth(X34184),X34183),esk486_2(X34183,X34184))))
| c_List_Olinorder__class_Osorted(X34184,X34183)
| ~ class_Orderings_Olinorder(X34184) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__equals__nth__mono])])])])]) ).
fof(i_0_7546,plain,
! [X30875,X30876,X30877,X30878,X30879,X30880] :
( ~ hBOOL(hAPP(hAPP(c_member(X30880),X30879),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30878,tc_fun(X30880,tc_HOL_Obool)),X30877),X30876)))
| ~ hBOOL(hAPP(hAPP(c_member(X30878),X30875),X30877))
| hBOOL(hAPP(hAPP(c_member(X30880),X30879),hAPP(X30876,X30875))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__D])]) ).
fof(i_0_7547,plain,
! [X30869,X30870,X30871,X30872,X30873,X30874] :
( ~ hBOOL(hAPP(hAPP(c_member(X30874),X30873),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30872,tc_fun(X30874,tc_HOL_Obool)),X30871),X30870)))
| hBOOL(hAPP(hAPP(c_member(X30874),X30873),hAPP(X30870,X30869)))
| ~ hBOOL(hAPP(hAPP(c_member(X30872),X30869),X30871)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5585])]) ).
fof(i_0_7548,plain,
! [X33567,X33568,X33569] :
( ~ class_Groups_Omonoid__add(X33569)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33569),X33568),hAPP(c_List_Ofoldl(X33569,X33569,c_Groups_Oplus__class_Oplus(X33569),c_Groups_Ozero__class_Ozero(X33569)),X33567)) = hAPP(c_List_Ofoldl(X33569,X33569,c_Groups_Oplus__class_Oplus(X33569),X33568),X33567) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__absorb0])]) ).
fof(i_0_7549,plain,
! [X32758,X32759,X32760,X32761,X32762,X32763] :
( X32763 = X32762
| hAPP(hAPP(c_List_Olist__update(X32761,hAPP(hAPP(c_List_Olist__update(X32761,X32760),X32763),X32759)),X32762),X32758) = hAPP(hAPP(c_List_Olist__update(X32761,hAPP(hAPP(c_List_Olist__update(X32761,X32760),X32762),X32758)),X32763),X32759) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__swap])]) ).
fof(i_0_7550,plain,
! [X30464,X30465,X30466] : hAPP(hAPP(c_Relation_Orel__comp(X30466,X30466,X30466),X30465),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30466,X30466),tc_HOL_Obool),X30464),X30465)) = hAPP(hAPP(c_Relation_Orel__comp(X30466,X30466,X30466),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30466,X30466),tc_HOL_Obool),X30464),X30465)),X30465),
inference(variable_rename,[status(thm)],[fact_rel__pow__commute]) ).
fof(i_0_7551,plain,
! [X34486,X34487,X34488,X34489,X34490,X34491,X34492,X34493,X34494,X34495] :
( ( X34486 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X34488,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ epred2_3(X34488,X34487,X34486) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34486))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34490))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34490),X34486))
| X34487 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34486),X34489)),X34490)
| hBOOL(hAPP(X34488,X34489))
| ~ epred2_3(X34488,X34487,X34486) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34486),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34486),X34492))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34487 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34486),X34491)),X34492)
| hBOOL(hAPP(X34488,X34491))
| ~ epred2_3(X34488,X34487,X34486) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34493))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),esk503_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34493))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X34493,X34494,X34495)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34493))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk502_3(X34493,X34494,X34495))),esk503_3(X34493,X34494,X34495))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34493))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( ~ hBOOL(hAPP(X34495,esk502_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34493))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X34493,X34494,X34495)))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),esk503_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X34493,X34494,X34495)))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X34493,X34494,X34495)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X34493,X34494,X34495)))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk502_3(X34493,X34494,X34495))),esk503_3(X34493,X34494,X34495))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X34493,X34494,X34495)))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( ~ hBOOL(hAPP(X34495,esk502_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X34493,X34494,X34495)))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X34493,X34494,X34495)),X34493))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),esk503_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X34493,X34494,X34495)),X34493))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X34493,X34494,X34495)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X34493,X34494,X34495)),X34493))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk502_3(X34493,X34494,X34495))),esk503_3(X34493,X34494,X34495))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X34493,X34494,X34495)),X34493))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( ~ hBOOL(hAPP(X34495,esk502_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X34493,X34494,X34495)),X34493))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk500_3(X34493,X34494,X34495))),esk501_3(X34493,X34494,X34495))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),esk503_3(X34493,X34494,X34495)))
| X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk500_3(X34493,X34494,X34495))),esk501_3(X34493,X34494,X34495))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X34493,X34494,X34495)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk500_3(X34493,X34494,X34495))),esk501_3(X34493,X34494,X34495))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk502_3(X34493,X34494,X34495))),esk503_3(X34493,X34494,X34495))
| X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk500_3(X34493,X34494,X34495))),esk501_3(X34493,X34494,X34495))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( ~ hBOOL(hAPP(X34495,esk502_3(X34493,X34494,X34495)))
| X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk500_3(X34493,X34494,X34495))),esk501_3(X34493,X34494,X34495))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34495,esk500_3(X34493,X34494,X34495)))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),esk503_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,esk500_3(X34493,X34494,X34495)))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X34493,X34494,X34495)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34495,esk500_3(X34493,X34494,X34495)))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk502_3(X34493,X34494,X34495))),esk503_3(X34493,X34494,X34495))
| ~ hBOOL(hAPP(X34495,esk500_3(X34493,X34494,X34495)))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( ~ hBOOL(hAPP(X34495,esk502_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,esk500_3(X34493,X34494,X34495)))
| X34493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34493))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),esk503_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34493))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X34493,X34494,X34495)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34493))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk502_3(X34493,X34494,X34495))),esk503_3(X34493,X34494,X34495))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34493))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( ~ hBOOL(hAPP(X34495,esk502_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34493))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),esk503_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X34493,X34494,X34495)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk502_3(X34493,X34494,X34495))),esk503_3(X34493,X34494,X34495))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( ~ hBOOL(hAPP(X34495,esk502_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X34493,X34494,X34495)),X34493))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),esk503_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X34493,X34494,X34495)),X34493))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X34493,X34494,X34495)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X34493,X34494,X34495)),X34493))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk502_3(X34493,X34494,X34495))),esk503_3(X34493,X34494,X34495))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X34493,X34494,X34495)),X34493))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( ~ hBOOL(hAPP(X34495,esk502_3(X34493,X34494,X34495)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X34493,X34494,X34495)),X34493))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk500_3(X34493,X34494,X34495))),esk501_3(X34493,X34494,X34495))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),esk503_3(X34493,X34494,X34495)))
| X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk500_3(X34493,X34494,X34495))),esk501_3(X34493,X34494,X34495))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X34493,X34494,X34495)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk500_3(X34493,X34494,X34495))),esk501_3(X34493,X34494,X34495))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk502_3(X34493,X34494,X34495))),esk503_3(X34493,X34494,X34495))
| X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk500_3(X34493,X34494,X34495))),esk501_3(X34493,X34494,X34495))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( ~ hBOOL(hAPP(X34495,esk502_3(X34493,X34494,X34495)))
| X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk500_3(X34493,X34494,X34495))),esk501_3(X34493,X34494,X34495))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34495,esk500_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34493),esk503_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,esk500_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X34493,X34494,X34495)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34495,esk500_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( X34494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34493),esk502_3(X34493,X34494,X34495))),esk503_3(X34493,X34494,X34495))
| ~ hBOOL(hAPP(X34495,esk500_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) )
& ( ~ hBOOL(hAPP(X34495,esk502_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,esk500_3(X34493,X34494,X34495)))
| ~ hBOOL(hAPP(X34495,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34495,X34494,X34493) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5189])])])])])]) ).
fof(i_0_7552,plain,
! [X24880,X24881,X24882] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24882),X24881))
| hAPP(c_Finite__Set_Ocard(X24882),hAPP(hAPP(c_Set_Oinsert(X24882),X24880),X24881)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X24882),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24882,tc_HOL_Obool)),X24881),hAPP(hAPP(c_Set_Oinsert(X24882),X24880),c_Orderings_Obot__class_Obot(tc_fun(X24882,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert])]) ).
cnf(i_0_7553,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5586]) ).
cnf(i_0_7554,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5587]) ).
cnf(i_0_7555,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5588]) ).
cnf(i_0_7556,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5589]) ).
fof(i_0_7557,plain,
! [X21748,X21749,X21750,X21751] :
( ~ class_Fields_Olinordered__field(X21751)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21751),X21750),X21749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21751),c_Groups_Ozero__class_Ozero(X21751)),X21748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21751),c_Groups_Ozero__class_Ozero(X21751)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21751),X21749),X21750)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21751),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21751),X21748),X21749)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21751),X21748),X21750))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono])]) ).
fof(i_0_7558,plain,
! [X21612,X21613,X21614,X21615] :
( ~ class_Fields_Olinordered__field(X21615)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21615),X21614),X21613))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21615),c_Groups_Ozero__class_Ozero(X21615)),X21612))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21615),c_Groups_Ozero__class_Ozero(X21615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21615),X21613),X21614)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21615),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21615),X21612),X21613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21615),X21612),X21614))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono])]) ).
fof(i_0_7559,plain,
! [X26429,X26430,X26431] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X26431,X26431),tc_HOL_Obool)),X26430),X26429))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26431,tc_HOL_Obool)),hAPP(c_Relation_OField(X26431),X26430)),hAPP(c_Relation_OField(X26431),X26429))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__Field])]) ).
fof(i_0_7560,plain,
! [X26829,X26830,X26831,X26832,X26833,X26834] :
( ~ c_Finite__Set_Ofolding(X26834,X26833,X26832,X26831)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26834),X26830))
| hAPP(c_Fun_Ocomp(X26833,X26833,X26833,hAPP(X26832,X26829)),hAPP(X26831,X26830)) = hAPP(c_Fun_Ocomp(X26833,X26833,X26833,hAPP(X26831,X26830)),hAPP(X26832,X26829)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H])]) ).
fof(i_0_7561,plain,
! [X34472,X34473,X34474,X34475,X34476,X34477,X34478,X34479,X34480,X34481] :
( ( X34472 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X34474,X34473))
| ~ epred1_3(X34474,X34473,X34472) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34472))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34476))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34476),X34472))
| X34473 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34472),X34475)),X34476)
| hBOOL(hAPP(X34474,X34476))
| ~ epred1_3(X34474,X34473,X34472) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34472),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34472),X34478))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34478),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34473 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34472),X34477)),X34478)
| hBOOL(hAPP(X34474,X34478))
| ~ epred1_3(X34474,X34473,X34472) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34479))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34479))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X34479,X34480,X34481)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34479))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk498_3(X34479,X34480,X34481))),esk499_3(X34479,X34480,X34481))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34479))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( ~ hBOOL(hAPP(X34481,esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34479))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X34479,X34480,X34481)))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X34479,X34480,X34481)))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X34479,X34480,X34481)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X34479,X34480,X34481)))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk498_3(X34479,X34480,X34481))),esk499_3(X34479,X34480,X34481))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X34479,X34480,X34481)))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( ~ hBOOL(hAPP(X34481,esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X34479,X34480,X34481)))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X34479,X34480,X34481)),X34479))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X34479,X34480,X34481)),X34479))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X34479,X34480,X34481)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X34479,X34480,X34481)),X34479))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk498_3(X34479,X34480,X34481))),esk499_3(X34479,X34480,X34481))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X34479,X34480,X34481)),X34479))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( ~ hBOOL(hAPP(X34481,esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X34479,X34480,X34481)),X34479))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk496_3(X34479,X34480,X34481))),esk497_3(X34479,X34480,X34481))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),esk499_3(X34479,X34480,X34481)))
| X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk496_3(X34479,X34480,X34481))),esk497_3(X34479,X34480,X34481))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X34479,X34480,X34481)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk496_3(X34479,X34480,X34481))),esk497_3(X34479,X34480,X34481))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk498_3(X34479,X34480,X34481))),esk499_3(X34479,X34480,X34481))
| X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk496_3(X34479,X34480,X34481))),esk497_3(X34479,X34480,X34481))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( ~ hBOOL(hAPP(X34481,esk499_3(X34479,X34480,X34481)))
| X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk496_3(X34479,X34480,X34481))),esk497_3(X34479,X34480,X34481))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34481,esk497_3(X34479,X34480,X34481)))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),esk499_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,esk497_3(X34479,X34480,X34481)))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X34479,X34480,X34481)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34481,esk497_3(X34479,X34480,X34481)))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk498_3(X34479,X34480,X34481))),esk499_3(X34479,X34480,X34481))
| ~ hBOOL(hAPP(X34481,esk497_3(X34479,X34480,X34481)))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( ~ hBOOL(hAPP(X34481,esk499_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,esk497_3(X34479,X34480,X34481)))
| X34479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34479))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34479))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X34479,X34480,X34481)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34479))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk498_3(X34479,X34480,X34481))),esk499_3(X34479,X34480,X34481))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34479))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( ~ hBOOL(hAPP(X34481,esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34479))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X34479,X34480,X34481)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk498_3(X34479,X34480,X34481))),esk499_3(X34479,X34480,X34481))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( ~ hBOOL(hAPP(X34481,esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X34479,X34480,X34481)),X34479))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X34479,X34480,X34481)),X34479))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X34479,X34480,X34481)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X34479,X34480,X34481)),X34479))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk498_3(X34479,X34480,X34481))),esk499_3(X34479,X34480,X34481))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X34479,X34480,X34481)),X34479))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( ~ hBOOL(hAPP(X34481,esk499_3(X34479,X34480,X34481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X34479,X34480,X34481)),X34479))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk496_3(X34479,X34480,X34481))),esk497_3(X34479,X34480,X34481))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),esk499_3(X34479,X34480,X34481)))
| X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk496_3(X34479,X34480,X34481))),esk497_3(X34479,X34480,X34481))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X34479,X34480,X34481)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk496_3(X34479,X34480,X34481))),esk497_3(X34479,X34480,X34481))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk498_3(X34479,X34480,X34481))),esk499_3(X34479,X34480,X34481))
| X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk496_3(X34479,X34480,X34481))),esk497_3(X34479,X34480,X34481))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( ~ hBOOL(hAPP(X34481,esk499_3(X34479,X34480,X34481)))
| X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk496_3(X34479,X34480,X34481))),esk497_3(X34479,X34480,X34481))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34481,esk497_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34479),esk499_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,esk497_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X34479,X34480,X34481)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34481,esk497_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( X34480 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34479),esk498_3(X34479,X34480,X34481))),esk499_3(X34479,X34480,X34481))
| ~ hBOOL(hAPP(X34481,esk497_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) )
& ( ~ hBOOL(hAPP(X34481,esk499_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,esk497_3(X34479,X34480,X34481)))
| ~ hBOOL(hAPP(X34481,X34480))
| epred1_3(X34481,X34480,X34479) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5188])])])])])]) ).
fof(i_0_7562,plain,
! [X30988,X30989,X30990,X30991,X30992] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30992,tc_fun(X30991,tc_HOL_Obool)),X30990),hAPP(hAPP(c_COMBB(tc_fun(X30991,tc_HOL_Obool),tc_fun(X30991,tc_HOL_Obool),X30992),hAPP(c_Set_Oinsert(X30991),X30989)),X30988)) = hAPP(hAPP(c_Set_Oinsert(X30991),X30989),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30992,tc_fun(X30991,tc_HOL_Obool)),X30990),X30988)),
inference(variable_rename,[status(thm)],[fact_INT__simps_I5_J]) ).
fof(i_0_7563,plain,
! [X30993,X30994,X30995,X30996,X30997] : hAPP(hAPP(c_Set_Oinsert(X30997),X30996),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30995,tc_fun(X30997,tc_HOL_Obool)),X30994),X30993)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30995,tc_fun(X30997,tc_HOL_Obool)),X30994),hAPP(hAPP(c_COMBB(tc_fun(X30997,tc_HOL_Obool),tc_fun(X30997,tc_HOL_Obool),X30995),hAPP(c_Set_Oinsert(X30997),X30996)),X30993)),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I5_J]) ).
fof(i_0_7564,plain,
! [X19721,X19722,X19723,X19724] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19724),X19723)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19722),X19723)),X19721)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19724),X19722)),X19723)),X19721),
inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).
cnf(i_0_7565,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X3))) = hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5590]) ).
fof(i_0_7566,plain,
! [X31906,X31907,X31908,X31909,X31910] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31910),tc_Option_Ooption(X31909),X31908,hAPP(c_Option_Omap(X31910,X31909),X31907)),hAPP(c_COMBK(tc_Option_Ooption(X31910),X31908),c_Option_Ooption_ONone(X31910))),X31906) = c_Option_Ooption_ONone(X31909),
inference(variable_rename,[status(thm)],[fact_option__map__o__empty]) ).
fof(i_0_7567,plain,
! [X22866,X22867,X22868,X22869,X22870] :
( ( X22870 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_New__DSequence_Oneg__decr__bind(X22869,X22868,X22867,X22866),X22870) = c_Lazy__Sequence_Ohit__bound(X22868) )
& ( X22870 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_New__DSequence_Oneg__decr__bind(X22869,X22868,X22867,X22866),X22870) = c_Lazy__Sequence_Ohb__bind(X22869,X22868,hAPP(X22867,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X22870),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X22869,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X22868))),X22866),X22870)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def])]) ).
fof(i_0_7568,plain,
! [X27990,X27991,X27992,X27993] :
( ~ c_Fun_Oinj__on(X27993,X27992,X27991,c_Orderings_Otop__class_Otop(tc_fun(X27993,tc_HOL_Obool)))
| c_Fun_Oinj__on(X27993,tc_fun(X27990,X27992),hAPP(hAPP(c_COMBB(X27992,tc_fun(X27990,X27992),X27993),c_COMBK(X27992,X27990)),X27991),c_Orderings_Otop__class_Otop(tc_fun(X27993,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).
fof(i_0_7569,plain,
! [X28092,X28093,X28094,X28095,X28096,X28097] :
( ~ c_Fun_Oinj__on(X28097,X28096,X28095,X28094)
| hBOOL(hAPP(hAPP(c_member(X28096),X28093),hAPP(c_Set_Oimage(X28097,X28096,X28095),X28094)))
| c_Fun_Oinj__on(X28097,X28096,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X28097,X28096),X28095),X28092),X28093),X28094) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5591])]) ).
fof(i_0_7570,plain,
! [X31414,X31415,X31416] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31416,tc_HOL_Obool)),X31415),X31414) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X31416,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31416,tc_HOL_Obool)),X31415),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31416,tc_HOL_Obool)),X31414),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31416,tc_HOL_Obool),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_Int__eq__Inter]) ).
fof(i_0_7571,plain,
! [X31403,X31404,X31405] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31405,tc_HOL_Obool)),X31404),X31403) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X31405,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31405,tc_HOL_Obool)),X31404),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31405,tc_HOL_Obool)),X31403),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31405,tc_HOL_Obool),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_Un__eq__Union]) ).
fof(i_0_7572,plain,
! [X21752,X21753,X21754,X21755] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21755)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21755),X21754),X21753))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21755),X21752),c_Groups_Ozero__class_Ozero(X21755)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21755),c_Groups_Ozero__class_Ozero(X21755)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21755),X21754),X21753)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21755),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21755),X21752),X21754)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21755),X21752),X21753))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg])]) ).
fof(i_0_7573,plain,
! [X21608,X21609,X21610,X21611] :
( ~ class_Fields_Olinordered__field(X21611)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21611),X21610),X21609))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21611),X21608),c_Groups_Ozero__class_Ozero(X21611)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21611),c_Groups_Ozero__class_Ozero(X21611)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21611),X21610),X21609)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21611),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21611),X21608),X21610)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21611),X21608),X21609))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg])]) ).
fof(i_0_7574,plain,
! [X32667,X32668,X32669,X32670,X32671] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32671),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32670)),X32669)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32671),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32668)),X32667)))
| hAPP(hAPP(c_List_Onth(tc_prod(X32670,X32668)),hAPP(hAPP(c_List_Ozip(X32670,X32668),X32669),X32667)),X32671) = hAPP(hAPP(c_Product__Type_OPair(X32670,X32668),hAPP(hAPP(c_List_Onth(X32670),X32669),X32671)),hAPP(hAPP(c_List_Onth(X32668),X32667),X32671)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__zip])]) ).
fof(i_0_7575,plain,
! [X19966,X19967,X19968] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19967),X19966)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19967),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19968),X19967),X19966))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19968,X19967)),
inference(variable_rename,[status(thm)],[fact_mod__mult2__eq]) ).
fof(i_0_7576,plain,
! [X24600,X24601,X24602] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24602),X24601))
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X24602)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24600),X24601)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24600),X24602)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24601),X24602)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24600),X24601))
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X24602)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24600),X24601)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24602),X24601)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24600),X24601))
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X24602)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24600),X24601)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24602),X24601)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5592])])]) ).
cnf(i_0_7577,plain,
( hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_List_Ofoldr(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5593]) ).
fof(i_0_7578,plain,
! [X32873,X32874,X32875,X32876,X32877] : hAPP(hAPP(c_List_Olist__update(X32877,hAPP(hAPP(c_List_Oappend(X32877),X32876),hAPP(hAPP(c_List_Olist_OCons(X32877),X32875),X32874))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32877)),X32876)),X32873) = hAPP(hAPP(c_List_Oappend(X32877),X32876),hAPP(hAPP(c_List_Olist_OCons(X32877),X32873),X32874)),
inference(variable_rename,[status(thm)],[fact_list__update__length]) ).
cnf(i_0_7579,plain,
( hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),X5),c_List_Oupt(X3,X2))),X1) = hAPP(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_5594]) ).
fof(i_0_7580,plain,
! [X33220,X33221] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X33221),tc_List_Olist(X33221)),tc_HOL_Obool)),c_List_Olistrel1(X33221,c_Transitive__Closure_Ortrancl(X33221,X33220))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33221),c_List_Olistrel1(X33221,X33220)))),
inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).
fof(i_0_7581,plain,
! [X30229,X30230,X30231] : c_Transitive__Closure_Ortrancl(X30231,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30231,X30231),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30231,X30230)),c_Transitive__Closure_Ortrancl(X30231,X30229))) = c_Transitive__Closure_Ortrancl(X30231,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30231,X30231),tc_HOL_Obool)),X30230),X30229)),
inference(variable_rename,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).
fof(i_0_7582,plain,
! [X23055,X23056,X23057,X23058] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23058),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23058),X23056),X23057)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23058),X23055),X23057)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23058),X23056),X23055))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23058),X23057),X23055))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23058),X23057),X23056))
| ~ class_Divides_Osemiring__div(X23058) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23058),X23056),X23055))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23058),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23058),X23056),X23057)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23058),X23055),X23057)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23058),X23057),X23055))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23058),X23057),X23056))
| ~ class_Divides_Osemiring__div(X23058) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__dvd__div])])]) ).
cnf(i_0_7583,plain,
hAPP(c_List_Orotate(X1,X2),hAPP(c_List_Orotate(X1,X3),X4)) = hAPP(c_List_Orotate(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4),
inference(split_conjunct,[status(thm)],[i_0_5595]) ).
cnf(i_0_7584,plain,
( c_List_Ofoldr(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2,X3) = hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Groups_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5596]) ).
fof(i_0_7585,plain,
! [X23408,X23409,X23410,X23411,X23413] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23410),X23408),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23410),esk94_3(X23408,X23409,X23410)),c_Groups_Ozero__class_Ozero(X23410))))
| ~ hBOOL(hAPP(X23409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23410),X23408),X23411)))
| ~ class_Rings_Odvd(X23410)
| ~ class_Rings_Osemiring__0(X23410) )
& ( hBOOL(hAPP(X23409,esk94_3(X23408,X23409,X23410)))
| ~ hBOOL(hAPP(X23409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23410),X23408),X23411)))
| ~ class_Rings_Odvd(X23410)
| ~ class_Rings_Osemiring__0(X23410) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23410),X23408),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23410),X23413),c_Groups_Ozero__class_Ozero(X23410))))
| ~ hBOOL(hAPP(X23409,X23413))
| hBOOL(hAPP(X23409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23410),X23408),esk95_3(X23408,X23409,X23410))))
| ~ class_Rings_Odvd(X23410)
| ~ class_Rings_Osemiring__0(X23410) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex])])])])]) ).
fof(i_0_7586,plain,
! [X32058,X32059,X32060] : hAPP(hAPP(c_List_Ozip(X32060,X32059),hAPP(hAPP(c_List_Omap(tc_prod(X32060,X32059),X32060),c_Product__Type_Ofst(X32060,X32059)),X32058)),hAPP(hAPP(c_List_Omap(tc_prod(X32060,X32059),X32059),c_Product__Type_Osnd(X32060,X32059)),X32058)) = X32058,
inference(variable_rename,[status(thm)],[fact_zip__map__fst__snd]) ).
fof(i_0_7587,plain,
! [X28098,X28099,X28100,X28101,X28102,X28103,X28104,X28105] :
( ~ class_Groups_Ocomm__monoid__mult(X28105)
| ~ c_Fun_Oinj__on(X28104,X28103,X28102,X28101)
| X28100 != hAPP(c_Set_Oimage(X28104,X28103,X28102),X28101)
| X28099 != hAPP(c_Fun_Ocomp(X28103,X28105,X28104,X28098),X28102)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28103,X28105),X28098),X28100) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28104,X28105),X28099),X28101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__cong])]) ).
fof(i_0_7588,plain,
! [X19604,X19605,X19606] :
( ~ class_Rings_Olinordered__ring(X19606)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19606),c_Groups_Ozero__class_Ozero(X19606)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19606),X19605),X19605)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19606),X19604),X19604)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).
fof(i_0_7589,plain,
! [X30325,X30326] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X30326),X30325)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30326),X30325)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30326),X30325))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X30326),X30325)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__nat__trancl__eq__le])]) ).
fof(i_0_7590,plain,
! [X26812,X26813,X26814,X26815,X26816,X26817] :
( ~ c_Finite__Set_Ofolding(X26817,X26816,X26815,X26814)
| hAPP(c_Fun_Ocomp(X26816,X26816,X26816,hAPP(X26815,X26813)),hAPP(X26815,X26812)) = hAPP(c_Fun_Ocomp(X26816,X26816,X26816,hAPP(X26815,X26812)),hAPP(X26815,X26813)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp])]) ).
fof(i_0_7591,plain,
! [X28708,X28709,X28710,X28711,X28712] : hAPP(hAPP(c_Product__Type_OSigma(X28712,X28711),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28712,tc_HOL_Obool)),X28710),X28709)),X28708) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28712,X28711),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28712,X28711),X28710),X28708)),hAPP(hAPP(c_Product__Type_OSigma(X28712,X28711),X28709),X28708)),
inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib1]) ).
fof(i_0_7592,plain,
! [X28682,X28683,X28684,X28685,X28686] : hAPP(hAPP(c_Product__Type_OSigma(X28686,X28685),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28686,tc_HOL_Obool)),X28684),X28683)),X28682) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28686,X28685),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28686,X28685),X28684),X28682)),hAPP(hAPP(c_Product__Type_OSigma(X28686,X28685),X28683),X28682)),
inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib1]) ).
fof(i_0_7593,plain,
! [X28639,X28640,X28641,X28642,X28643] : hAPP(hAPP(c_Product__Type_OSigma(X28643,X28642),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28643,tc_HOL_Obool)),X28641),X28640)),X28639) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28643,X28642),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28643,X28642),X28641),X28639)),hAPP(hAPP(c_Product__Type_OSigma(X28643,X28642),X28640),X28639)),
inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib1]) ).
fof(i_0_7594,plain,
! [X33823,X33824,X33825,X33826] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X33826),X33825),hAPP(c_List_Oset(X33826),c_List_Obutlast(X33826,X33824))))
| hBOOL(hAPP(hAPP(c_member(X33826),X33825),hAPP(c_List_Oset(X33826),c_List_Obutlast(X33826,hAPP(hAPP(c_List_Oappend(X33826),X33824),X33823))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X33826),X33825),hAPP(c_List_Oset(X33826),c_List_Obutlast(X33826,X33823))))
| hBOOL(hAPP(hAPP(c_member(X33826),X33825),hAPP(c_List_Oset(X33826),c_List_Obutlast(X33826,hAPP(hAPP(c_List_Oappend(X33826),X33824),X33823))))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlast__appendI])])]) ).
fof(i_0_7595,plain,
! [X28535,X28536,X28537] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28537,X28537),tc_HOL_Obool)),X28536),X28535))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28537,tc_HOL_Obool)),c_Wellfounded_Oacc(X28537,X28535)),c_Wellfounded_Oacc(X28537,X28536))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])]) ).
fof(i_0_7596,plain,
! [X32143,X32144,X32145,X32146,X32147,X32148] :
( ~ class_Orderings_Olinorder(X32148)
| hAPP(X32147,X32146) = hAPP(X32147,X32145)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32144,X32148,X32147),X32145),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32144,X32148,X32147),X32146),X32143)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32144,X32148,X32147),X32146),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32144,X32148,X32147),X32145),X32143)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__left__comm])]) ).
fof(i_0_7597,plain,
! [X31947,X31948,X31949,X31950,X31951] :
( hAPP(c_Map_Omap__of(X31951,X31950,X31949),X31948) != hAPP(c_Option_Ooption_OSome(X31950),X31947)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X31951,X31950)),hAPP(hAPP(c_Product__Type_OPair(X31951,X31950),X31948),X31947)),hAPP(c_List_Oset(tc_prod(X31951,X31950)),X31949))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeD])]) ).
fof(i_0_7598,plain,
! [X31942,X31943,X31944,X31945,X31946] :
( hAPP(c_Map_Omap__of(X31946,X31945,X31944),X31943) != hAPP(c_Option_Ooption_OSome(X31945),X31942)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X31946,X31945)),hAPP(hAPP(c_Product__Type_OPair(X31946,X31945),X31943),X31942)),hAPP(c_List_Oset(tc_prod(X31946,X31945)),X31944))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__SomeD])]) ).
fof(i_0_7599,plain,
! [X32043,X32044,X32045,X32046,X32047] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32047),X32046),hAPP(c_List_Oset(X32047),X32045)))
| hAPP(c_Map_Omap__of(X32047,X32044,hAPP(hAPP(c_List_Ozip(X32047,X32044),X32045),hAPP(hAPP(c_List_Omap(X32047,X32044),X32043),X32045))),X32046) = hAPP(c_Option_Ooption_OSome(X32044),hAPP(X32043,X32046)) )
& ( hBOOL(hAPP(hAPP(c_member(X32047),X32046),hAPP(c_List_Oset(X32047),X32045)))
| hAPP(c_Map_Omap__of(X32047,X32044,hAPP(hAPP(c_List_Ozip(X32047,X32044),X32045),hAPP(hAPP(c_List_Omap(X32047,X32044),X32043),X32045))),X32046) = c_Option_Ooption_ONone(X32044) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5597])]) ).
fof(i_0_7600,plain,
! [X22209,X22210] :
( X22210 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22209,X22210),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22209),X22210)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22209,X22210)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__mod])]) ).
fof(i_0_7601,plain,
! [X31015,X31016,X31017,X31018,X31019,X31020] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31020,tc_fun(X31019,tc_HOL_Obool)),X31018),hAPP(hAPP(c_COMBB(X31017,tc_fun(X31019,tc_HOL_Obool),X31020),X31016),X31015)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31017,tc_fun(X31019,tc_HOL_Obool)),hAPP(c_Set_Oimage(X31020,X31017,X31015),X31018)),X31016),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I10_J]) ).
fof(i_0_7602,plain,
! [X24282,X24283,X24284,X24285,X24286,X24287] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24287,tc_fun(X24286,tc_HOL_Obool)),X24285),hAPP(hAPP(c_COMBB(X24284,tc_fun(X24286,tc_HOL_Obool),X24287),X24283),X24282)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24284,tc_fun(X24286,tc_HOL_Obool)),hAPP(c_Set_Oimage(X24287,X24284,X24282),X24285)),X24283),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I10_J]) ).
fof(i_0_7603,plain,
! [X31009,X31010,X31011,X31012,X31013,X31014] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31014,tc_fun(X31013,tc_HOL_Obool)),hAPP(c_Set_Oimage(X31012,X31014,X31011),X31010)),X31009) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31012,tc_fun(X31013,tc_HOL_Obool)),X31010),hAPP(hAPP(c_COMBB(X31014,tc_fun(X31013,tc_HOL_Obool),X31012),X31009),X31011)),
inference(variable_rename,[status(thm)],[fact_INT__simps_I10_J]) ).
fof(i_0_7604,plain,
! [X24270,X24271,X24272,X24273,X24274,X24275] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24275,tc_fun(X24274,tc_HOL_Obool)),hAPP(c_Set_Oimage(X24273,X24275,X24272),X24271)),X24270) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24273,tc_fun(X24274,tc_HOL_Obool)),X24271),hAPP(hAPP(c_COMBB(X24275,tc_fun(X24274,tc_HOL_Obool),X24273),X24270),X24272)),
inference(variable_rename,[status(thm)],[fact_UN__simps_I10_J]) ).
fof(i_0_7605,plain,
! [X22008,X22009] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22009,X22008),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22009),X22008)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22009,X22008)))),
inference(variable_rename,[status(thm)],[fact_divmod__nat__rel]) ).
cnf(i_0_7606,plain,
hAPP(c_List_Orotate(X1,X2),X3) = hAPP(c_List_Orotate(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3),
inference(split_conjunct,[status(thm)],[i_0_5598]) ).
fof(i_0_7607,plain,
! [X22438,X22439,X22440] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22440,tc_HOL_Obool)),X22439),X22438))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22440,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22440,tc_HOL_Obool)),X22438)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22440,tc_HOL_Obool)),X22439))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono])]) ).
fof(i_0_7608,plain,
! [X28040,X28041,X28042] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28042),X28041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28042,tc_HOL_Obool)),X28041),hAPP(c_Set_Oimage(X28042,X28042,X28040),X28041)))
| c_Fun_Oinj__on(X28042,X28042,X28040,X28041) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).
fof(i_0_7609,plain,
! [X28670,X28671,X28672] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X28672,X28671),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28672,X28671),c_Orderings_Otop__class_Otop(tc_fun(X28672,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X28671,tc_HOL_Obool),X28672),X28670))) = hAPP(hAPP(c_Product__Type_OSigma(X28672,X28671),c_Orderings_Otop__class_Otop(tc_fun(X28672,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X28671,tc_HOL_Obool),X28672),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28671,tc_HOL_Obool)),X28670))),
inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV1]) ).
fof(i_0_7610,plain,
! [X28673,X28674,X28675] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X28675,X28674),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28675,X28674),X28673),hAPP(c_COMBK(tc_fun(X28674,tc_HOL_Obool),X28675),c_Orderings_Otop__class_Otop(tc_fun(X28674,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X28675,X28674),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28675,tc_HOL_Obool)),X28673)),hAPP(c_COMBK(tc_fun(X28674,tc_HOL_Obool),X28675),c_Orderings_Otop__class_Otop(tc_fun(X28674,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV2]) ).
fof(i_0_7611,plain,
! [X33207,X33208,X33209,X33210] :
( ~ hBOOL(hAPP(hAPP(c_member(X33210),X33209),c_Wellfounded_Oacc(X33210,X33208)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33210)),X33207),c_Wellfounded_Oacc(tc_List_Olist(X33210),c_List_Olistrel1(X33210,X33208))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33210)),hAPP(hAPP(c_List_Olist_OCons(X33210),X33209),X33207)),c_Wellfounded_Oacc(tc_List_Olist(X33210),c_List_Olistrel1(X33210,X33208)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I])]) ).
fof(i_0_7612,plain,
! [X21744,X21745,X21746,X21747] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21747),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21747),X21745),X21746)),X21744))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21747),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21747),X21744),X21746)),X21745))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21747),X21746),c_Groups_Ozero__class_Ozero(X21747)))
| ~ class_Fields_Olinordered__field(X21747) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21747),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21747),X21744),X21746)),X21745))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21747),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21747),X21745),X21746)),X21744))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21747),X21746),c_Groups_Ozero__class_Ozero(X21747)))
| ~ class_Fields_Olinordered__field(X21747) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq])])]) ).
fof(i_0_7613,plain,
! [X21616,X21617,X21618,X21619] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21619),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21619),X21617),X21618)),X21616))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21619),X21616),X21618)),X21617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21619),X21618),c_Groups_Ozero__class_Ozero(X21619)))
| ~ class_Fields_Olinordered__field(X21619) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21619),X21616),X21618)),X21617))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21619),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21619),X21617),X21618)),X21616))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21619),X21618),c_Groups_Ozero__class_Ozero(X21619)))
| ~ class_Fields_Olinordered__field(X21619) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq])])]) ).
fof(i_0_7614,plain,
! [X22861,X22862,X22863,X22864,X22865] :
( ( X22865 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_New__DSequence_Opos__decr__bind(X22864,X22863,X22862,X22861),X22865) = c_Lazy__Sequence_Oempty(X22863) )
& ( X22865 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_New__DSequence_Opos__decr__bind(X22864,X22863,X22862,X22861),X22865) = c_Lazy__Sequence_Obind(X22864,X22863,hAPP(X22862,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X22865),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X22864,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X22863)),X22861),X22865)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def])]) ).
cnf(i_0_7615,plain,
( c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Relation_OId(X1)))
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_5533]) ).
fof(i_0_7616,plain,
! [X21985,X21986,X21987] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21987,tc_fun(X21987,tc_HOL_Obool))),X21986),X21985))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21987,tc_HOL_Obool)),c_Wellfounded_Oaccp(X21987,X21985)),c_Wellfounded_Oaccp(X21987,X21986))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])]) ).
fof(i_0_7617,plain,
! [X27860,X27861,X27862,X27863,X27864,X27865] :
( ~ c_Finite__Set_Ofolding__idem(X27865,X27864,X27863,X27862)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27865),X27861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27865,tc_HOL_Obool)),X27860),X27861))
| hAPP(c_Fun_Ocomp(X27864,X27864,X27864,hAPP(X27862,X27861)),hAPP(X27862,X27860)) = hAPP(X27862,X27861) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Osubset__comp__idem])]) ).
fof(i_0_7618,plain,
! [X32824,X32825,X32826] :
( ~ class_Orderings_Olinorder(X32826)
| ~ hBOOL(hAPP(hAPP(c_member(X32826),X32825),hAPP(c_List_Oset(X32826),X32824)))
| c_List_Olinorder__class_Oinsort__insert__key(X32826,X32826,c_COMBI(X32826),X32825,X32824) = X32824 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__triv])]) ).
fof(i_0_7619,plain,
! [X20190,X20191,X20192] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20192),X20191)),X20190))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20190),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20192),hAPP(c_Nat_OSuc,X20191))))
| X20191 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20190),X20192)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20192)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20192),X20191)),X20190))
| X20191 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20190),X20192)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20192)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20190),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20192),hAPP(c_Nat_OSuc,X20191))))
| X20191 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20190),X20192)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20192)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div__lemma])])]) ).
fof(i_0_7620,plain,
! [X24498,X24499,X24500,X24501,X24502] :
( ~ class_Groups_Oab__group__add(X24502)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24501),X24500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24501,tc_HOL_Obool)),X24499),X24500))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24501,X24502),X24498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24501,tc_HOL_Obool)),X24500),X24499)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24502),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24501,X24502),X24498),X24500)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24501,X24502),X24498),X24499)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff])]) ).
cnf(i_0_7621,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5599]) ).
fof(i_0_7622,plain,
! [X33442,X33443,X33444] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33444),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33443)),X33442)))
| X33442 = hAPP(hAPP(c_List_Oappend(X33443),hAPP(hAPP(c_List_Otake(X33443),X33444),X33442)),hAPP(hAPP(c_List_Olist_OCons(X33443),hAPP(hAPP(c_List_Onth(X33443),X33442),X33444)),hAPP(hAPP(c_List_Odrop(X33443),hAPP(c_Nat_OSuc,X33444)),X33442))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_id__take__nth__drop])]) ).
fof(i_0_7623,plain,
! [X26209,X26210,X26211,X26212,X26213,X26214] :
( hBOOL(hAPP(hAPP(c_member(X26214),X26213),X26212))
| hAPP(c_Set_Oimage(X26214,tc_Option_Ooption(X26211),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26214,tc_Option_Ooption(X26211)),X26210),X26213),hAPP(c_Option_Ooption_OSome(X26211),X26209))),X26212) = hAPP(c_Set_Oimage(X26214,tc_Option_Ooption(X26211),X26210),X26212) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5600])]) ).
cnf(i_0_7624,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5538]) ).
cnf(i_0_7625,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5539]) ).
cnf(i_0_7626,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5540]) ).
cnf(i_0_7627,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5541]) ).
fof(i_0_7628,plain,
! [X26376,X26377] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26377),X26376)),c_Wellfounded_Oless__than))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26377),X26376)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26377),X26376))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X26377),X26376)),c_Wellfounded_Oless__than)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__than__iff])]) ).
cnf(i_0_7629,plain,
c_Int_Opred(c_Int_OBit0(X1)) = c_Int_OBit1(c_Int_Opred(X1)),
inference(split_conjunct,[status(thm)],[i_0_5601]) ).
fof(i_0_7630,plain,
! [X23688,X23689,X23690,X23691,X23692,X23693] : hAPP(c_Set_Oimage(X23693,X23692,X23691),hAPP(c_Set_Oimage(X23690,X23693,X23689),X23688)) = hAPP(c_Set_Oimage(X23690,X23692,hAPP(hAPP(c_COMBB(X23693,X23692,X23690),X23691),X23689)),X23688),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_7631,plain,
! [X26199,X26200,X26201,X26202,X26203] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X26202),X26199),X26201))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26202,X26203),X26200),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26202,tc_HOL_Obool)),X26201),hAPP(hAPP(c_Set_Oinsert(X26202),X26199),c_Orderings_Obot__class_Obot(tc_fun(X26202,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26203),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26202,X26203),X26200),X26201)),hAPP(X26200,X26199))
| hAPP(X26200,X26199) = c_Groups_Ozero__class_Ozero(X26203)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26202),X26201))
| ~ class_Fields_Ofield(X26203) )
& ( hBOOL(hAPP(hAPP(c_member(X26202),X26199),X26201))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26202,X26203),X26200),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26202,tc_HOL_Obool)),X26201),hAPP(hAPP(c_Set_Oinsert(X26202),X26199),c_Orderings_Obot__class_Obot(tc_fun(X26202,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26202,X26203),X26200),X26201)
| hAPP(X26200,X26199) = c_Groups_Ozero__class_Ozero(X26203)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26202),X26201))
| ~ class_Fields_Ofield(X26203) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5602])])]) ).
cnf(i_0_7632,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),c_Transitive__Closure_Otrancl(X1,X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5543]) ).
fof(i_0_7633,plain,
! [X31923,X31924,X31925,X31926,X31927] :
( hAPP(hAPP(c_List_Omap(X31927,X31926),X31925),X31924) != hAPP(hAPP(c_List_Omap(X31927,X31926),X31925),X31923)
| ~ c_Fun_Oinj__on(X31927,X31926,X31925,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31927,tc_HOL_Obool)),hAPP(c_List_Oset(X31927),X31924)),hAPP(c_List_Oset(X31927),X31923)))
| X31924 = X31923 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__inj__on])]) ).
fof(i_0_7634,plain,
! [X31918,X31919,X31920,X31921,X31922] :
( ( hAPP(hAPP(c_List_Omap(X31922,X31921),X31920),X31919) != hAPP(hAPP(c_List_Omap(X31922,X31921),X31920),X31918)
| X31919 = X31918
| ~ c_Fun_Oinj__on(X31922,X31921,X31920,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31922,tc_HOL_Obool)),hAPP(c_List_Oset(X31922),X31919)),hAPP(c_List_Oset(X31922),X31918))) )
& ( X31919 != X31918
| hAPP(hAPP(c_List_Omap(X31922,X31921),X31920),X31919) = hAPP(hAPP(c_List_Omap(X31922,X31921),X31920),X31918)
| ~ c_Fun_Oinj__on(X31922,X31921,X31920,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31922,tc_HOL_Obool)),hAPP(c_List_Oset(X31922),X31919)),hAPP(c_List_Oset(X31922),X31918))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__eq__map])])]) ).
fof(i_0_7635,plain,
! [X20357,X20358,X20359] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20357),X20358))
| hBOOL(hAPP(X20359,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20358)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20357))))
| ~ hBOOL(hAPP(X20359,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20358),X20357)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20358),X20357))
| hBOOL(hAPP(X20359,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X20359,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20358),X20357)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20358),X20357))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20357),X20358))
| hBOOL(hAPP(X20359,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20358),X20357)))) )
& ( ~ hBOOL(hAPP(X20359,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20357),X20358))
| hBOOL(hAPP(X20359,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20358),X20357)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20358),X20357))
| ~ hBOOL(hAPP(X20359,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20358)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20357))))
| hBOOL(hAPP(X20359,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20358),X20357)))) )
& ( ~ hBOOL(hAPP(X20359,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X20359,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20358)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20357))))
| hBOOL(hAPP(X20359,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20358),X20357)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int__split])])]) ).
fof(i_0_7636,plain,
! [X23355,X23356,X23357,X23358,X23359] :
( ~ class_Rings_Ocomm__semiring__1(X23359)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23359),hAPP(hAPP(c_Power_Opower__class_Opower(X23359),X23358),X23357)),X23356))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23355),X23357))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23359),hAPP(hAPP(c_Power_Opower__class_Opower(X23359),X23358),X23355)),X23356)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__dvd])]) ).
cnf(i_0_7637,plain,
c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))),
inference(split_conjunct,[status(thm)],[i_0_5603]) ).
fof(i_0_7638,plain,
! [X31635,X31636,X31637,X31638,X31639] : c_Map_Omap__add(X31639,X31638,X31637,c_Map_Omap__add(X31639,X31638,X31636,X31635)) = c_Map_Omap__add(X31639,X31638,c_Map_Omap__add(X31639,X31638,X31637,X31636),X31635),
inference(variable_rename,[status(thm)],[fact_map__add__assoc]) ).
fof(i_0_7639,plain,
! [X30562,X30563,X30564,X30565,X30566] :
( ~ c_Relation_Osingle__valued(X30566,X30565,hAPP(c_Relation_Oconverse(X30565,X30566),X30564))
| hAPP(c_Relation_OImage(X30565,X30566,X30564),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30565,tc_HOL_Obool)),X30563),X30562)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30566,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30565,X30566,X30564),X30563)),hAPP(c_Relation_OImage(X30565,X30566,X30564),X30562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__Int__eq])]) ).
fof(i_0_7640,plain,
! [X21587,X21588,X21589,X21590,X21591] :
( ~ class_Fields_Olinordered__field(X21591)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21591),c_Groups_Ozero__class_Ozero(X21591)),X21590))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21591),X21590),X21589))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),X21588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21591),X21588),X21587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),X21587)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21589),X21588))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__le])]) ).
fof(i_0_7641,plain,
! [X19371,X19372,X19373,X19374,X19375] :
( ~ class_Rings_Oordered__semiring(X19375)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19375),X19374),X19373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19375),X19372),X19371))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19375),c_Groups_Ozero__class_Ozero(X19375)),X19374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19375),c_Groups_Ozero__class_Ozero(X19375)),X19372))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19375),X19374),X19372)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19375),X19373),X19371))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).
fof(i_0_7642,plain,
! [X19366,X19367,X19368,X19369,X19370] :
( ~ class_Rings_Oordered__semiring(X19370)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19370),X19369),X19368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19370),X19367),X19366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19370),c_Groups_Ozero__class_Ozero(X19370)),X19368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19370),c_Groups_Ozero__class_Ozero(X19370)),X19367))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19370),X19369),X19367)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19370),X19368),X19366))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).
fof(i_0_7643,plain,
! [X21592,X21593,X21594,X21595,X21596] :
( ~ class_Fields_Olinordered__field(X21596)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21596),c_Groups_Ozero__class_Ozero(X21596)),X21595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21596),X21595),X21594))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21596),c_Groups_Ozero__class_Ozero(X21596)),X21593))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21596),X21593),X21592))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21596),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21596),X21595),X21592)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21596),X21594),X21593))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less])]) ).
fof(i_0_7644,plain,
! [X21597,X21598,X21599,X21600,X21601] :
( ~ class_Fields_Olinordered__field(X21601)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),X21600))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),X21600),X21599))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),X21598))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),X21598),X21597))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),X21597)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21599),X21598))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less2])]) ).
fof(i_0_7645,plain,
! [X19581,X19582,X19583,X19584,X19585] :
( ~ class_Rings_Olinordered__semiring__strict(X19585)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19585),X19584),X19583))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19585),X19582),X19581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19585),c_Groups_Ozero__class_Ozero(X19585)),X19584))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19585),c_Groups_Ozero__class_Ozero(X19585)),X19582))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19585),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19585),X19584),X19582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19585),X19583),X19581))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).
fof(i_0_7646,plain,
! [X19576,X19577,X19578,X19579,X19580] :
( ~ class_Rings_Olinordered__semiring__strict(X19580)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19580),X19579),X19578))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19580),X19577),X19576))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19580),c_Groups_Ozero__class_Ozero(X19580)),X19579))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19580),c_Groups_Ozero__class_Ozero(X19580)),X19577))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19580),X19579),X19577)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19580),X19578),X19576))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).
fof(i_0_7647,plain,
! [X19586,X19587,X19588,X19589,X19590] :
( ~ class_Rings_Olinordered__semiring__strict(X19590)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19590),X19589),X19588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19590),X19587),X19586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19590),c_Groups_Ozero__class_Ozero(X19590)),X19589))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19590),c_Groups_Ozero__class_Ozero(X19590)),X19587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19590),X19589),X19587)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19590),X19588),X19586))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).
fof(i_0_7648,plain,
! [X19591,X19592,X19593,X19594,X19595] :
( ~ class_Rings_Olinordered__semiring__strict(X19595)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19595),X19594),X19593))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19595),X19592),X19591))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19595),c_Groups_Ozero__class_Ozero(X19595)),X19593))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19595),c_Groups_Ozero__class_Ozero(X19595)),X19592))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19595),X19594),X19592)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19595),X19593),X19591))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).
fof(i_0_7649,plain,
! [X25403,X25404,X25405,X25406,X25407] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25406),X25404),X25405))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25406,X25407),X25403),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25406,tc_HOL_Obool)),X25405),hAPP(hAPP(c_Set_Oinsert(X25406),X25404),c_Orderings_Obot__class_Obot(tc_fun(X25406,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25407),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25406,X25407),X25403),X25405)),hAPP(X25403,X25404))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25406),X25405))
| ~ class_Groups_Oab__group__add(X25407) )
& ( hBOOL(hAPP(hAPP(c_member(X25406),X25404),X25405))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25406,X25407),X25403),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25406,tc_HOL_Obool)),X25405),hAPP(hAPP(c_Set_Oinsert(X25406),X25404),c_Orderings_Obot__class_Obot(tc_fun(X25406,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25406,X25407),X25403),X25405)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25406),X25405))
| ~ class_Groups_Oab__group__add(X25407) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5604])])]) ).
fof(i_0_7650,plain,
! [X25398,X25399,X25400,X25401,X25402] :
( ~ class_Rings_Oring(X25402)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25401),X25400))
| ~ hBOOL(hAPP(hAPP(c_member(X25401),X25399),X25400))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25401,X25402),X25398),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25401,tc_HOL_Obool)),X25400),hAPP(hAPP(c_Set_Oinsert(X25401),X25399),c_Orderings_Obot__class_Obot(tc_fun(X25401,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25402),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25401,X25402),X25398),X25400)),hAPP(X25398,X25399)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring])]) ).
fof(i_0_7651,plain,
! [X23535,X23536,X23537] :
( ~ class_Fields_Ofield(X23537)
| X23536 = c_Groups_Oone__class_Oone(X23537)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23537),hAPP(c_Power_Opower__class_Opower(X23537),X23536)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23535)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X23537),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23537),hAPP(hAPP(c_Power_Opower__class_Opower(X23537),X23536),X23535)),c_Groups_Oone__class_Oone(X23537))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23537),X23536),c_Groups_Oone__class_Oone(X23537))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_geometric__sum])]) ).
fof(i_0_7652,plain,
! [X32446,X32447] :
( ~ class_Groups_Oordered__ab__group__add__abs(X32447)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32447),hAPP(c_Groups_Oabs__class_Oabs(X32447),hAPP(c_List_Omonoid__add__class_Olistsum(X32447),X32446))),hAPP(c_List_Omonoid__add__class_Olistsum(X32447),hAPP(hAPP(c_List_Omap(X32447,X32447),c_Groups_Oabs__class_Oabs(X32447)),X32446)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__abs])]) ).
cnf(i_0_7653,plain,
hAPP(c_List_Oset(X1),c_List_Oconcat(X1,X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)),c_List_Oset(X1)),
inference(split_conjunct,[status(thm)],[i_0_5605]) ).
fof(i_0_7654,plain,
! [X17683,X17684,X17685,X17686,X17687,X17688] :
( ~ c_Natural_Oevaln(X17688,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17687),c_Com_Ovname_OLoc(X17686)),hAPP(X17685,X17687)),X17684,X17683)
| c_Natural_Oevaln(c_Com_Ocom_OLocal(X17686,X17685,X17688),X17687,X17684,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17683),c_Com_Ovname_OLoc(X17686)),hAPP(hAPP(c_Natural_Ogetlocs,X17687),X17686))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OLocal])]) ).
fof(i_0_7655,plain,
! [X23759,X23760,X23761] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X23761)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23760),X23759)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23760),X23761)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23759),X23761)),
inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).
fof(i_0_7656,plain,
! [X23595,X23596,X23597,X23598,X23599] :
( ~ class_Groups_Oab__group__add(X23599)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23598),X23597))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23597),X23596))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23599),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23599),X23595),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23598),X23596))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23599),X23595),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23598),X23597))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23599),X23595),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23597),X23596)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl])]) ).
fof(i_0_7657,plain,
! [X23590,X23591,X23592,X23593,X23594] :
( ~ class_Groups_Ocomm__monoid__add(X23594)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23593),X23592))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23592),X23591))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23594),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23594),X23590),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23593),X23592))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23594),X23590),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23592),X23591))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23594),X23590),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23593),X23591)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl])]) ).
fof(i_0_7658,plain,
! [X19556,X19557,X19558,X19559] :
( ~ class_Rings_Olinordered__semiring__strict(X19559)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19559),X19558),X19557)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19559),X19556),X19557)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19559),c_Groups_Ozero__class_Ozero(X19559)),X19557))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19559),X19558),X19556)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).
fof(i_0_7659,plain,
! [X19552,X19553,X19554,X19555] :
( ~ class_Rings_Olinordered__semiring__strict(X19555)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19555),X19554),X19553)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19555),X19554),X19552)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19555),c_Groups_Ozero__class_Ozero(X19555)),X19554))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19555),X19553),X19552)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).
fof(i_0_7660,plain,
! [X19600,X19601,X19602,X19603] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19603),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19603),X19602),X19601)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19603),X19602),X19600)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19603),X19601),X19600))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19603),c_Groups_Ozero__class_Ozero(X19603)),X19602))
| ~ class_Rings_Olinordered__ring__strict(X19603) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19603),X19601),X19600))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19603),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19603),X19602),X19601)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19603),X19602),X19600)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19603),c_Groups_Ozero__class_Ozero(X19603)),X19602))
| ~ class_Rings_Olinordered__ring__strict(X19603) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).
fof(i_0_7661,plain,
! [X19572,X19573,X19574,X19575] :
( ~ class_Rings_Olinordered__semiring(X19575)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19575),X19574),X19573)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19575),X19572),X19573)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19575),c_Groups_Ozero__class_Ozero(X19575)),X19573))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19575),X19574),X19572)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).
fof(i_0_7662,plain,
! [X19568,X19569,X19570,X19571] :
( ~ class_Rings_Olinordered__semiring__strict(X19571)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19571),X19570),X19569)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19571),X19568),X19569)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19571),c_Groups_Ozero__class_Ozero(X19571)),X19569))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19571),X19570),X19568)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).
fof(i_0_7663,plain,
! [X20954,X20955,X20956,X20957] :
( ~ class_Rings_Olinordered__semidom(X20957)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20957),hAPP(hAPP(c_Power_Opower__class_Opower(X20957),X20956),X20955)),hAPP(hAPP(c_Power_Opower__class_Opower(X20957),X20954),X20955)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20957),c_Groups_Ozero__class_Ozero(X20957)),X20954))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20957),X20956),X20954)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).
fof(i_0_7664,plain,
! [X19564,X19565,X19566,X19567] :
( ~ class_Rings_Olinordered__semiring(X19567)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19567),X19566),X19565)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19567),X19566),X19564)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19567),c_Groups_Ozero__class_Ozero(X19567)),X19566))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19567),X19565),X19564)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).
fof(i_0_7665,plain,
! [X19560,X19561,X19562,X19563] :
( ~ class_Rings_Olinordered__semiring__strict(X19563)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19563),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19563),X19562),X19561)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19563),X19562),X19560)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19563),c_Groups_Ozero__class_Ozero(X19563)),X19562))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19563),X19561),X19560)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).
fof(i_0_7666,plain,
! [X18869,X18870,X18871,X18872] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18872),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18872),X18871),X18870)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18872),X18871),X18869)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18872),X18870),X18869))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18872),c_Groups_Ozero__class_Ozero(X18872)),X18871))
| ~ class_Rings_Olinordered__ring__strict(X18872) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18872),X18870),X18869))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18872),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18872),X18871),X18870)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18872),X18871),X18869)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18872),c_Groups_Ozero__class_Ozero(X18872)),X18871))
| ~ class_Rings_Olinordered__ring__strict(X18872) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).
cnf(i_0_7667,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oconcat(X1,X2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)),
inference(split_conjunct,[status(thm)],[i_0_5606]) ).
fof(i_0_7668,plain,
! [X24372,X24373,X24374,X24375] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24375),X24374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24375,tc_HOL_Obool)),X24374),X24373))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24375,tc_Nat_Onat),X24372),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24375,tc_HOL_Obool)),X24373),X24374)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24375,tc_Nat_Onat),X24372),X24373)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24375,tc_Nat_Onat),X24372),X24374)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat])]) ).
fof(i_0_7669,plain,
! [X29069,X29070,X29071,X29073] :
( ( hBOOL(hAPP(hAPP(c_member(X29071),esk298_3(X29069,X29070,X29071)),X29070))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29071),hAPP(c_Finite__Set_Ofold1(X29071,c_Orderings_Oord__class_Omin(X29071)),X29070)),X29069))
| X29070 = c_Orderings_Obot__class_Obot(tc_fun(X29071,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29071),X29070))
| ~ class_Orderings_Olinorder(X29071) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29071),esk298_3(X29069,X29070,X29071)),X29069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29071),hAPP(c_Finite__Set_Ofold1(X29071,c_Orderings_Oord__class_Omin(X29071)),X29070)),X29069))
| X29070 = c_Orderings_Obot__class_Obot(tc_fun(X29071,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29071),X29070))
| ~ class_Orderings_Olinorder(X29071) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29071),X29073),X29070))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29071),X29073),X29069))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29071),hAPP(c_Finite__Set_Ofold1(X29071,c_Orderings_Oord__class_Omin(X29071)),X29070)),X29069))
| X29070 = c_Orderings_Obot__class_Obot(tc_fun(X29071,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29071),X29070))
| ~ class_Orderings_Olinorder(X29071) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__strict__below__iff])])])])]) ).
fof(i_0_7670,plain,
! [X29061,X29062,X29063,X29065] :
( ( hBOOL(hAPP(hAPP(c_member(X29063),esk297_3(X29061,X29062,X29063)),X29062))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29063),hAPP(c_Finite__Set_Ofold1(X29063,c_Orderings_Oord__class_Omin(X29063)),X29062)),X29061))
| X29062 = c_Orderings_Obot__class_Obot(tc_fun(X29063,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29063),X29062))
| ~ class_Orderings_Olinorder(X29063) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29063),esk297_3(X29061,X29062,X29063)),X29061))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29063),hAPP(c_Finite__Set_Ofold1(X29063,c_Orderings_Oord__class_Omin(X29063)),X29062)),X29061))
| X29062 = c_Orderings_Obot__class_Obot(tc_fun(X29063,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29063),X29062))
| ~ class_Orderings_Olinorder(X29063) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29063),X29065),X29062))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29063),X29065),X29061))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29063),hAPP(c_Finite__Set_Ofold1(X29063,c_Orderings_Oord__class_Omin(X29063)),X29062)),X29061))
| X29062 = c_Orderings_Obot__class_Obot(tc_fun(X29063,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29063),X29062))
| ~ class_Orderings_Olinorder(X29063) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__below__iff])])])])]) ).
fof(i_0_7671,plain,
! [X30863,X30864,X30865,X30866,X30867,X30868] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30868,tc_fun(X30867,tc_HOL_Obool)),X30866),X30865),X30864))
| ~ hBOOL(hAPP(hAPP(c_member(X30868),X30863),X30866))
| hBOOL(hAPP(hAPP(X30865,X30863),X30864)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF1__D])]) ).
fof(i_0_7672,plain,
! [X30857,X30858,X30859,X30860,X30861,X30862] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30862,tc_fun(X30861,tc_HOL_Obool)),X30860),X30859),X30858))
| hBOOL(hAPP(hAPP(X30859,X30857),X30858))
| ~ hBOOL(hAPP(hAPP(c_member(X30862),X30857),X30860)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5607])]) ).
fof(i_0_7673,plain,
! [X20838,X20839,X20840,X20841] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20841),hAPP(hAPP(c_Power_Opower__class_Opower(X20841),X20840),X20839)),hAPP(hAPP(c_Power_Opower__class_Opower(X20841),X20840),X20838)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20839),X20838))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20841),c_Groups_Oone__class_Oone(X20841)),X20840))
| ~ class_Rings_Olinordered__semidom(X20841) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20839),X20838))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20841),hAPP(hAPP(c_Power_Opower__class_Opower(X20841),X20840),X20839)),hAPP(hAPP(c_Power_Opower__class_Opower(X20841),X20840),X20838)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20841),c_Groups_Oone__class_Oone(X20841)),X20840))
| ~ class_Rings_Olinordered__semidom(X20841) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).
fof(i_0_7674,plain,
! [X20834,X20835,X20836,X20837] :
( ~ class_Rings_Olinordered__semidom(X20837)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20837),c_Groups_Oone__class_Oone(X20837)),X20836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20837),hAPP(hAPP(c_Power_Opower__class_Opower(X20837),X20836),X20835)),hAPP(hAPP(c_Power_Opower__class_Opower(X20837),X20836),X20834)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20835),X20834)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).
fof(i_0_7675,plain,
! [X20981,X20982,X20983,X20984] :
( ~ class_Rings_Olinordered__semidom(X20984)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20984),c_Groups_Oone__class_Oone(X20984)),X20983))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20984),hAPP(hAPP(c_Power_Opower__class_Opower(X20984),X20983),X20982)),hAPP(hAPP(c_Power_Opower__class_Opower(X20984),X20983),X20981)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20982),X20981)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).
fof(i_0_7676,plain,
! [X20977,X20978,X20979,X20980] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20980),hAPP(hAPP(c_Power_Opower__class_Opower(X20980),X20979),X20978)),hAPP(hAPP(c_Power_Opower__class_Opower(X20980),X20979),X20977)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20978),X20977))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20980),c_Groups_Oone__class_Oone(X20980)),X20979))
| ~ class_Rings_Olinordered__semidom(X20980) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20978),X20977))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20980),hAPP(hAPP(c_Power_Opower__class_Opower(X20980),X20979),X20978)),hAPP(hAPP(c_Power_Opower__class_Opower(X20980),X20979),X20977)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20980),c_Groups_Oone__class_Oone(X20980)),X20979))
| ~ class_Rings_Olinordered__semidom(X20980) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).
fof(i_0_7677,plain,
! [X32578,X32579,X32580] :
( X32580 = c_List_Olist_ONil(X32579)
| hBOOL(hAPP(hAPP(c_member(X32579),hAPP(c_Product__Type_Ofst(X32579,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X32579,X32580),X32578))),hAPP(c_List_Oset(X32579),X32580))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select])]) ).
fof(i_0_7678,plain,
! [X28751,X28752,X28753,X28754] : hAPP(c_Finite__Set_Ocard(tc_prod(X28754,X28753)),hAPP(hAPP(c_Product__Type_OSigma(X28754,X28753),hAPP(hAPP(c_Set_Oinsert(X28754),X28752),c_Orderings_Obot__class_Obot(tc_fun(X28754,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X28753,tc_HOL_Obool),X28754),X28751))) = hAPP(c_Finite__Set_Ocard(X28753),X28751),
inference(variable_rename,[status(thm)],[fact_card__cartesian__product__singleton]) ).
fof(i_0_7679,plain,
! [X17858,X17859,X17860] :
( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17860)),X17859),X17858))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17860))),X17859),X17858)) )
& ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17860))),X17859),X17858))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17860)),X17859),X17858)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I9_J])]) ).
fof(i_0_7680,plain,
! [X17715,X17716,X17717] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17717))),X17716),X17715))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17717)),X17716),X17715)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OBody])]) ).
fof(i_0_7681,plain,
! [X22103,X22104,X22105,X22106,X22107] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22107,X22106,tc_HOL_Obool),X22105),hAPP(hAPP(c_Product__Type_OPair(X22107,X22106),X22104),X22103)))
| hBOOL(hAPP(hAPP(X22105,X22104),X22103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD])]) ).
fof(i_0_7682,plain,
! [X28231,X28232,X28233] : c_Fun_Oinj__on(tc_prod(X28233,X28232),tc_prod(X28232,X28233),hAPP(c_Product__Type_Oprod_Oprod__case(X28233,X28232,tc_prod(X28232,X28233)),hAPP(c_COMBC(X28232,X28233,tc_prod(X28232,X28233)),c_Product__Type_OPair(X28232,X28233))),X28231),
inference(variable_rename,[status(thm)],[fact_swap__inj__on]) ).
fof(i_0_7683,plain,
! [X29098,X29099,X29100] :
( ( hBOOL(hAPP(hAPP(c_member(X29100),esk304_3(X29098,X29099,X29100)),X29099))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29100,tc_Nat_Onat),X29098),X29099)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29100),X29099)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X29098,esk304_3(X29098,X29099,X29100))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29100,tc_Nat_Onat),X29098),X29099)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29100),X29099)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat])])])]) ).
fof(i_0_7684,plain,
! [X26155,X26156,X26157,X26158] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26157,tc_Nat_Onat),X26155),X26156)))
| ~ hBOOL(hAPP(hAPP(c_member(X26157),X26158),X26156))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X26155,X26158)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26157),X26156)) )
& ( hBOOL(hAPP(hAPP(c_member(X26157),esk212_3(X26155,X26156,X26157)),X26156))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26157,tc_Nat_Onat),X26155),X26156)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26157),X26156)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X26155,esk212_3(X26155,X26156,X26157))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26157,tc_Nat_Onat),X26155),X26156)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26157),X26156)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat__iff])])])])]) ).
fof(i_0_7685,plain,
! [X23482,X23483,X23484,X23485] :
( ~ class_Groups_Ocomm__monoid__add(X23485)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23485),X23484),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23483),hAPP(c_Nat_OSuc,X23482))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23485),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23485,tc_Nat_Onat),X23484),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23483,X23482)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl])]) ).
fof(i_0_7686,plain,
! [X19596,X19597,X19598,X19599] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19599),X19598),X19597)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19599),X19598),X19596)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19599),X19596),X19597))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19599),X19598),c_Groups_Ozero__class_Ozero(X19599)))
| ~ class_Rings_Olinordered__ring__strict(X19599) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19599),X19596),X19597))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19599),X19598),X19597)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19599),X19598),X19596)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19599),X19598),c_Groups_Ozero__class_Ozero(X19599)))
| ~ class_Rings_Olinordered__ring__strict(X19599) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).
fof(i_0_7687,plain,
! [X18888,X18889,X18890,X18891] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18891),X18890),X18889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18891),X18890),X18888)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18891),X18888),X18889))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18891),X18890),c_Groups_Ozero__class_Ozero(X18891)))
| ~ class_Rings_Olinordered__ring__strict(X18891) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18891),X18888),X18889))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18891),X18890),X18889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18891),X18890),X18888)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18891),X18890),c_Groups_Ozero__class_Ozero(X18891)))
| ~ class_Rings_Olinordered__ring__strict(X18891) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).
fof(i_0_7688,plain,
! [X26239,X26240,X26241,X26242] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26242,tc_Option_Ooption(X26241)),hAPP(c_COMBK(tc_Option_Ooption(X26241),X26242),c_Option_Ooption_ONone(X26241))),X26240),c_Option_Ooption_ONone(X26241)),X26239) = c_Option_Ooption_ONone(X26241),
inference(variable_rename,[status(thm)],[fact_empty__upd__none]) ).
fof(i_0_7689,plain,
! [X27060,X27061,X27062] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27062,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27062,tc_HOL_Obool)),X27061),X27060)),X27061)),
inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).
fof(i_0_7690,plain,
! [X27057,X27058,X27059] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27059,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27059,tc_HOL_Obool)),X27058),X27057)),X27057)),
inference(variable_rename,[status(thm)],[fact_Int__lower2]) ).
fof(i_0_7691,plain,
! [X22423,X22424,X22425] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22425,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22425,tc_HOL_Obool)),X22424),X22423)),X22424)),
inference(variable_rename,[status(thm)],[fact_Diff__subset]) ).
fof(i_0_7692,plain,
! [X32472,X32473,X32474,X32475,X32476] :
( ~ class_Groups_Ocomm__monoid__add(X32476)
| ~ hBOOL(hAPP(hAPP(c_member(X32475),X32474),hAPP(c_List_Oset(X32475),X32473)))
| hAPP(c_List_Omonoid__add__class_Olistsum(X32476),hAPP(hAPP(c_List_Omap(X32475,X32476),X32472),X32473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32476),hAPP(X32472,X32474)),hAPP(c_List_Omonoid__add__class_Olistsum(X32476),hAPP(hAPP(c_List_Omap(X32475,X32476),X32472),c_List_Oremove1(X32475,X32474,X32473)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__map__remove1])]) ).
fof(i_0_7693,plain,
! [X27106,X27107,X27108,X27109] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27109,tc_HOL_Obool)),X27108),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27109,tc_HOL_Obool)),X27107),X27106)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27109,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27109,tc_HOL_Obool)),X27108),X27107)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27109,tc_HOL_Obool)),X27108),X27106)),
inference(variable_rename,[status(thm)],[fact_Int__Un__distrib]) ).
fof(i_0_7694,plain,
! [X27252,X27253,X27254,X27255] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27255,tc_HOL_Obool)),X27254),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27255,tc_HOL_Obool)),X27253),X27252)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27255,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27255,tc_HOL_Obool)),X27254),X27253)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27255,tc_HOL_Obool)),X27254),X27252)),
inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib]) ).
fof(i_0_7695,plain,
! [X27102,X27103,X27104,X27105] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27105,tc_HOL_Obool)),X27104),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27105,tc_HOL_Obool)),X27103),X27102)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27105,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27105,tc_HOL_Obool)),X27104),X27103)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27105,tc_HOL_Obool)),X27104),X27102)),
inference(variable_rename,[status(thm)],[fact_Un__Int__distrib]) ).
fof(i_0_7696,plain,
! [X27370,X27371,X27372,X27373] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27373,tc_HOL_Obool)),X27372),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27373,tc_HOL_Obool)),X27371),X27370)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27373,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27373,tc_HOL_Obool)),X27372),X27371)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27373,tc_HOL_Obool)),X27372),X27370)),
inference(variable_rename,[status(thm)],[fact_Diff__Int]) ).
fof(i_0_7697,plain,
! [X27366,X27367,X27368,X27369] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27369,tc_HOL_Obool)),X27368),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27369,tc_HOL_Obool)),X27367),X27366)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27369,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27369,tc_HOL_Obool)),X27368),X27367)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27369,tc_HOL_Obool)),X27368),X27366)),
inference(variable_rename,[status(thm)],[fact_Diff__Un]) ).
fof(i_0_7698,plain,
! [X22506,X22507,X22508,X22509,X22510,X22511] : c_Product__Type_Oprod_Oprod__rec(X22511,X22510,X22509,X22508,hAPP(hAPP(c_Product__Type_OPair(X22511,X22510),X22507),X22506)) = hAPP(hAPP(X22508,X22507),X22506),
inference(variable_rename,[status(thm)],[fact_prod_Orecs]) ).
fof(i_0_7699,plain,
! [X22907,X22908,X22909,X22910,X22911] : hAPP(c_New__DSequence_Oneg__bind(X22911,X22910,X22909,X22908),X22907) = c_Lazy__Sequence_Ohb__bind(X22911,X22910,hAPP(X22909,X22907),hAPP(hAPP(c_COMBC(X22911,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X22910))),X22908),X22907)),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__bind__def]) ).
fof(i_0_7700,plain,
! [X23577,X23578,X23579,X23580] :
( ~ class_Groups_Ocomm__monoid__add(X23580)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23580),X23579),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23578)),hAPP(c_Nat_OSuc,X23577))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23580),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23580,tc_Nat_Onat),X23579),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23578),X23577)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl])]) ).
fof(i_0_7701,plain,
! [X23762,X23763,X23764] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X23764)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23763,X23762)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23763),X23764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23762),X23764)),
inference(variable_rename,[status(thm)],[fact_image__add__atLeastAtMost]) ).
cnf(i_0_7702,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Ofoldr(X2,X2,c_Orderings_Oord__class_Omax(X2),X1,X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(hAPP(c_List_Onth(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5608]) ).
fof(i_0_7703,plain,
! [X29223,X29224,X29225,X29226] :
( ( hBOOL(hAPP(hAPP(c_member(X29226),X29225),X29224))
| ~ hBOOL(hAPP(hAPP(c_member(X29226),X29225),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29226,tc_HOL_Obool)),X29224),hAPP(c_Set_OCollect(X29226),X29223)))) )
& ( hBOOL(hAPP(X29223,X29225))
| ~ hBOOL(hAPP(hAPP(c_member(X29226),X29225),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29226,tc_HOL_Obool)),X29224),hAPP(c_Set_OCollect(X29226),X29223)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29226),X29225),X29224))
| ~ hBOOL(hAPP(X29223,X29225))
| hBOOL(hAPP(hAPP(c_member(X29226),X29225),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29226,tc_HOL_Obool)),X29224),hAPP(c_Set_OCollect(X29226),X29223)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__Collect])])]) ).
fof(i_0_7704,plain,
! [X33934,X33935,X33936,X33937] :
( ~ hBOOL(hAPP(hAPP(c_member(X33937),X33936),hAPP(c_List_Oset(X33937),X33935)))
| hBOOL(hAPP(X33934,X33936))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33937)),hAPP(c_List_Ofilter(X33937,X33934),X33935))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33937)),X33935))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5609])]) ).
fof(i_0_7705,plain,
! [X23572,X23573,X23574,X23575,X23576] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23576),X23573),X23575))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23576),X23574),X23575))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23576,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23576,X23575),X23574)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23576,X23573),X23572)))
| ~ class_Orderings_Olinorder(X23576) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23576),X23574),X23572))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23576),X23574),X23575))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23576,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23576,X23575),X23574)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23576,X23573),X23572)))
| ~ class_Orderings_Olinorder(X23576) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])]) ).
fof(i_0_7706,plain,
! [X18199,X18200,X18201,X18202,X18203] : c_Sum__Type_Osum_Osum__size(X18203,X18202,X18201,X18200,hAPP(c_Sum__Type_OInl(X18203,X18202),X18199)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X18201,X18199)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_sum_Osize_I1_J]) ).
fof(i_0_7707,plain,
! [X18194,X18195,X18196,X18197,X18198] : c_Sum__Type_Osum_Osum__size(X18198,X18197,X18196,X18195,hAPP(c_Sum__Type_OInr(X18197,X18198),X18194)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X18195,X18194)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_sum_Osize_I2_J]) ).
fof(i_0_7708,plain,
! [X27805,X27806,X27807,X27808,X27809,X27810] :
( ~ c_Finite__Set_Ofolding__idem(X27810,X27809,X27808,X27807)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27810),X27806))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27810),X27805))
| hAPP(X27807,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27810,tc_HOL_Obool)),X27806),X27805)) = hAPP(c_Fun_Ocomp(X27809,X27809,X27809,hAPP(X27807,X27806)),hAPP(X27807,X27805)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Ounion__idem])]) ).
cnf(i_0_7709,plain,
c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_5610]) ).
cnf(i_0_7710,plain,
c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_5611]) ).
fof(i_0_7711,plain,
! [X29777,X29778,X29779] :
( ~ c_Wellfounded_Owf(X29779,X29778)
| ~ c_Wellfounded_Owf(X29779,X29777)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29779,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29779,X29779),X29778)),hAPP(c_Relation_ORange(X29779,X29779),X29777)) != c_Orderings_Obot__class_Obot(tc_fun(X29779,tc_HOL_Obool))
| c_Wellfounded_Owf(X29779,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29779,X29779),tc_HOL_Obool)),X29778),X29777)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Un])]) ).
fof(i_0_7712,plain,
! [X20332,X20333,X20334] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20333),X20334)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20332),X20334)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20333),X20332))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20334),X20332))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20334),X20333)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20333),X20332))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20333),X20334)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20332),X20334)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20334),X20332))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20334),X20333)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).
fof(i_0_7713,plain,
! [X20413,X20414,X20415] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20414),X20415)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20413),X20415)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20414),X20413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20415),X20413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20415),X20414)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20414),X20413))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20414),X20415)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20413),X20415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20415),X20413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20415),X20414)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).
cnf(i_0_7714,plain,
c_Relation_Oirrefl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))),
inference(split_conjunct,[status(thm)],[i_0_5612]) ).
fof(i_0_7715,plain,
! [X18865,X18866,X18867,X18868] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),X18867),c_Groups_Ozero__class_Ozero(X18868)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),c_Groups_Ozero__class_Ozero(X18868)),X18867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18865)))
| ~ class_Rings_Olinordered__ring__strict(X18868) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),X18865),X18866))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),c_Groups_Ozero__class_Ozero(X18868)),X18867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18865)))
| ~ class_Rings_Olinordered__ring__strict(X18868) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),X18867),c_Groups_Ozero__class_Ozero(X18868)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),X18866),X18865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18865)))
| ~ class_Rings_Olinordered__ring__strict(X18868) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),X18865),X18866))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),X18866),X18865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18865)))
| ~ class_Rings_Olinordered__ring__strict(X18868) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),c_Groups_Ozero__class_Ozero(X18868)),X18867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),X18866),X18865))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18865)))
| ~ class_Rings_Olinordered__ring__strict(X18868) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),X18867),c_Groups_Ozero__class_Ozero(X18868)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),X18865),X18866))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18868),X18867),X18865)))
| ~ class_Rings_Olinordered__ring__strict(X18868) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).
fof(i_0_7716,plain,
! [X18861,X18862,X18863,X18864] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),X18862),c_Groups_Ozero__class_Ozero(X18864)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),c_Groups_Ozero__class_Ozero(X18864)),X18862))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18863),X18862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18861),X18862)))
| ~ class_Rings_Olinordered__ring__strict(X18864) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),X18861),X18863))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),c_Groups_Ozero__class_Ozero(X18864)),X18862))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18863),X18862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18861),X18862)))
| ~ class_Rings_Olinordered__ring__strict(X18864) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),X18862),c_Groups_Ozero__class_Ozero(X18864)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),X18863),X18861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18863),X18862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18861),X18862)))
| ~ class_Rings_Olinordered__ring__strict(X18864) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),X18861),X18863))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),X18863),X18861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18863),X18862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18861),X18862)))
| ~ class_Rings_Olinordered__ring__strict(X18864) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),c_Groups_Ozero__class_Ozero(X18864)),X18862))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),X18863),X18861))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18863),X18862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18861),X18862)))
| ~ class_Rings_Olinordered__ring__strict(X18864) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),X18862),c_Groups_Ozero__class_Ozero(X18864)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),X18861),X18863))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18863),X18862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18864),X18861),X18862)))
| ~ class_Rings_Olinordered__ring__strict(X18864) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).
fof(i_0_7717,plain,
! [X25233,X25234,X25235,X25236] :
( ( hBOOL(hAPP(hAPP(c_member(X25236),X25235),X25233))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25236,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25236),X25235),X25234)),X25233)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25236,tc_HOL_Obool)),X25234),X25233))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25236,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25236),X25235),X25234)),X25233)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25236),X25235),X25233))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25236,tc_HOL_Obool)),X25234),X25233))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25236,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25236),X25235),X25234)),X25233)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).
fof(i_0_7718,plain,
! [X26137,X26138,X26139] :
( ~ class_Groups_Ocomm__monoid__add(X26139)
| ~ class_Groups_Ocomm__monoid__mult(X26139)
| ~ c_Nat__Transfer_Onat__set(X26138)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26139),X26137),X26138) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X26139),hAPP(hAPP(c_COMBB(tc_Int_Oint,X26139,tc_Nat_Onat),X26137),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X26138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J])]) ).
fof(i_0_7719,plain,
! [X23788,X23789,X23790] :
( ~ class_Groups_Ocomm__monoid__add(X23790)
| ~ class_Groups_Ocomm__monoid__mult(X23790)
| ~ c_Nat__Transfer_Onat__set(X23789)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X23790),X23788),X23789) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23790),hAPP(hAPP(c_COMBB(tc_Int_Oint,X23790,tc_Nat_Onat),X23788),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23789)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J])]) ).
fof(i_0_7720,plain,
! [X32362,X32363,X32364,X32365] : c_Map_Omap__of(X32365,X32364,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X32365,X32364)),X32363),X32362)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32365,tc_Option_Ooption(X32364)),c_Map_Omap__of(X32365,X32364,X32362)),hAPP(c_Product__Type_Ofst(X32365,X32364),X32363)),hAPP(c_Option_Ooption_OSome(X32364),hAPP(c_Product__Type_Osnd(X32365,X32364),X32363))),
inference(variable_rename,[status(thm)],[fact_map__of_Osimps_I2_J]) ).
fof(i_0_7721,plain,
! [X27594,X27595,X27596,X27597,X27598] :
( ~ class_Groups_Ocomm__monoid__mult(X27598)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27597),X27596))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27597),X27595))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27597,tc_HOL_Obool)),X27596),X27595) != c_Orderings_Obot__class_Obot(tc_fun(X27597,tc_HOL_Obool))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27597,X27598),X27594),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27597,tc_HOL_Obool)),X27596),X27595)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27598),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27597,X27598),X27594),X27596)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27597,X27598),X27594),X27595)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint])]) ).
fof(i_0_7722,plain,
! [X27589,X27590,X27591,X27592,X27593] :
( ~ class_Groups_Ocomm__monoid__mult(X27593)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27592),X27591))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27592),X27590))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27592,tc_HOL_Obool)),X27591),X27590) != c_Orderings_Obot__class_Obot(tc_fun(X27592,tc_HOL_Obool))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27592,X27593),X27589),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27592,tc_HOL_Obool)),X27591),X27590)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27593),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27592,X27593),X27589),X27591)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27592,X27593),X27589),X27590)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint])]) ).
fof(i_0_7723,plain,
! [X27579,X27580,X27581,X27582,X27583] :
( ~ class_Groups_Ocomm__monoid__add(X27583)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27582),X27581))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27582),X27580))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27582,tc_HOL_Obool)),X27581),X27580) != c_Orderings_Obot__class_Obot(tc_fun(X27582,tc_HOL_Obool))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27582,X27583),X27579),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27582,tc_HOL_Obool)),X27581),X27580)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27583),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27582,X27583),X27579),X27581)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27582,X27583),X27579),X27580)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint])]) ).
fof(i_0_7724,plain,
! [X26032,X26033,X26034] :
( ~ class_Groups_Ocomm__monoid__add(X26034)
| ~ class_Groups_Ocomm__monoid__mult(X26034)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X26034),X26033),X26032) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26034),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26034,tc_Int_Oint),X26033),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X26032)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J])]) ).
fof(i_0_7725,plain,
! [X23727,X23728,X23729] :
( ~ class_Groups_Ocomm__monoid__add(X23729)
| ~ class_Groups_Ocomm__monoid__mult(X23729)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23729),X23728),X23727) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X23729),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23729,tc_Int_Oint),X23728),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23727)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J])]) ).
cnf(i_0_7726,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))) ),
inference(split_conjunct,[status(thm)],[i_0_5613]) ).
fof(i_0_7727,plain,
! [X33211,X33212] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X33212),tc_List_Olist(X33212)),tc_HOL_Obool)),c_List_Olistrel(X33212,X33211)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33212),c_List_Olistrel1(X33212,X33211)))),
inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).
fof(i_0_7728,plain,
! [X22231,X22232,X22233,X22234] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22233))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22233))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22234,X22233),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22232),X22231)))
| X22234 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22233),X22232)),X22231) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22233),X22231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22231),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22233))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22234,X22233),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22232),X22231)))
| X22234 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22233),X22232)),X22231) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22233))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22231),X22233))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22234,X22233),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22232),X22231)))
| X22234 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22233),X22232)),X22231) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22233),X22231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22231),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22231),X22233))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22234,X22233),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22232),X22231)))
| X22234 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22233),X22232)),X22231) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5614])])]) ).
fof(i_0_7729,plain,
! [X23782,X23783] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),X23783)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23782),X23783))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X23783),X23782),
inference(variable_rename,[status(thm)],[fact_image__add__int__atLeastLessThan]) ).
fof(i_0_7730,plain,
! [X33322,X33323,X33324,X33325] : hAPP(hAPP(c_List_Odrop(X33325),X33324),hAPP(hAPP(c_List_Oappend(X33325),X33323),X33322)) = hAPP(hAPP(c_List_Oappend(X33325),hAPP(hAPP(c_List_Odrop(X33325),X33324),X33323)),hAPP(hAPP(c_List_Odrop(X33325),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33325)),X33323))),X33322)),
inference(variable_rename,[status(thm)],[fact_drop__append]) ).
fof(i_0_7731,plain,
! [X33050,X33051,X33052,X33053] : hAPP(hAPP(c_List_Otake(X33053),X33052),hAPP(hAPP(c_List_Oappend(X33053),X33051),X33050)) = hAPP(hAPP(c_List_Oappend(X33053),hAPP(hAPP(c_List_Otake(X33053),X33052),X33051)),hAPP(hAPP(c_List_Otake(X33053),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33052),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33053)),X33051))),X33050)),
inference(variable_rename,[status(thm)],[fact_take__append]) ).
fof(i_0_7732,plain,
! [X32411,X32412,X32413] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32413,tc_HOL_Obool)),hAPP(c_List_Oset(X32413),c_List_Osublist(X32413,X32412,X32411))),hAPP(c_List_Oset(X32413),X32412))),
inference(variable_rename,[status(thm)],[fact_set__sublist__subset]) ).
fof(i_0_7733,plain,
! [X32019,X32020,X32021] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32021,tc_HOL_Obool)),hAPP(c_List_Oset(X32021),c_List_Oremove1(X32021,X32020,X32019))),hAPP(c_List_Oset(X32021),X32019))),
inference(variable_rename,[status(thm)],[fact_set__remove1__subset]) ).
fof(i_0_7734,plain,
! [X28409,X28410,X28411,X28412] :
( ~ c_Fun_Oinj__on(X28412,X28411,X28410,X28409)
| c_Fun_Oinj__on(X28411,X28412,c_Fun_Othe__inv__into(X28412,X28411,X28409,X28410),hAPP(c_Set_Oimage(X28412,X28411,X28410),X28409)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into])]) ).
fof(i_0_7735,plain,
! [X29850,X29851,X29852] : hAPP(c_Relation_ODomain(X29852,X29851),hAPP(c_Set_OCollect(tc_prod(X29852,X29851)),hAPP(c_Product__Type_Oprod_Oprod__case(X29852,X29851,tc_HOL_Obool),X29850))) = hAPP(c_Set_OCollect(X29852),hAPP(hAPP(c_COMBB(tc_fun(X29851,tc_HOL_Obool),tc_HOL_Obool,X29852),c_HOL_OEx(X29851)),X29850)),
inference(variable_rename,[status(thm)],[fact_Domain__Collect__split]) ).
cnf(i_0_7736,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),
inference(split_conjunct,[status(thm)],[i_0_5615]) ).
fof(i_0_7737,plain,
! [X33615,X33616,X33617,X33618,X33619] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X33619,X33618,X33617)
| hAPP(hAPP(c_Finite__Set_Ofold(X33619,X33618,X33617),X33616),hAPP(c_List_Oset(X33619),X33615)) = hAPP(c_List_Ofoldl(X33618,X33619,hAPP(c_COMBC(X33619,X33618,X33618),X33617),X33616),X33615) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__set])]) ).
fof(i_0_7738,plain,
! [X25384,X25385,X25386,X25387] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25387),X25386),X25385))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25387,tc_Nat_Onat),X25384),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25387,tc_HOL_Obool)),X25385),hAPP(hAPP(c_Set_Oinsert(X25387),X25386),c_Orderings_Obot__class_Obot(tc_fun(X25387,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25387,tc_Nat_Onat),X25384),X25385)),hAPP(X25384,X25386)) )
& ( hBOOL(hAPP(hAPP(c_member(X25387),X25386),X25385))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25387,tc_Nat_Onat),X25384),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25387,tc_HOL_Obool)),X25385),hAPP(hAPP(c_Set_Oinsert(X25387),X25386),c_Orderings_Obot__class_Obot(tc_fun(X25387,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25387,tc_Nat_Onat),X25384),X25385) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5616])]) ).
fof(i_0_7739,plain,
! [X23278,X23279,X23280,X23281] :
( ~ class_Groups_Oab__group__add(X23281)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23280,X23281),hAPP(hAPP(c_COMBB(X23281,X23281,X23280),c_Groups_Ouminus__class_Ouminus(X23281)),X23279)),X23278) = hAPP(c_Groups_Ouminus__class_Ouminus(X23281),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23280,X23281),X23279),X23278)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__negf])]) ).
fof(i_0_7740,plain,
! [X26035,X26036,X26037,X26038] :
( ~ class_Fields_Olinordered__field(X26038)
| hAPP(c_Groups_Oabs__class_Oabs(X26038),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26037,X26038),X26036),X26035)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26037,X26038),hAPP(hAPP(c_COMBB(X26038,X26038,X26037),c_Groups_Oabs__class_Oabs(X26038)),X26036)),X26035) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setprod])]) ).
fof(i_0_7741,plain,
! [X32637,X32638,X32639,X32641,X32642,X32643,X32644,X32646] :
( ( hBOOL(hAPP(hAPP(c_member(X32639),esk448_3(X32637,X32638,X32639)),hAPP(c_List_Oset(X32639),X32638)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32641),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32639)),X32638)))
| hBOOL(hAPP(X32637,hAPP(hAPP(c_List_Onth(X32639),X32638),X32641))) )
& ( ~ hBOOL(hAPP(X32637,esk448_3(X32637,X32638,X32639)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32641),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32639)),X32638)))
| hBOOL(hAPP(X32637,hAPP(hAPP(c_List_Onth(X32639),X32638),X32641))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk449_3(X32642,X32643,X32644)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32644)),X32643)))
| ~ hBOOL(hAPP(hAPP(c_member(X32644),X32646),hAPP(c_List_Oset(X32644),X32643)))
| hBOOL(hAPP(X32642,X32646)) )
& ( ~ hBOOL(hAPP(X32642,hAPP(hAPP(c_List_Onth(X32644),X32643),esk449_3(X32642,X32643,X32644))))
| ~ hBOOL(hAPP(hAPP(c_member(X32644),X32646),hAPP(c_List_Oset(X32644),X32643)))
| hBOOL(hAPP(X32642,X32646)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__set__conv__all__nth])])])])])]) ).
fof(i_0_7742,plain,
! [X24408,X24409,X24410,X24411] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24411,tc_HOL_Obool)),X24410),X24409))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24411,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24411),X24408),X24410)),hAPP(hAPP(c_Set_Oinsert(X24411),X24408),X24409))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).
cnf(i_0_7743,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5570]) ).
cnf(i_0_7744,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5571]) ).
cnf(i_0_7745,plain,
( c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X1,X2)))
| ~ c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5617]) ).
fof(i_0_7746,plain,
! [X34070,X34071,X34072,X34073,X34074] :
( ( c_List_Olinorder__class_Osorted(X34072,X34071)
| ~ c_List_Olinorder__class_Osorted(X34072,hAPP(hAPP(c_List_Oappend(X34072),X34071),X34070))
| ~ class_Orderings_Olinorder(X34072) )
& ( c_List_Olinorder__class_Osorted(X34072,X34070)
| ~ c_List_Olinorder__class_Osorted(X34072,hAPP(hAPP(c_List_Oappend(X34072),X34071),X34070))
| ~ class_Orderings_Olinorder(X34072) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X34072),X34073),hAPP(c_List_Oset(X34072),X34071)))
| ~ hBOOL(hAPP(hAPP(c_member(X34072),X34074),hAPP(c_List_Oset(X34072),X34070)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34072),X34073),X34074))
| ~ c_List_Olinorder__class_Osorted(X34072,hAPP(hAPP(c_List_Oappend(X34072),X34071),X34070))
| ~ class_Orderings_Olinorder(X34072) )
& ( hBOOL(hAPP(hAPP(c_member(X34072),esk483_3(X34070,X34071,X34072)),hAPP(c_List_Oset(X34072),X34071)))
| ~ c_List_Olinorder__class_Osorted(X34072,X34071)
| ~ c_List_Olinorder__class_Osorted(X34072,X34070)
| c_List_Olinorder__class_Osorted(X34072,hAPP(hAPP(c_List_Oappend(X34072),X34071),X34070))
| ~ class_Orderings_Olinorder(X34072) )
& ( hBOOL(hAPP(hAPP(c_member(X34072),esk484_3(X34070,X34071,X34072)),hAPP(c_List_Oset(X34072),X34070)))
| ~ c_List_Olinorder__class_Osorted(X34072,X34071)
| ~ c_List_Olinorder__class_Osorted(X34072,X34070)
| c_List_Olinorder__class_Osorted(X34072,hAPP(hAPP(c_List_Oappend(X34072),X34071),X34070))
| ~ class_Orderings_Olinorder(X34072) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34072),esk483_3(X34070,X34071,X34072)),esk484_3(X34070,X34071,X34072)))
| ~ c_List_Olinorder__class_Osorted(X34072,X34071)
| ~ c_List_Olinorder__class_Osorted(X34072,X34070)
| c_List_Olinorder__class_Osorted(X34072,hAPP(hAPP(c_List_Oappend(X34072),X34071),X34070))
| ~ class_Orderings_Olinorder(X34072) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__append])])])])]) ).
fof(i_0_7747,plain,
! [X20966,X20967,X20968] :
( ~ class_Rings_Olinordered__semidom(X20968)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20968),c_Groups_Oone__class_Oone(X20968)),X20967))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20968),hAPP(hAPP(c_Power_Opower__class_Opower(X20968),X20967),X20966)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20968),X20967),hAPP(hAPP(c_Power_Opower__class_Opower(X20968),X20967),X20966)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).
fof(i_0_7748,plain,
! [X22431,X22432,X22433,X22434] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22434,tc_HOL_Obool)),X22433),X22432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22434,tc_HOL_Obool)),X22432),X22431))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22434,tc_HOL_Obool)),X22432),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22434,tc_HOL_Obool)),X22431),X22433)) = X22433 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__diff])]) ).
fof(i_0_7749,plain,
! [X26517,X26518,X26519] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26519,tc_HOL_Obool)),X26518),X26517))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X26519,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X26519),X26518)),hAPP(c_Set_OPow(X26519),X26517))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__mono])]) ).
fof(i_0_7750,plain,
! [X26668,X26669,X26670,X26671,X26672,X26673] : hAPP(hAPP(c_Fun_Ocomp(X26673,X26672,X26671,hAPP(c_COMBK(X26672,X26673),X26670)),X26669),X26668) = X26670,
inference(variable_rename,[status(thm)],[fact_K__record__comp]) ).
fof(i_0_7751,plain,
! [X33354,X33355,X33356] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33356,tc_HOL_Obool)),hAPP(c_List_Oset(X33356),hAPP(hAPP(c_List_Odrop(X33356),X33355),X33354))),hAPP(c_List_Oset(X33356),X33354))),
inference(variable_rename,[status(thm)],[fact_set__drop__subset]) ).
fof(i_0_7752,plain,
! [X33102,X33103,X33104] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33104,tc_HOL_Obool)),hAPP(c_List_Oset(X33104),hAPP(hAPP(c_List_Otake(X33104),X33103),X33102))),hAPP(c_List_Oset(X33104),X33102))),
inference(variable_rename,[status(thm)],[fact_set__take__subset]) ).
fof(i_0_7753,plain,
! [X21724,X21725,X21726,X21727] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21727),X21725),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21727),X21724),X21726)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21727),X21725),X21726)),X21724))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21727),c_Groups_Ozero__class_Ozero(X21727)),X21726))
| ~ class_Fields_Olinordered__field(X21727) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21727),X21725),X21726)),X21724))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21727),X21725),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21727),X21724),X21726)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21727),c_Groups_Ozero__class_Ozero(X21727)),X21726))
| ~ class_Fields_Olinordered__field(X21727) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq])])]) ).
fof(i_0_7754,plain,
! [X21728,X21729,X21730,X21731] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21731),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21731),X21729),X21730)),X21728))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21731),X21729),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21731),X21728),X21730)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21731),c_Groups_Ozero__class_Ozero(X21731)),X21730))
| ~ class_Fields_Olinordered__field(X21731) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21731),X21729),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21731),X21728),X21730)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21731),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21731),X21729),X21730)),X21728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21731),c_Groups_Ozero__class_Ozero(X21731)),X21730))
| ~ class_Fields_Olinordered__field(X21731) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq])])]) ).
fof(i_0_7755,plain,
! [X21736,X21737,X21738,X21739] :
( ~ class_Fields_Olinordered__field(X21739)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21739),c_Groups_Ozero__class_Ozero(X21739)),X21738))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21739),X21737),X21738)),X21736))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21739),X21737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21739),X21736),X21738))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos])]) ).
fof(i_0_7756,plain,
! [X21636,X21637,X21638,X21639] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21639),X21637),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21639),X21636),X21638)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21639),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21639),X21637),X21638)),X21636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21639),c_Groups_Ozero__class_Ozero(X21639)),X21638))
| ~ class_Fields_Olinordered__field(X21639) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21639),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21639),X21637),X21638)),X21636))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21639),X21637),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21639),X21636),X21638)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21639),c_Groups_Ozero__class_Ozero(X21639)),X21638))
| ~ class_Fields_Olinordered__field(X21639) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])]) ).
fof(i_0_7757,plain,
! [X21632,X21633,X21634,X21635] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21635),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21635),X21633),X21634)),X21632))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21635),X21633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21635),X21632),X21634)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21635),c_Groups_Ozero__class_Ozero(X21635)),X21634))
| ~ class_Fields_Olinordered__field(X21635) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21635),X21633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21635),X21632),X21634)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21635),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21635),X21633),X21634)),X21632))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21635),c_Groups_Ozero__class_Ozero(X21635)),X21634))
| ~ class_Fields_Olinordered__field(X21635) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq])])]) ).
fof(i_0_7758,plain,
! [X21624,X21625,X21626,X21627] :
( ~ class_Fields_Olinordered__field(X21627)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21627),c_Groups_Ozero__class_Ozero(X21627)),X21626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21627),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21627),X21625),X21626)),X21624))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21627),X21625),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21627),X21624),X21626))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos])]) ).
fof(i_0_7759,plain,
! [X31687,X31688,X31689] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31689),X31688))
| c_Smallcheck_Osmall_H(X31687,X31689,X31688) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31689),X31688))
| c_Smallcheck_Osmall_H(X31687,X31689,X31688) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X31687,X31689,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X31688),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X31687,X31688)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5618])]) ).
fof(i_0_7760,plain,
! [X26039,X26040,X26041,X26042] :
( ~ class_Groups_Ocomm__monoid__mult(X26042)
| ~ class_Rings_Oring__1(X26042)
| hAPP(c_Int_Oring__1__class_Oof__int(X26042),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26041,tc_Int_Oint),X26040),X26039)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26041,X26042),hAPP(hAPP(c_COMBB(tc_Int_Oint,X26042,X26041),c_Int_Oring__1__class_Oof__int(X26042)),X26040)),X26039) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setprod])]) ).
fof(i_0_7761,plain,
! [X26049,X26050,X26051,X26052] :
( ~ class_Groups_Ocomm__monoid__mult(X26052)
| ~ class_Rings_Osemiring__1(X26052)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26052),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26051,tc_Nat_Onat),X26050),X26049)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26051,X26052),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26052,X26051),c_Nat_Osemiring__1__class_Oof__nat(X26052)),X26050)),X26049) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setprod])]) ).
cnf(i_0_7762,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate(X1,X3),X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5550]) ).
cnf(i_0_7763,plain,
( X3 = c_List_Olist_ONil(X1)
| c_List_Oconcat(X1,X2) != c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5619]) ).
cnf(i_0_7764,plain,
( X3 = c_List_Olist_ONil(X1)
| c_List_Olist_ONil(X1) != c_List_Oconcat(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5620]) ).
fof(i_0_7765,plain,
! [X30358,X30359,X30360,X30361] : hAPP(c_Relation_Oconverse(X30361,X30360),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X30361,X30360),tc_HOL_Obool)),X30359),X30358)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X30360,X30361),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X30361,X30360),X30359)),hAPP(c_Relation_Oconverse(X30361,X30360),X30358)),
inference(variable_rename,[status(thm)],[fact_converse__Int]) ).
fof(i_0_7766,plain,
! [X30351,X30352,X30353,X30354] : hAPP(c_Relation_Oconverse(X30354,X30353),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30354,X30353),tc_HOL_Obool)),X30352),X30351)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30353,X30354),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X30354,X30353),X30352)),hAPP(c_Relation_Oconverse(X30354,X30353),X30351)),
inference(variable_rename,[status(thm)],[fact_converse__Un]) ).
fof(i_0_7767,plain,
! [X30518,X30519,X30520,X30521] : hAPP(hAPP(c_Nat_Ocompow(X30521,X30521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30520),X30519)),X30518) = hAPP(c_Fun_Ocomp(X30521,X30521,X30521,hAPP(hAPP(c_Nat_Ocompow(X30521,X30521),X30520),X30518)),hAPP(hAPP(c_Nat_Ocompow(X30521,X30521),X30519),X30518)),
inference(variable_rename,[status(thm)],[fact_funpow__add]) ).
fof(i_0_7768,plain,
! [X23235,X23236,X23237,X23238] :
( ~ class_Rings_Oring__1(X23238)
| hAPP(c_Int_Oring__1__class_Oof__int(X23238),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23237,tc_Int_Oint),X23236),X23235)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23237,X23238),hAPP(hAPP(c_COMBB(tc_Int_Oint,X23238,X23237),c_Int_Oring__1__class_Oof__int(X23238)),X23236)),X23235) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setsum])]) ).
fof(i_0_7769,plain,
! [X23218,X23219,X23220,X23221] :
( ~ class_Rings_Osemiring__1(X23221)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23221),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23220,tc_Nat_Onat),X23219),X23218)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23220,X23221),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X23221,X23220),c_Nat_Osemiring__1__class_Oof__nat(X23221)),X23219)),X23218) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setsum])]) ).
fof(i_0_7770,plain,
! [X28112] : c_Fun_Oinj__on(X28112,tc_fun(X28112,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28112,tc_fun(X28112,tc_HOL_Obool),tc_fun(X28112,tc_HOL_Obool)),c_Set_Oinsert(X28112)),c_Orderings_Obot__class_Obot(tc_fun(X28112,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X28112,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_inj__singleton]) ).
fof(i_0_7771,plain,
! [X22925,X22926,X22927,X22928,X22929] : hAPP(c_New__DSequence_Opos__bind(X22929,X22928,X22927,X22926),X22925) = c_Lazy__Sequence_Obind(X22929,X22928,hAPP(X22927,X22925),hAPP(hAPP(c_COMBC(X22929,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X22928)),X22926),X22925)),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__bind__def]) ).
fof(i_0_7772,plain,
! [X28701,X28702,X28703,X28704] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28704),X28703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28702),X28701))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28704,X28702)),hAPP(hAPP(c_Product__Type_OSigma(X28704,X28702),X28703),hAPP(c_COMBK(tc_fun(X28702,tc_HOL_Obool),X28704),X28701)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__product])]) ).
fof(i_0_7773,plain,
! [X24503,X24504,X24505] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24505),X24504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24505,tc_HOL_Obool)),X24503),X24504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24505),X24503)),hAPP(c_Finite__Set_Ocard(X24505),X24504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24505,tc_HOL_Obool)),X24503),X24504)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).
fof(i_0_7774,plain,
! [X24559,X24560,X24561,X24562,X24563] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24563),X24562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24561,tc_HOL_Obool)),X24560),hAPP(c_Set_Oimage(X24563,X24561,X24559),X24562)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24561),X24560)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).
cnf(i_0_7775,plain,
( c_List_Oupt(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X1,X2)),c_List_Oupt(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5621]) ).
fof(i_0_7776,plain,
! [X28004,X28005,X28006,X28007,X28008] :
( ~ c_Fun_Oinj__on(X28008,X28007,X28006,X28005)
| ~ c_Fun_Oinj__on(X28008,X28007,X28006,X28004)
| c_Fun_Oinj__on(X28008,X28007,X28006,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28008,tc_HOL_Obool)),X28005),X28004)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Int])]) ).
fof(i_0_7777,plain,
! [X33406,X33407,X33408,X33409] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33409),X33408)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33407)),X33406)))
| hAPP(hAPP(c_List_Onth(X33407),hAPP(hAPP(c_List_Odrop(X33407),X33409),X33406)),X33408) = hAPP(hAPP(c_List_Onth(X33407),X33406),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33409),X33408)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop])]) ).
fof(i_0_7778,plain,
! [X23506,X23507,X23508,X23509] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X23508)),X23507))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23509),X23506),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23507,hAPP(c_Nat_OSuc,X23508))) = c_Groups_Ozero__class_Ozero(X23509)
| ~ class_Groups_Ocomm__monoid__add(X23509) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X23508)),X23507))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23509),X23506),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23507,hAPP(c_Nat_OSuc,X23508))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23509),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23509),X23506),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23507,X23508))),hAPP(X23506,hAPP(c_Nat_OSuc,X23508)))
| ~ class_Groups_Ocomm__monoid__add(X23509) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5622])])]) ).
fof(i_0_7779,plain,
! [X34351,X34352,X34353,X34354] :
( ~ class_Orderings_Olinorder(X34354)
| ~ c_List_Olinorder__class_Osorted(X34354,hAPP(c_List_Orev(X34354),X34353))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34352),X34351))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34351),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34354)),X34353)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34354),hAPP(hAPP(c_List_Onth(X34354),X34353),X34351)),hAPP(hAPP(c_List_Onth(X34354),X34353),X34352))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__rev__nth__mono])]) ).
fof(i_0_7780,plain,
! [X32859,X32860,X32861,X32862,X32863,X32864] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32864)),X32863) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32862)),X32861)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32864)),X32860) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32862)),X32859)
| hAPP(hAPP(c_List_Ozip(X32864,X32862),hAPP(hAPP(c_List_Oappend(X32864),X32863),X32860)),hAPP(hAPP(c_List_Oappend(X32862),X32861),X32859)) = hAPP(hAPP(c_List_Oappend(tc_prod(X32864,X32862)),hAPP(hAPP(c_List_Ozip(X32864,X32862),X32863),X32861)),hAPP(hAPP(c_List_Ozip(X32864,X32862),X32860),X32859)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__append])]) ).
fof(i_0_7781,plain,
! [X33584,X33585,X33586,X33587,X33588] : c_List_Olist_Olist__size(X33588,X33587,hAPP(hAPP(c_List_Omap(X33586,X33588),X33585),X33584)) = c_List_Olist_Olist__size(X33586,hAPP(c_Fun_Ocomp(X33588,tc_Nat_Onat,X33586,X33587),X33585),X33584),
inference(variable_rename,[status(thm)],[fact_list__size__map]) ).
fof(i_0_7782,plain,
! [X28995,X28996,X28997,X28998] :
( ~ c_Relation_Orefl__on(X28998,X28997,X28996)
| ~ hBOOL(hAPP(hAPP(c_member(X28998),X28995),X28997))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X28998,X28998)),hAPP(hAPP(c_Product__Type_OPair(X28998,X28998),X28995),X28995)),X28996)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD])]) ).
fof(i_0_7783,plain,
! [X25308,X25309,X25310,X25311,X25312] :
( ~ hBOOL(hAPP(hAPP(c_member(X25312),X25311),X25310))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25309,tc_HOL_Obool)),hAPP(X25308,X25311)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25312,tc_fun(X25309,tc_HOL_Obool)),X25310),X25308))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__upper])]) ).
fof(i_0_7784,plain,
! [X33182,X33183,X33184,X33185] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33185) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X33184),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33185)),hAPP(hAPP(c_List_Olist_OCons(X33184),X33183),X33182)) = c_List_Olist_ONil(X33184) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33185) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X33184),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33185)),hAPP(hAPP(c_List_Olist_OCons(X33184),X33183),X33182)) = hAPP(hAPP(c_List_Olist_OCons(X33184),X33183),hAPP(hAPP(c_List_Otake(X33184),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33185)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33182)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons__number__of])]) ).
fof(i_0_7785,plain,
! [X17779,X17780,X17781,X17783,X17784,X17785,X17786] :
( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17780),X17779),esk13_3(X17779,X17780,X17781)))
| ~ hBOOL(hAPP(X17781,X17779))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17781,X17780)),X17779),X17779)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17781,X17780)),esk13_3(X17779,X17780,X17781)),X17779))
| ~ hBOOL(hAPP(X17781,X17779))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17781,X17780)),X17779),X17779)) )
& ( hBOOL(hAPP(X17785,X17783))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17785,X17784)),X17783),X17783)) )
& ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17784),X17783),X17786))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17785,X17784)),X17786),X17783))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17785,X17784)),X17783),X17783)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I7_J])])])])])]) ).
fof(i_0_7786,plain,
! [X22936,X22937,X22938,X22939,X22940,X22941] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22941,tc_fun(X22940,tc_HOL_Obool))),X22939),X22938))
| ~ hBOOL(hAPP(hAPP(X22939,X22937),X22936))
| hBOOL(hAPP(hAPP(X22938,X22937),X22936)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_7787,plain,
! [X22930,X22931,X22932,X22933,X22934,X22935] :
( ~ hBOOL(hAPP(hAPP(X22935,X22934),X22933))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22932,tc_fun(X22931,tc_HOL_Obool))),X22935),X22930))
| hBOOL(hAPP(hAPP(X22930,X22934),X22933)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_7788,plain,
! [X29082,X29083,X29084] :
( ~ class_Orderings_Olinorder(X29084)
| X29083 = c_Orderings_Obot__class_Obot(tc_fun(X29084,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29084,tc_HOL_Obool)),X29083),X29082))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29084),X29082))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29084),hAPP(c_Finite__Set_Ofold1(X29084,c_Orderings_Oord__class_Omin(X29084)),X29082)),hAPP(c_Finite__Set_Ofold1(X29084,c_Orderings_Oord__class_Omin(X29084)),X29083))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__antimono])]) ).
fof(i_0_7789,plain,
! [X25076,X25077,X25078,X25079] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25079),X25078),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25079,tc_HOL_Obool)),X25077),X25076)))
| hBOOL(hAPP(hAPP(c_member(X25079),X25078),X25077))
| hBOOL(hAPP(hAPP(c_member(X25079),X25078),X25076)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25079),X25078),X25077))
| hBOOL(hAPP(hAPP(c_member(X25079),X25078),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25079,tc_HOL_Obool)),X25077),X25076))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25079),X25078),X25076))
| hBOOL(hAPP(hAPP(c_member(X25079),X25078),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25079,tc_HOL_Obool)),X25077),X25076))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__iff])])]) ).
fof(i_0_7790,plain,
! [X24963,X24964,X24965,X24966] :
( ~ hBOOL(hAPP(hAPP(c_member(X24966),X24965),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24966,tc_HOL_Obool)),X24964),X24963)))
| hBOOL(hAPP(hAPP(c_member(X24966),X24965),X24964))
| hBOOL(hAPP(hAPP(c_member(X24966),X24965),X24963)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5623])]) ).
fof(i_0_7791,plain,
! [X21801,X21802,X21803] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21803),c_Groups_Ozero__class_Ozero(X21803)),esk78_3(X21801,X21802,X21803)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21803),X21802),X21801))
| ~ class_Fields_Olinordered__field(X21803) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21803),X21802),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21803),X21801),esk78_3(X21801,X21802,X21803))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21803),X21802),X21801))
| ~ class_Fields_Olinordered__field(X21803) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__le__epsilon])])])]) ).
fof(i_0_7792,plain,
! [X27154,X27155,X27156,X27157,X27158] : c_Map_Orestrict__map(X27158,X27157,c_Map_Orestrict__map(X27158,X27157,X27156,X27155),X27154) = c_Map_Orestrict__map(X27158,X27157,X27156,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27158,tc_HOL_Obool)),X27155),X27154)),
inference(variable_rename,[status(thm)],[fact_restrict__restrict]) ).
fof(i_0_7793,plain,
! [X33589,X33590,X33591,X33592,X33593,X33594] : hAPP(c_List_Ofoldl(X33594,X33593,X33592,X33591),hAPP(hAPP(c_List_Olist_OCons(X33593),X33590),X33589)) = hAPP(c_List_Ofoldl(X33594,X33593,X33592,hAPP(hAPP(X33592,X33591),X33590)),X33589),
inference(variable_rename,[status(thm)],[fact_foldl__Cons]) ).
fof(i_0_7794,plain,
! [X34362,X34363] :
( ( X34362 != c_List_Olist_ONil(tc_List_Olist(X34363))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34363))),c_List_Otranspose(X34363,X34362)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34363),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34363))),X34362))) )
& ( X34362 = c_List_Olist_ONil(tc_List_Olist(X34363))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34363))),c_List_Otranspose(X34363,X34362)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34363)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34363)),X34362),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34363),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34363))),X34362))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__transpose__sorted])])]) ).
fof(i_0_7795,plain,
! [X20827,X20828,X20829,X20830] :
( ~ class_Rings_Olinordered__semidom(X20830)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20830),X20829),X20828))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20830),c_Groups_Ozero__class_Ozero(X20830)),X20829))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20827))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20830),hAPP(hAPP(c_Power_Opower__class_Opower(X20830),X20829),X20827)),hAPP(hAPP(c_Power_Opower__class_Opower(X20830),X20828),X20827))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).
fof(i_0_7796,plain,
! [X20842,X20843,X20844,X20845] :
( ~ class_Rings_Olinordered__semidom(X20845)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20844),X20843))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20845),c_Groups_Ozero__class_Ozero(X20845)),X20842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20845),X20842),c_Groups_Oone__class_Oone(X20845)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20845),hAPP(hAPP(c_Power_Opower__class_Opower(X20845),X20842),X20843)),hAPP(hAPP(c_Power_Opower__class_Opower(X20845),X20842),X20844))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).
fof(i_0_7797,plain,
! [X20846,X20847,X20848,X20849] :
( ~ class_Rings_Olinordered__semidom(X20849)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20848),X20847))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20849),c_Groups_Ozero__class_Ozero(X20849)),X20846))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20849),X20846),c_Groups_Oone__class_Oone(X20849)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20849),hAPP(hAPP(c_Power_Opower__class_Opower(X20849),X20846),X20847)),hAPP(hAPP(c_Power_Opower__class_Opower(X20849),X20846),X20848))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).
fof(i_0_7798,plain,
! [X28346,X28347,X28348,X28349,X28350] : hAPP(c_Set_Ovimage(X28350,X28349,X28348),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28349,tc_HOL_Obool)),X28347),X28346)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28350,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28350,X28349,X28348),X28347)),hAPP(c_Set_Ovimage(X28350,X28349,X28348),X28346)),
inference(variable_rename,[status(thm)],[fact_vimage__Int]) ).
fof(i_0_7799,plain,
! [X28312,X28313,X28314,X28315,X28316] : hAPP(c_Set_Ovimage(X28316,X28315,X28314),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28315,tc_HOL_Obool)),X28313),X28312)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28316,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28316,X28315,X28314),X28313)),hAPP(c_Set_Ovimage(X28316,X28315,X28314),X28312)),
inference(variable_rename,[status(thm)],[fact_vimage__Un]) ).
fof(i_0_7800,plain,
! [X28279,X28280,X28281,X28282,X28283] : hAPP(c_Set_Ovimage(X28283,X28282,X28281),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28282,tc_HOL_Obool)),X28280),X28279)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28283,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28283,X28282,X28281),X28280)),hAPP(c_Set_Ovimage(X28283,X28282,X28281),X28279)),
inference(variable_rename,[status(thm)],[fact_vimage__Diff]) ).
fof(i_0_7801,plain,
! [X26589,X26590,X26591,X26592,X26593] : hAPP(c_Relation_OImage(X26593,X26592,X26591),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26593,tc_HOL_Obool)),X26590),X26589)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26592,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26593,X26592,X26591),X26590)),hAPP(c_Relation_OImage(X26593,X26592,X26591),X26589)),
inference(variable_rename,[status(thm)],[fact_Image__Un]) ).
fof(i_0_7802,plain,
! [X23849,X23850,X23851,X23852,X23853] : hAPP(c_Set_Oimage(X23853,X23852,X23851),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23853,tc_HOL_Obool)),X23850),X23849)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23852,tc_HOL_Obool)),hAPP(c_Set_Oimage(X23853,X23852,X23851),X23850)),hAPP(c_Set_Oimage(X23853,X23852,X23851),X23849)),
inference(variable_rename,[status(thm)],[fact_image__Un]) ).
fof(i_0_7803,plain,
! [X33684,X33685,X33686,X33687] :
( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33687)),X33686),c_List_Olists(X33687,X33684)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33687)),hAPP(hAPP(c_List_Oappend(X33687),X33686),X33685)),c_List_Olists(X33687,X33684))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33687)),X33685),c_List_Olists(X33687,X33684)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33687)),hAPP(hAPP(c_List_Oappend(X33687),X33686),X33685)),c_List_Olists(X33687,X33684))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33687)),X33686),c_List_Olists(X33687,X33684)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33687)),X33685),c_List_Olists(X33687,X33684)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33687)),hAPP(hAPP(c_List_Oappend(X33687),X33686),X33685)),c_List_Olists(X33687,X33684))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])]) ).
fof(i_0_7804,plain,
! [X26569,X26570,X26571] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26571,tc_HOL_Obool)),X26570),X26569))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X26571,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X26571,X26570)),c_Predicate_OPowp(X26571,X26569))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__mono])]) ).
fof(i_0_7805,plain,
! [X31655,X31656,X31657,X31658] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31658,tc_HOL_Obool)),c_Map_Odom(X31658,X31657,X31656)),c_Map_Odom(X31658,X31657,X31655)) != c_Orderings_Obot__class_Obot(tc_fun(X31658,tc_HOL_Obool))
| c_Map_Omap__add(X31658,X31657,X31656,X31655) = c_Map_Omap__add(X31658,X31657,X31655,X31656) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__comm])]) ).
fof(i_0_7806,plain,
! [X24714,X24715,X24716,X24717] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24717),X24716))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24715),X24714))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24717,X24715)),c_Sum__Type_OPlus(X24717,X24715,X24716,X24714))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).
fof(i_0_7807,plain,
! [X26857,X26858,X26859,X26860,X26861,X26862] :
( ~ c_Finite__Set_Ofolding(X26862,X26861,X26860,X26859)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26862),X26858))
| hBOOL(hAPP(hAPP(c_member(X26862),X26857),X26858))
| hAPP(X26859,hAPP(hAPP(c_Set_Oinsert(X26862),X26857),X26858)) = hAPP(c_Fun_Ocomp(X26861,X26861,X26861,hAPP(X26859,X26858)),hAPP(X26860,X26857)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5624])]) ).
fof(i_0_7808,plain,
! [X26437,X26438,X26439,X26440] :
( X26440 != X26439
| ~ hBOOL(hAPP(hAPP(c_member(X26438),X26440),X26437))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26438,X26438)),hAPP(hAPP(c_Product__Type_OPair(X26438,X26438),X26440),X26439)),c_Relation_OId__on(X26438,X26437))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__eqI])]) ).
fof(i_0_7809,plain,
! [X29111,X29112] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X29112),c_Int_OInteg))
| ~ hBOOL(hAPP(X29111,hAPP(c_Int_ORep__Integ,esk308_2(X29111,X29112))))
| hBOOL(hAPP(X29111,X29112)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct])])]) ).
fof(i_0_7810,plain,
! [X32865,X32866,X32867,X32868,X32869] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32869),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32868)),X32867)))
| hAPP(hAPP(c_List_Olist__update(X32868,hAPP(hAPP(c_List_Oappend(X32868),X32867),X32866)),X32869),X32865) = hAPP(hAPP(c_List_Oappend(X32868),hAPP(hAPP(c_List_Olist__update(X32868,X32867),X32869),X32865)),X32866) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__append1])]) ).
fof(i_0_7811,plain,
! [X23448,X23449,X23450] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23450),X23449)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23450),X23448)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23449),X23448))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23450)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23449),X23448))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23450),X23449)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23450),X23448)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23450)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel1])])]) ).
fof(i_0_7812,plain,
! [X23445,X23446,X23447] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23447),X23446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23447),X23445)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23447))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23446),X23445)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel])]) ).
fof(i_0_7813,plain,
! [X19111,X19112,X19113] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19113),X19112)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19111),X19112)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19112))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19113),X19111)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19112))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19113),X19112)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19111),X19112))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19113),X19111))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19113),X19112)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19111),X19112))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).
fof(i_0_7814,plain,
! [X23031,X23032,X23033] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X23033),X23032)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X23033),X23031)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X23033))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23032),X23031)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le])]) ).
fof(i_0_7815,plain,
! [X19701,X19702,X19703] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19703),X19702)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19703),X19701)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19702),X19701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19703)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19702),X19701))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19703),X19702)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19703),X19701)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19703)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).
fof(i_0_7816,plain,
! [X19108,X19109,X19110] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19110),X19109)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19110),X19108)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19110))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19109),X19108)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19110))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19110),X19109)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19110),X19108))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19109),X19108))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19110),X19109)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19110),X19108))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).
fof(i_0_7817,plain,
! [X20866,X20867,X20868] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20868),X20867)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20868),X20866)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20867),X20866)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).
fof(i_0_7818,plain,
! [X19728,X19729,X19730] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19730),X19729)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19730),X19728)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19729),X19728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19730)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19729),X19728))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19730),X19729)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19730),X19728)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19730)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).
fof(i_0_7819,plain,
! [X29667,X29668,X29669] :
( ~ c_Wellfounded_Owf(X29669,X29668)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29669,tc_HOL_Obool)),X29667),hAPP(c_Relation_OImage(X29669,X29669,X29668),X29667)))
| X29667 = c_Orderings_Obot__class_Obot(tc_fun(X29669,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfE__pf])]) ).
fof(i_0_7820,plain,
! [X26046,X26047,X26048] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26048,tc_Nat_Onat),X26047),X26046)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26048,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X26048),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X26047)),X26046),
inference(variable_rename,[status(thm)],[fact_int__setprod]) ).
fof(i_0_7821,plain,
! [X23491,X23492,X23493] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23493,tc_Nat_Onat),X23492),X23491)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23493,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X23493),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23492)),X23491),
inference(variable_rename,[status(thm)],[fact_int__setsum]) ).
fof(i_0_7822,plain,
! [X29330,X29331,X29332,X29333] : c_Fun_Ooverride__on(X29333,X29332,X29331,X29330,c_Orderings_Obot__class_Obot(tc_fun(X29333,tc_HOL_Obool))) = X29331,
inference(variable_rename,[status(thm)],[fact_override__on__emptyset]) ).
fof(i_0_7823,plain,
! [X30811,X30812,X30813,X30814,X30815] :
( ~ c_Finite__Set_Ofun__left__comm(X30815,X30814,X30813)
| hAPP(c_Fun_Ocomp(X30814,X30814,X30814,hAPP(X30813,X30812)),hAPP(X30813,X30811)) = hAPP(c_Fun_Ocomp(X30814,X30814,X30814,hAPP(X30813,X30811)),hAPP(X30813,X30812)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm])]) ).
fof(i_0_7824,plain,
! [X25686,X25687,X25688] : c_Hoare__Mirabelle_Ohoare__derivs(X25688,X25687,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25688)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25688),X25686),c_Com_Ocom_OSKIP),X25686)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25688),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I7_J]) ).
fof(i_0_7825,plain,
! [X25683,X25684,X25685] : c_Hoare__Mirabelle_Ohoare__derivs(X25685,X25684,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25685)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25685),X25683),c_Com_Ocom_OSKIP),X25683)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25685),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_hoare__derivs_OSkip]) ).
fof(i_0_7826,plain,
! [X18128,X18129,X18130,X18131,X18132] : c_Option_Ooption_Ooption__rec(X18132,X18131,X18130,X18129,hAPP(c_Option_Ooption_OSome(X18131),X18128)) = hAPP(X18129,X18128),
inference(variable_rename,[status(thm)],[fact_option_Orecs_I2_J]) ).
fof(i_0_7827,plain,
! [X32820,X32821,X32822,X32823] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32823),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32822)),X32821)))
| hBOOL(hAPP(hAPP(c_member(X32822),X32820),hAPP(c_List_Oset(X32822),hAPP(hAPP(c_List_Olist__update(X32822,X32821),X32823),X32820)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__memI])]) ).
fof(i_0_7828,plain,
! [X24988,X24989,X24990,X24991,X24992,X24993] :
( ~ hBOOL(hAPP(hAPP(c_member(X24993),X24992),X24991))
| ~ hBOOL(hAPP(hAPP(c_member(X24990),X24989),hAPP(X24988,X24992)))
| hBOOL(hAPP(hAPP(c_member(X24990),X24989),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24993,tc_fun(X24990,tc_HOL_Obool)),X24991),X24988))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__I])]) ).
fof(i_0_7829,plain,
! [X22177,X22178,X22179,X22180,X22181,X22182] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22182,X22181),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22180),X22179)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22182,X22181),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22178),X22177)))
| X22181 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X22180 = X22178 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient])]) ).
fof(i_0_7830,plain,
! [X22183,X22184,X22185,X22186,X22187,X22188] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22188,X22187),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22186),X22185)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22188,X22187),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22184),X22183)))
| X22187 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X22185 = X22183 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__remainder])]) ).
fof(i_0_7831,plain,
! [X27929,X27930,X27931,X27932] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27932),hAPP(c_Set_Oimage(X27931,X27932,X27930),X27929)))
| ~ c_Fun_Oinj__on(X27931,X27932,X27930,X27929)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X27931),X27929)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
fof(i_0_7832,plain,
! [X23300,X23301,X23302,X23303] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23303),X23302),X23301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23303),X23302),X23300)))
| X23302 = c_Groups_Ozero__class_Ozero(X23303)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23303),X23301),X23300))
| ~ class_Rings_Oidom(X23303) )
& ( X23302 != c_Groups_Ozero__class_Ozero(X23303)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23303),X23302),X23301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23303),X23302),X23300)))
| ~ class_Rings_Oidom(X23303) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23303),X23301),X23300))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23303),X23302),X23301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23303),X23302),X23300)))
| ~ class_Rings_Oidom(X23303) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left])])]) ).
fof(i_0_7833,plain,
! [X23304,X23305,X23306,X23307] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23307),X23306),X23305)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23307),X23304),X23305)))
| X23305 = c_Groups_Ozero__class_Ozero(X23307)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23307),X23306),X23304))
| ~ class_Rings_Oidom(X23307) )
& ( X23305 != c_Groups_Ozero__class_Ozero(X23307)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23307),X23306),X23305)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23307),X23304),X23305)))
| ~ class_Rings_Oidom(X23307) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23307),X23306),X23304))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23307),X23306),X23305)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23307),X23304),X23305)))
| ~ class_Rings_Oidom(X23307) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right])])]) ).
fof(i_0_7834,plain,
! [X30579,X30580,X30581,X30582] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30582,X30581),tc_HOL_Obool)),X30580),X30579))
| ~ c_Relation_Osingle__valued(X30582,X30581,X30579)
| c_Relation_Osingle__valued(X30582,X30581,X30580) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])]) ).
cnf(i_0_7835,plain,
c_Int_Osucc(c_Int_OBit1(X1)) = c_Int_OBit0(c_Int_Osucc(X1)),
inference(split_conjunct,[status(thm)],[i_0_5625]) ).
fof(i_0_7836,plain,
! [X19208,X19209,X19210,X19211] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19211),X19210),X19209)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19211),X19208),X19209)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19211),X19210),X19208))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19211) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19211),X19210),X19208))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19211),X19210),X19209)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19211),X19208),X19209)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19211) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_7837,plain,
! [X19187,X19188,X19189,X19190] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19190)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19190),X19189),X19188)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19190),X19187),X19188)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19190),X19189),X19187)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_7838,plain,
! [X19204,X19205,X19206,X19207] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19207),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19207),X19206),X19205)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19207),X19206),X19204)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19207),X19205),X19204))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19207) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19207),X19205),X19204))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19207),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19207),X19206),X19205)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19207),X19206),X19204)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19207) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_7839,plain,
! [X19183,X19184,X19185,X19186] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19186)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19186),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19186),X19185),X19184)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19186),X19185),X19183)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19186),X19184),X19183)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_7840,plain,
! [X18257,X18258,X18259,X18260] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18260)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18260),X18259),X18258)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18260),X18257),X18258)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),X18259),X18257)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_7841,plain,
! [X18236,X18237,X18238,X18239] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18239),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18239),X18238),X18237)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18239),X18236),X18237)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18239),X18238),X18236))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18239) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18239),X18238),X18236))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18239),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18239),X18238),X18237)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18239),X18236),X18237)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18239) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_7842,plain,
! [X18261,X18262,X18263,X18264] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18264)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18264),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18264),X18263),X18262)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18264),X18263),X18261)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18264),X18262),X18261)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_7843,plain,
! [X18240,X18241,X18242,X18243] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18243),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18243),X18242),X18241)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18243),X18242),X18240)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18243),X18241),X18240))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18243) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18243),X18241),X18240))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18243),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18243),X18242),X18241)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18243),X18242),X18240)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18243) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_7844,plain,
! [X17759,X17760,X17761,X17762,X17764,X17765,X17766,X17767,X17768] :
( ( c_Natural_Oevaln(X17761,X17760,X17759,esk11_4(X17759,X17760,X17761,X17762))
| ~ hBOOL(hAPP(X17762,X17760))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17762,X17761),X17760,X17759,X17760) )
& ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X17762,X17761),esk11_4(X17759,X17760,X17761,X17762),X17759,X17760)
| ~ hBOOL(hAPP(X17762,X17760))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17762,X17761),X17760,X17759,X17760) )
& ( hBOOL(hAPP(X17767,X17765))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17767,X17766),X17765,X17764,X17765) )
& ( ~ c_Natural_Oevaln(X17766,X17765,X17764,X17768)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17767,X17766),X17768,X17764,X17765)
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17767,X17766),X17765,X17764,X17765) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I7_J])])])])])]) ).
fof(i_0_7845,plain,
! [X17964,X17965,X17966,X17967] :
( ( X17965 = hAPP(c_Nat_OSuc,esk21_4(X17964,X17965,X17966,X17967))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17967),X17966,X17965,X17964) )
& ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17967)),X17966,esk21_4(X17964,X17965,X17966,X17967),X17964)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17967),X17966,X17965,X17964) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5626])])])]) ).
fof(i_0_7846,plain,
! [X34189,X34190,X34191,X34192] :
( ~ class_Orderings_Olinorder(X34192)
| ~ c_List_Olinorder__class_Osorted(X34192,X34191)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34190),X34189))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34189),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34192)),X34191)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34192),hAPP(hAPP(c_List_Onth(X34192),X34191),X34190)),hAPP(hAPP(c_List_Onth(X34192),X34191),X34189))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__nth__mono])]) ).
fof(i_0_7847,plain,
! [X30467,X30468,X30469] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30469,X30469),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30468)),X30467) = hAPP(hAPP(c_Relation_Orel__comp(X30469,X30469,X30469),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30469,X30469),tc_HOL_Obool),X30468),X30467)),X30467),
inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I2_J]) ).
fof(i_0_7848,plain,
! [X21679,X21680,X21681,X21682] :
( ~ class_Fields_Ofield(X21682)
| X21681 = c_Groups_Ozero__class_Ozero(X21682)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21682),X21680),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21682),X21679),X21681)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21682),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21682),X21681),X21680)),X21679)),X21681) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff])]) ).
fof(i_0_7849,plain,
! [X21662,X21663,X21664,X21665] :
( ~ class_Fields_Ofield(X21665)
| X21664 = c_Groups_Ozero__class_Ozero(X21665)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21665),X21663),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21665),X21662),X21664)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21665),X21664),X21663)),X21662)),X21664) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])]) ).
fof(i_0_7850,plain,
! [X34141,X34142,X34143,X34144,X34145,X34146] :
( ~ class_Orderings_Olinorder(X34146)
| ~ c_List_Olinorder__class_Osorted(X34146,hAPP(hAPP(c_List_Omap(X34145,X34146),X34144),X34143))
| ~ hBOOL(hAPP(X34142,X34141))
| hAPP(c_List_Ofilter(X34145,X34142),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34145,X34146,X34144),X34141),X34143)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34145,X34146,X34144),X34141),hAPP(c_List_Ofilter(X34145,X34142),X34143)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__insort])]) ).
cnf(i_0_7851,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X3))) = hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5627]) ).
cnf(i_0_7852,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = c_Groups_Oone__class_Oone(X2)
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5405]) ).
fof(i_0_7853,plain,
! [X24734,X24735,X24736] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24736,tc_HOL_Obool)),X24735),hAPP(hAPP(c_Set_Oinsert(X24736),X24734),c_Orderings_Obot__class_Obot(tc_fun(X24736,tc_HOL_Obool)))))
| X24735 = c_Orderings_Obot__class_Obot(tc_fun(X24736,tc_HOL_Obool))
| X24735 = hAPP(hAPP(c_Set_Oinsert(X24736),X24734),c_Orderings_Obot__class_Obot(tc_fun(X24736,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__singletonD])]) ).
fof(i_0_7854,plain,
! [X25072,X25073,X25074,X25075] :
( ( hBOOL(hAPP(hAPP(c_member(X25075),X25074),X25073))
| ~ hBOOL(hAPP(hAPP(c_member(X25075),X25074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25075,tc_HOL_Obool)),X25073),X25072))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25075),X25074),X25072))
| ~ hBOOL(hAPP(hAPP(c_member(X25075),X25074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25075,tc_HOL_Obool)),X25073),X25072))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25075),X25074),X25073))
| hBOOL(hAPP(hAPP(c_member(X25075),X25074),X25072))
| hBOOL(hAPP(hAPP(c_member(X25075),X25074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25075,tc_HOL_Obool)),X25073),X25072))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5628])])]) ).
fof(i_0_7855,plain,
! [X24971,X24972,X24973,X24974] :
( ( hBOOL(hAPP(hAPP(c_member(X24974),X24973),X24972))
| ~ hBOOL(hAPP(hAPP(c_member(X24974),X24973),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24974,tc_HOL_Obool)),X24972),X24971))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24974),X24973),X24971))
| ~ hBOOL(hAPP(hAPP(c_member(X24974),X24973),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24974,tc_HOL_Obool)),X24972),X24971))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffE])])]) ).
fof(i_0_7856,plain,
! [X25064,X25065,X25066,X25067] :
( ~ hBOOL(hAPP(hAPP(c_member(X25067),X25066),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25067,tc_HOL_Obool)),X25065),X25064)))
| ~ hBOOL(hAPP(hAPP(c_member(X25067),X25066),X25064)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5629])]) ).
fof(i_0_7857,plain,
! [X25620,X25621,X25622,X25625,X25626,X25627,X25628,X25629] :
( ( X25621 = hAPP(hAPP(c_Set_Oinsert(X25622),esk190_3(X25620,X25621,X25622)),esk191_3(X25620,X25621,X25622))
| hAPP(c_Finite__Set_Ocard(X25622),X25621) != hAPP(c_Nat_OSuc,X25620) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25622),esk190_3(X25620,X25621,X25622)),esk191_3(X25620,X25621,X25622)))
| hAPP(c_Finite__Set_Ocard(X25622),X25621) != hAPP(c_Nat_OSuc,X25620) )
& ( hAPP(c_Finite__Set_Ocard(X25622),esk191_3(X25620,X25621,X25622)) = X25620
| hAPP(c_Finite__Set_Ocard(X25622),X25621) != hAPP(c_Nat_OSuc,X25620) )
& ( X25620 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| esk191_3(X25620,X25621,X25622) = c_Orderings_Obot__class_Obot(tc_fun(X25622,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(X25622),X25621) != hAPP(c_Nat_OSuc,X25620) )
& ( X25625 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X25626 != hAPP(hAPP(c_Set_Oinsert(X25627),X25628),X25629)
| hBOOL(hAPP(hAPP(c_member(X25627),X25628),X25629))
| hAPP(c_Finite__Set_Ocard(X25627),X25629) != X25625
| hAPP(c_Finite__Set_Ocard(X25627),X25626) = hAPP(c_Nat_OSuc,X25625) )
& ( X25629 != c_Orderings_Obot__class_Obot(tc_fun(X25627,tc_HOL_Obool))
| X25626 != hAPP(hAPP(c_Set_Oinsert(X25627),X25628),X25629)
| hBOOL(hAPP(hAPP(c_member(X25627),X25628),X25629))
| hAPP(c_Finite__Set_Ocard(X25627),X25629) != X25625
| hAPP(c_Finite__Set_Ocard(X25627),X25626) = hAPP(c_Nat_OSuc,X25625) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5630])])])])])]) ).
fof(i_0_7858,plain,
! [X27848,X27849,X27850,X27851,X27852,X27853] :
( ~ c_Finite__Set_Ofolding__idem(X27853,X27852,X27851,X27850)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27853),X27849))
| ~ hBOOL(hAPP(hAPP(c_member(X27853),X27848),X27849))
| hAPP(c_Fun_Ocomp(X27852,X27852,X27852,hAPP(X27850,X27849)),hAPP(X27851,X27848)) = hAPP(X27850,X27849) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oin__comp__idem])]) ).
fof(i_0_7859,plain,
! [X33192,X33193,X33194] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33194),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33193)),X33192)))
| hAPP(hAPP(c_List_Otake(X33193),hAPP(c_Nat_OSuc,X33194)),X33192) = hAPP(hAPP(c_List_Oappend(X33193),hAPP(hAPP(c_List_Otake(X33193),X33194),X33192)),hAPP(hAPP(c_List_Olist_OCons(X33193),hAPP(hAPP(c_List_Onth(X33193),X33192),X33194)),c_List_Olist_ONil(X33193))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc__conv__app__nth])]) ).
fof(i_0_7860,plain,
! [X27623,X27624,X27625] :
( ~ class_Orderings_Olinorder(X27625)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27625),X27624))
| X27624 = c_Orderings_Obot__class_Obot(tc_fun(X27625,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27625),X27623))
| X27623 = c_Orderings_Obot__class_Obot(tc_fun(X27625,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27625,tc_HOL_Obool)),X27624),X27623) != c_Orderings_Obot__class_Obot(tc_fun(X27625,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X27625,c_Orderings_Oord__class_Omin(X27625),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27625,tc_HOL_Obool)),X27624),X27623)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27625),c_Big__Operators_Olattice_OInf__fin(X27625,c_Orderings_Oord__class_Omin(X27625),X27624)),c_Big__Operators_Olattice_OInf__fin(X27625,c_Orderings_Oord__class_Omin(X27625),X27623)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint])]) ).
fof(i_0_7861,plain,
! [X27626,X27627,X27628] :
( ~ class_Orderings_Olinorder(X27628)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27628),X27627))
| X27627 = c_Orderings_Obot__class_Obot(tc_fun(X27628,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27628),X27626))
| X27626 = c_Orderings_Obot__class_Obot(tc_fun(X27628,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27628,tc_HOL_Obool)),X27627),X27626) != c_Orderings_Obot__class_Obot(tc_fun(X27628,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X27628,c_Orderings_Oord__class_Omax(X27628),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27628,tc_HOL_Obool)),X27627),X27626)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27628),c_Big__Operators_Olattice_OSup__fin(X27628,c_Orderings_Oord__class_Omax(X27628),X27627)),c_Big__Operators_Olattice_OSup__fin(X27628,c_Orderings_Oord__class_Omax(X27628),X27626)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint])]) ).
fof(i_0_7862,plain,
! [X30487,X30488,X30489,X30490] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X30490,X30489),tc_fun(X30490,X30489)),X30488),c_Fun_Ocomp(X30489,X30489,X30490,X30487)) = c_Fun_Ocomp(X30489,X30489,X30490,hAPP(hAPP(c_Nat_Ocompow(X30489,X30489),X30488),X30487)),
inference(variable_rename,[status(thm)],[fact_comp__funpow]) ).
fof(i_0_7863,plain,
! [X23017,X23018,X23019,X23020,X23021,X23022] : hAPP(hAPP(c_Product__Type_Ocurry(X23022,X23021,X23020,X23019),X23018),X23017) = hAPP(X23019,hAPP(hAPP(c_Product__Type_OPair(X23022,X23021),X23018),X23017)),
inference(variable_rename,[status(thm)],[fact_curry__conv]) ).
fof(i_0_7864,plain,
! [X22996,X22997,X22998,X22999,X23000,X23001] : hAPP(hAPP(c_Product__Type_Ocurry(X23001,X23000,X22999,X22998),X22997),X22996) = hAPP(X22998,hAPP(hAPP(c_Product__Type_OPair(X23001,X23000),X22997),X22996)),
inference(variable_rename,[status(thm)],[fact_curry__def]) ).
fof(i_0_7865,plain,
! [X27906,X27907,X27908,X27909,X27910] :
( ( hAPP(c_Set_Oimage(X27910,X27909,X27908),X27907) != hAPP(c_Set_Oimage(X27910,X27909,X27908),X27906)
| X27907 = X27906
| ~ c_Fun_Oinj__on(X27910,X27909,X27908,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27910,tc_HOL_Obool)),X27907),X27906)) )
& ( X27907 != X27906
| hAPP(c_Set_Oimage(X27910,X27909,X27908),X27907) = hAPP(c_Set_Oimage(X27910,X27909,X27908),X27906)
| ~ c_Fun_Oinj__on(X27910,X27909,X27908,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27910,tc_HOL_Obool)),X27907),X27906)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff])])]) ).
fof(i_0_7866,plain,
! [X21732,X21733,X21734,X21735] :
( ~ class_Fields_Olinordered__field(X21735)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21735),c_Groups_Ozero__class_Ozero(X21735)),X21734))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21735),X21733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21735),X21732),X21734)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21735),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21735),X21733),X21734)),X21732)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le])]) ).
fof(i_0_7867,plain,
! [X21628,X21629,X21630,X21631] :
( ~ class_Fields_Olinordered__field(X21631)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21631),c_Groups_Ozero__class_Ozero(X21631)),X21630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21631),X21629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21631),X21628),X21630)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21631),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21631),X21629),X21630)),X21628)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less])]) ).
fof(i_0_7868,plain,
! [X28990,X28991,X28992,X28993,X28994] :
( ~ c_Relation_Orefl__on(X28994,X28993,X28992)
| ~ c_Relation_Orefl__on(X28994,X28991,X28990)
| c_Relation_Orefl__on(X28994,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28994,tc_HOL_Obool)),X28993),X28991),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28994,X28994),tc_HOL_Obool)),X28992),X28990)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Int])]) ).
fof(i_0_7869,plain,
! [X28985,X28986,X28987,X28988,X28989] :
( ~ c_Relation_Orefl__on(X28989,X28988,X28987)
| ~ c_Relation_Orefl__on(X28989,X28986,X28985)
| c_Relation_Orefl__on(X28989,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28989,tc_HOL_Obool)),X28988),X28986),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28989,X28989),tc_HOL_Obool)),X28987),X28985)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Un])]) ).
fof(i_0_7870,plain,
! [X33066,X33067,X33068,X33069] : c_Map_Omap__upds(X33069,X33068,X33067,c_List_Olist_ONil(X33069),X33066) = X33067,
inference(variable_rename,[status(thm)],[fact_map__upds__Nil1]) ).
fof(i_0_7871,plain,
! [X33070,X33071,X33072,X33073] : c_Map_Omap__upds(X33073,X33072,X33071,X33070,c_List_Olist_ONil(X33072)) = X33071,
inference(variable_rename,[status(thm)],[fact_map__upds__Nil2]) ).
fof(i_0_7872,plain,
! [X18137,X18138,X18139,X18140] : c_Option_Ooption_Ooption__rec(X18140,X18139,X18138,X18137,c_Option_Ooption_ONone(X18139)) = X18138,
inference(variable_rename,[status(thm)],[fact_option_Orecs_I1_J]) ).
fof(i_0_7873,plain,
! [X29831,X29832,X29833,X29834,X29835] : hAPP(c_Relation_ODomain(X29835,X29834),hAPP(hAPP(c_Set_Oinsert(tc_prod(X29835,X29834)),hAPP(hAPP(c_Product__Type_OPair(X29835,X29834),X29833),X29832)),X29831)) = hAPP(hAPP(c_Set_Oinsert(X29835),X29833),hAPP(c_Relation_ODomain(X29835,X29834),X29831)),
inference(variable_rename,[status(thm)],[fact_Domain__insert]) ).
fof(i_0_7874,plain,
! [X29740,X29741,X29742,X29743,X29744] : hAPP(c_Relation_ORange(X29744,X29743),hAPP(hAPP(c_Set_Oinsert(tc_prod(X29744,X29743)),hAPP(hAPP(c_Product__Type_OPair(X29744,X29743),X29742),X29741)),X29740)) = hAPP(hAPP(c_Set_Oinsert(X29743),X29741),hAPP(c_Relation_ORange(X29744,X29743),X29740)),
inference(variable_rename,[status(thm)],[fact_Range__insert]) ).
fof(i_0_7875,plain,
! [X22452,X22453,X22454,X22455] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22455,tc_HOL_Obool)),X22454),X22453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22455,tc_HOL_Obool)),X22453),X22452))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22455,tc_HOL_Obool)),X22454),X22452)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_7876,plain,
! [X22468,X22469,X22470,X22471] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22471,tc_HOL_Obool)),X22470),X22469))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22471,tc_HOL_Obool)),X22469),X22468))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22471,tc_HOL_Obool)),X22470),X22468)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_7877,plain,
! [X22472,X22473,X22474,X22475] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22475,tc_HOL_Obool)),X22474),X22473))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22475,tc_HOL_Obool)),X22473),X22472))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22475,tc_HOL_Obool)),X22474),X22472)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_7878,plain,
! [X22520,X22521,X22522,X22523] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22523,tc_HOL_Obool)),X22522),X22521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22523,tc_HOL_Obool)),X22521),X22520))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22523,tc_HOL_Obool)),X22522),X22520)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).
fof(i_0_7879,plain,
! [X25062,X25063] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25063),X25062))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25063)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25062))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25063)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25062)))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25063),X25062)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J])]) ).
fof(i_0_7880,plain,
! [X22817,X22818,X22819,X22820,X22821] : hAPP(hAPP(c_Product__Type_Oscomp(X22821,X22820,X22821,X22819),hAPP(c_Product__Type_OPair(X22820,X22821),X22818)),X22817) = hAPP(X22817,X22818),
inference(variable_rename,[status(thm)],[fact_Pair__scomp]) ).
cnf(i_0_7881,plain,
( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X2),c_List_Oupt(X1,X3)) = c_List_Oupt(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_5631]) ).
fof(i_0_7882,plain,
! [X20149,X20150,X20151] :
( ~ class_Divides_Osemiring__div(X20151)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20151),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20151),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20151),X20150),X20149)),X20149)),c_Divides_Odiv__class_Omod(X20151,X20150,X20149)) = X20150 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality])]) ).
fof(i_0_7883,plain,
! [X20201,X20202,X20203] :
( ~ class_Divides_Osemiring__div(X20203)
| X20202 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20203),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20203),X20202),X20201)),X20201)),c_Divides_Odiv__class_Omod(X20203,X20202,X20201)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__decomp])]) ).
cnf(i_0_7884,plain,
hAPP(c_List_Orotate(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(c_List_Orotate(X3,X2),X5)),
inference(split_conjunct,[status(thm)],[i_0_5632]) ).
cnf(i_0_7885,plain,
c_Transitive__Closure_Otrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) = hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_5633]) ).
fof(i_0_7886,plain,
! [X17718,X17719,X17720] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17720)),X17719),X17718))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17720))),X17719),X17718)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I6_J])]) ).
fof(i_0_7887,plain,
! [X24807,X24808] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24808,tc_fun(X24808,tc_HOL_Obool)),X24807),hAPP(hAPP(c_COMBC(X24808,tc_fun(X24808,tc_HOL_Obool),tc_fun(X24808,tc_HOL_Obool)),c_Set_Oinsert(X24808)),c_Orderings_Obot__class_Obot(tc_fun(X24808,tc_HOL_Obool)))) = X24807,
inference(variable_rename,[status(thm)],[fact_UN__singleton]) ).
fof(i_0_7888,plain,
! [X33314,X33315,X33316,X33317] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33317),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33316)),X33315)))
| hAPP(hAPP(c_List_Olist__update(X33316,X33315),X33317),X33314) = hAPP(hAPP(c_List_Oappend(X33316),hAPP(hAPP(c_List_Otake(X33316),X33317),X33315)),hAPP(hAPP(c_List_Olist_OCons(X33316),X33314),hAPP(hAPP(c_List_Odrop(X33316),hAPP(c_Nat_OSuc,X33317)),X33315))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upd__conv__take__nth__drop])]) ).
fof(i_0_7889,plain,
! [X32338,X32339,X32340,X32341,X32342,X32343] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32343),hAPP(X32342,X32341)),hAPP(X32342,X32340)))
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32339,X32343,X32342),X32341),hAPP(hAPP(c_List_Olist_OCons(X32339),X32340),X32338)) = hAPP(hAPP(c_List_Olist_OCons(X32339),X32341),hAPP(hAPP(c_List_Olist_OCons(X32339),X32340),X32338))
| ~ class_Orderings_Olinorder(X32343) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32343),hAPP(X32342,X32341)),hAPP(X32342,X32340)))
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32339,X32343,X32342),X32341),hAPP(hAPP(c_List_Olist_OCons(X32339),X32340),X32338)) = hAPP(hAPP(c_List_Olist_OCons(X32339),X32340),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32339,X32343,X32342),X32341),X32338))
| ~ class_Orderings_Olinorder(X32343) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5634])])]) ).
fof(i_0_7890,plain,
! [X32570,X32571] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32571)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32570)))
| c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32571),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32570)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32571)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32571)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32570))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32571)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32570)))
| c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32571),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32570)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5635])]) ).
fof(i_0_7891,plain,
! [X26493,X26494,X26495] : hAPP(c_Set_OPow(X26495),hAPP(hAPP(c_Set_Oinsert(X26495),X26494),X26493)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X26495,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X26495),X26493)),hAPP(c_Set_Oimage(tc_fun(X26495,tc_HOL_Obool),tc_fun(X26495,tc_HOL_Obool),hAPP(c_Set_Oinsert(X26495),X26494)),hAPP(c_Set_OPow(X26495),X26493))),
inference(variable_rename,[status(thm)],[fact_Pow__insert]) ).
fof(i_0_7892,plain,
! [X17373,X17374,X17375,X17376,X17377] :
( ~ hBOOL(hAPP(X17377,X17376))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17375),X17376),X17374))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17377,X17375,X17373)),X17376),X17374)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OIfTrue])]) ).
fof(i_0_7893,plain,
! [X28361,X28362,X28363,X28364] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28364),hAPP(c_Set_Ovimage(X28364,X28363,X28362),X28361)))
| hAPP(c_Set_Oimage(X28364,X28363,X28362),c_Orderings_Otop__class_Otop(tc_fun(X28364,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28363,tc_HOL_Obool))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28363),X28361)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageD])]) ).
fof(i_0_7894,plain,
! [X33692,X33693,X33694,X33695] :
( ( hBOOL(hAPP(hAPP(c_member(X33695),X33694),X33692))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33695)),hAPP(hAPP(c_List_Olist_OCons(X33695),X33694),X33693)),c_List_Olists(X33695,X33692))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33695)),X33693),c_List_Olists(X33695,X33692)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33695)),hAPP(hAPP(c_List_Olist_OCons(X33695),X33694),X33693)),c_List_Olists(X33695,X33692))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X33695),X33694),X33692))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33695)),X33693),c_List_Olists(X33695,X33692)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33695)),hAPP(hAPP(c_List_Olist_OCons(X33695),X33694),X33693)),c_List_Olists(X33695,X33692))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])]) ).
fof(i_0_7895,plain,
! [X25229,X25230,X25231,X25232] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25232,tc_HOL_Obool)),X25230),hAPP(hAPP(c_Set_Oinsert(X25232),X25231),X25229)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25232,tc_HOL_Obool)),X25230),X25229))
| hBOOL(hAPP(hAPP(c_member(X25232),X25231),X25230)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25232,tc_HOL_Obool)),X25230),X25229))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25232,tc_HOL_Obool)),X25230),hAPP(hAPP(c_Set_Oinsert(X25232),X25231),X25229)))
| hBOOL(hAPP(hAPP(c_member(X25232),X25231),X25230)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5636])])]) ).
fof(i_0_7896,plain,
! [X22529,X22530] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X22530))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(X22530),X22529))),X22530)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range])]) ).
fof(i_0_7897,plain,
! [X27086,X27087,X27088,X27089] :
( ( hBOOL(hAPP(hAPP(c_member(X27089),X27088),X27087))
| ~ hBOOL(hAPP(hAPP(c_member(X27089),X27088),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27089,tc_HOL_Obool)),X27087),X27086))) )
& ( hBOOL(hAPP(hAPP(c_member(X27089),X27088),X27086))
| ~ hBOOL(hAPP(hAPP(c_member(X27089),X27088),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27089,tc_HOL_Obool)),X27087),X27086))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X27089),X27088),X27087))
| ~ hBOOL(hAPP(hAPP(c_member(X27089),X27088),X27086))
| hBOOL(hAPP(hAPP(c_member(X27089),X27088),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27089,tc_HOL_Obool)),X27087),X27086))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])]) ).
fof(i_0_7898,plain,
! [X27082,X27083,X27084,X27085] :
( ~ hBOOL(hAPP(hAPP(c_member(X27085),X27084),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27085,tc_HOL_Obool)),X27083),X27082)))
| hBOOL(hAPP(hAPP(c_member(X27085),X27084),X27083)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD1])]) ).
fof(i_0_7899,plain,
! [X26981,X26982,X26983,X26984] :
( ( hBOOL(hAPP(hAPP(c_member(X26984),X26983),X26982))
| ~ hBOOL(hAPP(hAPP(c_member(X26984),X26983),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26984,tc_HOL_Obool)),X26982),X26981))) )
& ( hBOOL(hAPP(hAPP(c_member(X26984),X26983),X26981))
| ~ hBOOL(hAPP(hAPP(c_member(X26984),X26983),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26984,tc_HOL_Obool)),X26982),X26981))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5637])])]) ).
fof(i_0_7900,plain,
! [X25068,X25069,X25070,X25071] :
( ~ hBOOL(hAPP(hAPP(c_member(X25071),X25070),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25071,tc_HOL_Obool)),X25069),X25068)))
| hBOOL(hAPP(hAPP(c_member(X25071),X25070),X25069)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffD1])]) ).
fof(i_0_7901,plain,
! [X27078,X27079,X27080,X27081] :
( ~ hBOOL(hAPP(hAPP(c_member(X27081),X27080),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27081,tc_HOL_Obool)),X27079),X27078)))
| hBOOL(hAPP(hAPP(c_member(X27081),X27080),X27078)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD2])]) ).
fof(i_0_7902,plain,
! [X24749,X24750,X24751,X24752] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24752,tc_HOL_Obool)),X24751),hAPP(hAPP(c_Set_Oinsert(X24752),X24750),X24749)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24752,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24752,tc_HOL_Obool)),X24751),X24749)),hAPP(hAPP(c_Set_Oinsert(X24752),X24750),c_Orderings_Obot__class_Obot(tc_fun(X24752,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_Diff__insert]) ).
fof(i_0_7903,plain,
! [X32484,X32485] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32485),X32484))
| c_List_Oupto(X32485,X32484) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X32485),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32485),c_Groups_Oone__class_Oone(tc_Int_Oint)),X32484))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X32485),X32484))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32485),X32484))
| c_List_Oupto(X32485,X32484) = c_List_Olist_ONil(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X32485),X32484))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5638])])]) ).
fof(i_0_7904,plain,
! [X29013,X29014,X29015] :
( ~ class_Groups_Oab__semigroup__mult(X29015)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29015),X29014))
| X29014 = c_Orderings_Obot__class_Obot(tc_fun(X29015,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29015),X29013))
| X29013 = c_Orderings_Obot__class_Obot(tc_fun(X29015,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29015,tc_HOL_Obool)),X29014),X29013) != c_Orderings_Obot__class_Obot(tc_fun(X29015,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ofold1(X29015,c_Groups_Otimes__class_Otimes(X29015)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29015,tc_HOL_Obool)),X29014),X29013)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29015),hAPP(c_Finite__Set_Ofold1(X29015,c_Groups_Otimes__class_Otimes(X29015)),X29014)),hAPP(c_Finite__Set_Ofold1(X29015,c_Groups_Otimes__class_Otimes(X29015)),X29013)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un])]) ).
fof(i_0_7905,plain,
! [X30833,X30834,X30835,X30836,X30837,X30838] :
( ~ c_Finite__Set_Ofun__left__comm(X30838,X30837,X30836)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30838),X30835))
| hBOOL(hAPP(hAPP(c_member(X30838),X30834),X30835))
| hAPP(hAPP(c_Finite__Set_Ofold(X30838,X30837,X30836),X30833),hAPP(hAPP(c_Set_Oinsert(X30838),X30834),X30835)) = hAPP(hAPP(X30836,X30834),hAPP(hAPP(c_Finite__Set_Ofold(X30838,X30837,X30836),X30833),X30835)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5639])]) ).
cnf(i_0_7906,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = c_Groups_Oone__class_Oone(X2)
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5422]) ).
fof(i_0_7907,plain,
! [X17368,X17369,X17370,X17371,X17372] :
( hBOOL(hAPP(X17372,X17371))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17370),X17371),X17369))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17372,X17368,X17370)),X17371),X17369)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5640])]) ).
fof(i_0_7908,plain,
! [X24298,X24299] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),esk145_2(X24298,X24299)),esk146_2(X24298,X24299)))
| c_Orderings_Oorder_Omono(tc_Nat_Onat,X24299,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24298)
| ~ class_Orderings_Oorder(X24299) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24299),hAPP(X24298,esk145_2(X24298,X24299))),hAPP(X24298,esk146_2(X24298,X24299))))
| c_Orderings_Oorder_Omono(tc_Nat_Onat,X24299,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24298)
| ~ class_Orderings_Oorder(X24299) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OmonoI])])])]) ).
fof(i_0_7909,plain,
! [X27854,X27855,X27856,X27857,X27858,X27859] :
( ~ c_Finite__Set_Ofolding__idem(X27859,X27858,X27857,X27856)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27859),X27855))
| hAPP(X27856,hAPP(hAPP(c_Set_Oinsert(X27859),X27854),X27855)) = hAPP(c_Fun_Ocomp(X27858,X27858,X27858,hAPP(X27856,X27855)),hAPP(X27857,X27854)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oinsert__idem])]) ).
fof(i_0_7910,plain,
! [X32224,X32225,X32226,X32227,X32228] :
( ( hAPP(c_Map_Omap__of(X32228,X32226,hAPP(hAPP(c_List_Ozip(X32228,X32226),X32227),X32225)),X32224) != c_Option_Ooption_ONone(X32226)
| ~ hBOOL(hAPP(hAPP(c_member(X32228),X32224),hAPP(c_List_Oset(X32228),X32227)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32228)),X32227) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32226)),X32225) )
& ( hBOOL(hAPP(hAPP(c_member(X32228),X32224),hAPP(c_List_Oset(X32228),X32227)))
| hAPP(c_Map_Omap__of(X32228,X32226,hAPP(hAPP(c_List_Ozip(X32228,X32226),X32227),X32225)),X32224) = c_Option_Ooption_ONone(X32226)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32228)),X32227) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32226)),X32225) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5641])])]) ).
fof(i_0_7911,plain,
! [X22813,X22814,X22815,X22816] : hAPP(hAPP(c_Product__Type_Oscomp(X22816,X22815,X22814,tc_prod(X22815,X22814)),X22813),c_Product__Type_OPair(X22815,X22814)) = X22813,
inference(variable_rename,[status(thm)],[fact_scomp__Pair]) ).
fof(i_0_7912,plain,
! [X29316,X29317] : hAPP(c_Set_OPow(X29317),X29316) = hAPP(c_Set_OCollect(tc_fun(X29317,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X29317,tc_HOL_Obool),tc_fun(X29317,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X29317,tc_HOL_Obool))),X29316)),
inference(variable_rename,[status(thm)],[fact_Pow__def]) ).
fof(i_0_7913,plain,
! [X34267,X34268] : hAPP(c_List_Orev(X34268),X34267) = hAPP(c_List_Ofoldl(tc_List_Olist(X34268),X34268,hAPP(c_COMBC(X34268,tc_List_Olist(X34268),tc_List_Olist(X34268)),c_List_Olist_OCons(X34268)),c_List_Olist_ONil(X34268)),X34267),
inference(variable_rename,[status(thm)],[fact_rev__foldl__cons]) ).
cnf(i_0_7914,plain,
( c_List_Ofoldr(X2,X2,c_Orderings_Oord__class_Omax(X2),X1,X3) = X3
| X1 != c_List_Olist_ONil(X2)
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5608]) ).
fof(i_0_7915,plain,
! [X23471,X23472] :
( ~ class_Rings_Ocomm__semiring__1(X23472)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23472),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23472),c_Groups_Oone__class_Oone(X23472)),c_Groups_Oone__class_Oone(X23472))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23472),c_Nat_Osemiring__1__class_Oof__nat(X23472)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X23471))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23472),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23472),X23471)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23472),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23472),X23471)),c_Groups_Oone__class_Oone(X23472))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gauss__sum])]) ).
cnf(i_0_7916,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_5436]) ).
fof(i_0_7917,plain,
! [X31928,X31929,X31930,X31931,X31932,X31933] :
( hBOOL(hAPP(hAPP(c_member(X31933),X31932),hAPP(c_List_Oset(X31933),X31931)))
| hAPP(hAPP(c_List_Omap(X31933,X31930),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31933,X31930),X31929),X31932),X31928)),X31931) = hAPP(hAPP(c_List_Omap(X31933,X31930),X31929),X31931) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5642])]) ).
fof(i_0_7918,plain,
! [X29885,X29886,X29887] :
( ~ c_Wellfounded_Oacyclic(X29887,X29886)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29887,X29887),tc_HOL_Obool)),X29885),X29886))
| c_Wellfounded_Oacyclic(X29887,X29885) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__subset])]) ).
fof(i_0_7919,plain,
! [X29625,X29626,X29627] :
( ~ c_Wellfounded_Owf(X29627,X29626)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29627,X29627),tc_HOL_Obool)),X29625),X29626))
| c_Wellfounded_Owf(X29627,X29625) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__subset])]) ).
fof(i_0_7920,plain,
! [X32029,X32030,X32031,X32032] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32030),X32032),hAPP(c_List_Oset(X32030),c_List_Oremove1(X32030,X32031,X32029))))
| hBOOL(hAPP(hAPP(c_member(X32030),X32032),hAPP(c_List_Oset(X32030),X32029)))
| X32032 = X32031 )
& ( ~ hBOOL(hAPP(hAPP(c_member(X32030),X32032),hAPP(c_List_Oset(X32030),X32029)))
| hBOOL(hAPP(hAPP(c_member(X32030),X32032),hAPP(c_List_Oset(X32030),c_List_Oremove1(X32030,X32031,X32029))))
| X32032 = X32031 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__remove1])])]) ).
fof(i_0_7921,plain,
! [X27169,X27170,X27171,X27172] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27172,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27172,tc_HOL_Obool)),X27171),X27170)),X27169) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27172,tc_HOL_Obool)),X27171),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27172,tc_HOL_Obool)),X27170),X27169)),
inference(variable_rename,[status(thm)],[fact_Int__assoc]) ).
fof(i_0_7922,plain,
! [X23892,X23893,X23894,X23895] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23895,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23895,tc_HOL_Obool)),X23894),X23893)),X23892) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23895,tc_HOL_Obool)),X23894),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23895,tc_HOL_Obool)),X23893),X23892)),
inference(variable_rename,[status(thm)],[fact_Un__assoc]) ).
fof(i_0_7923,plain,
! [X27256,X27257,X27258,X27259] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27259,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27259,tc_HOL_Obool)),X27258),X27257)),X27256) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27259,tc_HOL_Obool)),X27258),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27259,tc_HOL_Obool)),X27257),X27256)),
inference(variable_rename,[status(thm)],[fact_Int__Diff]) ).
fof(i_0_7924,plain,
! [X20441,X20442,X20443] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20443),X20442))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20442),X20441)),X20443))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).
fof(i_0_7925,plain,
! [X32407,X32408,X32409,X32410] :
( hBOOL(hAPP(hAPP(c_member(X32410),X32409),hAPP(c_List_Oset(X32410),X32408)))
| ~ hBOOL(hAPP(hAPP(c_member(X32410),X32409),hAPP(c_List_Oset(X32410),c_List_Osublist(X32410,X32408,X32407)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5643])]) ).
fof(i_0_7926,plain,
! [X32403,X32404,X32405,X32406] :
( ~ hBOOL(hAPP(hAPP(c_member(X32406),X32405),hAPP(c_List_Oset(X32406),c_List_Osublist(X32406,X32404,X32403))))
| hBOOL(hAPP(hAPP(c_member(X32406),X32405),hAPP(c_List_Oset(X32406),X32404))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__sublistD])]) ).
fof(i_0_7927,plain,
! [X32025,X32026,X32027,X32028] :
( hBOOL(hAPP(hAPP(c_member(X32028),X32027),hAPP(c_List_Oset(X32028),X32026)))
| ~ hBOOL(hAPP(hAPP(c_member(X32028),X32027),hAPP(c_List_Oset(X32028),c_List_Oremove1(X32028,X32025,X32026)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5644])]) ).
fof(i_0_7928,plain,
! [X17731,X17732,X17733,X17734,X17735,X17736] :
( ~ hBOOL(hAPP(X17736,X17735))
| ~ c_Natural_Oevaln(X17734,X17735,X17733,X17732)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17736,X17734),X17732,X17733,X17731)
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17736,X17734),X17735,X17733,X17731) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OWhileTrue])]) ).
fof(i_0_7929,plain,
! [X33861,X33862,X33863] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33863,tc_HOL_Obool)),hAPP(c_List_Oset(X33863),hAPP(c_List_Ofilter(X33863,X33862),X33861))),hAPP(c_List_Oset(X33863),X33861))),
inference(variable_rename,[status(thm)],[fact_filter__is__subset]) ).
fof(i_0_7930,plain,
! [X18811,X18812,X18813,X18814,X18815] :
( ( X18814 = X18813
| X18812 = X18811
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18814),X18812)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18813),X18811)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18814),X18811)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18813),X18812))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18815) )
& ( X18814 != X18813
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18814),X18812)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18813),X18811)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18814),X18811)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18813),X18812))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18815) )
& ( X18812 != X18811
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18814),X18812)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18813),X18811)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18814),X18811)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18813),X18812))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18815) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).
fof(i_0_7931,plain,
! [X18798,X18799,X18800,X18801,X18802] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18801),X18800)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18799),X18798)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18801),X18798)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18799),X18800))
| X18801 = X18799
| X18800 = X18798
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18802) )
& ( X18801 != X18799
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18801),X18800)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18799),X18798)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18801),X18798)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18799),X18800))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18802) )
& ( X18800 != X18798
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18801),X18800)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18799),X18798)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18801),X18798)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18802),X18799),X18800))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18802) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).
cnf(i_0_7932,plain,
( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X1,X3)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_5645]) ).
fof(i_0_7933,plain,
! [X29356,X29357] :
( ( ~ c_Predicate_Oreflp(X29357,X29356)
| c_Relation_Orefl__on(X29357,c_Orderings_Otop__class_Otop(tc_fun(X29357,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X29357,X29357)),hAPP(c_Product__Type_Oprod_Oprod__case(X29357,X29357,tc_HOL_Obool),X29356))) )
& ( ~ c_Relation_Orefl__on(X29357,c_Orderings_Otop__class_Otop(tc_fun(X29357,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X29357,X29357)),hAPP(c_Product__Type_Oprod_Oprod__case(X29357,X29357,tc_HOL_Obool),X29356)))
| c_Predicate_Oreflp(X29357,X29356) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflp__def])]) ).
fof(i_0_7934,plain,
! [X20433,X20434,X20435] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20433),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20434),X20435)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20433),X20435)),X20434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20435),X20434)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20433),X20435)),X20434))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20433),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20434),X20435)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20435),X20434)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).
cnf(i_0_7935,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_5646]) ).
fof(i_0_7936,plain,
! [X28297,X28298,X28299,X28300,X28301] :
( ~ hBOOL(hAPP(hAPP(c_member(X28301),X28300),hAPP(c_Set_Ovimage(X28301,X28299,X28298),X28297)))
| hBOOL(hAPP(hAPP(c_member(X28299),hAPP(X28298,X28300)),X28297)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageD])]) ).
fof(i_0_7937,plain,
! [X28292,X28293,X28294,X28295,X28296] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28296),X28295),hAPP(c_Set_Ovimage(X28296,X28294,X28293),X28292)))
| hBOOL(hAPP(hAPP(c_member(X28294),hAPP(X28293,X28295)),X28292)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28294),hAPP(X28293,X28295)),X28292))
| hBOOL(hAPP(hAPP(c_member(X28296),X28295),hAPP(c_Set_Ovimage(X28296,X28294,X28293),X28292))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__eq])]) ).
fof(i_0_7938,plain,
! [X19714,X19715,X19716,X19717] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19716,X19717)),X19715),X19714))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19716,X19717)),X19715),X19714))
| ~ class_Orderings_Oord(X19717) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19716,X19717)),X19714),X19715))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19716,X19717)),X19715),X19714))
| ~ class_Orderings_Oord(X19717) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19716,X19717)),X19715),X19714))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19716,X19717)),X19714),X19715))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19716,X19717)),X19715),X19714))
| ~ class_Orderings_Oord(X19717) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5647])])]) ).
fof(i_0_7939,plain,
! [X33398,X33399,X33400,X33401] : hAPP(hAPP(c_List_Odrop(X33401),X33400),hAPP(hAPP(c_List_Olist_OCons(X33401),X33399),X33398)) = c_Nat_Onat_Onat__case(tc_List_Olist(X33401),hAPP(hAPP(c_List_Olist_OCons(X33401),X33399),X33398),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X33401),tc_List_Olist(X33401)),c_List_Odrop(X33401)),X33398),X33400),
inference(variable_rename,[status(thm)],[fact_drop__Cons]) ).
fof(i_0_7940,plain,
! [X19613,X19614,X19615] :
( ~ class_Rings_Olinordered__idom(X19615)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19615),c_Groups_Ozero__class_Ozero(X19615)),X19614))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19615),c_Groups_Ozero__class_Ozero(X19615)),X19613))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19615),X19613),c_Groups_Oone__class_Oone(X19615)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19615),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19615),X19614),X19613)),X19614)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).
fof(i_0_7941,plain,
! [X19610,X19611,X19612] :
( ~ class_Rings_Olinordered__idom(X19612)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19612),c_Groups_Ozero__class_Ozero(X19612)),X19611))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19612),c_Groups_Ozero__class_Ozero(X19612)),X19610))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19612),X19610),c_Groups_Oone__class_Oone(X19612)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19612),X19610),X19611)),X19611)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).
fof(i_0_7942,plain,
! [X32396,X32397,X32398,X32399] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X32399),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32398),X32397)))
| hAPP(c_Random_Opick(X32398,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X32398)),X32397),X32396)),X32399) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X32398),X32397) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X32399),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32398),X32397)))
| hAPP(c_Random_Opick(X32398,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X32398)),X32397),X32396)),X32399) = hAPP(c_Random_Opick(X32398,X32396),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X32399),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32398),X32397))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5648])]) ).
cnf(i_0_7943,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5586]) ).
cnf(i_0_7944,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5588]) ).
cnf(i_0_7945,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5587]) ).
cnf(i_0_7946,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5589]) ).
fof(i_0_7947,plain,
! [X31308,X31309,X31310,X31311,X31312,X31313,X31314] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31310,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31310,tc_HOL_Obool),X31309)),X31308) != c_Orderings_Obot__class_Obot(tc_fun(X31310,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31310,tc_HOL_Obool)),X31311),X31309))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31310,tc_HOL_Obool)),X31311),X31308) = c_Orderings_Obot__class_Obot(tc_fun(X31310,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31314,tc_HOL_Obool)),esk402_3(X31312,X31313,X31314)),X31313))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31314,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31314,tc_HOL_Obool),X31313)),X31312) = c_Orderings_Obot__class_Obot(tc_fun(X31314,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31314,tc_HOL_Obool)),esk402_3(X31312,X31313,X31314)),X31312) != c_Orderings_Obot__class_Obot(tc_fun(X31314,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31314,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31314,tc_HOL_Obool),X31313)),X31312) = c_Orderings_Obot__class_Obot(tc_fun(X31314,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__disjoint])])])])])]) ).
fof(i_0_7948,plain,
! [X20086,X20087,X20088] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20088))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20087))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20087),X20086))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20088),X20086)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20088),X20087))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])]) ).
fof(i_0_7949,plain,
! [X29811,X29812,X29813,X29814] : hAPP(c_Relation_ODomain(X29814,X29813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29814,X29813),tc_HOL_Obool)),X29812),X29811)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29814,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29814,X29813),X29812)),hAPP(c_Relation_ODomain(X29814,X29813),X29811)),
inference(variable_rename,[status(thm)],[fact_Domain__Un__eq]) ).
fof(i_0_7950,plain,
! [X29720,X29721,X29722,X29723] : hAPP(c_Relation_ORange(X29723,X29722),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29723,X29722),tc_HOL_Obool)),X29721),X29720)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29722,tc_HOL_Obool)),hAPP(c_Relation_ORange(X29723,X29722),X29721)),hAPP(c_Relation_ORange(X29723,X29722),X29720)),
inference(variable_rename,[status(thm)],[fact_Range__Un__eq]) ).
fof(i_0_7951,plain,
! [X32778,X32779,X32780,X32781,X32782,X32783] : hAPP(hAPP(c_List_Omap(X32783,X32782),X32781),hAPP(hAPP(c_List_Olist__update(X32783,X32780),X32779),X32778)) = hAPP(hAPP(c_List_Olist__update(X32782,hAPP(hAPP(c_List_Omap(X32783,X32782),X32781),X32780)),X32779),hAPP(X32781,X32778)),
inference(variable_rename,[status(thm)],[fact_map__update]) ).
fof(i_0_7952,plain,
! [X31640,X31641,X31642,X31643,X31644] : hAPP(c_Map_Omap__add(X31644,X31643,X31642,X31641),X31640) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X31643),X31643,hAPP(X31642,X31640),c_Option_Ooption_OSome(X31643)),hAPP(X31641,X31640)),
inference(variable_rename,[status(thm)],[fact_map__add__def]) ).
fof(i_0_7953,plain,
! [X32284,X32285,X32286,X32287] :
( ~ hBOOL(hAPP(hAPP(c_member(X32287),X32286),hAPP(c_List_Oset(X32287),hAPP(hAPP(c_List_Olist_OCons(X32287),X32285),X32284))))
| X32286 = X32285
| hBOOL(hAPP(hAPP(c_member(X32287),X32286),hAPP(c_List_Oset(X32287),X32284))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__ConsD])]) ).
fof(i_0_7954,plain,
! [X22733] :
( X22733 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22733)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X22733))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__decr])]) ).
fof(i_0_7955,plain,
! [X33348,X33349,X33350,X33351] :
( ~ hBOOL(hAPP(hAPP(c_member(X33351),X33350),hAPP(c_List_Oset(X33351),hAPP(hAPP(c_List_Odrop(X33351),X33349),X33348))))
| hBOOL(hAPP(hAPP(c_member(X33351),X33350),hAPP(c_List_Oset(X33351),X33348))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__dropD])]) ).
fof(i_0_7956,plain,
! [X33109,X33110,X33111,X33112] :
( ~ hBOOL(hAPP(hAPP(c_member(X33112),X33111),hAPP(c_List_Oset(X33112),hAPP(hAPP(c_List_Otake(X33112),X33110),X33109))))
| hBOOL(hAPP(hAPP(c_member(X33112),X33111),hAPP(c_List_Oset(X33112),X33109))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__takeD])]) ).
fof(i_0_7957,plain,
! [X28490,X28491,X28492,X28493,X28494] :
( ( X28494 != c_Option_Ooption_ONone(X28493)
| c_Map_Odom(X28492,X28493,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X28492,tc_Option_Ooption(X28493)),X28491),X28490),X28494)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28492,tc_HOL_Obool)),c_Map_Odom(X28492,X28493,X28491)),hAPP(hAPP(c_Set_Oinsert(X28492),X28490),c_Orderings_Obot__class_Obot(tc_fun(X28492,tc_HOL_Obool)))) )
& ( X28494 = c_Option_Ooption_ONone(X28493)
| c_Map_Odom(X28492,X28493,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X28492,tc_Option_Ooption(X28493)),X28491),X28490),X28494)) = hAPP(hAPP(c_Set_Oinsert(X28492),X28490),c_Map_Odom(X28492,X28493,X28491)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__fun__upd])]) ).
fof(i_0_7958,plain,
! [X20850,X20851,X20852] :
( ~ class_Rings_Olinordered__semidom(X20852)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20852),c_Groups_Ozero__class_Ozero(X20852)),X20851))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20852),X20851),c_Groups_Oone__class_Oone(X20852)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20852),hAPP(hAPP(c_Power_Opower__class_Opower(X20852),X20851),hAPP(c_Nat_OSuc,X20850))),c_Groups_Oone__class_Oone(X20852))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).
fof(i_0_7959,plain,
! [X31571,X31572,X31573] :
( ( hBOOL(hAPP(hAPP(c_member(X31573),X31572),esk425_3(X31571,X31572,X31573)))
| ~ hBOOL(hAPP(hAPP(c_member(X31573),X31572),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31573,tc_HOL_Obool),X31571))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31573,tc_HOL_Obool)),esk425_3(X31571,X31572,X31573)),X31571))
| ~ hBOOL(hAPP(hAPP(c_member(X31573),X31572),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31573,tc_HOL_Obool),X31571))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5649])])])]) ).
fof(i_0_7960,plain,
! [X20097,X20098,X20099] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20099),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20098),X20097))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20099),X20098)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20099),X20097))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg])]) ).
fof(i_0_7961,plain,
! [X26445,X26446,X26447] :
( ( hBOOL(hAPP(hAPP(c_member(X26447),esk224_3(X26445,X26446,X26447)),X26445))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26447,X26447)),X26446),c_Relation_OId__on(X26447,X26445))) )
& ( X26446 = hAPP(hAPP(c_Product__Type_OPair(X26447,X26447),esk224_3(X26445,X26446,X26447)),esk224_3(X26445,X26446,X26447))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26447,X26447)),X26446),c_Relation_OId__on(X26447,X26445))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__onE])])])]) ).
fof(i_0_7962,plain,
! [X28401,X28402,X28403,X28404] :
( ~ c_Fun_Oinj__on(X28404,X28403,X28402,c_Orderings_Otop__class_Otop(tc_fun(X28404,tc_HOL_Obool)))
| hAPP(c_Fun_Othe__inv__into(X28404,X28403,c_Orderings_Otop__class_Otop(tc_fun(X28404,tc_HOL_Obool)),X28402),hAPP(X28402,X28401)) = X28401 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__f__f])]) ).
fof(i_0_7963,plain,
! [X30816,X30817,X30818,X30819,X30820,X30821] :
( ~ c_Finite__Set_Ofun__left__comm(X30821,X30820,X30819)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30821),X30818))
| hAPP(hAPP(X30819,X30817),hAPP(hAPP(c_Finite__Set_Ofold(X30821,X30820,X30819),X30816),X30818)) = hAPP(hAPP(c_Finite__Set_Ofold(X30821,X30820,X30819),hAPP(hAPP(X30819,X30817),X30816)),X30818) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm])]) ).
fof(i_0_7964,plain,
! [X29799,X29800,X29801] :
( ~ c_Wellfounded_OwfP(X29801,X29800)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29801,tc_fun(X29801,tc_HOL_Obool))),X29799),X29800))
| c_Wellfounded_OwfP(X29801,X29799) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__subset])]) ).
fof(i_0_7965,plain,
! [X25144,X25145,X25146] :
( ( hAPP(hAPP(c_COMBC(X25146,tc_fun(X25146,tc_HOL_Obool),tc_HOL_Obool),c_member(X25146)),X25145) != hAPP(hAPP(c_COMBC(X25146,tc_fun(X25146,tc_HOL_Obool),tc_HOL_Obool),c_member(X25146)),X25144)
| X25145 = X25144 )
& ( X25145 != X25144
| hAPP(hAPP(c_COMBC(X25146,tc_fun(X25146,tc_HOL_Obool),tc_HOL_Obool),c_member(X25146)),X25145) = hAPP(hAPP(c_COMBC(X25146,tc_fun(X25146,tc_HOL_Obool),tc_HOL_Obool),c_member(X25146)),X25144) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_7966,plain,
! [X19454,X19455,X19456] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19456),X19455)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19456),X19454))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19455),X19454))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19456),X19455)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19456),X19454))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19455),X19454))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19456),X19455)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19456),X19454))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).
fof(i_0_7967,plain,
! [X19451,X19452,X19453] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19452))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19453),X19452)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19451),X19452))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19453),X19451))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19453),X19452)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19451),X19452))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19452))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19453),X19451))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19453),X19452)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19451),X19452))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).
fof(i_0_7968,plain,
! [X21485,X21486,X21487,X21488] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21488)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21488),X21487),X21486))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21488),c_Groups_Ozero__class_Ozero(X21488)),X21485))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21488),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21488),X21487),X21485)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21488),X21486),X21485))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono])]) ).
fof(i_0_7969,plain,
! [X20920,X20921,X20922,X20923] :
( ~ class_Rings_Olinordered__semidom(X20923)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20923),X20922),X20921))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20923),c_Groups_Ozero__class_Ozero(X20923)),X20922))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20923),hAPP(hAPP(c_Power_Opower__class_Opower(X20923),X20922),X20920)),hAPP(hAPP(c_Power_Opower__class_Opower(X20923),X20921),X20920))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).
fof(i_0_7970,plain,
! [X19392,X19393,X19394,X19395] :
( ~ class_Rings_Oordered__semiring(X19395)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19395),X19394),X19393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19395),c_Groups_Ozero__class_Ozero(X19395)),X19392))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19395),X19394),X19392)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19395),X19393),X19392))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).
fof(i_0_7971,plain,
! [X19384,X19385,X19386,X19387] :
( ~ class_Rings_Oordered__comm__semiring(X19387)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19387),X19386),X19385))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19387),c_Groups_Ozero__class_Ozero(X19387)),X19384))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19387),X19384),X19386)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19387),X19384),X19385))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).
fof(i_0_7972,plain,
! [X19388,X19389,X19390,X19391] :
( ~ class_Rings_Oordered__semiring(X19391)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19391),X19390),X19389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19391),c_Groups_Ozero__class_Ozero(X19391)),X19388))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19391),X19388),X19390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19391),X19388),X19389))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).
fof(i_0_7973,plain,
! [X21497,X21498,X21499,X21500] :
( ~ class_Fields_Olinordered__field(X21500)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21500),X21499),X21498))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21500),c_Groups_Ozero__class_Ozero(X21500)),X21497))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21500),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21500),X21499),X21497)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21500),X21498),X21497))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])]) ).
fof(i_0_7974,plain,
! [X18898,X18899,X18900,X18901] :
( ~ class_Rings_Olinordered__semiring__strict(X18901)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18901),X18900),X18899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18901),c_Groups_Ozero__class_Ozero(X18901)),X18898))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18901),X18900),X18898)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18901),X18899),X18898))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).
fof(i_0_7975,plain,
! [X18906,X18907,X18908,X18909] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X18909)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18909),X18908),X18907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18909),c_Groups_Ozero__class_Ozero(X18909)),X18906))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18909),X18906),X18908)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18909),X18906),X18907))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).
fof(i_0_7976,plain,
! [X18902,X18903,X18904,X18905] :
( ~ class_Rings_Olinordered__semiring__strict(X18905)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18905),X18904),X18903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18905),c_Groups_Ozero__class_Ozero(X18905)),X18902))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18905),X18902),X18904)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18905),X18902),X18903))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).
fof(i_0_7977,plain,
! [X32288,X32289,X32290,X32291,X32292,X32293] : hAPP(hAPP(c_List_Ozip(X32293,X32292),hAPP(hAPP(c_List_Olist_OCons(X32293),X32291),X32290)),hAPP(hAPP(c_List_Olist_OCons(X32292),X32289),X32288)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X32293,X32292)),hAPP(hAPP(c_Product__Type_OPair(X32293,X32292),X32291),X32289)),hAPP(hAPP(c_List_Ozip(X32293,X32292),X32290),X32288)),
inference(variable_rename,[status(thm)],[fact_zip__Cons__Cons]) ).
fof(i_0_7978,plain,
! [X21482,X21483,X21484] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),X21483),c_Groups_Ozero__class_Ozero(X21484)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),c_Groups_Ozero__class_Ozero(X21484)),X21483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21484),X21483),X21482)),c_Groups_Ozero__class_Ozero(X21484)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21484) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),c_Groups_Ozero__class_Ozero(X21484)),X21482))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),c_Groups_Ozero__class_Ozero(X21484)),X21483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21484),X21483),X21482)),c_Groups_Ozero__class_Ozero(X21484)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21484) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),X21483),c_Groups_Ozero__class_Ozero(X21484)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),X21482),c_Groups_Ozero__class_Ozero(X21484)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21484),X21483),X21482)),c_Groups_Ozero__class_Ozero(X21484)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21484) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),c_Groups_Ozero__class_Ozero(X21484)),X21482))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),X21482),c_Groups_Ozero__class_Ozero(X21484)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21484),X21483),X21482)),c_Groups_Ozero__class_Ozero(X21484)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21484) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),c_Groups_Ozero__class_Ozero(X21484)),X21483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),X21482),c_Groups_Ozero__class_Ozero(X21484)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21484),X21483),X21482)),c_Groups_Ozero__class_Ozero(X21484)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21484) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),X21483),c_Groups_Ozero__class_Ozero(X21484)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),c_Groups_Ozero__class_Ozero(X21484)),X21482))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21484),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21484),X21483),X21482)),c_Groups_Ozero__class_Ozero(X21484)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21484) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])]) ).
fof(i_0_7979,plain,
! [X19411,X19412,X19413] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),X19412),c_Groups_Ozero__class_Ozero(X19413)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),c_Groups_Ozero__class_Ozero(X19413)),X19412))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19413),X19412),X19411)),c_Groups_Ozero__class_Ozero(X19413)))
| ~ class_Rings_Olinordered__ring__strict(X19413) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),c_Groups_Ozero__class_Ozero(X19413)),X19411))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),c_Groups_Ozero__class_Ozero(X19413)),X19412))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19413),X19412),X19411)),c_Groups_Ozero__class_Ozero(X19413)))
| ~ class_Rings_Olinordered__ring__strict(X19413) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),X19412),c_Groups_Ozero__class_Ozero(X19413)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),X19411),c_Groups_Ozero__class_Ozero(X19413)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19413),X19412),X19411)),c_Groups_Ozero__class_Ozero(X19413)))
| ~ class_Rings_Olinordered__ring__strict(X19413) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),c_Groups_Ozero__class_Ozero(X19413)),X19411))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),X19411),c_Groups_Ozero__class_Ozero(X19413)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19413),X19412),X19411)),c_Groups_Ozero__class_Ozero(X19413)))
| ~ class_Rings_Olinordered__ring__strict(X19413) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),c_Groups_Ozero__class_Ozero(X19413)),X19412))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),X19411),c_Groups_Ozero__class_Ozero(X19413)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19413),X19412),X19411)),c_Groups_Ozero__class_Ozero(X19413)))
| ~ class_Rings_Olinordered__ring__strict(X19413) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),X19412),c_Groups_Ozero__class_Ozero(X19413)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),c_Groups_Ozero__class_Ozero(X19413)),X19411))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19413),X19412),X19411)),c_Groups_Ozero__class_Ozero(X19413)))
| ~ class_Rings_Olinordered__ring__strict(X19413) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).
fof(i_0_7980,plain,
! [X21513,X21514,X21515] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),X21514),c_Groups_Ozero__class_Ozero(X21515)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),c_Groups_Ozero__class_Ozero(X21515)),X21514))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21515),X21514),X21513)),c_Groups_Ozero__class_Ozero(X21515)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21515) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),c_Groups_Ozero__class_Ozero(X21515)),X21513))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),c_Groups_Ozero__class_Ozero(X21515)),X21514))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21515),X21514),X21513)),c_Groups_Ozero__class_Ozero(X21515)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21515) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),X21514),c_Groups_Ozero__class_Ozero(X21515)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),X21513),c_Groups_Ozero__class_Ozero(X21515)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21515),X21514),X21513)),c_Groups_Ozero__class_Ozero(X21515)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21515) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),c_Groups_Ozero__class_Ozero(X21515)),X21513))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),X21513),c_Groups_Ozero__class_Ozero(X21515)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21515),X21514),X21513)),c_Groups_Ozero__class_Ozero(X21515)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21515) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),c_Groups_Ozero__class_Ozero(X21515)),X21514))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),X21513),c_Groups_Ozero__class_Ozero(X21515)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21515),X21514),X21513)),c_Groups_Ozero__class_Ozero(X21515)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21515) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),X21514),c_Groups_Ozero__class_Ozero(X21515)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),c_Groups_Ozero__class_Ozero(X21515)),X21513))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21515),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21515),X21514),X21513)),c_Groups_Ozero__class_Ozero(X21515)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21515) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff])])]) ).
fof(i_0_7981,plain,
! [X25267,X25268] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25268),X25267))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X25268)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25267)))
| ~ c_Nat__Transfer_Onat__set(X25267)
| ~ c_Nat__Transfer_Ois__nat(X25268) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X25268)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25267)))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25268),X25267))
| ~ c_Nat__Transfer_Onat__set(X25267)
| ~ c_Nat__Transfer_Ois__nat(X25268) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I2_J])])]) ).
fof(i_0_7982,plain,
! [X30090,X30091,X30092] :
( ( hBOOL(hAPP(hAPP(c_member(X30092),esk362_3(X30090,X30091,X30092)),X30091))
| ~ hBOOL(hAPP(hAPP(c_member(X30092),X30090),X30091))
| c_Big__Operators_Olinorder__class_OMax(X30092,X30091) = X30090
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30092),X30091))
| ~ class_Orderings_Olinorder(X30092) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30092),esk362_3(X30090,X30091,X30092)),X30090))
| ~ hBOOL(hAPP(hAPP(c_member(X30092),X30090),X30091))
| c_Big__Operators_Olinorder__class_OMax(X30092,X30091) = X30090
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30092),X30091))
| ~ class_Orderings_Olinorder(X30092) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__eqI])])])]) ).
fof(i_0_7983,plain,
! [X23371,X23372,X23373] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23373),X23372)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23373),X23371)))
| X23373 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23372),X23371)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel])]) ).
fof(i_0_7984,plain,
! [X23368,X23369,X23370] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23369),X23368))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23370),X23369)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23370),X23368)))
| X23370 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23370),X23369)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23370),X23368)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23369),X23368))
| X23370 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mono])])]) ).
fof(i_0_7985,plain,
! [X23385,X23386,X23387] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23387),X23386)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23387),X23385)))
| X23387 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23386),X23385)) )
& ( X23387 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23387),X23386)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23387),X23385))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23386),X23385))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23387),X23386)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23387),X23385))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj])])]) ).
fof(i_0_7986,plain,
! [X22133] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22133)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22133)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22133))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__1__number__of])]) ).
fof(i_0_7987,plain,
! [X27933,X27934,X27935,X27936,X27937] :
( ~ c_Fun_Oinj__on(X27937,X27936,X27935,X27934)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27937,tc_HOL_Obool)),X27933),X27934))
| c_Fun_Oinj__on(X27937,X27936,X27935,X27933) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).
fof(i_0_7988,plain,
! [X33864,X33865,X33866] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33866)),hAPP(c_List_Ofilter(X33866,X33865),X33864))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33866)),X33864))),
inference(variable_rename,[status(thm)],[fact_length__filter__le]) ).
fof(i_0_7989,plain,
! [X30176,X30177,X30178] : hBOOL(hAPP(hAPP(c_member(tc_prod(X30178,X30178)),hAPP(hAPP(c_Product__Type_OPair(X30178,X30178),X30177),X30177)),c_Transitive__Closure_Ortrancl(X30178,X30176))),
inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).
cnf(i_0_7990,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5650]) ).
cnf(i_0_7991,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5651]) ).
fof(i_0_7992,plain,
! [X19286,X19287,X19288] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19288),X19287)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19288),X19286)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19287),X19286)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19287),X19286))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19288),X19287)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19288),X19286))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
cnf(i_0_7993,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5652]) ).
cnf(i_0_7994,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5653]) ).
fof(i_0_7995,plain,
! [X18314,X18315,X18316] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18316),X18315)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18316),X18314)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18315),X18314)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18315),X18314))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18316),X18315)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18316),X18314))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_7996,plain,
! [X23379,X23380,X23381] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23381),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23381),X23379))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23381),X23380)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23381),X23380))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23381),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23381),X23379)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__reduce])]) ).
fof(i_0_7997,plain,
! [X28390,X28391,X28392,X28393,X28394] :
( ~ c_Fun_Oinj__on(X28394,X28393,X28392,X28391)
| ~ hBOOL(hAPP(hAPP(c_member(X28394),X28390),X28391))
| hAPP(c_Fun_Othe__inv__into(X28394,X28393,X28391,X28392),hAPP(X28392,X28390)) = X28390 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f])]) ).
fof(i_0_7998,plain,
! [X22245] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22245)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22245)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22245))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg__1__number__of])]) ).
fof(i_0_7999,plain,
! [X28395,X28396,X28397,X28398,X28399,X28400] :
( ~ c_Fun_Oinj__on(X28400,X28399,X28398,X28397)
| hAPP(X28398,X28396) != X28395
| ~ hBOOL(hAPP(hAPP(c_member(X28400),X28396),X28397))
| hAPP(c_Fun_Othe__inv__into(X28400,X28399,X28397,X28398),X28395) = X28396 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq])]) ).
fof(i_0_8000,plain,
! [X30897,X30898,X30899,X30900,X30901] :
( ~ hBOOL(hAPP(hAPP(c_member(X30900),X30901),X30899))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30898),hAPP(X30897,X30901)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X30898),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30900,tc_fun(X30898,tc_HOL_Obool)),X30899),X30897))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__INT])])]) ).
fof(i_0_8001,plain,
! [X20992,X20993,X20994,X20995] :
( ~ class_Rings_Olinordered__semidom(X20995)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20994),X20993))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20995),c_Groups_Oone__class_Oone(X20995)),X20992))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20995),hAPP(hAPP(c_Power_Opower__class_Opower(X20995),X20992),X20994)),hAPP(hAPP(c_Power_Opower__class_Opower(X20995),X20992),X20993))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).
fof(i_0_8002,plain,
! [X20985,X20986,X20987,X20988] :
( ~ class_Rings_Olinordered__semidom(X20988)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20987),X20986))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20988),c_Groups_Oone__class_Oone(X20988)),X20985))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20988),hAPP(hAPP(c_Power_Opower__class_Opower(X20988),X20985),X20987)),hAPP(hAPP(c_Power_Opower__class_Opower(X20988),X20985),X20986))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).
fof(i_0_8003,plain,
! [X21489,X21490,X21491,X21492] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21492)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21492),X21491),X21490))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21492),X21489),c_Groups_Ozero__class_Ozero(X21492)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21492),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21492),X21490),X21489)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21492),X21491),X21489))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg])]) ).
fof(i_0_8004,plain,
! [X19380,X19381,X19382,X19383] :
( ~ class_Rings_Oordered__ring(X19383)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19383),X19382),X19381))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19383),X19380),c_Groups_Ozero__class_Ozero(X19383)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19383),X19381),X19380)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19383),X19382),X19380))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).
fof(i_0_8005,plain,
! [X19376,X19377,X19378,X19379] :
( ~ class_Rings_Oordered__ring(X19379)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19379),X19378),X19377))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19379),X19376),c_Groups_Ozero__class_Ozero(X19379)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19379),X19376),X19377)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19379),X19376),X19378))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).
fof(i_0_8006,plain,
! [X21493,X21494,X21495,X21496] :
( ~ class_Fields_Olinordered__field(X21496)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21496),X21495),X21494))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21496),X21493),c_Groups_Ozero__class_Ozero(X21496)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21496),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21496),X21494),X21493)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21496),X21495),X21493))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg])]) ).
fof(i_0_8007,plain,
! [X18910,X18911,X18912,X18913] :
( ~ class_Rings_Olinordered__ring__strict(X18913)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18913),X18912),X18911))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18913),X18910),c_Groups_Ozero__class_Ozero(X18913)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18913),X18911),X18910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18913),X18912),X18910))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).
fof(i_0_8008,plain,
! [X18914,X18915,X18916,X18917] :
( ~ class_Rings_Olinordered__ring__strict(X18917)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18917),X18916),X18915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18917),X18914),c_Groups_Ozero__class_Ozero(X18917)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18917),X18914),X18915)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18917),X18914),X18916))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).
fof(i_0_8009,plain,
! [X24918,X24919,X24920] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24920),X24919))
| ~ hBOOL(hAPP(hAPP(c_member(X24920),X24918),X24919))
| hAPP(c_Finite__Set_Ocard(X24920),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24920,tc_HOL_Obool)),X24919),hAPP(hAPP(c_Set_Oinsert(X24920),X24918),c_Orderings_Obot__class_Obot(tc_fun(X24920,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24920),X24919)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton])]) ).
fof(i_0_8010,plain,
! [X24915,X24916,X24917] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X24917),X24915),X24916))
| hAPP(c_Finite__Set_Ocard(X24917),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24917,tc_HOL_Obool)),X24916),hAPP(hAPP(c_Set_Oinsert(X24917),X24915),c_Orderings_Obot__class_Obot(tc_fun(X24917,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24917),X24916)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24917),X24916)) )
& ( hBOOL(hAPP(hAPP(c_member(X24917),X24915),X24916))
| hAPP(c_Finite__Set_Ocard(X24917),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24917,tc_HOL_Obool)),X24916),hAPP(hAPP(c_Set_Oinsert(X24917),X24915),c_Orderings_Obot__class_Obot(tc_fun(X24917,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X24917),X24916)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24917),X24916)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5654])])]) ).
fof(i_0_8011,plain,
! [X24550,X24551,X24552] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24552),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24552,tc_HOL_Obool)),X24550),X24551)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24552),X24550))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24552),X24551)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24552),X24550))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24552),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24552,tc_HOL_Obool)),X24550),X24551)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24552),X24551)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff2])])]) ).
cnf(i_0_8012,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5655]) ).
fof(i_0_8013,plain,
! [X20709,X20710,X20711] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20711),hAPP(c_Int_Onumber__class_Onumber__of(X20711),X20710)),hAPP(c_Int_Onumber__class_Onumber__of(X20711),X20709)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20711),hAPP(c_Int_Onumber__class_Onumber__of(X20711),X20709)),hAPP(c_Int_Onumber__class_Onumber__of(X20711),X20710)))
| ~ class_Int_Onumber(X20711)
| ~ class_Orderings_Olinorder(X20711) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20711),hAPP(c_Int_Onumber__class_Onumber__of(X20711),X20709)),hAPP(c_Int_Onumber__class_Onumber__of(X20711),X20710)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20711),hAPP(c_Int_Onumber__class_Onumber__of(X20711),X20710)),hAPP(c_Int_Onumber__class_Onumber__of(X20711),X20709)))
| ~ class_Int_Onumber(X20711)
| ~ class_Orderings_Olinorder(X20711) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5656])])]) ).
fof(i_0_8014,plain,
! [X25458,X25459,X25460,X25461] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X25461,tc_fun(X25460,tc_HOL_Obool))),X25459),X25458)),
inference(variable_rename,[status(thm)],[i_0_5657]) ).
fof(i_0_8015,plain,
! [X32830,X32831,X32832] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32832),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X32831)))
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X32831),X32832),X32830)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X32831)),X32830)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X32831),X32832)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__update__nat])]) ).
fof(i_0_8016,plain,
! [X26630,X26631,X26632,X26633,X26634,X26635] : hAPP(hAPP(c_Fun_Ocomp(X26635,X26634,X26633,X26632),X26631),X26630) = hAPP(X26632,hAPP(X26631,X26630)),
inference(variable_rename,[status(thm)],[fact_o__apply]) ).
fof(i_0_8017,plain,
! [X26606,X26607,X26608,X26609,X26610,X26611] : hAPP(hAPP(c_Fun_Ocomp(X26611,X26610,X26609,X26608),X26607),X26606) = hAPP(X26608,hAPP(X26607,X26606)),
inference(variable_rename,[status(thm)],[fact_o__def]) ).
fof(i_0_8018,plain,
! [X23172,X23173,X23174,X23175,X23176] :
( ~ class_Rings_Ocomm__semiring__1(X23176)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23176),X23175),X23174))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23176),X23173),X23172))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23176),X23175),X23173)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23176),X23174),X23172))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono])]) ).
fof(i_0_8019,plain,
! [X27033,X27034,X27035,X27036,X27037] :
( ~ class_Lattices_Osemilattice__inf(X27037)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27037),X27036),X27035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27037),X27034),X27033))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27037),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27037),X27036),X27034)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27037),X27035),X27033))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__mono])]) ).
fof(i_0_8020,plain,
! [X24016,X24017,X24018,X24019,X24020] :
( ~ class_Lattices_Osemilattice__sup(X24020)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24020),X24019),X24018))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24020),X24017),X24016))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24020),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24020),X24019),X24017)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24020),X24018),X24016))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__mono])]) ).
fof(i_0_8021,plain,
! [X22594,X22595,X22596,X22597,X22598] :
( ~ class_Orderings_Olinorder(X22598)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22598),X22597),X22596))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22598),X22595),X22594))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22598),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22598),X22597),X22595)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22598),X22596),X22594))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__mono])]) ).
fof(i_0_8022,plain,
! [X22265,X22266,X22267,X22268,X22269] :
( ~ class_Orderings_Olinorder(X22269)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22269),X22268),X22267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22269),X22266),X22265))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22269),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22269),X22268),X22266)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22269),X22267),X22265))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__mono])]) ).
fof(i_0_8023,plain,
! [X19191,X19192,X19193,X19194,X19195] :
( ~ class_Groups_Oordered__ab__semigroup__add(X19195)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19195),X19194),X19193))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19195),X19192),X19191))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19195),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19195),X19194),X19192)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19195),X19193),X19191))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_8024,plain,
! [X19424,X19425,X19426,X19427,X19428] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X19428)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19428),X19427),X19426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19428),X19425),X19424))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19428),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19428),X19427),X19425)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19428),X19426),X19424))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_8025,plain,
! [X19419,X19420,X19421,X19422,X19423] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X19423)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19423),X19422),X19421))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19423),X19420),X19419))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19423),X19422),X19420)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19423),X19421),X19419))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_8026,plain,
! [X18252,X18253,X18254,X18255,X18256] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18256)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),X18255),X18254))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),X18253),X18252))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18256),X18255),X18253)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18256),X18254),X18252))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_8027,plain,
! [X20729,X20730,X20731,X20732] :
( ~ class_Int_Onumber(X20732)
| ~ class_Rings_Oring(X20732)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20732),hAPP(c_Int_Onumber__class_Onumber__of(X20732),X20731)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20732),X20730),X20729)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20732),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20732),hAPP(c_Int_Onumber__class_Onumber__of(X20732),X20731)),X20730)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20732),hAPP(c_Int_Onumber__class_Onumber__of(X20732),X20731)),X20729)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of])]) ).
fof(i_0_8028,plain,
! [X20712,X20713,X20714,X20715] :
( ~ class_Int_Onumber(X20715)
| ~ class_Rings_Osemiring(X20715)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20715),hAPP(c_Int_Onumber__class_Onumber__of(X20715),X20714)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20715),X20713),X20712)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20715),hAPP(c_Int_Onumber__class_Onumber__of(X20715),X20714)),X20713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20715),hAPP(c_Int_Onumber__class_Onumber__of(X20715),X20714)),X20712)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])]) ).
fof(i_0_8029,plain,
! [X23321,X23322,X23323,X23324,X23325] :
( ~ class_Divides_Osemiring__div(X23325)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23325),X23324),X23323))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23325),X23322),X23321))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23325),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23325),X23323),X23324)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23325),X23321),X23322)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23325),X23323),X23321)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23325),X23324),X23322)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__div__if__dvd])]) ).
fof(i_0_8030,plain,
! [X30679,X30680,X30681,X30682] :
( ~ class_Lattices_Osemilattice__inf(X30682)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30682),X30681))
| hAPP(hAPP(c_Finite__Set_Ofold(X30682,X30682,c_Lattices_Osemilattice__inf__class_Oinf(X30682)),X30680),hAPP(hAPP(c_Set_Oinsert(X30682),X30679),X30681)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X30682),X30679),hAPP(hAPP(c_Finite__Set_Ofold(X30682,X30682,c_Lattices_Osemilattice__inf__class_Oinf(X30682)),X30680),X30681)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__insert])]) ).
fof(i_0_8031,plain,
! [X30675,X30676,X30677,X30678] :
( ~ class_Lattices_Osemilattice__sup(X30678)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30678),X30677))
| hAPP(hAPP(c_Finite__Set_Ofold(X30678,X30678,c_Lattices_Osemilattice__sup__class_Osup(X30678)),X30676),hAPP(hAPP(c_Set_Oinsert(X30678),X30675),X30677)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X30678),X30675),hAPP(hAPP(c_Finite__Set_Ofold(X30678,X30678,c_Lattices_Osemilattice__sup__class_Osup(X30678)),X30676),X30677)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__sup__insert])]) ).
fof(i_0_8032,plain,
! [X30687,X30688,X30689,X30690] :
( ~ class_Orderings_Olinorder(X30690)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30690),X30689))
| hAPP(hAPP(c_Finite__Set_Ofold(X30690,X30690,c_Orderings_Oord__class_Omax(X30690)),X30688),hAPP(hAPP(c_Set_Oinsert(X30690),X30687),X30689)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X30690),X30687),hAPP(hAPP(c_Finite__Set_Ofold(X30690,X30690,c_Orderings_Oord__class_Omax(X30690)),X30688),X30689)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert])]) ).
fof(i_0_8033,plain,
! [X30683,X30684,X30685,X30686] :
( ~ class_Orderings_Olinorder(X30686)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30686),X30685))
| hAPP(hAPP(c_Finite__Set_Ofold(X30686,X30686,c_Orderings_Oord__class_Omin(X30686)),X30684),hAPP(hAPP(c_Set_Oinsert(X30686),X30683),X30685)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X30686),X30683),hAPP(hAPP(c_Finite__Set_Ofold(X30686,X30686,c_Orderings_Oord__class_Omin(X30686)),X30684),X30685)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert])]) ).
fof(i_0_8034,plain,
! [X28374,X28375,X28376,X28377] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28377),X28376))
| ~ c_Fun_Oinj__on(X28375,X28377,X28374,c_Orderings_Otop__class_Otop(tc_fun(X28375,tc_HOL_Obool)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28375),hAPP(c_Set_Ovimage(X28375,X28377,X28374),X28376))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageI])]) ).
fof(i_0_8035,plain,
! [X31178,X31179,X31180,X31181,X31182] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31182)
| ~ hBOOL(hAPP(hAPP(c_member(X31181),X31180),X31179))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31182),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31181,X31182),X31179),X31178)),hAPP(X31178,X31180))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__leI])]) ).
fof(i_0_8036,plain,
! [X20823,X20824,X20825,X20826] :
( ~ class_Int_Onumber__ring(X20826)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20826),hAPP(c_Int_Onumber__class_Onumber__of(X20826),X20825)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20826),X20824),hAPP(c_Int_Onumber__class_Onumber__of(X20826),X20823))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20826),hAPP(c_Int_Onumber__class_Onumber__of(X20826),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20825),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20823)))),X20824) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff2])]) ).
fof(i_0_8037,plain,
! [X21928,X21929] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21929)),X21928))
| hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21929),X21928)) )
& ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21929),X21928))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21929)),X21928)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).
fof(i_0_8038,plain,
! [X24982,X24983,X24984,X24985,X24986,X24987] :
( ~ hBOOL(hAPP(hAPP(c_member(X24987),X24986),X24985))
| ~ hBOOL(hAPP(hAPP(X24984,X24986),X24983))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24987,tc_fun(X24982,tc_HOL_Obool)),X24985),X24984),X24983)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP1__I])]) ).
fof(i_0_8039,plain,
! [X31291,X31292,X31293,X31294] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31293),c_Complete__Lattice_OSup__class_OSup(X31293,X31292)),X31291))
| ~ hBOOL(hAPP(hAPP(c_member(X31293),X31294),X31292))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31293),X31294),X31291))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31293) )
& ( hBOOL(hAPP(hAPP(c_member(X31293),esk400_3(X31291,X31292,X31293)),X31292))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31293),c_Complete__Lattice_OSup__class_OSup(X31293,X31292)),X31291))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31293) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31293),esk400_3(X31291,X31292,X31293)),X31291))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31293),c_Complete__Lattice_OSup__class_OSup(X31293,X31292)),X31291))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31293) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__le__iff])])])])]) ).
fof(i_0_8040,plain,
! [X30691,X30692,X30693,X30694,X30695,X30696] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X30696,X30695,X30694)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30696),X30693))
| hAPP(hAPP(c_Finite__Set_Ofold(X30696,X30695,X30694),X30692),hAPP(hAPP(c_Set_Oinsert(X30696),X30691),X30693)) = hAPP(hAPP(X30694,X30691),hAPP(hAPP(c_Finite__Set_Ofold(X30696,X30695,X30694),X30692),X30693)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem])]) ).
fof(i_0_8041,plain,
! [X33607,X33608,X33609,X33610,X33611] :
( ( X33608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33608),X33607) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33609),hAPP(c_List_Oset(tc_Nat_Onat),X33607)))
| X33609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33608),X33607) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk467_2(X33610,X33611)),hAPP(c_List_Oset(tc_Nat_Onat),X33610)))
| X33611 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33611),X33610) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( esk467_2(X33610,X33611) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X33611 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33611),X33610) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__eq__0__conv])])])])])]) ).
fof(i_0_8042,plain,
! [X17488,X17489,X17490,X17491,X17492,X17493] :
( ( ~ hBOOL(hAPP(X17493,X17490))
| hBOOL(hAPP(X17493,X17490))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17493,X17492,X17491),X17490,X17489,X17488) )
& ( c_Natural_Oevaln(X17491,X17490,X17489,X17488)
| hBOOL(hAPP(X17493,X17490))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17493,X17492,X17491),X17490,X17489,X17488) )
& ( ~ hBOOL(hAPP(X17493,X17490))
| c_Natural_Oevaln(X17492,X17490,X17489,X17488)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17493,X17492,X17491),X17490,X17489,X17488) )
& ( c_Natural_Oevaln(X17491,X17490,X17489,X17488)
| c_Natural_Oevaln(X17492,X17490,X17489,X17488)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17493,X17492,X17491),X17490,X17489,X17488) )
& ( ~ hBOOL(hAPP(X17493,X17490))
| ~ c_Natural_Oevaln(X17492,X17490,X17489,X17488)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17493,X17492,X17491),X17490,X17489,X17488) )
& ( hBOOL(hAPP(X17493,X17490))
| ~ c_Natural_Oevaln(X17491,X17490,X17489,X17488)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17493,X17492,X17491),X17490,X17489,X17488) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5658])])]) ).
fof(i_0_8043,plain,
! [X17482,X17483,X17484,X17485,X17486,X17487] :
( ( ~ hBOOL(hAPP(X17487,X17484))
| hBOOL(hAPP(X17487,X17484))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17487,X17486,X17485),X17484,X17483,X17482) )
& ( c_Natural_Oevaln(X17485,X17484,X17483,X17482)
| hBOOL(hAPP(X17487,X17484))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17487,X17486,X17485),X17484,X17483,X17482) )
& ( ~ hBOOL(hAPP(X17487,X17484))
| c_Natural_Oevaln(X17486,X17484,X17483,X17482)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17487,X17486,X17485),X17484,X17483,X17482) )
& ( c_Natural_Oevaln(X17485,X17484,X17483,X17482)
| c_Natural_Oevaln(X17486,X17484,X17483,X17482)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17487,X17486,X17485),X17484,X17483,X17482) )
& ( ~ hBOOL(hAPP(X17487,X17484))
| ~ c_Natural_Oevaln(X17486,X17484,X17483,X17482)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17487,X17486,X17485),X17484,X17483,X17482) )
& ( hBOOL(hAPP(X17487,X17484))
| ~ c_Natural_Oevaln(X17485,X17484,X17483,X17482)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17487,X17486,X17485),X17484,X17483,X17482) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5659])])]) ).
fof(i_0_8044,plain,
! [X17335,X17336,X17337,X17338,X17339,X17340] :
( ( ~ hBOOL(hAPP(X17340,X17337))
| hBOOL(hAPP(X17340,X17337))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17340,X17339,X17338),X17337,X17336,X17335) )
& ( c_Natural_Oevaln(X17338,X17337,X17336,X17335)
| hBOOL(hAPP(X17340,X17337))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17340,X17339,X17338),X17337,X17336,X17335) )
& ( ~ hBOOL(hAPP(X17340,X17337))
| c_Natural_Oevaln(X17339,X17337,X17336,X17335)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17340,X17339,X17338),X17337,X17336,X17335) )
& ( c_Natural_Oevaln(X17338,X17337,X17336,X17335)
| c_Natural_Oevaln(X17339,X17337,X17336,X17335)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17340,X17339,X17338),X17337,X17336,X17335) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5660])])]) ).
fof(i_0_8045,plain,
! [X17315,X17316,X17317,X17318,X17319,X17320] :
( ~ c_Natural_Oevaln(X17320,X17319,X17318,X17317)
| ~ c_Natural_Oevaln(X17316,X17317,X17318,X17315)
| c_Natural_Oevaln(c_Com_Ocom_OSemi(X17320,X17316),X17319,X17318,X17315) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OSemi])]) ).
fof(i_0_8046,plain,
! [X19106,X19107] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19107))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19107),X19106))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19106))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19107),X19106))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19107))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19106))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19107),X19106))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])]) ).
fof(i_0_8047,plain,
! [X19620,X19621] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19620))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19620),X19621))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).
fof(i_0_8048,plain,
! [X20115,X20116,X20117] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20117),X20116)),X20115)),X20116) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20115),X20116),
inference(variable_rename,[status(thm)],[fact_mod__mult__self4]) ).
fof(i_0_8049,plain,
! [X31360,X31361,X31362] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31362,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X31362,tc_HOL_Obool),tc_HOL_Obool)),X31361),X31360)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31362,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31362,tc_HOL_Obool),X31361)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31362,tc_HOL_Obool),X31360)),
inference(variable_rename,[status(thm)],[fact_Union__Un__distrib]) ).
fof(i_0_8050,plain,
! [X31381,X31382,X31383] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31383,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X31383,tc_HOL_Obool),tc_HOL_Obool)),X31382),X31381)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31383,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31383,tc_HOL_Obool),X31382)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31383,tc_HOL_Obool),X31381)),
inference(variable_rename,[status(thm)],[fact_Inter__Un__distrib]) ).
fof(i_0_8051,plain,
! [X20170,X20171,X20172,X20173,X20174,X20175,X20176,X20177] :
( ( X20170 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20172,X20171))
| ~ hBOOL(hAPP(X20172,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20171,X20170))) )
& ( X20170 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20174),X20170))
| X20171 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20170),X20173)),X20174)
| hBOOL(hAPP(X20172,X20174))
| ~ hBOOL(hAPP(X20172,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20171,X20170))) )
& ( X20175 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20177,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20176,X20175))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk64_3(X20175,X20176,X20177)),X20175))
| X20175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20177,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20176,X20175))) )
& ( X20176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20175),esk63_3(X20175,X20176,X20177))),esk64_3(X20175,X20176,X20177))
| X20175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20177,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20176,X20175))) )
& ( ~ hBOOL(hAPP(X20177,esk64_3(X20175,X20176,X20177)))
| X20175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20177,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20176,X20175))) )
& ( X20175 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X20177,X20176))
| hBOOL(hAPP(X20177,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20176,X20175))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk64_3(X20175,X20176,X20177)),X20175))
| ~ hBOOL(hAPP(X20177,X20176))
| hBOOL(hAPP(X20177,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20176,X20175))) )
& ( X20176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20175),esk63_3(X20175,X20176,X20177))),esk64_3(X20175,X20176,X20177))
| ~ hBOOL(hAPP(X20177,X20176))
| hBOOL(hAPP(X20177,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20176,X20175))) )
& ( ~ hBOOL(hAPP(X20177,esk64_3(X20175,X20176,X20177)))
| ~ hBOOL(hAPP(X20177,X20176))
| hBOOL(hAPP(X20177,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20176,X20175))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mod])])])])])]) ).
fof(i_0_8052,plain,
! [X33696,X33697,X33698,X33699,X33700,X33701,X33702] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33698)),X33697),c_List_Olists(X33698,X33696)))
| ~ hBOOL(hAPP(hAPP(c_member(X33698),X33699),hAPP(c_List_Oset(X33698),X33697)))
| hBOOL(hAPP(hAPP(c_member(X33698),X33699),X33696)) )
& ( hBOOL(hAPP(hAPP(c_member(X33702),esk468_3(X33700,X33701,X33702)),hAPP(c_List_Oset(X33702),X33701)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33702)),X33701),c_List_Olists(X33702,X33700))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X33702),esk468_3(X33700,X33701,X33702)),X33700))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33702)),X33701),c_List_Olists(X33702,X33700))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lists__conv__set])])])])])]) ).
fof(i_0_8053,plain,
! [X33556,X33557,X33558,X33559] : c_List_Olist_Olist__size(X33559,X33558,hAPP(hAPP(c_List_Olist_OCons(X33559),X33557),X33556)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X33558,X33557)),c_List_Olist_Olist__size(X33559,X33558,X33556))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_list_Osize_I2_J]) ).
fof(i_0_8054,plain,
! [X23350,X23351,X23352,X23353,X23354] :
( ~ class_Rings_Ocomm__semiring__1(X23354)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23354),X23353),X23352))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23351),X23350))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23354),hAPP(hAPP(c_Power_Opower__class_Opower(X23354),X23353),X23351)),hAPP(hAPP(c_Power_Opower__class_Opower(X23354),X23352),X23350))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__le])]) ).
fof(i_0_8055,plain,
! [X26310,X26311,X26312,X26313] : c_Map_Orestrict__map(X26313,X26312,X26311,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26313,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26313),X26310),c_Orderings_Obot__class_Obot(tc_fun(X26313,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26313,tc_Option_Ooption(X26312)),X26311),X26310),c_Option_Ooption_ONone(X26312)),
inference(variable_rename,[status(thm)],[fact_restrict__complement__singleton__eq]) ).
fof(i_0_8056,plain,
! [X32414,X32415,X32416] : c_Random_Oselect__weight(X32416,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X32416)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X32416),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X32415)),X32414)) = c_Random_Oselect__weight(X32416,X32414),
inference(variable_rename,[status(thm)],[fact_select__weight__cons__zero]) ).
fof(i_0_8057,plain,
! [X19912,X19913,X19914,X19915] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19914))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19914))
| X19914 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19915,X19914) = X19912
| X19915 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19914),X19913)),X19912) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19914),X19912))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19912),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19914))
| X19914 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19915,X19914) = X19912
| X19915 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19914),X19913)),X19912) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19912))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19912),X19914))
| X19914 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19915,X19914) = X19912
| X19915 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19914),X19913)),X19912) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19914),X19912))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19912),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19912))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19912),X19914))
| X19914 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19915,X19914) = X19912
| X19915 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19914),X19913)),X19912) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5661])])]) ).
fof(i_0_8058,plain,
! [X34206,X34207] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X34207)),c_List_Otranspose__rel(X34207)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34207)),c_List_Olist_ONil(X34207)),X34206)))
| c_List_Otranspose(X34207,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34207)),c_List_Olist_ONil(X34207)),X34206)) = c_List_Otranspose(X34207,X34206) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I2_J])]) ).
cnf(i_0_8059,plain,
c_List_Ofoldr(X1,X2,X3,c_List_Olist_ONil(X1),X4) = X4,
inference(split_conjunct,[status(thm)],[i_0_5662]) ).
fof(i_0_8060,plain,
! [X27421,X27422,X27423] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27423,tc_HOL_Obool)),X27422),X27421) != c_Orderings_Obot__class_Obot(tc_fun(X27423,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27423,tc_HOL_Obool)),X27422),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27423,tc_HOL_Obool)),X27421))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27423,tc_HOL_Obool)),X27422),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27423,tc_HOL_Obool)),X27421)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27423,tc_HOL_Obool)),X27422),X27421) = c_Orderings_Obot__class_Obot(tc_fun(X27423,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl])]) ).
fof(i_0_8061,plain,
! [X24587,X24588,X24589] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24589),X24588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24589,tc_HOL_Obool)),X24587),X24588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24589),X24588)),hAPP(c_Finite__Set_Ocard(X24589),X24587)))
| X24587 = X24588 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).
fof(i_0_8062,plain,
! [X31288,X31289,X31290] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31290,tc_HOL_Obool)),X31289),X31288))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31290,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31290,tc_HOL_Obool),X31288)),X31289)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__lower])]) ).
fof(i_0_8063,plain,
! [X30346,X30347,X30348,X30349,X30350] : hAPP(c_Relation_Oconverse(X30350,X30349),hAPP(hAPP(c_Relation_Orel__comp(X30350,X30348,X30349),X30347),X30346)) = hAPP(hAPP(c_Relation_Orel__comp(X30349,X30348,X30350),hAPP(c_Relation_Oconverse(X30348,X30349),X30346)),hAPP(c_Relation_Oconverse(X30350,X30348),X30347)),
inference(variable_rename,[status(thm)],[fact_converse__rel__comp]) ).
fof(i_0_8064,plain,
! [X19941,X19942,X19943,X19944] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19943))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19943))
| X19943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19944),X19943) = X19942
| X19944 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19943),X19942)),X19941) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19943),X19941))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19941),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19943))
| X19943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19944),X19943) = X19942
| X19944 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19943),X19942)),X19941) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19943))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19941))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19941),X19943))
| X19943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19944),X19943) = X19942
| X19944 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19943),X19942)),X19941) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19943),X19941))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19941),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19941))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19941),X19943))
| X19943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19944),X19943) = X19942
| X19944 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19943),X19942)),X19941) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5663])])]) ).
fof(i_0_8065,plain,
! [X22257,X22258,X22259,X22260] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22260),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22260),X22259),X22258)),X22257))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22260),X22259),X22257))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22260),X22258),X22257))
| ~ class_Orderings_Olinorder(X22260) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22260),X22259),X22257))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22260),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22260),X22259),X22258)),X22257))
| ~ class_Orderings_Olinorder(X22260) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22260),X22258),X22257))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22260),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22260),X22259),X22258)),X22257))
| ~ class_Orderings_Olinorder(X22260) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj])])]) ).
fof(i_0_8066,plain,
! [X22353,X22354,X22355,X22356] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22356),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22356),X22355),X22354)),X22353))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22356),X22355),X22353))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22356),X22354),X22353))
| ~ class_Orderings_Olinorder(X22356) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22356),X22355),X22353))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22356),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22356),X22355),X22354)),X22353))
| ~ class_Orderings_Olinorder(X22356) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22356),X22354),X22353))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22356),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22356),X22355),X22354)),X22353))
| ~ class_Orderings_Olinorder(X22356) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj])])]) ).
fof(i_0_8067,plain,
! [X20160,X20161,X20162,X20163,X20164,X20165,X20166,X20167] :
( ( X20160 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20162,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X20162,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20161),X20160))) )
& ( X20160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20164),X20160))
| X20161 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20160),X20163)),X20164)
| hBOOL(hAPP(X20162,X20163))
| ~ hBOOL(hAPP(X20162,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20161),X20160))) )
& ( X20165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20167,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20166),X20165))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_3(X20165,X20166,X20167)),X20165))
| X20165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20167,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20166),X20165))) )
& ( X20166 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20165),esk61_3(X20165,X20166,X20167))),esk62_3(X20165,X20166,X20167))
| X20165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20167,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20166),X20165))) )
& ( ~ hBOOL(hAPP(X20167,esk61_3(X20165,X20166,X20167)))
| X20165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20167,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20166),X20165))) )
& ( X20165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X20167,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20167,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20166),X20165))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_3(X20165,X20166,X20167)),X20165))
| ~ hBOOL(hAPP(X20167,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20167,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20166),X20165))) )
& ( X20166 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20165),esk61_3(X20165,X20166,X20167))),esk62_3(X20165,X20166,X20167))
| ~ hBOOL(hAPP(X20167,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20167,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20166),X20165))) )
& ( ~ hBOOL(hAPP(X20167,esk61_3(X20165,X20166,X20167)))
| ~ hBOOL(hAPP(X20167,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20167,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20166),X20165))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div])])])])])]) ).
fof(i_0_8068,plain,
! [X25968,X25969,X25970] :
( ~ class_Orderings_Olinorder(X25970)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25970),X25969))
| X25968 = c_Orderings_Obot__class_Obot(tc_fun(X25970,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25970,tc_HOL_Obool)),X25968),X25969))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25970),c_Big__Operators_Olattice_OSup__fin(X25970,c_Orderings_Oord__class_Omax(X25970),X25968)),c_Big__Operators_Olattice_OSup__fin(X25970,c_Orderings_Oord__class_Omax(X25970),X25969)) = c_Big__Operators_Olattice_OSup__fin(X25970,c_Orderings_Oord__class_Omax(X25970),X25969) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem])]) ).
fof(i_0_8069,plain,
! [X25965,X25966,X25967] :
( ~ class_Orderings_Olinorder(X25967)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25967),X25966))
| X25965 = c_Orderings_Obot__class_Obot(tc_fun(X25967,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25967,tc_HOL_Obool)),X25965),X25966))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25967),c_Big__Operators_Olattice_OInf__fin(X25967,c_Orderings_Oord__class_Omin(X25967),X25965)),c_Big__Operators_Olattice_OInf__fin(X25967,c_Orderings_Oord__class_Omin(X25967),X25966)) = c_Big__Operators_Olattice_OInf__fin(X25967,c_Orderings_Oord__class_Omin(X25967),X25966) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem])]) ).
cnf(i_0_8070,plain,
hAPP(c_List_Orotate(X1,hAPP(c_Nat_OSuc,X2)),X3) = hAPP(c_List_Orotate1(X1),hAPP(c_List_Orotate(X1,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_5664]) ).
fof(i_0_8071,plain,
! [X30839,X30840,X30841,X30842,X30843,X30844] :
( ~ c_Finite__Set_Ofun__left__comm(X30844,X30843,X30842)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30844),X30841))
| hBOOL(hAPP(hAPP(c_member(X30844),X30840),X30841))
| hAPP(hAPP(c_Finite__Set_Ofold(X30844,X30843,X30842),X30839),hAPP(hAPP(c_Set_Oinsert(X30844),X30840),X30841)) = hAPP(hAPP(c_Finite__Set_Ofold(X30844,X30843,X30842),hAPP(hAPP(X30842,X30840),X30839)),X30841) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5665])]) ).
fof(i_0_8072,plain,
! [X31603,X31604,X31605,X31606,X31607] :
( ~ hBOOL(hAPP(hAPP(c_member(X31607),X31606),c_Map_Odom(X31607,X31605,X31604)))
| hAPP(c_Map_Omap__add(X31607,X31605,X31603,X31604),X31606) = hAPP(X31604,X31606) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__dom__app__simps_I1_J])]) ).
fof(i_0_8073,plain,
! [X17726,X17727,X17728,X17729,X17730] :
( ~ hBOOL(hAPP(X17730,X17729))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17728),X17729),X17727))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17730,X17728)),X17727),X17726))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17730,X17728)),X17729),X17726)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OWhileTrue])]) ).
cnf(i_0_8074,plain,
( c_List_Oupt(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X3
| c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_5666]) ).
fof(i_0_8075,plain,
! [X31322,X31323] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X31323,tc_HOL_Obool),tc_HOL_Obool)),X31322),hAPP(c_Set_OPow(X31323),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31323,tc_HOL_Obool),X31322)))),
inference(variable_rename,[status(thm)],[fact_subset__Pow__Union]) ).
fof(i_0_8076,plain,
! [X32183,X32184,X32185,X32186,X32187] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32187)),X32186) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32185)),X32184)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32187)),X32183) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32185)),X32184)
| ~ hBOOL(hAPP(c_List_Odistinct(X32185),X32184))
| c_Map_Omap__of(X32185,X32187,hAPP(hAPP(c_List_Ozip(X32185,X32187),X32184),X32186)) != c_Map_Omap__of(X32185,X32187,hAPP(hAPP(c_List_Ozip(X32185,X32187),X32184),X32183))
| X32186 = X32183 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__zip__inject])]) ).
fof(i_0_8077,plain,
! [X26985,X26986,X26987,X26988] :
( ~ hBOOL(hAPP(hAPP(c_member(X26988),X26987),X26986))
| ~ hBOOL(hAPP(hAPP(c_member(X26988),X26987),X26985))
| hBOOL(hAPP(hAPP(c_member(X26988),X26987),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26988,tc_HOL_Obool)),X26986),X26985))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntI])]) ).
fof(i_0_8078,plain,
! [X31599,X31600,X31601,X31602] : c_Map_Odom(X31602,X31601,c_Map_Omap__add(X31602,X31601,X31600,X31599)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31602,tc_HOL_Obool)),c_Map_Odom(X31602,X31601,X31599)),c_Map_Odom(X31602,X31601,X31600)),
inference(variable_rename,[status(thm)],[fact_dom__map__add]) ).
fof(i_0_8079,plain,
! [X23607,X23608,X23609,X23610] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23609),X23608))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23610),X23607),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23608),hAPP(c_Nat_OSuc,X23609))) = c_Groups_Ozero__class_Ozero(X23610)
| ~ class_Groups_Ocomm__monoid__add(X23610) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23609),X23608))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23610),X23607),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23608),hAPP(c_Nat_OSuc,X23609))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23610),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23610),X23607),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23608),X23609))),hAPP(X23607,X23609))
| ~ class_Groups_Ocomm__monoid__add(X23610) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5667])])]) ).
fof(i_0_8080,plain,
! [X22499,X22500,X22501,X22502,X22503,X22504] :
( ( hBOOL(hAPP(X22504,hAPP(c_Product__Type_Ofst(X22500,X22499),hAPP(hAPP(c_Product__Type_OPair(X22500,X22499),X22503),X22501))))
| ~ hBOOL(hAPP(X22502,X22501))
| ~ hBOOL(hAPP(X22504,X22503)) )
& ( hBOOL(hAPP(X22502,hAPP(c_Product__Type_Osnd(X22500,X22499),hAPP(hAPP(c_Product__Type_OPair(X22500,X22499),X22503),X22501))))
| ~ hBOOL(hAPP(X22502,X22501))
| ~ hBOOL(hAPP(X22504,X22503)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conjI__realizer])])]) ).
fof(i_0_8081,plain,
! [X31036,X31037,X31038,X31039,X31040,X31041] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31041)
| hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31040,tc_fun(X31039,X31041)),X31038),X31037),X31036) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31040,X31041),X31038),hAPP(hAPP(c_COMBC(X31040,X31039,X31041),X31037),X31036)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__apply])]) ).
fof(i_0_8082,plain,
! [X24198,X24199,X24200,X24201,X24202,X24203] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X24203)
| hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24202,tc_fun(X24201,X24203)),X24200),X24199),X24198) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24202,X24203),X24200),hAPP(hAPP(c_COMBC(X24202,X24201,X24203),X24199),X24198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__apply])]) ).
fof(i_0_8083,plain,
! [X24547,X24548,X24549] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24549),X24548))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24549),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24549,tc_HOL_Obool)),X24548),X24547))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24549),X24547))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24549),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24549,tc_HOL_Obool)),X24548),X24547))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24549),X24548))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24549),X24547))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24549),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24549,tc_HOL_Obool)),X24548),X24547))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])]) ).
fof(i_0_8084,plain,
! [X23842,X23843,X23844,X23845] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23845,tc_HOL_Obool)),X23844),X23843),X23842))
| hBOOL(hAPP(X23844,X23842))
| hBOOL(hAPP(X23843,X23842)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5668])]) ).
fof(i_0_8085,plain,
! [X27363,X27364,X27365] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27365,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27365,tc_HOL_Obool)),X27364),X27363)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27365,tc_HOL_Obool)),X27364),X27363)) = X27364,
inference(variable_rename,[status(thm)],[fact_Un__Diff__Int]) ).
fof(i_0_8086,plain,
! [X33688,X33689,X33690] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33690,tc_HOL_Obool)),X33689),X33688))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X33690),tc_HOL_Obool)),c_List_Olists(X33690,X33689)),c_List_Olists(X33690,X33688))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__mono])]) ).
fof(i_0_8087,plain,
! [X21740,X21741,X21742,X21743] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21743),X21741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21743),X21740),X21742)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21743),X21740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21743),X21741),X21742)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21743),X21742),c_Groups_Ozero__class_Ozero(X21743)))
| ~ class_Fields_Olinordered__field(X21743) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21743),X21740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21743),X21741),X21742)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21743),X21741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21743),X21740),X21742)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21743),X21742),c_Groups_Ozero__class_Ozero(X21743)))
| ~ class_Fields_Olinordered__field(X21743) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq])])]) ).
fof(i_0_8088,plain,
! [X21620,X21621,X21622,X21623] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21623),X21621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21623),X21620),X21622)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21623),X21620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21623),X21621),X21622)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21623),X21622),c_Groups_Ozero__class_Ozero(X21623)))
| ~ class_Fields_Olinordered__field(X21623) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21623),X21620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21623),X21621),X21622)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21623),X21621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21623),X21620),X21622)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21623),X21622),c_Groups_Ozero__class_Ozero(X21623)))
| ~ class_Fields_Olinordered__field(X21623) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq])])]) ).
fof(i_0_8089,plain,
! [X29780,X29781] :
( ( ~ c_Wellfounded_OwfP(X29781,X29780)
| c_Wellfounded_Owf(X29781,hAPP(c_Set_OCollect(tc_prod(X29781,X29781)),hAPP(c_Product__Type_Oprod_Oprod__case(X29781,X29781,tc_HOL_Obool),X29780))) )
& ( ~ c_Wellfounded_Owf(X29781,hAPP(c_Set_OCollect(tc_prod(X29781,X29781)),hAPP(c_Product__Type_Oprod_Oprod__case(X29781,X29781,tc_HOL_Obool),X29780)))
| c_Wellfounded_OwfP(X29781,X29780) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__def])]) ).
fof(i_0_8090,plain,
! [X20017,X20018] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20017),X20018)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20017),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20018)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20017),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20017),X20018)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20018)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])]) ).
fof(i_0_8091,plain,
! [X28644,X28645,X28646,X28647,X28648,X28649] :
( ( hAPP(hAPP(c_Product__Type_OSigma(X28646,X28649),X28645),hAPP(c_COMBK(tc_fun(X28649,tc_HOL_Obool),X28646),X28647)) != hAPP(hAPP(c_Product__Type_OSigma(X28646,X28649),X28644),hAPP(c_COMBK(tc_fun(X28649,tc_HOL_Obool),X28646),X28647))
| X28645 = X28644
| ~ hBOOL(hAPP(hAPP(c_member(X28649),X28648),X28647)) )
& ( X28645 != X28644
| hAPP(hAPP(c_Product__Type_OSigma(X28646,X28649),X28645),hAPP(c_COMBK(tc_fun(X28649,tc_HOL_Obool),X28646),X28647)) = hAPP(hAPP(c_Product__Type_OSigma(X28646,X28649),X28644),hAPP(c_COMBK(tc_fun(X28649,tc_HOL_Obool),X28646),X28647))
| ~ hBOOL(hAPP(hAPP(c_member(X28649),X28648),X28647)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2])])]) ).
fof(i_0_8092,plain,
! [X19910,X19911] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19911))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19911),X19910)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19911,X19910) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19911),X19910) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial])]) ).
fof(i_0_8093,plain,
! [X30034,X30035] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30035,tc_HOL_Obool)),esk351_2(X30034,X30035)),hAPP(c_Relation_OImage(X30035,X30035,X30034),esk351_2(X30034,X30035))))
| c_Wellfounded_Owf(X30035,X30034) )
& ( esk351_2(X30034,X30035) != c_Orderings_Obot__class_Obot(tc_fun(X30035,tc_HOL_Obool))
| c_Wellfounded_Owf(X30035,X30034) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfI__pf])])])]) ).
fof(i_0_8094,plain,
! [X22041,X22042,X22043,X22044,X22045] :
( ~ hBOOL(hAPP(hAPP(X22045,X22044),X22043))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22042,X22041,tc_HOL_Obool),X22045),hAPP(hAPP(c_Product__Type_OPair(X22042,X22041),X22044),X22043))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitI])]) ).
fof(i_0_8095,plain,
! [X22036,X22037,X22038,X22039,X22040] :
( ~ hBOOL(hAPP(hAPP(X22040,X22039),X22038))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22037,X22036,tc_HOL_Obool),X22040),hAPP(hAPP(c_Product__Type_OPair(X22037,X22036),X22039),X22038))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__caseI])]) ).
fof(i_0_8096,plain,
! [X20019,X20020] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20019),X20020)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20019))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20020),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20019))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20019),X20020)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20020),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__neg__iff])])]) ).
fof(i_0_8097,plain,
! [X20444,X20445,X20446] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20446),X20445)),X20444))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20446),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20444),X20445))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20446),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20444),X20445)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20446),X20445)),X20444)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).
fof(i_0_8098,plain,
! [X20406,X20407,X20408] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20408),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20407),X20406)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20408),X20406)),X20407)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20408),X20406)),X20407))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20408),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20407),X20406))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).
fof(i_0_8099,plain,
! [X24509,X24510,X24511] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24511),X24510))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24511,tc_HOL_Obool)),X24510),X24509))
| hAPP(c_Finite__Set_Ocard(X24511),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24511,tc_HOL_Obool)),X24509),X24510)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24511),X24509)),hAPP(c_Finite__Set_Ocard(X24511),X24510)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset])]) ).
fof(i_0_8100,plain,
! [X27836,X27837,X27838,X27839,X27840] :
( ~ c_Finite__Set_Ofolding__idem(X27840,X27839,X27838,X27837)
| hAPP(c_Fun_Ocomp(X27839,X27839,X27839,hAPP(X27838,X27836)),hAPP(X27838,X27836)) = hAPP(X27838,X27836) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__comp])]) ).
cnf(i_0_8101,plain,
c_Int_Opred(c_Int_OBit1(X1)) = c_Int_OBit0(X1),
inference(split_conjunct,[status(thm)],[i_0_5669]) ).
fof(i_0_8102,plain,
! [X21036,X21037,X21038] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21038)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21038)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21037)),X21036)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21037)),X21036) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21037)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21038)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21037)),X21036)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21038)),X21036)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21038))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21037)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21038)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21037)),X21036)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21038),X21037))),X21036)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21038))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5670])])]) ).
cnf(i_0_8103,plain,
c_Transitive__Closure_Otrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_5671]) ).
cnf(i_0_8104,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X3,X4))) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Oupt(X3,X4)))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5672]) ).
cnf(i_0_8105,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Oupt(X3,X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X3,X4)))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5673]) ).
fof(i_0_8106,plain,
! [X26432,X26433,X26434] : hAPP(c_Relation_OField(X26434),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X26434,X26434),tc_HOL_Obool)),X26433),X26432)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26434,tc_HOL_Obool)),hAPP(c_Relation_OField(X26434),X26433)),hAPP(c_Relation_OField(X26434),X26432)),
inference(variable_rename,[status(thm)],[fact_Field__Un]) ).
fof(i_0_8107,plain,
! [X32204,X32205,X32206,X32207,X32208] :
( ( hAPP(hAPP(c_List_Omap(tc_prod(X32208,X32206),X32208),c_Product__Type_Ofst(X32208,X32206)),X32204) = X32207
| hAPP(hAPP(c_List_Ozip(X32208,X32206),X32207),X32205) != X32204
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32208)),X32207) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32206)),X32205) )
& ( hAPP(hAPP(c_List_Omap(tc_prod(X32208,X32206),X32206),c_Product__Type_Osnd(X32208,X32206)),X32204) = X32205
| hAPP(hAPP(c_List_Ozip(X32208,X32206),X32207),X32205) != X32204
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32208)),X32207) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32206)),X32205) )
& ( hAPP(hAPP(c_List_Omap(tc_prod(X32208,X32206),X32208),c_Product__Type_Ofst(X32208,X32206)),X32204) != X32207
| hAPP(hAPP(c_List_Omap(tc_prod(X32208,X32206),X32206),c_Product__Type_Osnd(X32208,X32206)),X32204) != X32205
| hAPP(hAPP(c_List_Ozip(X32208,X32206),X32207),X32205) = X32204
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32208)),X32207) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32206)),X32205) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__eq__conv])])]) ).
fof(i_0_8108,plain,
! [X26232,X26233,X26234,X26235,X26236,X26237,X26238] :
( ( X26233 != X26235
| X26233 = X26235
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26238,tc_Option_Ooption(X26237)),X26236),X26235),hAPP(c_Option_Ooption_OSome(X26237),X26234)),X26233) != hAPP(c_Option_Ooption_OSome(X26237),X26232) )
& ( hAPP(X26236,X26233) = hAPP(c_Option_Ooption_OSome(X26237),X26232)
| X26233 = X26235
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26238,tc_Option_Ooption(X26237)),X26236),X26235),hAPP(c_Option_Ooption_OSome(X26237),X26234)),X26233) != hAPP(c_Option_Ooption_OSome(X26237),X26232) )
& ( X26233 != X26235
| X26234 = X26232
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26238,tc_Option_Ooption(X26237)),X26236),X26235),hAPP(c_Option_Ooption_OSome(X26237),X26234)),X26233) != hAPP(c_Option_Ooption_OSome(X26237),X26232) )
& ( hAPP(X26236,X26233) = hAPP(c_Option_Ooption_OSome(X26237),X26232)
| X26234 = X26232
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26238,tc_Option_Ooption(X26237)),X26236),X26235),hAPP(c_Option_Ooption_OSome(X26237),X26234)),X26233) != hAPP(c_Option_Ooption_OSome(X26237),X26232) )
& ( X26233 != X26235
| X26234 != X26232
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26238,tc_Option_Ooption(X26237)),X26236),X26235),hAPP(c_Option_Ooption_OSome(X26237),X26234)),X26233) = hAPP(c_Option_Ooption_OSome(X26237),X26232) )
& ( X26233 = X26235
| hAPP(X26236,X26233) != hAPP(c_Option_Ooption_OSome(X26237),X26232)
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26238,tc_Option_Ooption(X26237)),X26236),X26235),hAPP(c_Option_Ooption_OSome(X26237),X26234)),X26233) = hAPP(c_Option_Ooption_OSome(X26237),X26232) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__Some__unfold])])]) ).
fof(i_0_8109,plain,
! [X26973,X26974,X26975,X26976] :
( ( hBOOL(hAPP(X26975,X26973))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26976,tc_HOL_Obool)),X26975),X26974),X26973)) )
& ( hBOOL(hAPP(X26974,X26973))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26976,tc_HOL_Obool)),X26975),X26974),X26973)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5674])])]) ).
fof(i_0_8110,plain,
! [X27165,X27166,X27167,X27168] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27168,tc_HOL_Obool)),X27167),X27166),X27165))
| hBOOL(hAPP(X27167,X27165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])]) ).
fof(i_0_8111,plain,
! [X27161,X27162,X27163,X27164] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27164,tc_HOL_Obool)),X27163),X27162),X27161))
| hBOOL(hAPP(X27162,X27161)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])]) ).
cnf(i_0_8112,plain,
hAPP(c_List_Orotate1(X1),hAPP(c_List_Orotate(X1,X2),X3)) = hAPP(c_List_Orotate(X1,X2),hAPP(c_List_Orotate1(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_5675]) ).
fof(i_0_8113,plain,
! [X32312,X32313,X32314,X32315,X32316,X32317] :
( ( hBOOL(hAPP(hAPP(X32316,X32315),X32313))
| ~ c_List_Olistrelp(X32317,X32316,hAPP(hAPP(c_List_Olist_OCons(X32317),X32315),X32314),hAPP(hAPP(c_List_Olist_OCons(X32317),X32313),X32312)) )
& ( c_List_Olistrelp(X32317,X32316,X32314,X32312)
| ~ c_List_Olistrelp(X32317,X32316,hAPP(hAPP(c_List_Olist_OCons(X32317),X32315),X32314),hAPP(hAPP(c_List_Olist_OCons(X32317),X32313),X32312)) )
& ( ~ hBOOL(hAPP(hAPP(X32316,X32315),X32313))
| ~ c_List_Olistrelp(X32317,X32316,X32314,X32312)
| c_List_Olistrelp(X32317,X32316,hAPP(hAPP(c_List_Olist_OCons(X32317),X32315),X32314),hAPP(hAPP(c_List_Olist_OCons(X32317),X32313),X32312)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J])])]) ).
fof(i_0_8114,plain,
! [X32306,X32307,X32308,X32309,X32310,X32311] :
( ~ hBOOL(hAPP(hAPP(X32311,X32310),X32309))
| ~ c_List_Olistrelp(X32308,X32311,X32307,X32306)
| c_List_Olistrelp(X32308,X32311,hAPP(hAPP(c_List_Olist_OCons(X32308),X32310),X32307),hAPP(hAPP(c_List_Olist_OCons(X32308),X32309),X32306)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_OCons])]) ).
cnf(i_0_8115,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5676]) ).
fof(i_0_8116,plain,
! [X29109] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X29109),c_Int_OInteg))
| X29109 = hAPP(c_Int_ORep__Integ,esk307_1(X29109)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__cases])])]) ).
fof(i_0_8117,plain,
! [X31497,X31498,X31499] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31499,tc_HOL_Obool)),esk416_3(X31497,X31498,X31499)),X31498))
| hBOOL(hAPP(hAPP(c_member(X31499),X31497),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31499,tc_HOL_Obool),X31498))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X31499),X31497),esk416_3(X31497,X31498,X31499)))
| hBOOL(hAPP(hAPP(c_member(X31499),X31497),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31499,tc_HOL_Obool),X31498))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterI])])])]) ).
fof(i_0_8118,plain,
! [X33778,X33779,X33780,X33783,X33784,X33785,X33786,X33787] :
( ( X33779 = hAPP(hAPP(c_List_Olist_OCons(X33780),esk475_3(X33778,X33779,X33780)),esk476_3(X33778,X33779,X33780))
| X33779 = c_List_Olist_ONil(X33780)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33780)),X33779),c_List_Olists(X33780,X33778))) )
& ( hBOOL(hAPP(hAPP(c_member(X33780),esk475_3(X33778,X33779,X33780)),X33778))
| X33779 = c_List_Olist_ONil(X33780)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33780)),X33779),c_List_Olists(X33780,X33778))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33780)),esk476_3(X33778,X33779,X33780)),c_List_Olists(X33780,X33778)))
| X33779 = c_List_Olist_ONil(X33780)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33780)),X33779),c_List_Olists(X33780,X33778))) )
& ( X33784 != c_List_Olist_ONil(X33785)
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33785)),X33784),c_List_Olists(X33785,X33783))) )
& ( X33784 != hAPP(hAPP(c_List_Olist_OCons(X33785),X33786),X33787)
| ~ hBOOL(hAPP(hAPP(c_member(X33785),X33786),X33783))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33785)),X33787),c_List_Olists(X33785,X33783)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33785)),X33784),c_List_Olists(X33785,X33783))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists_Osimps])])])])])]) ).
fof(i_0_8119,plain,
! [X27569,X27570,X27571,X27572,X27573] :
( ~ c_Finite__Set_Ofolding__one(X27573,X27572,X27571)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27573),X27570))
| X27570 = c_Orderings_Obot__class_Obot(tc_fun(X27573,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27573),X27569))
| X27569 = c_Orderings_Obot__class_Obot(tc_fun(X27573,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27573,tc_HOL_Obool)),X27570),X27569) != c_Orderings_Obot__class_Obot(tc_fun(X27573,tc_HOL_Obool))
| hAPP(X27571,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27573,tc_HOL_Obool)),X27570),X27569)) = hAPP(hAPP(X27572,hAPP(X27571,X27570)),hAPP(X27571,X27569)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint])]) ).
fof(i_0_8120,plain,
! [X20271,X20272,X20273,X20274] :
( ~ class_Divides_Oring__div(X20274)
| c_Divides_Odiv__class_Omod(X20274,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20274),X20273),X20272),X20271) = c_Divides_Odiv__class_Omod(X20274,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20274),c_Divides_Odiv__class_Omod(X20274,X20273,X20271)),c_Divides_Odiv__class_Omod(X20274,X20272,X20271)),X20271) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__eq])]) ).
fof(i_0_8121,plain,
! [X19815,X19816,X19817,X19818] :
( ~ class_Divides_Osemiring__div(X19818)
| c_Divides_Odiv__class_Omod(X19818,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19818),X19817),X19816),X19815) = c_Divides_Odiv__class_Omod(X19818,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19818),c_Divides_Odiv__class_Omod(X19818,X19817,X19815)),c_Divides_Odiv__class_Omod(X19818,X19816,X19815)),X19815) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])]) ).
fof(i_0_8122,plain,
! [X19779,X19780,X19781,X19782] :
( ~ class_Divides_Osemiring__div(X19782)
| c_Divides_Odiv__class_Omod(X19782,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19782),X19781),X19780),X19779) = c_Divides_Odiv__class_Omod(X19782,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19782),c_Divides_Odiv__class_Omod(X19782,X19781,X19779)),c_Divides_Odiv__class_Omod(X19782,X19780,X19779)),X19779) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])]) ).
fof(i_0_8123,plain,
! [X23317,X23318,X23319,X23320] :
( ~ class_Divides_Osemiring__div(X23320)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23320),X23319),X23318))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23320),X23319),X23317))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23320),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23320),X23318),X23317)),X23319) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23320),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23320),X23318),X23319)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23320),X23317),X23319)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add])]) ).
fof(i_0_8124,plain,
! [X20969,X20970,X20971] :
( ~ class_Rings_Olinordered__semidom(X20971)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20971),c_Groups_Oone__class_Oone(X20971)),X20970))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20971),c_Groups_Oone__class_Oone(X20971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20971),X20970),hAPP(hAPP(c_Power_Opower__class_Opower(X20971),X20970),X20969)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).
fof(i_0_8125,plain,
! [X19341,X19342] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19342),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19342),X19341),X19341)),c_Groups_Ozero__class_Ozero(X19342)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19342),X19341),c_Groups_Ozero__class_Ozero(X19342)))
| ~ class_Groups_Olinordered__ab__group__add(X19342) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19342),X19341),c_Groups_Ozero__class_Ozero(X19342)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19342),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19342),X19341),X19341)),c_Groups_Ozero__class_Ozero(X19342)))
| ~ class_Groups_Olinordered__ab__group__add(X19342) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])]) ).
fof(i_0_8126,plain,
! [X18331,X18332] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18332),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18332),X18331),X18331)),c_Groups_Ozero__class_Ozero(X18332)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18332),X18331),c_Groups_Ozero__class_Ozero(X18332)))
| ~ class_Rings_Olinordered__idom(X18332) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18332),X18331),c_Groups_Ozero__class_Ozero(X18332)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18332),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18332),X18331),X18331)),c_Groups_Ozero__class_Ozero(X18332)))
| ~ class_Rings_Olinordered__idom(X18332) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_8127,plain,
! [X18327,X18328] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18328),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18328),X18327),X18327)),c_Groups_Ozero__class_Ozero(X18328)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18328),X18327),c_Groups_Ozero__class_Ozero(X18328)))
| ~ class_Groups_Olinordered__ab__group__add(X18328) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18328),X18327),c_Groups_Ozero__class_Ozero(X18328)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18328),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18328),X18327),X18327)),c_Groups_Ozero__class_Ozero(X18328)))
| ~ class_Groups_Olinordered__ab__group__add(X18328) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero])])]) ).
fof(i_0_8128,plain,
! [X29972,X29973] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk341_2(X29972,X29973)),X29973))
| c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X29972),X29973) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29972),esk341_2(X29972,X29973)))
| c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X29972),X29973) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff__nat])])])]) ).
fof(i_0_8129,plain,
! [X31214,X31215,X31216,X31217] :
( ~ hBOOL(hAPP(hAPP(c_member(X31217),X31216),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31217,tc_HOL_Obool),X31215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31217,tc_HOL_Obool)),X31214),X31215))
| hBOOL(hAPP(hAPP(c_member(X31217),X31216),X31214)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterE])]) ).
fof(i_0_8130,plain,
! [X31210,X31211,X31212,X31213] :
( ~ hBOOL(hAPP(hAPP(c_member(X31213),X31212),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31213,tc_HOL_Obool),X31211)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31213,tc_HOL_Obool)),X31210),X31211))
| hBOOL(hAPP(hAPP(c_member(X31213),X31212),X31210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterD])]) ).
fof(i_0_8131,plain,
! [X21050,X21051] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21051))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21051),X21050)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21051),X21050) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg__trivial])]) ).
fof(i_0_8132,plain,
! [X24598,X24599] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X24599,X24598)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X24599,X24598),tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(X24598),c_Orderings_Otop__class_Otop(tc_fun(X24598,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24599),c_Orderings_Otop__class_Otop(tc_fun(X24599,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).
fof(i_0_8133,plain,
! [X25977,X25978,X25979] :
( ~ class_Orderings_Olinorder(X25979)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25979),X25978))
| X25978 = c_Orderings_Obot__class_Obot(tc_fun(X25979,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25979),X25977))
| X25977 = c_Orderings_Obot__class_Obot(tc_fun(X25979,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25979,c_Orderings_Oord__class_Omin(X25979),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25979,tc_HOL_Obool)),X25978),X25977)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25979),c_Big__Operators_Olattice_OInf__fin(X25979,c_Orderings_Oord__class_Omin(X25979),X25978)),c_Big__Operators_Olattice_OInf__fin(X25979,c_Orderings_Oord__class_Omin(X25979),X25977)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem])]) ).
fof(i_0_8134,plain,
! [X25980,X25981,X25982] :
( ~ class_Orderings_Olinorder(X25982)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25982),X25981))
| X25981 = c_Orderings_Obot__class_Obot(tc_fun(X25982,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25982),X25980))
| X25980 = c_Orderings_Obot__class_Obot(tc_fun(X25982,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25982,c_Orderings_Oord__class_Omax(X25982),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25982,tc_HOL_Obool)),X25981),X25980)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25982),c_Big__Operators_Olattice_OSup__fin(X25982,c_Orderings_Oord__class_Omax(X25982),X25981)),c_Big__Operators_Olattice_OSup__fin(X25982,c_Orderings_Oord__class_Omax(X25982),X25980)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem])]) ).
fof(i_0_8135,plain,
! [X24975,X24976,X24977,X24978] :
( ~ hBOOL(hAPP(hAPP(c_member(X24978),X24977),X24976))
| hBOOL(hAPP(hAPP(c_member(X24978),X24977),X24975))
| hBOOL(hAPP(hAPP(c_member(X24978),X24977),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24978,tc_HOL_Obool)),X24976),X24975))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5677])]) ).
fof(i_0_8136,plain,
! [X20102,X20103,X20104] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20104),X20103))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20102))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20104),X20102)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20103),X20102))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1])]) ).
fof(i_0_8137,plain,
! [X20066,X20067,X20068] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20068))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20068),X20067))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20066),X20067)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20066),X20068))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono2])]) ).
fof(i_0_8138,plain,
! [X18936,X18937,X18938] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18938),X18937))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18936))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18936),X18938)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18936),X18937))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).
fof(i_0_8139,plain,
! [X19448,X19449,X19450] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19450),X19449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19448))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19450),X19448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19449),X19448))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).
fof(i_0_8140,plain,
! [X19445,X19446,X19447] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19447),X19446))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19445))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19445),X19447)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19445),X19446))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).
fof(i_0_8141,plain,
! [X31768,X31769,X31770] :
( ( ~ c_Fun_Oinj__on(tc_List_Olist(X31770),tc_List_Olist(X31769),hAPP(c_List_Omap(X31770,X31769),X31768),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31770),tc_HOL_Obool)))
| c_Fun_Oinj__on(X31770,X31769,X31768,c_Orderings_Otop__class_Otop(tc_fun(X31770,tc_HOL_Obool))) )
& ( ~ c_Fun_Oinj__on(X31770,X31769,X31768,c_Orderings_Otop__class_Otop(tc_fun(X31770,tc_HOL_Obool)))
| c_Fun_Oinj__on(tc_List_Olist(X31770),tc_List_Olist(X31769),hAPP(c_List_Omap(X31770,X31769),X31768),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31770),tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__map])]) ).
fof(i_0_8142,plain,
! [X31760,X31761,X31762] :
( ~ c_Fun_Oinj__on(tc_List_Olist(X31762),tc_List_Olist(X31761),hAPP(c_List_Omap(X31762,X31761),X31760),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31762),tc_HOL_Obool)))
| c_Fun_Oinj__on(X31762,X31761,X31760,c_Orderings_Otop__class_Otop(tc_fun(X31762,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapD])]) ).
fof(i_0_8143,plain,
! [X24412,X24413,X24414,X24415] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24415,tc_HOL_Obool)),X24414),X24413))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24415,tc_HOL_Obool)),X24414),hAPP(hAPP(c_Set_Oinsert(X24415),X24412),X24413))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).
fof(i_0_8144,plain,
! [X30964,X30965,X30966,X30967,X30968] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30968,tc_fun(X30967,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X30968),X30966),X30965)),X30964) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30967,tc_HOL_Obool)),hAPP(X30964,X30966)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30968,tc_fun(X30967,tc_HOL_Obool)),X30965),X30964)),
inference(variable_rename,[status(thm)],[fact_INT__insert]) ).
fof(i_0_8145,plain,
! [X24458,X24459,X24460,X24461,X24462] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24462,tc_fun(X24461,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24462),X24460),X24459)),X24458) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24461,tc_HOL_Obool)),hAPP(X24458,X24460)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24462,tc_fun(X24461,tc_HOL_Obool)),X24459),X24458)),
inference(variable_rename,[status(thm)],[fact_UN__insert]) ).
fof(i_0_8146,plain,
! [X29074,X29075,X29076,X29077] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29076),X29074),hAPP(c_Finite__Set_Ofold1(X29076,c_Orderings_Oord__class_Omin(X29076)),X29075)))
| ~ hBOOL(hAPP(hAPP(c_member(X29076),X29077),X29075))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29076),X29074),X29077))
| X29075 = c_Orderings_Obot__class_Obot(tc_fun(X29076,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29076),X29075))
| ~ class_Orderings_Olinorder(X29076) )
& ( hBOOL(hAPP(hAPP(c_member(X29076),esk299_3(X29074,X29075,X29076)),X29075))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29076),X29074),hAPP(c_Finite__Set_Ofold1(X29076,c_Orderings_Oord__class_Omin(X29076)),X29075)))
| X29075 = c_Orderings_Obot__class_Obot(tc_fun(X29076,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29076),X29075))
| ~ class_Orderings_Olinorder(X29076) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29076),X29074),esk299_3(X29074,X29075,X29076)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29076),X29074),hAPP(c_Finite__Set_Ofold1(X29076,c_Orderings_Oord__class_Omin(X29076)),X29075)))
| X29075 = c_Orderings_Obot__class_Obot(tc_fun(X29076,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29076),X29075))
| ~ class_Orderings_Olinorder(X29076) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strict__below__fold1__iff])])])])]) ).
fof(i_0_8147,plain,
! [X29056,X29057,X29058,X29059] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29058),X29056),hAPP(c_Finite__Set_Ofold1(X29058,c_Orderings_Oord__class_Omin(X29058)),X29057)))
| ~ hBOOL(hAPP(hAPP(c_member(X29058),X29059),X29057))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29058),X29056),X29059))
| X29057 = c_Orderings_Obot__class_Obot(tc_fun(X29058,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29058),X29057))
| ~ class_Orderings_Olinorder(X29058) )
& ( hBOOL(hAPP(hAPP(c_member(X29058),esk296_3(X29056,X29057,X29058)),X29057))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29058),X29056),hAPP(c_Finite__Set_Ofold1(X29058,c_Orderings_Oord__class_Omin(X29058)),X29057)))
| X29057 = c_Orderings_Obot__class_Obot(tc_fun(X29058,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29058),X29057))
| ~ class_Orderings_Olinorder(X29058) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29058),X29056),esk296_3(X29056,X29057,X29058)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29058),X29056),hAPP(c_Finite__Set_Ofold1(X29058,c_Orderings_Oord__class_Omin(X29058)),X29057)))
| X29057 = c_Orderings_Obot__class_Obot(tc_fun(X29058,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29058),X29057))
| ~ class_Orderings_Olinorder(X29058) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Obelow__fold1__iff])])])])]) ).
fof(i_0_8148,plain,
! [X29045,X29046,X29047,X29048] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29047),X29045),hAPP(c_Finite__Set_Ofold1(X29047,c_Lattices_Osemilattice__inf__class_Oinf(X29047)),X29046)))
| ~ hBOOL(hAPP(hAPP(c_member(X29047),X29048),X29046))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29047),X29045),X29048))
| X29046 = c_Orderings_Obot__class_Obot(tc_fun(X29047,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29047),X29046))
| ~ class_Lattices_Osemilattice__inf(X29047) )
& ( hBOOL(hAPP(hAPP(c_member(X29047),esk295_3(X29045,X29046,X29047)),X29046))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29047),X29045),hAPP(c_Finite__Set_Ofold1(X29047,c_Lattices_Osemilattice__inf__class_Oinf(X29047)),X29046)))
| X29046 = c_Orderings_Obot__class_Obot(tc_fun(X29047,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29047),X29046))
| ~ class_Lattices_Osemilattice__inf(X29047) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29047),X29045),esk295_3(X29045,X29046,X29047)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29047),X29045),hAPP(c_Finite__Set_Ofold1(X29047,c_Lattices_Osemilattice__inf__class_Oinf(X29047)),X29046)))
| X29046 = c_Orderings_Obot__class_Obot(tc_fun(X29047,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29047),X29046))
| ~ class_Lattices_Osemilattice__inf(X29047) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__fold1__iff])])])])]) ).
cnf(i_0_8149,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk490_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
| c_List_Oconcat(X1,X2) = c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5619]) ).
cnf(i_0_8150,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk489_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
| c_List_Olist_ONil(X1) = c_List_Oconcat(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_5620]) ).
fof(i_0_8151,plain,
! [X20360,X20361,X20362] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20362),X20361),X20360))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20362),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20362),X20361),X20360)),c_Groups_Ozero__class_Ozero(X20362)))
| ~ class_Groups_Oordered__ab__group__add(X20362) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20362),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20362),X20361),X20360)),c_Groups_Ozero__class_Ozero(X20362)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20362),X20361),X20360))
| ~ class_Groups_Oordered__ab__group__add(X20362) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).
fof(i_0_8152,plain,
! [X20363,X20364,X20365] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20365),X20364),X20363))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20365),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20365),X20364),X20363)),c_Groups_Ozero__class_Ozero(X20365)))
| ~ class_Groups_Oordered__ab__group__add(X20365) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20365),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20365),X20364),X20363)),c_Groups_Ozero__class_Ozero(X20365)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20365),X20364),X20363))
| ~ class_Groups_Oordered__ab__group__add(X20365) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).
fof(i_0_8153,plain,
! [X20105,X20106,X20107] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20107),X20106))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20105),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20106),X20105)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20107),X20105))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])]) ).
cnf(i_0_8154,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,c_Code__Numeral_OSuc__code__numeral(X4)) = hAPP(hAPP(X3,X4),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,X4)),
inference(split_conjunct,[status(thm)],[i_0_5678]) ).
cnf(i_0_8155,plain,
c_Code__Numeral_OSuc__code__numeral(X1) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))),
inference(split_conjunct,[status(thm)],[i_0_5679]) ).
fof(i_0_8156,plain,
! [X32682,X32683,X32684] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32684),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32683)),X32682)))
| hBOOL(hAPP(hAPP(c_member(X32683),hAPP(hAPP(c_List_Onth(X32683),X32682),X32684)),hAPP(c_List_Oset(X32683),X32682))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__mem])]) ).
fof(i_0_8157,plain,
! [X19622,X19623] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19622))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19623),X19622))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).
fof(i_0_8158,plain,
! [X19624,X19625] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19625))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19624))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19624),X19625))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).
fof(i_0_8159,plain,
! [X28196,X28197] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28197),X28196))
| hAPP(c_Finite__Set_Ocard(X28197),X28196) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X28197,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X28197),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28196) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).
fof(i_0_8160,plain,
! [X28194,X28195] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28195),X28194))
| hAPP(c_Finite__Set_Ocard(X28195),X28194) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X28195,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X28195),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28194) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28195),X28194))
| hAPP(c_Finite__Set_Ocard(X28195),X28194) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5680])]) ).
fof(i_0_8161,plain,
! [X21675,X21676,X21677,X21678] :
( ~ class_Fields_Ofield(X21678)
| X21677 = c_Groups_Ozero__class_Ozero(X21678)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21678),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21678),X21676),X21677)),X21675) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21678),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21678),X21676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21678),X21677),X21675))),X21677) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff])]) ).
fof(i_0_8162,plain,
! [X21654,X21655,X21656,X21657] :
( ~ class_Fields_Ofield(X21657)
| X21656 = c_Groups_Ozero__class_Ozero(X21657)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21657),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21657),X21655),X21656)),X21654) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21657),X21655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21657),X21656),X21654))),X21656) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff])]) ).
fof(i_0_8163,plain,
! [X21658,X21659,X21660,X21661] :
( ~ class_Fields_Ofield__inverse__zero(X21661)
| X21660 = c_Groups_Ozero__class_Ozero(X21661)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21661),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21661),X21659),X21660)),X21658) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21661),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21661),X21659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21661),X21658),X21660))),X21660) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__num])]) ).
fof(i_0_8164,plain,
! [X32674,X32675,X32676,X32678,X32679,X32680,X32681] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk453_3(X32674,X32675,X32676)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32676)),X32674)))
| ~ hBOOL(hAPP(hAPP(c_member(X32676),X32675),hAPP(c_List_Oset(X32676),X32674))) )
& ( hAPP(hAPP(c_List_Onth(X32676),X32674),esk453_3(X32674,X32675,X32676)) = X32675
| ~ hBOOL(hAPP(hAPP(c_member(X32676),X32675),hAPP(c_List_Oset(X32676),X32674))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32681),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32680)),X32678)))
| hAPP(hAPP(c_List_Onth(X32680),X32678),X32681) != X32679
| hBOOL(hAPP(hAPP(c_member(X32680),X32679),hAPP(c_List_Oset(X32680),X32678))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__conv__nth])])])])])]) ).
fof(i_0_8165,plain,
! [X19021,X19022,X19023,X19024] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19024),X19023))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19022),X19021))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19024),X19022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19023),X19021))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).
fof(i_0_8166,plain,
! [X19298,X19299,X19300,X19301] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19301),X19300))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19299),X19298))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19301),X19299)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19300),X19298))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_8167,plain,
! [X19514,X19515,X19516,X19517] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19517),X19516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19515),X19514))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19517),X19515)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19516),X19514))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).
fof(i_0_8168,plain,
! [X20416,X20417,X20418] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20418),X20417))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20416),X20418))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20418),X20416)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20417),X20416))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).
fof(i_0_8169,plain,
! [X20293,X20294,X20295] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20295),X20294))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20295),X20293))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20293),X20294)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20293),X20295))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).
fof(i_0_8170,plain,
! [X18301,X18302,X18303,X18304] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18304),X18303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18302),X18301))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18304),X18302)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18303),X18301))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_8171,plain,
! [X18704,X18705,X18706,X18707,X18708] :
( ~ class_Rings_Ocomm__semiring__1(X18708)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),X18707),X18706)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),X18705),X18704)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),X18705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),X18707),X18706)),X18704)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).
fof(i_0_8172,plain,
! [X23297,X23298,X23299] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23299,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X23299),X23298)),hAPP(c_SetInterval_Oord__class_OlessThan(X23299),X23297)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23299),X23298),X23297))
| ~ class_Orderings_Olinorder(X23299) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23299),X23298),X23297))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23299,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X23299),X23298)),hAPP(c_SetInterval_Oord__class_OlessThan(X23299),X23297)))
| ~ class_Orderings_Olinorder(X23299) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff])])]) ).
fof(i_0_8173,plain,
! [X24097,X24098,X24099] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24099,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24099),X24098)),hAPP(c_SetInterval_Oord__class_OatMost(X24099),X24097)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24099),X24098),X24097))
| ~ class_Orderings_Oorder(X24099) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24099),X24098),X24097))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24099,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24099),X24098)),hAPP(c_SetInterval_Oord__class_OatMost(X24099),X24097)))
| ~ class_Orderings_Oorder(X24099) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff])])]) ).
fof(i_0_8174,plain,
! [X23768,X23769,X23770] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23770,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X23770),X23769)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X23770),X23768)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23770),X23768),X23769))
| ~ class_Orderings_Olinorder(X23770) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23770),X23768),X23769))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23770,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X23770),X23769)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X23770),X23768)))
| ~ class_Orderings_Olinorder(X23770) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff])])]) ).
fof(i_0_8175,plain,
! [X24161,X24162,X24163] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24163,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X24163),X24162)),hAPP(c_SetInterval_Oord__class_OatLeast(X24163),X24161)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24163),X24161),X24162))
| ~ class_Orderings_Oorder(X24163) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24163),X24161),X24162))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24163,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X24163),X24162)),hAPP(c_SetInterval_Oord__class_OatLeast(X24163),X24161)))
| ~ class_Orderings_Oorder(X24163) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff])])]) ).
fof(i_0_8176,plain,
! [X23314,X23315,X23316] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23316,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X23316),X23315)),hAPP(c_SetInterval_Oord__class_OlessThan(X23316),X23314)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23316),X23315),X23314))
| ~ class_Orderings_Olinorder(X23316) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23316),X23315),X23314))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23316,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X23316),X23315)),hAPP(c_SetInterval_Oord__class_OlessThan(X23316),X23314)))
| ~ class_Orderings_Olinorder(X23316) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff])])]) ).
cnf(i_0_8177,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Relation_OId(X1)),X3) = X3,
inference(split_conjunct,[status(thm)],[i_0_5681]) ).
fof(i_0_8178,plain,
! [X21584,X21585,X21586] :
( ~ class_Fields_Olinordered__field(X21586)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21586),X21585),c_Groups_Ozero__class_Ozero(X21586)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21586),c_Groups_Ozero__class_Ozero(X21586)),X21584))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21586),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21586),X21585),X21584)),c_Groups_Ozero__class_Ozero(X21586))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos])]) ).
fof(i_0_8179,plain,
! [X21602,X21603,X21604] :
( ~ class_Fields_Olinordered__field(X21604)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21604),c_Groups_Ozero__class_Ozero(X21604)),X21603))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21604),X21602),c_Groups_Ozero__class_Ozero(X21604)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21604),X21603),X21602)),c_Groups_Ozero__class_Ozero(X21604))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg])]) ).
fof(i_0_8180,plain,
! [X19399,X19400,X19401] :
( ~ class_Rings_Oordered__cancel__semiring(X19401)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19401),X19400),c_Groups_Ozero__class_Ozero(X19401)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19401),c_Groups_Ozero__class_Ozero(X19401)),X19399))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19401),X19400),X19399)),c_Groups_Ozero__class_Ozero(X19401))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).
fof(i_0_8181,plain,
! [X19360,X19361,X19362] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19362),c_Groups_Ozero__class_Ozero(X19362)),X19361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19362),X19360),c_Groups_Ozero__class_Ozero(X19362)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19362),X19361),X19360)),c_Groups_Ozero__class_Ozero(X19362)))
| ~ class_Rings_Oordered__cancel__semiring(X19362) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19362),X19361),c_Groups_Ozero__class_Ozero(X19362)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19362),c_Groups_Ozero__class_Ozero(X19362)),X19360))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19362),X19361),X19360)),c_Groups_Ozero__class_Ozero(X19362)))
| ~ class_Rings_Oordered__cancel__semiring(X19362) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).
fof(i_0_8182,plain,
! [X19405,X19406,X19407] :
( ~ class_Rings_Oordered__cancel__semiring(X19407)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19407),c_Groups_Ozero__class_Ozero(X19407)),X19406))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19407),X19405),c_Groups_Ozero__class_Ozero(X19407)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19407),X19406),X19405)),c_Groups_Ozero__class_Ozero(X19407))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).
fof(i_0_8183,plain,
! [X19402,X19403,X19404] :
( ~ class_Rings_Oordered__cancel__semiring(X19404)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19404),c_Groups_Ozero__class_Ozero(X19404)),X19403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19404),X19402),c_Groups_Ozero__class_Ozero(X19404)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19404),X19402),X19403)),c_Groups_Ozero__class_Ozero(X19404))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).
fof(i_0_8184,plain,
! [X21504,X21505,X21506] :
( ~ class_Fields_Olinordered__field(X21506)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21506),X21505),c_Groups_Ozero__class_Ozero(X21506)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21506),c_Groups_Ozero__class_Ozero(X21506)),X21504))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21506),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21506),X21505),X21504)),c_Groups_Ozero__class_Ozero(X21506))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])]) ).
fof(i_0_8185,plain,
! [X21507,X21508,X21509] :
( ~ class_Fields_Olinordered__field(X21509)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21509),c_Groups_Ozero__class_Ozero(X21509)),X21508))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21509),X21507),c_Groups_Ozero__class_Ozero(X21509)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21509),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21509),X21508),X21507)),c_Groups_Ozero__class_Ozero(X21509))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__neg])]) ).
fof(i_0_8186,plain,
! [X18892,X18893,X18894] :
( ~ class_Rings_Olinordered__semiring__strict(X18894)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18894),X18893),c_Groups_Ozero__class_Ozero(X18894)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18894),c_Groups_Ozero__class_Ozero(X18894)),X18892))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18894),X18893),X18892)),c_Groups_Ozero__class_Ozero(X18894))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).
fof(i_0_8187,plain,
! [X18876,X18877,X18878] :
( ~ class_Rings_Olinordered__semiring__strict(X18878)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18878),c_Groups_Ozero__class_Ozero(X18878)),X18877))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18878),X18876),c_Groups_Ozero__class_Ozero(X18878)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18878),X18877),X18876)),c_Groups_Ozero__class_Ozero(X18878))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).
fof(i_0_8188,plain,
! [X18879,X18880,X18881] :
( ~ class_Rings_Olinordered__semiring__strict(X18881)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18881),c_Groups_Ozero__class_Ozero(X18881)),X18880))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18881),X18879),c_Groups_Ozero__class_Ozero(X18881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18881),X18879),X18880)),c_Groups_Ozero__class_Ozero(X18881))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).
fof(i_0_8189,plain,
! [X32294,X32295,X32296] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32296,tc_HOL_Obool)),hAPP(c_List_Oset(X32296),X32295)),hAPP(c_List_Oset(X32296),hAPP(hAPP(c_List_Olist_OCons(X32296),X32294),X32295)))),
inference(variable_rename,[status(thm)],[fact_set__subset__Cons]) ).
fof(i_0_8190,plain,
! [X33972,X33973,X33974,X33975] : c_List_Otranspose(X33975,hAPP(hAPP(c_List_Omap(tc_List_Olist(X33974),tc_List_Olist(X33975)),hAPP(c_List_Omap(X33974,X33975),X33973)),X33972)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X33974),tc_List_Olist(X33975)),hAPP(c_List_Omap(X33974,X33975),X33973)),c_List_Otranspose(X33974,X33972)),
inference(variable_rename,[status(thm)],[fact_transpose__map__map]) ).
cnf(i_0_8191,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))) = X2
| ~ class_Fields_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5682]) ).
cnf(i_0_8192,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))) = X2
| ~ class_Fields_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5683]) ).
fof(i_0_8193,plain,
! [X23164,X23165,X23166,X23167] :
( ~ class_Rings_Ocomm__semiring__1(X23167)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23167),X23166),X23165)),X23164))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23167),X23166),X23164)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__left])]) ).
fof(i_0_8194,plain,
! [X23160,X23161,X23162,X23163] :
( ~ class_Rings_Ocomm__semiring__1(X23163)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23163),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23163),X23162),X23161)),X23160))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23163),X23161),X23160)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__right])]) ).
fof(i_0_8195,plain,
! [X24043,X24044,X24045,X24046] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24046),X24045),X24043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24046),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24046),X24045),X24044)),X24043))
| ~ class_Lattices_Osemilattice__sup(X24046) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24046),X24044),X24043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24046),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24046),X24045),X24044)),X24043))
| ~ class_Lattices_Osemilattice__sup(X24046) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24046),X24045),X24043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24046),X24044),X24043))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24046),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24046),X24045),X24044)),X24043))
| ~ class_Lattices_Osemilattice__sup(X24046) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__sup__iff])])]) ).
fof(i_0_8196,plain,
! [X24012,X24013,X24014,X24015] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24015),X24014),X24012))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24015),X24014),X24013)),X24012))
| ~ class_Lattices_Osemilattice__sup(X24015) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24015),X24013),X24012))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24015),X24014),X24013)),X24012))
| ~ class_Lattices_Osemilattice__sup(X24015) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5684])])]) ).
fof(i_0_8197,plain,
! [X22621,X22622,X22623,X22624] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22624),X22623),X22621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22624),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22624),X22623),X22622)),X22621))
| ~ class_Orderings_Olinorder(X22624) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22624),X22622),X22621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22624),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22624),X22623),X22622)),X22621))
| ~ class_Orderings_Olinorder(X22624) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22624),X22623),X22621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22624),X22622),X22621))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22624),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22624),X22623),X22622)),X22621))
| ~ class_Orderings_Olinorder(X22624) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff])])]) ).
fof(i_0_8198,plain,
! [X22590,X22591,X22592,X22593] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22593),X22592),X22590))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22593),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22593),X22592),X22591)),X22590))
| ~ class_Orderings_Olinorder(X22593) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22593),X22591),X22590))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22593),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22593),X22592),X22591)),X22590))
| ~ class_Orderings_Olinorder(X22593) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5685])])]) ).
fof(i_0_8199,plain,
! [X22566,X22567,X22568,X22569] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22569),X22568),X22566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22569),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22569),X22568),X22567)),X22566))
| ~ class_Orderings_Olinorder(X22569) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22569),X22567),X22566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22569),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22569),X22568),X22567)),X22566))
| ~ class_Orderings_Olinorder(X22569) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22569),X22568),X22566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22569),X22567),X22566))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22569),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22569),X22568),X22567)),X22566))
| ~ class_Orderings_Olinorder(X22569) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj])])]) ).
fof(i_0_8200,plain,
! [X32655,X32656,X32657,X32658] :
( ( hAPP(hAPP(c_List_Onth(X32658),X32657),X32656) != hAPP(hAPP(c_List_Onth(X32658),X32657),X32655)
| X32656 = X32655
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32655),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32658)),X32657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32656),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32658)),X32657)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32658),X32657)) )
& ( X32656 != X32655
| hAPP(hAPP(c_List_Onth(X32658),X32657),X32656) = hAPP(hAPP(c_List_Onth(X32658),X32657),X32655)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32655),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32658)),X32657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32656),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32658)),X32657)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32658),X32657)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__eq__iff__index__eq])])]) ).
fof(i_0_8201,plain,
! [X32647,X32648,X32649,X32650,X32651,X32652] :
( ( ~ hBOOL(hAPP(c_List_Odistinct(X32648),X32647))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32649),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32648)),X32647)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32650),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32648)),X32647)))
| X32649 = X32650
| hAPP(hAPP(c_List_Onth(X32648),X32647),X32649) != hAPP(hAPP(c_List_Onth(X32648),X32647),X32650) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk450_2(X32651,X32652)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32652)),X32651)))
| hBOOL(hAPP(c_List_Odistinct(X32652),X32651)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk451_2(X32651,X32652)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32652)),X32651)))
| hBOOL(hAPP(c_List_Odistinct(X32652),X32651)) )
& ( esk450_2(X32651,X32652) != esk451_2(X32651,X32652)
| hBOOL(hAPP(c_List_Odistinct(X32652),X32651)) )
& ( hAPP(hAPP(c_List_Onth(X32652),X32651),esk450_2(X32651,X32652)) = hAPP(hAPP(c_List_Onth(X32652),X32651),esk451_2(X32651,X32652))
| hBOOL(hAPP(c_List_Odistinct(X32652),X32651)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__conv__nth])])])])])]) ).
fof(i_0_8202,plain,
! [X31974,X31975,X31976,X31977] :
( ( hBOOL(hAPP(c_List_Odistinct(X31976),X31974))
| ~ hBOOL(hAPP(c_List_Odistinct(X31977),hAPP(hAPP(c_List_Omap(X31976,X31977),X31975),X31974))) )
& ( c_Fun_Oinj__on(X31976,X31977,X31975,hAPP(c_List_Oset(X31976),X31974))
| ~ hBOOL(hAPP(c_List_Odistinct(X31977),hAPP(hAPP(c_List_Omap(X31976,X31977),X31975),X31974))) )
& ( ~ hBOOL(hAPP(c_List_Odistinct(X31976),X31974))
| ~ c_Fun_Oinj__on(X31976,X31977,X31975,hAPP(c_List_Oset(X31976),X31974))
| hBOOL(hAPP(c_List_Odistinct(X31977),hAPP(hAPP(c_List_Omap(X31976,X31977),X31975),X31974))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__map])])]) ).
fof(i_0_8203,plain,
! [X25947,X25948] :
( ~ class_Orderings_Olinorder(X25948)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25948),X25947))
| X25947 = c_Orderings_Obot__class_Obot(tc_fun(X25948,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25948),c_Big__Operators_Olattice_OInf__fin(X25948,c_Orderings_Oord__class_Omin(X25948),X25947)),c_Big__Operators_Olattice_OSup__fin(X25948,c_Orderings_Oord__class_Omax(X25948),X25947))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup])]) ).
fof(i_0_8204,plain,
! [X27957,X27958,X27959,X27960,X27961] :
( ~ c_Fun_Oinj__on(X27961,X27960,X27959,X27958)
| c_Fun_Oinj__on(X27961,X27960,X27959,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27961,tc_HOL_Obool)),X27958),X27957)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff])]) ).
cnf(i_0_8205,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5686]) ).
fof(i_0_8206,plain,
! [X30697,X30698,X30699,X30700,X30701,X30702] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X30702,X30701,X30700)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30702),X30699))
| hAPP(hAPP(c_Finite__Set_Ofold(X30702,X30701,X30700),X30698),hAPP(hAPP(c_Set_Oinsert(X30702),X30697),X30699)) = hAPP(hAPP(c_Finite__Set_Ofold(X30702,X30701,X30700),hAPP(hAPP(X30700,X30697),X30698)),X30699) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2])]) ).
fof(i_0_8207,plain,
! [X25332,X25333,X25334] :
( ~ hBOOL(hAPP(hAPP(c_member(X25334),X25333),X25332))
| hAPP(hAPP(c_Set_Oinsert(X25334),X25333),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25334,tc_HOL_Obool)),X25332),hAPP(hAPP(c_Set_Oinsert(X25334),X25333),c_Orderings_Obot__class_Obot(tc_fun(X25334,tc_HOL_Obool))))) = X25332 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff])]) ).
fof(i_0_8208,plain,
! [X24542,X24543] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24543),c_Orderings_Otop__class_Otop(tc_fun(X24543,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24542),c_Orderings_Otop__class_Otop(tc_fun(X24542,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X24543,X24542)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X24543,X24542),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).
fof(i_0_8209,plain,
! [X24538,X24539] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24539),c_Orderings_Otop__class_Otop(tc_fun(X24539,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24539,X24538)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X24539,X24538),tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24538),c_Orderings_Otop__class_Otop(tc_fun(X24538,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24539,X24538)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X24539,X24538),tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24539),c_Orderings_Otop__class_Otop(tc_fun(X24539,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24538),c_Orderings_Otop__class_Otop(tc_fun(X24538,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24539,X24538)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X24539,X24538),tc_HOL_Obool)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff])])]) ).
fof(i_0_8210,plain,
! [X23502,X23503,X23504,X23505] :
( ~ class_Groups_Ocomm__monoid__add(X23505)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23504),X23503))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23505),X23502),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23504,X23503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23505),hAPP(X23502,X23504)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23505),X23502),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23504),X23503))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc])]) ).
fof(i_0_8211,plain,
! [X28302,X28303,X28304,X28305,X28306] :
( ~ hBOOL(hAPP(hAPP(c_member(X28306),hAPP(X28305,X28304)),X28303))
| hBOOL(hAPP(hAPP(c_member(X28302),X28304),hAPP(c_Set_Ovimage(X28302,X28306,X28305),X28303))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI2])]) ).
cnf(i_0_8212,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(c_List_Ohd(X2),hAPP(c_List_Orotate(X2,X3),X1)) = hAPP(hAPP(c_List_Onth(X2),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5687]) ).
fof(i_0_8213,plain,
! [X34099,X34100,X34101] :
( ( ~ c_List_Olinorder__class_Osorted(X34101,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34101,X34101,c_COMBI(X34101)),X34100),X34099))
| c_List_Olinorder__class_Osorted(X34101,X34099)
| ~ class_Orderings_Olinorder(X34101) )
& ( ~ c_List_Olinorder__class_Osorted(X34101,X34099)
| c_List_Olinorder__class_Osorted(X34101,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34101,X34101,c_COMBI(X34101)),X34100),X34099))
| ~ class_Orderings_Olinorder(X34101) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort])])]) ).
fof(i_0_8214,plain,
! [X23603,X23604,X23605,X23606] :
( ~ class_Groups_Ocomm__monoid__add(X23606)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23605),X23604))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23606),X23603),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23605),X23604)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23606),hAPP(X23603,X23605)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23606),X23603),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23605)),X23604))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc])]) ).
fof(i_0_8215,plain,
! [X22443,X22444,X22445] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22443,tc_HOL_Obool)),X22445),X22444))
| X22445 != X22444 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22443,tc_HOL_Obool)),X22444),X22445))
| X22445 != X22444 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22443,tc_HOL_Obool)),X22445),X22444))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22443,tc_HOL_Obool)),X22444),X22445))
| X22445 = X22444 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_8216,plain,
! [X22242,X22243,X22244] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22244,tc_HOL_Obool)),X22243),X22242))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22244,tc_HOL_Obool)),X22242),X22243))
| X22243 = X22242 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_8217,plain,
! [X34332,X34333,X34334] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34334),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34333)),X34332)))
| hAPP(hAPP(c_List_Onth(X34333),hAPP(c_List_Orev(X34333),X34332)),X34334) = hAPP(hAPP(c_List_Onth(X34333),X34332),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34333)),X34332)),hAPP(c_Nat_OSuc,X34334))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__nth])]) ).
fof(i_0_8218,plain,
! [X31061,X31062,X31063,X31064,X31065] :
( ~ hBOOL(hAPP(hAPP(c_member(X31065),X31064),X31063))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31062,tc_HOL_Obool)),hAPP(X31061,X31064)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31065,tc_fun(X31062,tc_HOL_Obool)),X31063),X31061)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31065,tc_fun(X31062,tc_HOL_Obool)),X31063),X31061) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__absorb])]) ).
fof(i_0_8219,plain,
! [X25317,X25318,X25319,X25320,X25321] :
( ~ hBOOL(hAPP(hAPP(c_member(X25321),X25320),X25319))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25318,tc_HOL_Obool)),hAPP(X25317,X25320)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25321,tc_fun(X25318,tc_HOL_Obool)),X25319),X25317)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25321,tc_fun(X25318,tc_HOL_Obool)),X25319),X25317) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__absorb])]) ).
fof(i_0_8220,plain,
! [X32764,X32765,X32766,X32767,X32768] : hAPP(hAPP(c_List_Olist__update(X32768,hAPP(hAPP(c_List_Olist__update(X32768,X32767),X32766),X32765)),X32766),X32764) = hAPP(hAPP(c_List_Olist__update(X32768,X32767),X32766),X32764),
inference(variable_rename,[status(thm)],[fact_list__update__overwrite]) ).
fof(i_0_8221,plain,
! [X18623,X18624] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X18624)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18623))),
inference(variable_rename,[status(thm)],[fact_negative__zless]) ).
fof(i_0_8222,plain,
! [X25742,X25743,X25744] :
( ~ class_Rings_Oring__1(X25744)
| ~ hBOOL(hAPP(hAPP(c_member(X25744),X25743),c_Int_Oring__1__class_OInts(X25744)))
| ~ hBOOL(hAPP(hAPP(c_member(X25744),X25742),c_Int_Oring__1__class_OInts(X25744)))
| hBOOL(hAPP(hAPP(c_member(X25744),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25744),X25743),X25742)),c_Int_Oring__1__class_OInts(X25744))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__diff])]) ).
fof(i_0_8223,plain,
! [X25739,X25740,X25741] :
( ~ class_Rings_Oring__1(X25741)
| ~ hBOOL(hAPP(hAPP(c_member(X25741),X25740),c_Int_Oring__1__class_OInts(X25741)))
| ~ hBOOL(hAPP(hAPP(c_member(X25741),X25739),c_Int_Oring__1__class_OInts(X25741)))
| hBOOL(hAPP(hAPP(c_member(X25741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25741),X25740),X25739)),c_Int_Oring__1__class_OInts(X25741))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__mult])]) ).
fof(i_0_8224,plain,
! [X25656,X25657,X25658] :
( ~ class_Rings_Osemiring__1(X25658)
| ~ hBOOL(hAPP(hAPP(c_member(X25658),X25657),c_Nat_Osemiring__1__class_ONats(X25658)))
| ~ hBOOL(hAPP(hAPP(c_member(X25658),X25656),c_Nat_Osemiring__1__class_ONats(X25658)))
| hBOOL(hAPP(hAPP(c_member(X25658),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25658),X25657),X25656)),c_Nat_Osemiring__1__class_ONats(X25658))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__mult])]) ).
fof(i_0_8225,plain,
! [X25736,X25737,X25738] :
( ~ class_Rings_Oring__1(X25738)
| ~ hBOOL(hAPP(hAPP(c_member(X25738),X25737),c_Int_Oring__1__class_OInts(X25738)))
| ~ hBOOL(hAPP(hAPP(c_member(X25738),X25736),c_Int_Oring__1__class_OInts(X25738)))
| hBOOL(hAPP(hAPP(c_member(X25738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25738),X25737),X25736)),c_Int_Oring__1__class_OInts(X25738))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).
fof(i_0_8226,plain,
! [X25653,X25654,X25655] :
( ~ class_Rings_Osemiring__1(X25655)
| ~ hBOOL(hAPP(hAPP(c_member(X25655),X25654),c_Nat_Osemiring__1__class_ONats(X25655)))
| ~ hBOOL(hAPP(hAPP(c_member(X25655),X25653),c_Nat_Osemiring__1__class_ONats(X25655)))
| hBOOL(hAPP(hAPP(c_member(X25655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25655),X25654),X25653)),c_Nat_Osemiring__1__class_ONats(X25655))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__add])]) ).
fof(i_0_8227,plain,
! [X19357,X19358,X19359] :
( ~ class_Groups_Oordered__comm__monoid__add(X19359)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19359),X19358),c_Groups_Ozero__class_Ozero(X19359)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19359),X19357),c_Groups_Ozero__class_Ozero(X19359)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19359),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19359),X19358),X19357)),c_Groups_Ozero__class_Ozero(X19359))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_8228,plain,
! [X19535,X19536,X19537] :
( ~ class_Groups_Oordered__comm__monoid__add(X19537)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19537),X19536),c_Groups_Ozero__class_Ozero(X19537)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19537),X19535),c_Groups_Ozero__class_Ozero(X19537)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19537),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19537),X19536),X19535)),c_Groups_Ozero__class_Ozero(X19537))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_8229,plain,
! [X19532,X19533,X19534] :
( ~ class_Groups_Oordered__comm__monoid__add(X19534)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19534),X19533),c_Groups_Ozero__class_Ozero(X19534)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19534),X19532),c_Groups_Ozero__class_Ozero(X19534)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19534),X19533),X19532)),c_Groups_Ozero__class_Ozero(X19534))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_8230,plain,
! [X18321,X18322,X18323] :
( ~ class_Groups_Oordered__comm__monoid__add(X18323)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18323),X18322),c_Groups_Ozero__class_Ozero(X18323)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18323),X18321),c_Groups_Ozero__class_Ozero(X18323)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18323),X18322),X18321)),c_Groups_Ozero__class_Ozero(X18323))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_8231,plain,
! [X33667,X33668,X33669] : c_List_Olist_Olist__size(X33669,X33668,X33667) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X33669,tc_Nat_Onat),X33668),X33667))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33669)),X33667)),
inference(variable_rename,[status(thm)],[fact_list__size__conv__listsum]) ).
fof(i_0_8232,plain,
! [X28473,X28474,X28475,X28476] : c_Map_Odom(X28476,X28475,c_Map_Orestrict__map(X28476,X28475,X28474,X28473)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28476,tc_HOL_Obool)),c_Map_Odom(X28476,X28475,X28474)),X28473),
inference(variable_rename,[status(thm)],[fact_dom__restrict]) ).
fof(i_0_8233,plain,
! [X31938,X31939,X31940,X31941] :
( c_Map_Omap__of(X31941,X31940,X31939) != c_Map_Omap__of(X31941,X31940,X31938)
| hAPP(c_Set_Oimage(tc_prod(X31941,X31940),X31941,c_Product__Type_Ofst(X31941,X31940)),hAPP(c_List_Oset(tc_prod(X31941,X31940)),X31939)) = hAPP(c_Set_Oimage(tc_prod(X31941,X31940),X31941,c_Product__Type_Ofst(X31941,X31940)),hAPP(c_List_Oset(tc_prod(X31941,X31940)),X31938)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__eq__dom])]) ).
fof(i_0_8234,plain,
! [X28045,X28046] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28046),c_Orderings_Otop__class_Otop(tc_fun(X28046,tc_HOL_Obool))))
| ~ c_Fun_Oinj__on(X28046,X28046,X28045,c_Orderings_Otop__class_Otop(tc_fun(X28046,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(X28046,X28046,X28045),c_Orderings_Otop__class_Otop(tc_fun(X28046,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X28046,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
fof(i_0_8235,plain,
! [X32468,X32469,X32470,X32471] :
( ~ class_Rings_Osemiring__1(X32471)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32471),hAPP(hAPP(c_List_Omap(X32470,X32471),hAPP(c_COMBK(X32471,X32470),X32469)),X32468)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32471),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X32471),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32470)),X32468))),X32469) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__triv])]) ).
fof(i_0_8236,plain,
! [X20996,X20997,X20998] :
( ~ class_Rings_Oring__1(X20998)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20998),hAPP(c_Groups_Ouminus__class_Ouminus(X20998),X20997)),X20996) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20998),hAPP(hAPP(c_Power_Opower__class_Opower(X20998),hAPP(c_Groups_Ouminus__class_Ouminus(X20998),c_Groups_Oone__class_Oone(X20998))),X20996)),hAPP(hAPP(c_Power_Opower__class_Opower(X20998),X20997),X20996)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).
fof(i_0_8237,plain,
! [X25247,X25248,X25249,X25250] : hBOOL(hAPP(hAPP(c_member(X25250),hAPP(X25249,X25248)),hAPP(c_Set_Oimage(X25247,X25250,X25249),c_Orderings_Otop__class_Otop(tc_fun(X25247,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(i_0_8238,plain,
! [X20733,X20734,X20735,X20736] :
( ~ class_Int_Onumber(X20736)
| ~ class_Rings_Oring(X20736)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20736),X20735),X20734)),hAPP(c_Int_Onumber__class_Onumber__of(X20736),X20733)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20736),X20735),hAPP(c_Int_Onumber__class_Onumber__of(X20736),X20733))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20736),X20734),hAPP(c_Int_Onumber__class_Onumber__of(X20736),X20733))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of])]) ).
fof(i_0_8239,plain,
! [X20716,X20717,X20718,X20719] :
( ~ class_Int_Onumber(X20719)
| ~ class_Rings_Osemiring(X20719)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20719),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20719),X20718),X20717)),hAPP(c_Int_Onumber__class_Onumber__of(X20719),X20716)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20719),X20718),hAPP(c_Int_Onumber__class_Onumber__of(X20719),X20716))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20719),X20717),hAPP(c_Int_Onumber__class_Onumber__of(X20719),X20716))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])]) ).
fof(i_0_8240,plain,
! [X31593,X31594,X31595,X31596,X31597,X31598] :
( ( hAPP(X31595,X31594) = c_Option_Ooption_ONone(X31597)
| hAPP(X31595,X31594) = hAPP(c_Option_Ooption_OSome(X31597),X31593)
| hAPP(c_Map_Omap__add(X31598,X31597,X31596,X31595),X31594) != hAPP(c_Option_Ooption_OSome(X31597),X31593) )
& ( hAPP(X31596,X31594) = hAPP(c_Option_Ooption_OSome(X31597),X31593)
| hAPP(X31595,X31594) = hAPP(c_Option_Ooption_OSome(X31597),X31593)
| hAPP(c_Map_Omap__add(X31598,X31597,X31596,X31595),X31594) != hAPP(c_Option_Ooption_OSome(X31597),X31593) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__SomeD])])]) ).
fof(i_0_8241,plain,
! [X31587,X31588,X31589,X31590,X31591,X31592] :
( ( hAPP(X31589,X31588) = c_Option_Ooption_ONone(X31591)
| hAPP(X31589,X31588) = hAPP(c_Option_Ooption_OSome(X31591),X31587)
| hAPP(c_Map_Omap__add(X31592,X31591,X31590,X31589),X31588) != hAPP(c_Option_Ooption_OSome(X31591),X31587) )
& ( hAPP(X31590,X31588) = hAPP(c_Option_Ooption_OSome(X31591),X31587)
| hAPP(X31589,X31588) = hAPP(c_Option_Ooption_OSome(X31591),X31587)
| hAPP(c_Map_Omap__add(X31592,X31591,X31590,X31589),X31588) != hAPP(c_Option_Ooption_OSome(X31591),X31587) )
& ( hAPP(X31589,X31588) != hAPP(c_Option_Ooption_OSome(X31591),X31587)
| hAPP(c_Map_Omap__add(X31592,X31591,X31590,X31589),X31588) = hAPP(c_Option_Ooption_OSome(X31591),X31587) )
& ( hAPP(X31589,X31588) != c_Option_Ooption_ONone(X31591)
| hAPP(X31590,X31588) != hAPP(c_Option_Ooption_OSome(X31591),X31587)
| hAPP(c_Map_Omap__add(X31592,X31591,X31590,X31589),X31588) = hAPP(c_Option_Ooption_OSome(X31591),X31587) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__Some__iff])])]) ).
fof(i_0_8242,plain,
! [X27795,X27796,X27797] :
( ~ class_Lattices_Olattice(X27797)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27797),X27796))
| X27796 = c_Orderings_Obot__class_Obot(tc_fun(X27797,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27797),X27795))
| X27795 = c_Orderings_Obot__class_Obot(tc_fun(X27797,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27797,tc_HOL_Obool)),X27796),X27795) != c_Orderings_Obot__class_Obot(tc_fun(X27797,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X27797,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27797,tc_HOL_Obool)),X27796),X27795)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27797),c_Big__Operators_Olattice__class_OInf__fin(X27797,X27796)),c_Big__Operators_Olattice__class_OInf__fin(X27797,X27795)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint])]) ).
fof(i_0_8243,plain,
! [X27611,X27612,X27613] :
( ~ class_Orderings_Olinorder(X27613)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27613),X27612))
| X27612 = c_Orderings_Obot__class_Obot(tc_fun(X27613,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27613),X27611))
| X27611 = c_Orderings_Obot__class_Obot(tc_fun(X27613,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27613,tc_HOL_Obool)),X27612),X27611) != c_Orderings_Obot__class_Obot(tc_fun(X27613,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X27613,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27613,tc_HOL_Obool)),X27612),X27611)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27613),c_Big__Operators_Olinorder__class_OMin(X27613,X27612)),c_Big__Operators_Olinorder__class_OMin(X27613,X27611)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint])]) ).
fof(i_0_8244,plain,
! [X27614,X27615,X27616] :
( ~ class_Orderings_Olinorder(X27616)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27616),X27615))
| X27615 = c_Orderings_Obot__class_Obot(tc_fun(X27616,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27616),X27614))
| X27614 = c_Orderings_Obot__class_Obot(tc_fun(X27616,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27616,tc_HOL_Obool)),X27615),X27614) != c_Orderings_Obot__class_Obot(tc_fun(X27616,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X27616,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27616,tc_HOL_Obool)),X27615),X27614)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27616),c_Big__Operators_Olinorder__class_OMax(X27616,X27615)),c_Big__Operators_Olinorder__class_OMax(X27616,X27614)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint])]) ).
fof(i_0_8245,plain,
! [X27605,X27606,X27607] :
( ~ class_Lattices_Olattice(X27607)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27607),X27606))
| X27606 = c_Orderings_Obot__class_Obot(tc_fun(X27607,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27607),X27605))
| X27605 = c_Orderings_Obot__class_Obot(tc_fun(X27607,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27607,tc_HOL_Obool)),X27606),X27605) != c_Orderings_Obot__class_Obot(tc_fun(X27607,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X27607,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27607,tc_HOL_Obool)),X27606),X27605)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27607),c_Big__Operators_Olattice__class_OSup__fin(X27607,X27606)),c_Big__Operators_Olattice__class_OSup__fin(X27607,X27605)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint])]) ).
fof(i_0_8246,plain,
! [X23136,X23137,X23138,X23139] :
( ~ class_Rings_Ocomm__semiring__1(X23139)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23139),X23138),X23137))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23139),hAPP(hAPP(c_Power_Opower__class_Opower(X23139),X23138),X23136)),hAPP(hAPP(c_Power_Opower__class_Opower(X23139),X23137),X23136))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__same])]) ).
fof(i_0_8247,plain,
! [X19200,X19201,X19202,X19203] :
( ~ class_Groups_Oordered__ab__semigroup__add(X19203)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19203),X19202),X19201))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19203),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19203),X19202),X19200)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19203),X19201),X19200))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_8248,plain,
! [X19196,X19197,X19198,X19199] :
( ~ class_Groups_Oordered__ab__semigroup__add(X19199)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19199),X19198),X19197))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19199),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19199),X19196),X19198)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19199),X19196),X19197))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_8249,plain,
! [X18244,X18245,X18246,X18247] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18247)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18247),X18246),X18245))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18247),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18247),X18246),X18244)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18247),X18245),X18244))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_8250,plain,
! [X18248,X18249,X18250,X18251] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18251)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18251),X18250),X18249))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18251),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18251),X18248),X18250)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18251),X18248),X18249))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_8251,plain,
! [X29066,X29067,X29068] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X29068)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29068),X29067))
| X29067 = c_Orderings_Obot__class_Obot(tc_fun(X29068,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29068),X29066))
| X29066 = c_Orderings_Obot__class_Obot(tc_fun(X29068,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ofold1(X29068,c_Groups_Otimes__class_Otimes(X29068)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29068,tc_HOL_Obool)),X29067),X29066)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29068),hAPP(c_Finite__Set_Ofold1(X29068,c_Groups_Otimes__class_Otimes(X29068)),X29067)),hAPP(c_Finite__Set_Ofold1(X29068,c_Groups_Otimes__class_Otimes(X29068)),X29066)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un2])]) ).
fof(i_0_8252,plain,
! [X34319,X34320,X34321] : hAPP(c_List_Orev(X34321),hAPP(hAPP(c_List_Odrop(X34321),X34320),X34319)) = hAPP(hAPP(c_List_Otake(X34321),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34321)),X34319)),X34320)),hAPP(c_List_Orev(X34321),X34319)),
inference(variable_rename,[status(thm)],[fact_rev__drop]) ).
fof(i_0_8253,plain,
! [X34322,X34323,X34324] : hAPP(c_List_Orev(X34324),hAPP(hAPP(c_List_Otake(X34324),X34323),X34322)) = hAPP(hAPP(c_List_Odrop(X34324),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34324)),X34322)),X34323)),hAPP(c_List_Orev(X34324),X34322)),
inference(variable_rename,[status(thm)],[fact_rev__take]) ).
fof(i_0_8254,plain,
! [X24889,X24890,X24891] :
( ~ class_Orderings_Olinorder(X24891)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24891),X24890),X24889))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24891,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24891),X24890),c_Orderings_Obot__class_Obot(tc_fun(X24891,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X24891,X24890,X24889)) = c_SetInterval_Oord__class_OatLeastAtMost(X24891,X24890,X24889) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J])]) ).
fof(i_0_8255,plain,
! [X24781,X24782] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24782,tc_HOL_Obool)),X24781),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24782,tc_HOL_Obool)),X24781)))
| X24781 = c_Orderings_Obot__class_Obot(tc_fun(X24782,tc_HOL_Obool)) )
& ( X24781 != c_Orderings_Obot__class_Obot(tc_fun(X24782,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24782,tc_HOL_Obool)),X24781),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24782,tc_HOL_Obool)),X24781))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq])]) ).
fof(i_0_8256,plain,
! [X26220,X26221,X26222,X26223,X26224,X26225,X26226] :
( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26226,tc_Option_Ooption(X26225)),X26224),X26223),hAPP(c_Option_Ooption_OSome(X26225),X26222)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26226,tc_Option_Ooption(X26225)),X26221),X26223),hAPP(c_Option_Ooption_OSome(X26225),X26220))
| X26222 = X26220 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__eqD1])]) ).
fof(i_0_8257,plain,
! [X21099,X21100,X21101] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21101),c_Int_OPls))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21101)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21100)),X21099)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21101),c_Int_OPls))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21101)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21100)),X21099)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21101),X21100))),X21099) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5688])]) ).
fof(i_0_8258,plain,
! [X22120,X22121] : c_Divides_Opdivmod(X22121,X22120) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22121)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22120))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22121),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22120))),
inference(variable_rename,[status(thm)],[fact_pdivmod__def]) ).
fof(i_0_8259,plain,
! [X31301,X31302,X31303] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31303,tc_HOL_Obool)),X31302),X31301))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31303,tc_HOL_Obool)),X31302),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31303,tc_HOL_Obool),X31301))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__upper])]) ).
fof(i_0_8260,plain,
! [X30663,X30664,X30665,X30666] : hAPP(c_Finite__Set_Ofold__image(X30666,X30665,X30664),X30663) = c_Finite__Set_Ofold(X30665,X30666,hAPP(hAPP(c_COMBB(X30666,tc_fun(X30666,X30666),X30665),X30664),X30663)),
inference(variable_rename,[status(thm)],[fact_fold__image__def]) ).
fof(i_0_8261,plain,
! [X22722,X22723] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22723)),X22722) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22723),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22723)),X22722),
inference(variable_rename,[status(thm)],[fact_max__Suc1]) ).
fof(i_0_8262,plain,
! [X31286,X31287] : hAPP(c_Relation_OField(X31287),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X31287,X31287),tc_HOL_Obool),X31286)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X31287,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X31287,X31287),tc_HOL_Obool),tc_fun(X31287,tc_HOL_Obool),c_Relation_OField(X31287)),X31286)),
inference(variable_rename,[status(thm)],[fact_Field__Union]) ).
fof(i_0_8263,plain,
! [X23034,X23035] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23034),X23035)),X23035))
| X23034 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23035)) )
& ( X23034 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23034),X23035)),X23035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23035)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel2])])]) ).
fof(i_0_8264,plain,
! [X23036,X23037] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23037),X23036)),X23037))
| X23036 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23037)) )
& ( X23036 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23037),X23036)),X23037))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23037)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel1])])]) ).
fof(i_0_8265,plain,
! [X24077,X24078,X24079] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24079,tc_HOL_Obool)),X24078),X24077))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24079,tc_HOL_Obool)),X24078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24079,tc_HOL_Obool)),X24077),X24078)) = X24077 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__partition])]) ).
fof(i_0_8266,plain,
! [X31719,X31720,X31721] :
( ~ c_Fun_Oinj__on(X31721,X31720,X31719,c_Orderings_Otop__class_Otop(tc_fun(X31721,tc_HOL_Obool)))
| c_Fun_Oinj__on(tc_List_Olist(X31721),tc_List_Olist(X31720),hAPP(c_List_Omap(X31721,X31720),X31719),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31721),tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapI])]) ).
fof(i_0_8267,plain,
! [X27392,X27393,X27394] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27394,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27394,tc_HOL_Obool)),X27393),X27392)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27394,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27394,tc_HOL_Obool)),X27393)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27394,tc_HOL_Obool)),X27392)),
inference(variable_rename,[status(thm)],[fact_Compl__Int]) ).
fof(i_0_8268,plain,
! [X27389,X27390,X27391] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27391,tc_HOL_Obool)),X27390),X27389)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27391,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27391,tc_HOL_Obool)),X27390)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27391,tc_HOL_Obool)),X27389)),
inference(variable_rename,[status(thm)],[fact_Compl__Un]) ).
fof(i_0_8269,plain,
! [X26783,X26784,X26785,X26786,X26787] :
( ( hBOOL(hAPP(hAPP(X26786,X26784),X26783))
| ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X26787,X26786,X26785),X26784),X26783)) )
& ( hBOOL(hAPP(X26785,X26783))
| ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X26787,X26786,X26785),X26784),X26783)) )
& ( ~ hBOOL(hAPP(hAPP(X26786,X26784),X26783))
| ~ hBOOL(hAPP(X26785,X26783))
| hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X26787,X26786,X26785),X26784),X26783)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_peek__and__def])])]) ).
fof(i_0_8270,plain,
! [X28326,X28327,X28328,X28329,X28330] :
( ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X28330,X28329,X28328),X28327),X28326))
| hBOOL(hAPP(X28327,hAPP(X28328,X28326))) )
& ( ~ hBOOL(hAPP(X28327,hAPP(X28328,X28326)))
| hBOOL(hAPP(hAPP(c_Set_Ovimage(X28330,X28329,X28328),X28327),X28326)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__code])]) ).
fof(i_0_8271,plain,
! [X31274,X31275,X31276,X31278] :
( ( hBOOL(hAPP(hAPP(c_member(X31276),esk398_3(X31274,X31275,X31276)),X31275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31276),c_Complete__Lattice_OInf__class_OInf(X31276,X31275)),X31274))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31276)
| ~ class_Orderings_Olinorder(X31276) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31276),esk398_3(X31274,X31275,X31276)),X31274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31276),c_Complete__Lattice_OInf__class_OInf(X31276,X31275)),X31274))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31276)
| ~ class_Orderings_Olinorder(X31276) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X31276),X31278),X31275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31276),X31278),X31274))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31276),c_Complete__Lattice_OInf__class_OInf(X31276,X31275)),X31274))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31276)
| ~ class_Orderings_Olinorder(X31276) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__less__iff])])])])]) ).
fof(i_0_8272,plain,
! [X20767,X20768,X20769,X20770] :
( ~ class_Int_Onumber__ring(X20770)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20770),hAPP(c_Int_Onumber__class_Onumber__of(X20770),X20769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20770),hAPP(c_Int_Onumber__class_Onumber__of(X20770),X20768)),X20767)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20770),hAPP(c_Int_Onumber__class_Onumber__of(X20770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20769),X20768))),X20767) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])]) ).
fof(i_0_8273,plain,
! [X20810,X20811,X20812,X20813] :
( ~ class_Int_Onumber__ring(X20813)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20813),hAPP(c_Int_Onumber__class_Onumber__of(X20813),X20812)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20813),hAPP(c_Int_Onumber__class_Onumber__of(X20813),X20811)),X20810)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20813),hAPP(c_Int_Onumber__class_Onumber__of(X20813),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20812),X20811))),X20810) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1])]) ).
fof(i_0_8274,plain,
! [X20749,X20750,X20751,X20752] :
( ~ class_Int_Onumber__ring(X20752)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20752),hAPP(c_Int_Onumber__class_Onumber__of(X20752),X20751)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20752),hAPP(c_Int_Onumber__class_Onumber__of(X20752),X20750)),X20749)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20752),hAPP(c_Int_Onumber__class_Onumber__of(X20752),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20751),X20750))),X20749) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])]) ).
fof(i_0_8275,plain,
! [X31959,X31960,X31961] : hAPP(c_Option_Omap(X31961,X31960),X31959) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(X31960),X31961,c_Option_Ooption_ONone(X31960),hAPP(hAPP(c_COMBB(X31960,tc_Option_Ooption(X31960),X31961),c_Option_Ooption_OSome(X31960)),X31959)),
inference(variable_rename,[status(thm)],[fact_Option_Omap__def]) ).
fof(i_0_8276,plain,
! [X24892,X24893,X24894] :
( ~ class_Orderings_Olinorder(X24894)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24894),X24893),X24892))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24894,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24894),X24893),c_Orderings_Obot__class_Obot(tc_fun(X24894,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X24894,X24893,X24892)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24894,X24893),X24892) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J])]) ).
fof(i_0_8277,plain,
! [X32632,X32633,X32634,X32635,X32636] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32636),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32635)),X32634)))
| hAPP(hAPP(c_List_Onth(X32633),hAPP(hAPP(c_List_Omap(X32635,X32633),X32632),X32634)),X32636) = hAPP(X32632,hAPP(hAPP(c_List_Onth(X32635),X32634),X32636)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map])]) ).
fof(i_0_8278,plain,
! [X23346,X23347,X23348,X23349] :
( ~ class_Rings_Ocomm__semiring__1(X23349)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23348),X23347))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23349),hAPP(hAPP(c_Power_Opower__class_Opower(X23349),X23346),X23348)),hAPP(hAPP(c_Power_Opower__class_Opower(X23349),X23346),X23347))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__power__dvd])]) ).
fof(i_0_8279,plain,
! [X22051,X22052] :
( ( X22051 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nitpick_Onat__gcd(X22052,X22051) = X22052
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22052),X22051))) )
& ( X22051 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nitpick_Onat__gcd(X22052,X22051) = c_Nitpick_Onat__gcd(X22051,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22052,X22051))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22052),X22051))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opsimps])])]) ).
fof(i_0_8280,plain,
! [X31206,X31207,X31208,X31209] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31209,tc_HOL_Obool)),X31208),X31207))
| ~ hBOOL(hAPP(hAPP(c_member(X31209),X31206),X31208))
| hBOOL(hAPP(hAPP(c_member(X31209),X31206),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31209,tc_HOL_Obool),X31207))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnionI])]) ).
fof(i_0_8281,plain,
! [X18885,X18886,X18887] :
( ~ class_Rings_Olinordered__semiring__strict(X18887)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18887),c_Groups_Ozero__class_Ozero(X18887)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18887),X18886),X18885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18887),c_Groups_Ozero__class_Ozero(X18887)),X18885))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18887),c_Groups_Ozero__class_Ozero(X18887)),X18886)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).
fof(i_0_8282,plain,
! [X18882,X18883,X18884] :
( ~ class_Rings_Olinordered__semiring__strict(X18884)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18884),c_Groups_Ozero__class_Ozero(X18884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18884),X18883),X18882)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18884),c_Groups_Ozero__class_Ozero(X18884)),X18883))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18884),c_Groups_Ozero__class_Ozero(X18884)),X18882)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).
fof(i_0_8283,plain,
! [X27599,X27600,X27601] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27601),X27600))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27601),X27599))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27601,tc_HOL_Obool)),X27600),X27599) != c_Orderings_Obot__class_Obot(tc_fun(X27601,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(X27601),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27601,tc_HOL_Obool)),X27600),X27599)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27601),X27600)),hAPP(c_Finite__Set_Ocard(X27601),X27599)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint])]) ).
fof(i_0_8284,plain,
! [X22478,X22479] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22479)),X22478) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22479)),X22478),
inference(variable_rename,[status(thm)],[fact_min__Suc1]) ).
fof(i_0_8285,plain,
! [X32040,X32041,X32042] :
( ~ class_Orderings_Olinorder(X32042)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32042),X32041))
| c_List_Olinorder__class_Osorted__list__of__set(X32042,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32042,tc_HOL_Obool)),X32041),hAPP(hAPP(c_Set_Oinsert(X32042),X32040),c_Orderings_Obot__class_Obot(tc_fun(X32042,tc_HOL_Obool))))) = c_List_Oremove1(X32042,X32040,c_List_Olinorder__class_Osorted__list__of__set(X32042,X32041)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__remove])]) ).
fof(i_0_8286,plain,
! [X24540,X24541] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X24541,X24540)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X24541,X24540),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24540),c_Orderings_Otop__class_Otop(tc_fun(X24540,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).
fof(i_0_8287,plain,
! [X26507,X26508,X26509] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26509,tc_HOL_Obool)),X26508),hAPP(c_Set_OPow(X26509),X26507)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26509,tc_HOL_Obool)),X26508),X26507)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowD])]) ).
fof(i_0_8288,plain,
! [X26504,X26505,X26506] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26506,tc_HOL_Obool)),X26505),hAPP(c_Set_OPow(X26506),X26504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26506,tc_HOL_Obool)),X26505),X26504)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26506,tc_HOL_Obool)),X26505),X26504))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26506,tc_HOL_Obool)),X26505),hAPP(c_Set_OPow(X26506),X26504))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__iff])]) ).
fof(i_0_8289,plain,
! [X20664,X20665] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20665)),X20664)))
| X20665 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X20664 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X20665 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20665)),X20664))) )
& ( X20664 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20665)),X20664))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])]) ).
fof(i_0_8290,plain,
! [X23830,X23831,X23832,X23833] :
( ~ class_Orderings_Olinorder(X23833)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23833),X23832),X23831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23833),X23831),X23830))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23833,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23833,X23832,X23831)),c_SetInterval_Oord__class_OatLeastAtMost(X23833,X23831,X23830)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X23833,X23832,X23830) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J])]) ).
fof(i_0_8291,plain,
! [X24125,X24126,X24127,X24128] :
( ~ class_Orderings_Olinorder(X24128)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24128),X24127),X24126))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24128),X24126),X24125))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24128,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24128,X24127,X24126)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24128,X24126,X24125)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X24128,X24127,X24125) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J])]) ).
fof(i_0_8292,plain,
! [X24082,X24083,X24084,X24085] :
( ~ class_Orderings_Olinorder(X24085)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24085),X24084),X24083))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24085),X24083),X24082))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24085,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24085,X24084,X24083)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24085,X24083,X24082)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X24085,X24084,X24082) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J])]) ).
fof(i_0_8293,plain,
! [X24110,X24111,X24112,X24113] :
( ~ class_Orderings_Olinorder(X24113)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24113),X24112),X24111))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24113),X24111),X24110))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24113,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24113,X24112,X24111)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24113,X24111,X24110)) = c_SetInterval_Oord__class_OatLeastAtMost(X24113,X24112,X24110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J])]) ).
fof(i_0_8294,plain,
! [X23988,X23989,X23990] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23990,tc_HOL_Obool)),X23989),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23990,tc_HOL_Obool)),X23989),X23988))),
inference(variable_rename,[status(thm)],[fact_Un__upper1]) ).
fof(i_0_8295,plain,
! [X23991,X23992,X23993] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23993,tc_HOL_Obool)),X23992),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23993,tc_HOL_Obool)),X23991),X23992))),
inference(variable_rename,[status(thm)],[fact_Un__upper2]) ).
fof(i_0_8296,plain,
! [X30173,X30174,X30175] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30175,X30175)),X30174),X30173))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30175,X30175)),X30174),c_Transitive__Closure_Ortrancl(X30175,X30173))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])]) ).
fof(i_0_8297,plain,
! [X24871,X24872,X24873,X24874] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24874),X24873))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24872),X24871))
| hAPP(c_Finite__Set_Ocard(tc_sum(X24874,X24872)),c_Sum__Type_OPlus(X24874,X24872,X24873,X24871)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24874),X24873)),hAPP(c_Finite__Set_Ocard(X24872),X24871)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).
fof(i_0_8298,plain,
! [X24609,X24610,X24611,X24612] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24612),X24611))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24610),X24609))
| hAPP(c_Finite__Set_Ocard(tc_sum(X24612,X24610)),c_Sum__Type_OPlus(X24612,X24610,X24611,X24609)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24612),X24611)),hAPP(c_Finite__Set_Ocard(X24610),X24609)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24612),X24611))
| hAPP(c_Finite__Set_Ocard(tc_sum(X24612,X24610)),c_Sum__Type_OPlus(X24612,X24610,X24611,X24609)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24610),X24609))
| hAPP(c_Finite__Set_Ocard(tc_sum(X24612,X24610)),c_Sum__Type_OPlus(X24612,X24610,X24611,X24609)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus__conv__if])])]) ).
fof(i_0_8299,plain,
! [X24025,X24026,X24027,X24028] :
( ~ class_Lattices_Osemilattice__sup(X24028)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24028),X24027),X24026))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24028),X24025),X24026))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24028),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24028),X24027),X24025)),X24026)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI])]) ).
fof(i_0_8300,plain,
! [X24021,X24022,X24023,X24024] :
( ~ class_Lattices_Osemilattice__sup(X24024)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24024),X24023),X24022))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24024),X24021),X24022))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24024),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24024),X24023),X24021)),X24022)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__least])]) ).
fof(i_0_8301,plain,
! [X22603,X22604,X22605,X22606] :
( ~ class_Orderings_Olinorder(X22606)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22606),X22605),X22604))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22606),X22603),X22604))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22606),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22606),X22605),X22603)),X22604)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI])]) ).
fof(i_0_8302,plain,
! [X22599,X22600,X22601,X22602] :
( ~ class_Orderings_Olinorder(X22602)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22602),X22601),X22600))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22602),X22599),X22600))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22602),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22602),X22601),X22599)),X22600)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__least])]) ).
fof(i_0_8303,plain,
! [X27173,X27174,X27175,X27176] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27176,tc_HOL_Obool)),X27175),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27176,tc_HOL_Obool)),X27174),X27173)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27176,tc_HOL_Obool)),X27174),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27176,tc_HOL_Obool)),X27175),X27173)),
inference(variable_rename,[status(thm)],[fact_Int__left__commute]) ).
fof(i_0_8304,plain,
! [X23896,X23897,X23898,X23899] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23899,tc_HOL_Obool)),X23898),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23899,tc_HOL_Obool)),X23897),X23896)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23899,tc_HOL_Obool)),X23897),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23899,tc_HOL_Obool)),X23898),X23896)),
inference(variable_rename,[status(thm)],[fact_Un__left__commute]) ).
fof(i_0_8305,plain,
! [X23968,X23969,X23970] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23970,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23970,tc_HOL_Obool)),X23969),X23968)),X23968) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23970,tc_HOL_Obool)),X23969),X23968),
inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel2]) ).
fof(i_0_8306,plain,
! [X22517,X22518,X22519] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22519,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22519,tc_HOL_Obool)),X22518),X22517)),X22517) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22519,tc_HOL_Obool)),X22518),X22517),
inference(variable_rename,[status(thm)],[fact_Diff__idemp]) ).
cnf(i_0_8307,plain,
( hAPP(c_List_Orotate(X1,X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_5689]) ).
fof(i_0_8308,plain,
! [X25045,X25046,X25047,X25048,X25049] :
( ~ hBOOL(hAPP(hAPP(c_member(X25049),X25048),X25047))
| hBOOL(hAPP(hAPP(c_member(X25046),hAPP(X25045,X25048)),hAPP(c_Set_Oimage(X25049,X25046,X25045),X25047))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_8309,plain,
! [X25679,X25680,X25681,X25682] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X25682,X25681,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25682)),X25680),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25682),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X25682,X25681,X25679)
| c_Hoare__Mirabelle_Ohoare__derivs(X25682,X25681,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X25682)),X25680),X25679)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert])]) ).
fof(i_0_8310,plain,
! [X23293,X23294] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23294),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23293)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23294))),X23293)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23294))),X23293))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23294),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23293))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__int__iff])]) ).
fof(i_0_8311,plain,
! [X30792,X30793,X30794,X30795,X30796] :
( ~ c_Finite__Set_Ofun__left__comm(X30796,X30795,X30794)
| c_Finite__Set_Ofun__left__comm(X30793,X30795,hAPP(hAPP(c_COMBB(X30796,tc_fun(X30795,X30795),X30793),X30794),X30792)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply])]) ).
fof(i_0_8312,plain,
! [X29122,X29123,X29124,X29125,X29126] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X29126,X29125,X29124)
| c_Finite__Set_Ofun__left__comm__idem(X29123,X29125,hAPP(hAPP(c_COMBB(X29126,tc_fun(X29125,X29125),X29123),X29124),X29122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply])]) ).
fof(i_0_8313,plain,
! [X27344,X27345,X27346,X27347] :
( ~ hBOOL(hAPP(hAPP(c_member(X27347),X27346),X27345))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27347,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X27347),X27346),X27344)),X27345) = hAPP(hAPP(c_Set_Oinsert(X27347),X27346),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27347,tc_HOL_Obool)),X27344),X27345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1])]) ).
fof(i_0_8314,plain,
! [X27328,X27329,X27330,X27331] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27331),X27330),X27329))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27331,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X27331),X27330),X27328)),X27329) = hAPP(hAPP(c_Set_Oinsert(X27331),X27330),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27331,tc_HOL_Obool)),X27328),X27329)) )
& ( hBOOL(hAPP(hAPP(c_member(X27331),X27330),X27329))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27331,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X27331),X27330),X27328)),X27329) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27331,tc_HOL_Obool)),X27328),X27329) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5690])]) ).
fof(i_0_8315,plain,
! [X27975,X27976,X27977,X27978,X27979] :
( ( hAPP(c_Set_Oimage(X27979,X27978,X27977),X27976) != hAPP(c_Set_Oimage(X27979,X27978,X27977),X27975)
| X27976 = X27975
| ~ c_Fun_Oinj__on(X27979,X27978,X27977,c_Orderings_Otop__class_Otop(tc_fun(X27979,tc_HOL_Obool))) )
& ( X27976 != X27975
| hAPP(c_Set_Oimage(X27979,X27978,X27977),X27976) = hAPP(c_Set_Oimage(X27979,X27978,X27977),X27975)
| ~ c_Fun_Oinj__on(X27979,X27978,X27977,c_Orderings_Otop__class_Otop(tc_fun(X27979,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__eq__iff])])]) ).
fof(i_0_8316,plain,
! [X26674,X26675,X26676,X26677,X26678,X26679,X26680] :
( hAPP(c_Fun_Ocomp(X26680,X26679,X26678,X26677),X26676) != X26675
| hAPP(X26677,hAPP(X26676,X26674)) = hAPP(X26675,X26674) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs])]) ).
fof(i_0_8317,plain,
! [X18615] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X18615)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_negative__zless__0]) ).
fof(i_0_8318,plain,
! [X33415,X33416,X33417] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33417),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33416)),X33415)))
| hAPP(hAPP(c_List_Olist_OCons(X33416),hAPP(hAPP(c_List_Onth(X33416),X33415),X33417)),hAPP(hAPP(c_List_Odrop(X33416),hAPP(c_Nat_OSuc,X33417)),X33415)) = hAPP(hAPP(c_List_Odrop(X33416),X33417),X33415) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop_H])]) ).
fof(i_0_8319,plain,
! [X28370,X28371,X28372,X28373] : hAPP(c_Set_Oimage(X28373,X28372,X28371),hAPP(c_Set_Ovimage(X28373,X28372,X28371),X28370)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28372,tc_HOL_Obool)),X28370),hAPP(c_Set_Oimage(X28373,X28372,X28371),c_Orderings_Otop__class_Otop(tc_fun(X28373,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_image__vimage__eq]) ).
fof(i_0_8320,plain,
! [X19636,X19637] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19637),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19636))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19637),X19636)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19637),X19636))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19637),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19636)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).
fof(i_0_8321,plain,
! [X23834,X23835,X23836,X23837] :
( ~ class_Orderings_Olinorder(X23837)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23837),X23836),X23835))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23837),X23835),X23834))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23837,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X23837,X23836,X23835)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23837,X23835,X23834)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23837,X23836),X23834) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J])]) ).
fof(i_0_8322,plain,
! [X24441] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24441))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24441))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24441)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24441)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J])]) ).
fof(i_0_8323,plain,
! [X24584,X24585,X24586] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24586),X24585))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24586,tc_HOL_Obool)),X24584),X24585))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24586),X24584)),hAPP(c_Finite__Set_Ocard(X24586),X24585))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).
fof(i_0_8324,plain,
! [X24594,X24595,X24596] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24596),X24595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24596,tc_HOL_Obool)),X24594),X24595))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24596),X24594)),hAPP(c_Finite__Set_Ocard(X24596),X24595))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).
fof(i_0_8325,plain,
! [X28485,X28486,X28487,X28488,X28489] :
( hAPP(X28489,X28488) != c_Option_Ooption_ONone(X28487)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28486,tc_HOL_Obool)),c_Map_Odom(X28486,X28487,X28489)),hAPP(hAPP(c_Set_Oinsert(X28486),X28488),X28485)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28486,tc_HOL_Obool)),c_Map_Odom(X28486,X28487,X28489)),X28485) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__minus])]) ).
fof(i_0_8326,plain,
! [X25080,X25081,X25082,X25083] :
( ~ hBOOL(hAPP(hAPP(c_member(X25083),X25082),X25081))
| hBOOL(hAPP(hAPP(c_member(X25083),X25082),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25083,tc_HOL_Obool)),X25081),X25080))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI1])]) ).
fof(i_0_8327,plain,
! [X24967,X24968,X24969,X24970] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X24970),X24969),X24968))
| hBOOL(hAPP(hAPP(c_member(X24970),X24969),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24970,tc_HOL_Obool)),X24967),X24968))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24970),X24969),X24967))
| hBOOL(hAPP(hAPP(c_member(X24970),X24969),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24970,tc_HOL_Obool)),X24967),X24968))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5691])])]) ).
fof(i_0_8328,plain,
! [X25084,X25085,X25086,X25087] :
( ~ hBOOL(hAPP(hAPP(c_member(X25087),X25086),X25085))
| hBOOL(hAPP(hAPP(c_member(X25087),X25086),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25087,tc_HOL_Obool)),X25084),X25085))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI2])]) ).
fof(i_0_8329,plain,
! [X28043,X28044] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28044),c_Orderings_Otop__class_Otop(tc_fun(X28044,tc_HOL_Obool))))
| hAPP(c_Set_Oimage(X28044,X28044,X28043),c_Orderings_Otop__class_Otop(tc_fun(X28044,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28044,tc_HOL_Obool))
| c_Fun_Oinj__on(X28044,X28044,X28043,c_Orderings_Otop__class_Otop(tc_fun(X28044,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).
fof(i_0_8330,plain,
! [X20701,X20702,X20703] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20703),X20702),X20701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20703),hAPP(c_Groups_Oabs__class_Oabs(X20703),X20702)),X20701))
| ~ class_Groups_Oordered__ab__group__add__abs(X20703) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20703),hAPP(c_Groups_Ouminus__class_Ouminus(X20703),X20702)),X20701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20703),hAPP(c_Groups_Oabs__class_Oabs(X20703),X20702)),X20701))
| ~ class_Groups_Oordered__ab__group__add__abs(X20703) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20703),X20702),X20701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20703),hAPP(c_Groups_Ouminus__class_Ouminus(X20703),X20702)),X20701))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20703),hAPP(c_Groups_Oabs__class_Oabs(X20703),X20702)),X20701))
| ~ class_Groups_Oordered__ab__group__add__abs(X20703) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])]) ).
fof(i_0_8331,plain,
! [X20698,X20699,X20700] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20700)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20700),X20699),X20698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20700),hAPP(c_Groups_Ouminus__class_Ouminus(X20700),X20699)),X20698))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20700),hAPP(c_Groups_Oabs__class_Oabs(X20700),X20699)),X20698)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__leI])]) ).
fof(i_0_8332,plain,
! [X20706,X20707,X20708] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20708),X20707),X20706))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20708),hAPP(c_Groups_Oabs__class_Oabs(X20708),X20707)),X20706))
| ~ class_Rings_Olinordered__idom(X20708) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20708),hAPP(c_Groups_Ouminus__class_Ouminus(X20708),X20707)),X20706))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20708),hAPP(c_Groups_Oabs__class_Oabs(X20708),X20707)),X20706))
| ~ class_Rings_Olinordered__idom(X20708) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20708),X20707),X20706))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20708),hAPP(c_Groups_Ouminus__class_Ouminus(X20708),X20707)),X20706))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20708),hAPP(c_Groups_Oabs__class_Oabs(X20708),X20707)),X20706))
| ~ class_Rings_Olinordered__idom(X20708) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])]) ).
fof(i_0_8333,plain,
! [X31613,X31614,X31615,X31616,X31617] :
( hBOOL(hAPP(hAPP(c_member(X31617),X31616),c_Map_Odom(X31617,X31615,X31614)))
| hAPP(c_Map_Omap__add(X31617,X31615,X31614,X31613),X31616) = hAPP(X31613,X31616) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5692])]) ).
fof(i_0_8334,plain,
! [X31608,X31609,X31610,X31611,X31612] :
( hBOOL(hAPP(hAPP(c_member(X31612),X31611),c_Map_Odom(X31612,X31610,X31609)))
| hAPP(c_Map_Omap__add(X31612,X31610,X31608,X31609),X31611) = hAPP(X31608,X31611) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5693])]) ).
fof(i_0_8335,plain,
! [X33673,X33674,X33675] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33675)),X33674),c_Wellfounded_Oacc(tc_List_Olist(X33675),c_List_Olistrel1(X33675,X33673))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33675)),X33674),c_List_Olists(X33675,c_Wellfounded_Oacc(X33675,X33673)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accI])]) ).
fof(i_0_8336,plain,
! [X18859,X18860] :
( ~ class_Rings_Olinordered__ring(X18860)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18860),X18859),X18859)),c_Groups_Ozero__class_Ozero(X18860))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5694])]) ).
fof(i_0_8337,plain,
! [X28378,X28379,X28380,X28381] :
( ~ c_Fun_Oinj__on(X28381,X28380,X28379,c_Orderings_Otop__class_Otop(tc_fun(X28381,tc_HOL_Obool)))
| hAPP(c_Set_Ovimage(X28381,X28380,X28379),hAPP(c_Set_Oimage(X28381,X28380,X28379),X28378)) = X28378 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq])]) ).
fof(i_0_8338,plain,
! [X24121,X24122,X24123,X24124] :
( ~ class_Orderings_Olinorder(X24124)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24124),X24123),X24122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24124),X24122),X24121))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24124,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24124,X24123,X24122)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24124,X24122),X24121)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X24124,X24123,X24121) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J])]) ).
fof(i_0_8339,plain,
! [X20129,X20130,X20131,X20132] :
( ~ class_Divides_Osemiring__div(X20132)
| X20131 = c_Groups_Ozero__class_Ozero(X20132)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20132),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20132),X20130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20132),X20131),X20129))),X20131) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20132),X20129),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20132),X20130),X20131)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])]) ).
fof(i_0_8340,plain,
! [X20133,X20134,X20135,X20136] :
( ~ class_Divides_Osemiring__div(X20136)
| X20135 = c_Groups_Ozero__class_Ozero(X20136)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20136),X20134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20136),X20133),X20135))),X20135) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20136),X20133),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20136),X20134),X20135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1])]) ).
fof(i_0_8341,plain,
! [X21666,X21667,X21668,X21669] :
( ~ class_Fields_Ofield__inverse__zero(X21669)
| X21668 = c_Groups_Ozero__class_Ozero(X21669)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21669),X21667),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21669),X21666),X21668)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21669),X21666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21669),X21667),X21668))),X21668) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])]) ).
fof(i_0_8342,plain,
! [X29470,X29471,X29472,X29473] :
( ~ class_Groups_Ocomm__monoid__mult(X29473)
| ~ c_Fun_Oinj__on(X29472,X29473,X29471,X29470)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29472,X29473),X29471),X29470) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29473,X29473),c_Fun_Oid(X29473)),hAPP(c_Set_Oimage(X29472,X29473,X29471),X29470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__id])]) ).
fof(i_0_8343,plain,
! [X29466,X29467,X29468,X29469] :
( ~ class_Groups_Ocomm__monoid__add(X29469)
| ~ c_Fun_Oinj__on(X29468,X29469,X29467,X29466)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29468,X29469),X29467),X29466) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29469,X29469),c_Fun_Oid(X29469)),hAPP(c_Set_Oimage(X29468,X29469,X29467),X29466)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex__id])]) ).
fof(i_0_8344,plain,
! [X29594,X29595] :
( ( ~ c_Wellfounded_Owf(X29595,X29594)
| c_Wellfounded_Owf(X29595,hAPP(hAPP(c_Relation_Orel__comp(X29595,X29595,X29595),X29594),X29594)) )
& ( ~ c_Wellfounded_Owf(X29595,hAPP(hAPP(c_Relation_Orel__comp(X29595,X29595,X29595),X29594),X29594))
| c_Wellfounded_Owf(X29595,X29594) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__comp__self])]) ).
fof(i_0_8345,plain,
! [X25462,X25463,X25464] :
( X25464 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X25463,X25463),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X25463,X25463),tc_HOL_Obool)),X25464),X25462)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__by__empty])]) ).
fof(i_0_8346,plain,
! [X33011,X33012,X33013] :
( ( hBOOL(hAPP(c_List_Odistinct(X33013),X33012))
| ~ hBOOL(hAPP(c_List_Odistinct(X33013),hAPP(hAPP(c_List_Oappend(X33013),X33012),X33011))) )
& ( hBOOL(hAPP(c_List_Odistinct(X33013),X33011))
| ~ hBOOL(hAPP(c_List_Odistinct(X33013),hAPP(hAPP(c_List_Oappend(X33013),X33012),X33011))) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33013,tc_HOL_Obool)),hAPP(c_List_Oset(X33013),X33012)),hAPP(c_List_Oset(X33013),X33011)) = c_Orderings_Obot__class_Obot(tc_fun(X33013,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_List_Odistinct(X33013),hAPP(hAPP(c_List_Oappend(X33013),X33012),X33011))) )
& ( ~ hBOOL(hAPP(c_List_Odistinct(X33013),X33012))
| ~ hBOOL(hAPP(c_List_Odistinct(X33013),X33011))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33013,tc_HOL_Obool)),hAPP(c_List_Oset(X33013),X33012)),hAPP(c_List_Oset(X33013),X33011)) != c_Orderings_Obot__class_Obot(tc_fun(X33013,tc_HOL_Obool))
| hBOOL(hAPP(c_List_Odistinct(X33013),hAPP(hAPP(c_List_Oappend(X33013),X33012),X33011))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__append])])]) ).
fof(i_0_8347,plain,
! [X33636,X33637,X33638] :
( ~ class_Orderings_Olinorder(X33638)
| c_Big__Operators_Olattice_OInf__fin(X33638,c_Orderings_Oord__class_Omin(X33638),hAPP(c_List_Oset(X33638),hAPP(hAPP(c_List_Olist_OCons(X33638),X33637),X33636))) = hAPP(c_List_Ofoldl(X33638,X33638,c_Orderings_Oord__class_Omin(X33638),X33637),X33636) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin__set__fold])]) ).
fof(i_0_8348,plain,
! [X33639,X33640,X33641] :
( ~ class_Orderings_Olinorder(X33641)
| c_Big__Operators_Olattice_OSup__fin(X33641,c_Orderings_Oord__class_Omax(X33641),hAPP(c_List_Oset(X33641),hAPP(hAPP(c_List_Olist_OCons(X33641),X33640),X33639))) = hAPP(c_List_Ofoldl(X33641,X33641,c_Orderings_Oord__class_Omax(X33641),X33640),X33639) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin__set__fold])]) ).
fof(i_0_8349,plain,
! [X23674,X23675,X23676,X23677] :
( ~ class_Groups_Ocomm__monoid__add(X23677)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23676),X23675))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23677),X23674),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23676,X23675)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23677),hAPP(X23674,X23676)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23677),X23674),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X23676,X23675))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head])]) ).
fof(i_0_8350,plain,
! [X30515,X30516,X30517] : hAPP(hAPP(c_Nat_Ocompow(X30517,X30517),hAPP(c_Nat_OSuc,X30516)),X30515) = hAPP(c_Fun_Ocomp(X30517,X30517,X30517,X30515),hAPP(hAPP(c_Nat_Ocompow(X30517,X30517),X30516),X30515)),
inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I2_J]) ).
fof(i_0_8351,plain,
! [X33655,X33656,X33657,X33658,X33659] :
( ~ hBOOL(hAPP(hAPP(c_member(X33659),X33658),hAPP(c_List_Oset(X33659),X33657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33656),hAPP(X33655,X33658)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33656),c_List_Olist_Olist__size(X33659,X33655,X33657))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation_H])]) ).
fof(i_0_8352,plain,
! [X33650,X33651,X33652,X33653,X33654] :
( ~ hBOOL(hAPP(hAPP(c_member(X33654),X33653),hAPP(c_List_Oset(X33654),X33652)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33651),hAPP(X33650,X33653)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33651),c_List_Olist_Olist__size(X33654,X33650,X33652))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation])]) ).
fof(i_0_8353,plain,
! [X32672,X32673] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32673),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X32672)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X32672),X32673)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X32672))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__listsum__nat])]) ).
fof(i_0_8354,plain,
! [X32971,X32972,X32973,X32974] : c_Map_Omap__of(X32974,X32973,hAPP(hAPP(c_List_Oappend(tc_prod(X32974,X32973)),X32972),X32971)) = c_Map_Omap__add(X32974,X32973,c_Map_Omap__of(X32974,X32973,X32971),c_Map_Omap__of(X32974,X32973,X32972)),
inference(variable_rename,[status(thm)],[fact_map__of__append]) ).
fof(i_0_8355,plain,
! [X20199,X20200] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20200),X20199))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20199),X20200) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20199),X20200)),X20200)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__div__geq])]) ).
fof(i_0_8356,plain,
! [X33707,X33708,X33709] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33709)),X33708),c_List_Olists(X33709,c_Wellfounded_Oacc(X33709,X33707))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33709)),X33708),c_Wellfounded_Oacc(tc_List_Olist(X33709),c_List_Olistrel1(X33709,X33707)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])]) ).
cnf(i_0_8357,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_5695]) ).
cnf(i_0_8358,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X2))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[i_0_5696]) ).
fof(i_0_8359,plain,
! [X23393,X23394,X23395] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23395),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23394),X23393)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23395),X23393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23393),X23394))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23395),X23394)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diffD])]) ).
fof(i_0_8360,plain,
! [X23396,X23397,X23398] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23398),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23397),X23396)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23398),X23397))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23396),X23397))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23398),X23396)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diffD1])]) ).
fof(i_0_8361,plain,
! [X21866,X21867] :
( ~ class_Rings_Osemiring__1(X21867)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21867),X21866) = c_Nat_Osemiring__1__class_Oof__nat__aux(X21867,hAPP(hAPP(c_COMBC(X21867,X21867,X21867),c_Groups_Oplus__class_Oplus(X21867)),c_Groups_Oone__class_Oone(X21867)),X21866,c_Groups_Ozero__class_Ozero(X21867)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code])]) ).
fof(i_0_8362,plain,
! [X32280,X32281,X32282,X32283] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32283)),X32282)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32283)),X32281)))
| X32282 != hAPP(hAPP(c_List_Olist_OCons(X32283),X32280),X32281) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_impossible__Cons])]) ).
fof(i_0_8363,plain,
! [X26490,X26491,X26492] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26492,tc_HOL_Obool)),X26491),X26490))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26492,tc_HOL_Obool)),X26491),hAPP(c_Set_OPow(X26492),X26490))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowI])]) ).
fof(i_0_8364,plain,
! [X21027,X21028,X21029,X21030,X21031] : hAPP(hAPP(c_Power_Opower_Opower(X21031,X21030,X21029),X21028),hAPP(c_Nat_OSuc,X21027)) = hAPP(hAPP(X21029,X21028),hAPP(hAPP(c_Power_Opower_Opower(X21031,X21030,X21029),X21028),X21027)),
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(i_0_8365,plain,
! [X31624,X31625,X31626,X31627,X31628] :
( ( hAPP(X31625,X31624) = c_Option_Ooption_ONone(X31627)
| hAPP(c_Map_Omap__add(X31628,X31627,X31626,X31625),X31624) != c_Option_Ooption_ONone(X31627) )
& ( hAPP(X31626,X31624) = c_Option_Ooption_ONone(X31627)
| hAPP(c_Map_Omap__add(X31628,X31627,X31626,X31625),X31624) != c_Option_Ooption_ONone(X31627) )
& ( hAPP(X31625,X31624) != c_Option_Ooption_ONone(X31627)
| hAPP(X31626,X31624) != c_Option_Ooption_ONone(X31627)
| hAPP(c_Map_Omap__add(X31628,X31627,X31626,X31625),X31624) = c_Option_Ooption_ONone(X31627) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__None])])]) ).
fof(i_0_8366,plain,
! [X25848,X25849,X25850] :
( ~ class_Orderings_Olinorder(X25850)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25850,tc_HOL_Obool)),X25849),X25848))
| X25849 = c_Orderings_Obot__class_Obot(tc_fun(X25850,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25850),X25848))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25850),c_Big__Operators_Olinorder__class_OMin(X25850,X25848)),c_Big__Operators_Olinorder__class_OMin(X25850,X25849))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__antimono])]) ).
fof(i_0_8367,plain,
! [X25845,X25846,X25847] :
( ~ class_Orderings_Olinorder(X25847)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25847,tc_HOL_Obool)),X25846),X25845))
| X25846 = c_Orderings_Obot__class_Obot(tc_fun(X25847,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25847),X25845))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25847),c_Big__Operators_Olinorder__class_OMax(X25847,X25846)),c_Big__Operators_Olinorder__class_OMax(X25847,X25845))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__mono])]) ).
fof(i_0_8368,plain,
! [X20392,X20393] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20393),X20392))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20393),X20392)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20393),X20392)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20393),X20392)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).
fof(i_0_8369,plain,
! [X25226,X25227,X25228] :
( ~ hBOOL(hAPP(hAPP(c_member(X25228),X25227),hAPP(hAPP(c_Set_Oinsert(X25228),X25226),c_Orderings_Obot__class_Obot(tc_fun(X25228,tc_HOL_Obool)))))
| X25227 = X25226 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singletonE])]) ).
fof(i_0_8370,plain,
! [X25223,X25224,X25225] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25225),X25224),hAPP(hAPP(c_Set_Oinsert(X25225),X25223),c_Orderings_Obot__class_Obot(tc_fun(X25225,tc_HOL_Obool)))))
| X25224 = X25223 )
& ( X25224 != X25223
| hBOOL(hAPP(hAPP(c_member(X25225),X25224),hAPP(hAPP(c_Set_Oinsert(X25225),X25223),c_Orderings_Obot__class_Obot(tc_fun(X25225,tc_HOL_Obool))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__iff])]) ).
fof(i_0_8371,plain,
! [X25242,X25243,X25244,X25245,X25246] :
( X25246 != hAPP(X25245,X25244)
| hBOOL(hAPP(hAPP(c_member(X25243),X25246),hAPP(c_Set_Oimage(X25242,X25243,X25245),c_Orderings_Otop__class_Otop(tc_fun(X25242,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
fof(i_0_8372,plain,
! [X28779,X28780,X28781,X28782] :
( ( X28782 != c_Orderings_Obot__class_Obot(tc_fun(X28781,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X28781,X28780),X28780,c_Product__Type_Osnd(X28781,X28780)),hAPP(hAPP(c_Product__Type_OSigma(X28781,X28780),X28782),hAPP(c_COMBK(tc_fun(X28780,tc_HOL_Obool),X28781),X28779))) = c_Orderings_Obot__class_Obot(tc_fun(X28780,tc_HOL_Obool)) )
& ( X28782 = c_Orderings_Obot__class_Obot(tc_fun(X28781,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X28781,X28780),X28780,c_Product__Type_Osnd(X28781,X28780)),hAPP(hAPP(c_Product__Type_OSigma(X28781,X28780),X28782),hAPP(c_COMBK(tc_fun(X28780,tc_HOL_Obool),X28781),X28779))) = X28779 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__image__times])]) ).
fof(i_0_8373,plain,
! [X28775,X28776,X28777,X28778] :
( ( X28778 != c_Orderings_Obot__class_Obot(tc_fun(X28777,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X28776,X28777),X28776,c_Product__Type_Ofst(X28776,X28777)),hAPP(hAPP(c_Product__Type_OSigma(X28776,X28777),X28775),hAPP(c_COMBK(tc_fun(X28777,tc_HOL_Obool),X28776),X28778))) = c_Orderings_Obot__class_Obot(tc_fun(X28776,tc_HOL_Obool)) )
& ( X28778 = c_Orderings_Obot__class_Obot(tc_fun(X28777,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X28776,X28777),X28776,c_Product__Type_Ofst(X28776,X28777)),hAPP(hAPP(c_Product__Type_OSigma(X28776,X28777),X28775),hAPP(c_COMBK(tc_fun(X28777,tc_HOL_Obool),X28776),X28778))) = X28775 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__image__times])]) ).
fof(i_0_8374,plain,
! [X24623,X24624,X24625,X24626,X24627] :
( ( X24626 = X24623
| X24626 = X24624
| hAPP(hAPP(c_Set_Oinsert(X24627),X24626),hAPP(hAPP(c_Set_Oinsert(X24627),X24625),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X24627),X24624),hAPP(hAPP(c_Set_Oinsert(X24627),X24623),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) )
& ( X24625 = X24624
| X24626 = X24624
| hAPP(hAPP(c_Set_Oinsert(X24627),X24626),hAPP(hAPP(c_Set_Oinsert(X24627),X24625),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X24627),X24624),hAPP(hAPP(c_Set_Oinsert(X24627),X24623),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) )
& ( X24626 = X24623
| X24625 = X24623
| hAPP(hAPP(c_Set_Oinsert(X24627),X24626),hAPP(hAPP(c_Set_Oinsert(X24627),X24625),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X24627),X24624),hAPP(hAPP(c_Set_Oinsert(X24627),X24623),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) )
& ( X24625 = X24624
| X24625 = X24623
| hAPP(hAPP(c_Set_Oinsert(X24627),X24626),hAPP(hAPP(c_Set_Oinsert(X24627),X24625),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X24627),X24624),hAPP(hAPP(c_Set_Oinsert(X24627),X24623),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) )
& ( X24626 != X24624
| X24625 != X24623
| hAPP(hAPP(c_Set_Oinsert(X24627),X24626),hAPP(hAPP(c_Set_Oinsert(X24627),X24625),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X24627),X24624),hAPP(hAPP(c_Set_Oinsert(X24627),X24623),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) )
& ( X24626 != X24623
| X24625 != X24624
| hAPP(hAPP(c_Set_Oinsert(X24627),X24626),hAPP(hAPP(c_Set_Oinsert(X24627),X24625),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X24627),X24624),hAPP(hAPP(c_Set_Oinsert(X24627),X24623),c_Orderings_Obot__class_Obot(tc_fun(X24627,tc_HOL_Obool)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])]) ).
fof(i_0_8375,plain,
! [X26150,X26151,X26152,X26153,X26154] :
( ~ class_Rings_Ocomm__semiring__1(X26154)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26153),X26152))
| ~ hBOOL(hAPP(hAPP(c_member(X26153),X26151),X26152))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X26154),hAPP(X26150,X26151)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26153,X26154),X26150),X26152))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__setprod])]) ).
fof(i_0_8376,plain,
! [X32807,X32808,X32809,X32810,X32811] :
( ( X32811 != X32808
| hAPP(hAPP(c_List_Onth(X32810),hAPP(hAPP(c_List_Olist__update(X32810,X32809),X32811),X32807)),X32808) = X32807
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32811),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32810)),X32809))) )
& ( X32811 = X32808
| hAPP(hAPP(c_List_Onth(X32810),hAPP(hAPP(c_List_Olist__update(X32810,X32809),X32811),X32807)),X32808) = hAPP(hAPP(c_List_Onth(X32810),X32809),X32808)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32811),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32810)),X32809))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update])])]) ).
fof(i_0_8377,plain,
! [X23463,X23464,X23465,X23466] :
( ~ class_Orderings_Oorder(X23466)
| ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,X23466,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23465)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23464),X23463))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23466),hAPP(X23465,X23464)),hAPP(X23465,X23463))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OmonoD])]) ).
fof(i_0_8378,plain,
! [X19308,X19309,X19310] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19310),X19308))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19310),X19309)),X19308)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19309),X19308))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19310),X19309)),X19308)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5697])])]) ).
fof(i_0_8379,plain,
! [X19305,X19306,X19307] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19307),X19306)),X19305))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19307),X19305)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_8380,plain,
! [X19302,X19303,X19304] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19304),X19303)),X19302))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19303),X19302)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_8381,plain,
! [X18294,X18295,X18296] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18296),X18295)),X18294))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18296),X18294)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_8382,plain,
! [X20491,X20492] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20492))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20492),hAPP(c_Nat_OSuc,X20491))),X20492)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])]) ).
fof(i_0_8383,plain,
! [X17899,X17900,X17901,X17902] :
( ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17902),X17901,hAPP(c_Nat_OSuc,X17900),X17899)
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17902)),X17901,X17900,X17899) )
& ( ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17902)),X17901,X17900,X17899)
| c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17902),X17901,hAPP(c_Nat_OSuc,X17900),X17899) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I9_J])]) ).
fof(i_0_8384,plain,
! [X17887,X17888,X17889,X17890] :
( ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17890)),X17889,X17888,X17887)
| c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17890),X17889,hAPP(c_Nat_OSuc,X17888),X17887) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OBody])]) ).
fof(i_0_8385,plain,
! [X26247,X26248,X26249,X26250,X26251] :
( hAPP(X26251,X26250) != c_Option_Ooption_ONone(X26249)
| c_Map_Oran(X26248,X26249,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26248,tc_Option_Ooption(X26249)),X26251),X26250),hAPP(c_Option_Ooption_OSome(X26249),X26247))) = hAPP(hAPP(c_Set_Oinsert(X26249),X26247),c_Map_Oran(X26248,X26249,X26251)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__map__upd])]) ).
fof(i_0_8386,plain,
! [X24100,X24101,X24102,X24103] :
( ~ class_Orderings_Olinorder(X24103)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24103),X24102),X24101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24103),X24101),X24100))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24103,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24103,X24102),X24101)),c_SetInterval_Oord__class_OatLeastAtMost(X24103,X24101,X24100)) = c_SetInterval_Oord__class_OatLeastAtMost(X24103,X24102,X24100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J])]) ).
fof(i_0_8387,plain,
! [X24104,X24105,X24106] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24106),X24105))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24106),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24105),X24104)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24106),X24105)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24105),X24104))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__add__Un])]) ).
fof(i_0_8388,plain,
! [X24757,X24758,X24759] : hAPP(hAPP(c_Set_Oinsert(X24759),X24758),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24759,tc_HOL_Obool)),X24757),hAPP(hAPP(c_Set_Oinsert(X24759),X24758),c_Orderings_Obot__class_Obot(tc_fun(X24759,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X24759),X24758),X24757),
inference(variable_rename,[status(thm)],[fact_insert__Diff__single]) ).
cnf(i_0_8389,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_5698]) ).
cnf(i_0_8390,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin)) ),
inference(split_conjunct,[status(thm)],[i_0_5699]) ).
cnf(i_0_8391,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin)) ),
inference(split_conjunct,[status(thm)],[i_0_5700]) ).
cnf(i_0_8392,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_5701]) ).
cnf(i_0_8393,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_5702]) ).
cnf(i_0_8394,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5536]) ).
fof(i_0_8395,plain,
! [X24581,X24582,X24583] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24583),X24582))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24583),X24582)),hAPP(c_Finite__Set_Ocard(X24583),hAPP(hAPP(c_Set_Oinsert(X24583),X24581),X24582)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).
fof(i_0_8396,plain,
! [X18485,X18486,X18487] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18487)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18486)),X18485)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18487),X18486))),X18485),
inference(variable_rename,[status(thm)],[fact_zadd__int__left]) ).
fof(i_0_8397,plain,
! [X31279,X31280,X31281,X31283] :
( ( hBOOL(hAPP(hAPP(c_member(X31281),esk399_3(X31279,X31280,X31281)),X31279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31281),X31280),c_Complete__Lattice_OSup__class_OSup(X31281,X31279)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31281)
| ~ class_Orderings_Olinorder(X31281) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31281),X31280),esk399_3(X31279,X31280,X31281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31281),X31280),c_Complete__Lattice_OSup__class_OSup(X31281,X31279)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31281)
| ~ class_Orderings_Olinorder(X31281) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X31281),X31283),X31279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31281),X31280),X31283))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31281),X31280),c_Complete__Lattice_OSup__class_OSup(X31281,X31279)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31281)
| ~ class_Orderings_Olinorder(X31281) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Sup__iff])])])])]) ).
fof(i_0_8398,plain,
! [X24442] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X24442))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24442)))
| ~ c_Nat__Transfer_Onat__set(X24442) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24442)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X24442))
| ~ c_Nat__Transfer_Onat__set(X24442) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I1_J])])]) ).
cnf(i_0_8399,plain,
hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_5703]) ).
fof(i_0_8400,plain,
! [X23291,X23292] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23292)),hAPP(c_Int_Onat,X23291)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23292),X23291))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23291))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23292)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23292),X23291))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23292)),hAPP(c_Int_Onat,X23291)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23291))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23292)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I4_J])])]) ).
fof(i_0_8401,plain,
! [X19114,X19115] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19115)),hAPP(c_Int_Onat,X19114)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19115),X19114))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19114))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19115)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19115),X19114))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19115)),hAPP(c_Int_Onat,X19114)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19114))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19115)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I3_J])])]) ).
fof(i_0_8402,plain,
! [X19649,X19650] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19650)),hAPP(c_Int_Onat,X19649)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19650),X19649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19650)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19650),X19649))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19650)),hAPP(c_Int_Onat,X19649)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19650)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I2_J])])]) ).
fof(i_0_8403,plain,
! [X24895,X24896,X24897] :
( ~ class_Orderings_Olinorder(X24897)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24897),X24896),X24895))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24897,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24897,X24896,X24895)),hAPP(hAPP(c_Set_Oinsert(X24897),X24895),c_Orderings_Obot__class_Obot(tc_fun(X24897,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X24897,X24896,X24895) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J])]) ).
fof(i_0_8404,plain,
! [X25251,X25252,X25253,X25254] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25254),X25253),X25252))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25254,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25254),X25253),X25251)),X25252) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25254,tc_HOL_Obool)),X25251),X25252) )
& ( hBOOL(hAPP(hAPP(c_member(X25254),X25253),X25252))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25254,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25254),X25253),X25251)),X25252) = hAPP(hAPP(c_Set_Oinsert(X25254),X25253),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25254,tc_HOL_Obool)),X25251),X25252)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5704])]) ).
fof(i_0_8405,plain,
! [X17341,X17342,X17343,X17344,X17345,X17346] :
( ~ hBOOL(hAPP(X17346,X17345))
| ~ c_Natural_Oevaln(X17344,X17345,X17343,X17342)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17346,X17344,X17341),X17345,X17343,X17342) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OIfTrue])]) ).
fof(i_0_8406,plain,
! [X30086,X30087,X30088] :
( ( hBOOL(hAPP(hAPP(c_member(X30088),esk361_3(X30086,X30087,X30088)),X30087))
| ~ hBOOL(hAPP(hAPP(c_member(X30088),X30086),X30087))
| c_Big__Operators_Olinorder__class_OMin(X30088,X30087) = X30086
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30088),X30087))
| ~ class_Orderings_Olinorder(X30088) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30088),X30086),esk361_3(X30086,X30087,X30088)))
| ~ hBOOL(hAPP(hAPP(c_member(X30088),X30086),X30087))
| c_Big__Operators_Olinorder__class_OMin(X30088,X30087) = X30086
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30088),X30087))
| ~ class_Orderings_Olinorder(X30088) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__eqI])])])]) ).
fof(i_0_8407,plain,
! [X32927,X32928,X32929,X32930,X32931] : hAPP(hAPP(c_List_Omap(X32931,X32930),X32929),hAPP(hAPP(c_List_Oappend(X32931),X32928),X32927)) = hAPP(hAPP(c_List_Oappend(X32930),hAPP(hAPP(c_List_Omap(X32931,X32930),X32929),X32928)),hAPP(hAPP(c_List_Omap(X32931,X32930),X32929),X32927)),
inference(variable_rename,[status(thm)],[fact_map__append]) ).
fof(i_0_8408,plain,
! [X31455,X31456] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31456,tc_HOL_Obool)),esk407_2(X31455,X31456)),X31455))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X31456),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31456,tc_HOL_Obool),X31455)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31456,tc_HOL_Obool)),X31455)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31456),esk407_2(X31455,X31456)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X31456),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31456,tc_HOL_Obool),X31455)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31456,tc_HOL_Obool)),X31455)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Union])])])]) ).
fof(i_0_8409,plain,
! [X23360,X23361,X23362,X23363] :
( ~ class_Divides_Osemiring__div(X23363)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23363),X23362),X23361))
| hAPP(hAPP(c_Power_Opower__class_Opower(X23363),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23363),X23361),X23362)),X23360) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23363),hAPP(hAPP(c_Power_Opower__class_Opower(X23363),X23361),X23360)),hAPP(hAPP(c_Power_Opower__class_Opower(X23363),X23362),X23360)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__power])]) ).
fof(i_0_8410,plain,
! [X20110,X20111] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20111))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X20110))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20111),X20110)),X20111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).
fof(i_0_8411,plain,
! [X20394,X20395] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20394))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20394),X20395)),X20394)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).
fof(i_0_8412,plain,
! [X20076,X20077] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20077))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20076))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20076),X20077)),X20076)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less__dividend])]) ).
cnf(i_0_8413,plain,
c_Map_Omap__comp(X1,X2,X3,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X4,X5) = c_Option_Ooption_ONone(X2),
inference(split_conjunct,[status(thm)],[i_0_5705]) ).
cnf(i_0_8414,plain,
c_Map_Omap__comp(X1,X2,X3,X4,hAPP(c_COMBK(tc_Option_Ooption(X1),X3),c_Option_Ooption_ONone(X1)),X5) = c_Option_Ooption_ONone(X2),
inference(split_conjunct,[status(thm)],[i_0_5706]) ).
cnf(i_0_8415,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5707]) ).
cnf(i_0_8416,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),
inference(split_conjunct,[status(thm)],[i_0_5708]) ).
fof(i_0_8417,plain,
! [X27150,X27151,X27152,X27153] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27153,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X27153),X27152),X27151)),hAPP(hAPP(c_Set_Oinsert(X27153),X27152),X27150)) = hAPP(hAPP(c_Set_Oinsert(X27153),X27152),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27153,tc_HOL_Obool)),X27151),X27150)),
inference(variable_rename,[status(thm)],[fact_insert__inter__insert]) ).
fof(i_0_8418,plain,
! [X20095,X20096] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20096),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20095))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20096),X20095)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0])]) ).
fof(i_0_8419,plain,
! [X20089,X20090] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20090))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20089),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20090),X20089)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0])]) ).
fof(i_0_8420,plain,
! [X20021,X20022] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20022),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20021))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20022),X20021)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0])]) ).
fof(i_0_8421,plain,
! [X19316,X19317,X19318,X19319,X19320] :
( ~ c_Natural_Oevaln(X19320,X19319,X19318,X19317)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19318),X19316))
| c_Natural_Oevaln(X19320,X19319,X19316,X19317) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__nonstrict])]) ).
fof(i_0_8422,plain,
! [X23152,X23153,X23154,X23155] :
( ~ class_Divides_Osemiring__div(X23155)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23155),X23154),c_Divides_Odiv__class_Omod(X23155,X23153,X23152)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23155),X23154),X23152))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23155),X23154),X23153)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__imp__dvd])]) ).
fof(i_0_8423,plain,
! [X23140,X23141,X23142,X23143] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23143),X23142),c_Divides_Odiv__class_Omod(X23143,X23140,X23141)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23143),X23142),X23140))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23143),X23142),X23141))
| ~ class_Divides_Osemiring__div(X23143) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23143),X23142),X23140))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23143),X23142),c_Divides_Odiv__class_Omod(X23143,X23140,X23141)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23143),X23142),X23141))
| ~ class_Divides_Osemiring__div(X23143) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__iff])])]) ).
fof(i_0_8424,plain,
! [X20143,X20144,X20145] :
( ~ class_Divides_Osemiring__div(X20145)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20145),c_Divides_Odiv__class_Omod(X20145,X20144,X20143)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20145),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20145),X20144),X20143)),X20143)) = X20144 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])]) ).
fof(i_0_8425,plain,
! [X21479,X21480,X21481] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),X21480),c_Groups_Ozero__class_Ozero(X21481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),X21480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21481),X21480),X21479)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21481) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),X21479),c_Groups_Ozero__class_Ozero(X21481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),X21480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21481),X21480),X21479)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21481) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),X21480),c_Groups_Ozero__class_Ozero(X21481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),X21479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21481),X21480),X21479)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21481) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),X21479),c_Groups_Ozero__class_Ozero(X21481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),X21479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21481),X21480),X21479)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21481) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),X21480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),X21479))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21481),X21480),X21479)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21481) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),X21480),c_Groups_Ozero__class_Ozero(X21481)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),X21479),c_Groups_Ozero__class_Ozero(X21481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21481),c_Groups_Ozero__class_Ozero(X21481)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21481),X21480),X21479)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21481) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff])])]) ).
fof(i_0_8426,plain,
! [X19414,X19415,X19416] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),X19415),c_Groups_Ozero__class_Ozero(X19416)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),X19415))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19416),X19415),X19414)))
| ~ class_Rings_Olinordered__ring__strict(X19416) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),X19414),c_Groups_Ozero__class_Ozero(X19416)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),X19415))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19416),X19415),X19414)))
| ~ class_Rings_Olinordered__ring__strict(X19416) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),X19415),c_Groups_Ozero__class_Ozero(X19416)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),X19414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19416),X19415),X19414)))
| ~ class_Rings_Olinordered__ring__strict(X19416) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),X19414),c_Groups_Ozero__class_Ozero(X19416)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),X19414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19416),X19415),X19414)))
| ~ class_Rings_Olinordered__ring__strict(X19416) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),X19415))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),X19414))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19416),X19415),X19414)))
| ~ class_Rings_Olinordered__ring__strict(X19416) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),X19415),c_Groups_Ozero__class_Ozero(X19416)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),X19414),c_Groups_Ozero__class_Ozero(X19416)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19416),c_Groups_Ozero__class_Ozero(X19416)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19416),X19415),X19414)))
| ~ class_Rings_Olinordered__ring__strict(X19416) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).
fof(i_0_8427,plain,
! [X21516,X21517,X21518] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),X21517),c_Groups_Ozero__class_Ozero(X21518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),X21517))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21517),X21516)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21518) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),X21516),c_Groups_Ozero__class_Ozero(X21518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),X21517))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21517),X21516)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21518) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),X21517),c_Groups_Ozero__class_Ozero(X21518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),X21516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21517),X21516)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21518) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),X21516),c_Groups_Ozero__class_Ozero(X21518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),X21516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21517),X21516)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21518) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),X21517))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),X21516))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21517),X21516)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21518) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),X21517),c_Groups_Ozero__class_Ozero(X21518)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),X21516),c_Groups_Ozero__class_Ozero(X21518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21518),c_Groups_Ozero__class_Ozero(X21518)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21517),X21516)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21518) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])]) ).
cnf(i_0_8428,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5650]) ).
cnf(i_0_8429,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5651]) ).
fof(i_0_8430,plain,
! [X19313,X19314,X19315] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19315),X19314))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19313),X19315)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19313),X19314))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).
fof(i_0_8431,plain,
! [X20321,X20322,X20323] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20323),X20322))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20323),X20321)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20322),X20321))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).
fof(i_0_8432,plain,
! [X20318,X20319,X20320] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20320),X20319))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20318),X20319)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20318),X20320))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).
fof(i_0_8433,plain,
! [X19971,X19972,X19973] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19973),X19972))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19973),X19971)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19972),X19971))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])]) ).
fof(i_0_8434,plain,
! [X19015,X19016,X19017] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19017),X19016))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19017),X19015)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19016),X19015))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).
fof(i_0_8435,plain,
! [X19018,X19019,X19020] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19020),X19019))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19018),X19020)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19018),X19019))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).
fof(i_0_8436,plain,
! [X19295,X19296,X19297] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19297),X19296))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19297),X19295)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19296),X19295))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
cnf(i_0_8437,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5652]) ).
cnf(i_0_8438,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5653]) ).
fof(i_0_8439,plain,
! [X18553,X18554,X18555] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18555),X18554))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18555),X18553)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18554),X18553))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).
fof(i_0_8440,plain,
! [X18305,X18306,X18307] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18307),X18306))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18307),X18305)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18306),X18305))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_8441,plain,
! [X33627,X33628,X33629] :
( ~ class_Lattices_Olattice(X33629)
| c_Big__Operators_Olattice__class_OInf__fin(X33629,hAPP(c_List_Oset(X33629),hAPP(hAPP(c_List_Olist_OCons(X33629),X33628),X33627))) = hAPP(c_List_Ofoldl(X33629,X33629,c_Lattices_Osemilattice__inf__class_Oinf(X33629),X33628),X33627) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__set__fold])]) ).
fof(i_0_8442,plain,
! [X33630,X33631,X33632] :
( ~ class_Orderings_Olinorder(X33632)
| c_Big__Operators_Olinorder__class_OMin(X33632,hAPP(c_List_Oset(X33632),hAPP(hAPP(c_List_Olist_OCons(X33632),X33631),X33630))) = hAPP(c_List_Ofoldl(X33632,X33632,c_Orderings_Oord__class_Omin(X33632),X33631),X33630) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__fin__set__fold])]) ).
fof(i_0_8443,plain,
! [X33633,X33634,X33635] :
( ~ class_Orderings_Olinorder(X33635)
| c_Big__Operators_Olinorder__class_OMax(X33635,hAPP(c_List_Oset(X33635),hAPP(hAPP(c_List_Olist_OCons(X33635),X33634),X33633))) = hAPP(c_List_Ofoldl(X33635,X33635,c_Orderings_Oord__class_Omax(X33635),X33634),X33633) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold])]) ).
fof(i_0_8444,plain,
! [X33624,X33625,X33626] :
( ~ class_Lattices_Olattice(X33626)
| c_Big__Operators_Olattice__class_OSup__fin(X33626,hAPP(c_List_Oset(X33626),hAPP(hAPP(c_List_Olist_OCons(X33626),X33625),X33624))) = hAPP(c_List_Ofoldl(X33626,X33626,c_Lattices_Osemilattice__sup__class_Osup(X33626),X33625),X33624) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__set__fold])]) ).
fof(i_0_8445,plain,
! [X20512,X20513,X20514] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20514),X20513))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20513),X20514))),X20512) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20513)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20514),X20512)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])]) ).
fof(i_0_8446,plain,
! [X20146,X20147,X20148] :
( ~ class_Divides_Osemiring__div(X20148)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20148),X20147),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20148),X20146),X20147))),c_Divides_Odiv__class_Omod(X20148,X20146,X20147)) = X20146 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality2])]) ).
cnf(i_0_8447,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_5709]) ).
fof(i_0_8448,plain,
! [X32784,X32785,X32786,X32787,X32788] : hAPP(hAPP(c_List_Olist__update(X32788,hAPP(hAPP(c_List_Olist_OCons(X32788),X32787),X32786)),hAPP(c_Nat_OSuc,X32785)),X32784) = hAPP(hAPP(c_List_Olist_OCons(X32788),X32787),hAPP(hAPP(c_List_Olist__update(X32788,X32786),X32785),X32784)),
inference(variable_rename,[status(thm)],[fact_list__update__code_I3_J]) ).
fof(i_0_8449,plain,
! [X18217,X18218,X18219,X18220,X18221,X18222] :
( ( X18220 = X18218
| c_Nitpick_Opair__box_OPairBox(X18222,X18221,X18220,X18219) != c_Nitpick_Opair__box_OPairBox(X18222,X18221,X18218,X18217) )
& ( X18219 = X18217
| c_Nitpick_Opair__box_OPairBox(X18222,X18221,X18220,X18219) != c_Nitpick_Opair__box_OPairBox(X18222,X18221,X18218,X18217) )
& ( X18220 != X18218
| X18219 != X18217
| c_Nitpick_Opair__box_OPairBox(X18222,X18221,X18220,X18219) = c_Nitpick_Opair__box_OPairBox(X18222,X18221,X18218,X18217) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject])])]) ).
fof(i_0_8450,plain,
! [X18464,X18465,X18466,X18467,X18468] :
( c_Sum__Type_OSumr(X18468,X18467,X18466,X18465) != c_Sum__Type_OSumr(X18468,X18467,X18466,X18464)
| X18465 = X18464 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sumr__inject])]) ).
fof(i_0_8451,plain,
! [X18469,X18470,X18471,X18472,X18473] :
( c_Sum__Type_OSuml(X18473,X18472,X18471,X18470) != c_Sum__Type_OSuml(X18473,X18472,X18471,X18469)
| X18470 = X18469 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suml__inject])]) ).
fof(i_0_8452,plain,
! [X28273,X28274,X28275,X28276,X28277,X28278] :
( hAPP(X28278,X28277) != X28276
| ~ hBOOL(hAPP(hAPP(c_member(X28275),X28276),X28274))
| hBOOL(hAPP(hAPP(c_member(X28273),X28277),hAPP(c_Set_Ovimage(X28273,X28275,X28278),X28274))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI])]) ).
fof(i_0_8453,plain,
! [X24957,X24958,X24959,X24960,X24961,X24962] :
( X24962 != hAPP(X24961,X24960)
| ~ hBOOL(hAPP(hAPP(c_member(X24959),X24960),X24958))
| hBOOL(hAPP(hAPP(c_member(X24957),X24962),hAPP(c_Set_Oimage(X24959,X24957,X24961),X24958))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_8454,plain,
! [X25039,X25040,X25041,X25042,X25043,X25044] :
( ~ hBOOL(hAPP(hAPP(c_member(X25044),X25043),X25042))
| X25041 != hAPP(X25040,X25043)
| hBOOL(hAPP(hAPP(c_member(X25039),X25041),hAPP(c_Set_Oimage(X25044,X25039,X25040),X25042))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_8455,plain,
! [X17347,X17348,X17349,X17350,X17351,X17352] :
( hBOOL(hAPP(X17352,X17351))
| ~ c_Natural_Oevaln(X17350,X17351,X17349,X17348)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17352,X17347,X17350),X17351,X17349,X17348) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5710])]) ).
fof(i_0_8456,plain,
! [X27890,X27891,X27892,X27893,X27894,X27895] :
( ( hAPP(X27893,X27891) != hAPP(X27893,X27890)
| X27891 = X27890
| ~ hBOOL(hAPP(hAPP(c_member(X27895),X27890),X27892))
| ~ hBOOL(hAPP(hAPP(c_member(X27895),X27891),X27892))
| ~ c_Fun_Oinj__on(X27895,X27894,X27893,X27892) )
& ( X27891 != X27890
| hAPP(X27893,X27891) = hAPP(X27893,X27890)
| ~ hBOOL(hAPP(hAPP(c_member(X27895),X27890),X27892))
| ~ hBOOL(hAPP(hAPP(c_member(X27895),X27891),X27892))
| ~ c_Fun_Oinj__on(X27895,X27894,X27893,X27892) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).
fof(i_0_8457,plain,
! [X27896,X27897,X27898,X27899,X27900,X27901] :
( ~ c_Fun_Oinj__on(X27901,X27900,X27899,X27898)
| hAPP(X27899,X27897) != hAPP(X27899,X27896)
| ~ hBOOL(hAPP(hAPP(c_member(X27901),X27897),X27898))
| ~ hBOOL(hAPP(hAPP(c_member(X27901),X27896),X27898))
| X27897 = X27896 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).
fof(i_0_8458,plain,
! [X27884,X27885,X27886,X27887,X27888,X27889] :
( ~ c_Fun_Oinj__on(X27889,X27888,X27887,X27886)
| X27885 = X27884
| ~ hBOOL(hAPP(hAPP(c_member(X27889),X27885),X27886))
| ~ hBOOL(hAPP(hAPP(c_member(X27889),X27884),X27886))
| hAPP(X27887,X27885) != hAPP(X27887,X27884) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).
fof(i_0_8459,plain,
! [X20572,X20573] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20572),X20573))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20572),X20573) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20573)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20572),X20573))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20572),X20573) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20572),X20573)),X20573))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20573)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5711])])]) ).
fof(i_0_8460,plain,
! [X20574,X20575] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20575))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20574),X20575))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20574),X20575) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20574),X20575)),X20575)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5712])]) ).
fof(i_0_8461,plain,
! [X20084,X20085] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20084),X20085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20085),X20084)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20085)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20084))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20085),X20084)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20085)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20084),X20085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20084))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20085),X20084)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20085)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])]) ).
fof(i_0_8462,plain,
! [X26549,X26550,X26551,X26552,X26553] :
( ~ c_Finite__Set_Ofolding__one__idem(X26553,X26552,X26551)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26553),X26550))
| X26549 = c_Orderings_Obot__class_Obot(tc_fun(X26553,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26553,tc_HOL_Obool)),X26549),X26550))
| hAPP(hAPP(X26552,hAPP(X26551,X26549)),hAPP(X26551,X26550)) = hAPP(X26551,X26550) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem])]) ).
fof(i_0_8463,plain,
! [X30436,X30437,X30438] :
( hAPP(hAPP(c_Relation_Orel__comp(X30438,X30438,X30438),hAPP(c_Relation_Oconverse(X30438,X30438),X30437)),X30437) != X30437
| hAPP(c_Relation_ODomain(X30438,X30438),X30437) != X30436
| c_Equiv__Relations_Oequiv(X30438,X30436,X30437) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__equivI])]) ).
fof(i_0_8464,plain,
! [X18098,X18099,X18100] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X18100,X18099,X18098)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X18099)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X18098))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_com_Osize_I13_J]) ).
fof(i_0_8465,plain,
! [X19076,X19077,X19078,X19079,X19080] :
( ~ class_Orderings_Oord(X19080)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19079,X19080)),X19078),X19077))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19080),hAPP(X19078,X19076)),hAPP(X19077,X19076))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_8466,plain,
! [X19038,X19039,X19040,X19041,X19042] :
( ~ class_Orderings_Oord(X19042)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19041,X19042)),X19040),X19039))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19042),hAPP(X19040,X19038)),hAPP(X19039,X19038))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_8467,plain,
! [X31763,X31764,X31765,X31766,X31767] :
( ( hAPP(hAPP(c_List_Omap(X31767,X31766),X31765),X31764) != hAPP(hAPP(c_List_Omap(X31767,X31766),X31765),X31763)
| X31764 = X31763
| ~ c_Fun_Oinj__on(X31767,X31766,X31765,c_Orderings_Otop__class_Otop(tc_fun(X31767,tc_HOL_Obool))) )
& ( X31764 != X31763
| hAPP(hAPP(c_List_Omap(X31767,X31766),X31765),X31764) = hAPP(hAPP(c_List_Omap(X31767,X31766),X31765),X31763)
| ~ c_Fun_Oinj__on(X31767,X31766,X31765,c_Orderings_Otop__class_Otop(tc_fun(X31767,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__map__eq__map])])]) ).
fof(i_0_8468,plain,
! [X31755,X31756,X31757,X31758,X31759] :
( hAPP(hAPP(c_List_Omap(X31759,X31758),X31757),X31756) != hAPP(hAPP(c_List_Omap(X31759,X31758),X31757),X31755)
| ~ c_Fun_Oinj__on(X31759,X31758,X31757,c_Orderings_Otop__class_Otop(tc_fun(X31759,tc_HOL_Obool)))
| X31756 = X31755 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__injective])]) ).
fof(i_0_8469,plain,
! [X32816,X32817,X32818,X32819] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32819),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32818)),X32817)))
| hAPP(hAPP(c_List_Onth(X32818),hAPP(hAPP(c_List_Olist__update(X32818,X32817),X32819),X32816)),X32819) = X32816 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__eq])]) ).
fof(i_0_8470,plain,
! [X24129,X24130,X24131] :
( ~ class_Groups_Ocomm__monoid__add(X24131)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24131),X24130),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24129))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24131),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24131),X24130),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24129))),hAPP(X24130,hAPP(c_Nat_OSuc,X24129))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc])]) ).
fof(i_0_8471,plain,
! [X24069,X24070,X24071,X24072] :
( ~ class_Orderings_Olinorder(X24072)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24072),X24071),X24070))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24072),X24070),X24069))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24072,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24072,X24071),X24070)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24072,X24070),X24069)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24072,X24071),X24069) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J])]) ).
fof(i_0_8472,plain,
! [X33835,X33836] : c_List_Obutlast(X33836,X33835) = hAPP(hAPP(c_List_Otake(X33836),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33836)),X33835)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33835),
inference(variable_rename,[status(thm)],[fact_butlast__conv__take]) ).
fof(i_0_8473,plain,
! [X29042,X29043,X29044] :
( ~ class_Lattices_Osemilattice__inf(X29044)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29044),X29043))
| ~ hBOOL(hAPP(hAPP(c_member(X29044),X29042),X29043))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29044),hAPP(c_Finite__Set_Ofold1(X29044,c_Lattices_Osemilattice__inf__class_Oinf(X29044)),X29043)),X29042)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__belowI])]) ).
fof(i_0_8474,plain,
! [X29050,X29051,X29052] :
( ~ class_Orderings_Olinorder(X29052)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29052),X29051))
| ~ hBOOL(hAPP(hAPP(c_member(X29052),X29050),X29051))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29052),hAPP(c_Finite__Set_Ofold1(X29052,c_Orderings_Oord__class_Omin(X29052)),X29051)),X29050)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI])]) ).
fof(i_0_8475,plain,
! [X19662] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X19662))))),
inference(variable_rename,[status(thm)],[i_0_5713]) ).
fof(i_0_8476,plain,
! [X34165,X34166,X34167,X34168] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X34167),X34168),hAPP(c_List_Oset(X34167),X34165)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34167),X34166),X34168))
| ~ c_List_Olinorder__class_Osorted(X34167,hAPP(hAPP(c_List_Olist_OCons(X34167),X34166),X34165))
| ~ class_Orderings_Olinorder(X34167) )
& ( c_List_Olinorder__class_Osorted(X34167,X34165)
| ~ c_List_Olinorder__class_Osorted(X34167,hAPP(hAPP(c_List_Olist_OCons(X34167),X34166),X34165))
| ~ class_Orderings_Olinorder(X34167) )
& ( hBOOL(hAPP(hAPP(c_member(X34167),esk485_3(X34165,X34166,X34167)),hAPP(c_List_Oset(X34167),X34165)))
| ~ c_List_Olinorder__class_Osorted(X34167,X34165)
| c_List_Olinorder__class_Osorted(X34167,hAPP(hAPP(c_List_Olist_OCons(X34167),X34166),X34165))
| ~ class_Orderings_Olinorder(X34167) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34167),X34166),esk485_3(X34165,X34166,X34167)))
| ~ c_List_Olinorder__class_Osorted(X34167,X34165)
| c_List_Olinorder__class_Osorted(X34167,hAPP(hAPP(c_List_Olist_OCons(X34167),X34166),X34165))
| ~ class_Orderings_Olinorder(X34167) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I2_J])])])])]) ).
fof(i_0_8477,plain,
! [X34065,X34066,X34067,X34068] :
( ( c_List_Olinorder__class_Osorted(X34067,X34065)
| ~ c_List_Olinorder__class_Osorted(X34067,hAPP(hAPP(c_List_Olist_OCons(X34067),X34066),X34065))
| ~ class_Orderings_Olinorder(X34067) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X34067),X34068),hAPP(c_List_Oset(X34067),X34065)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34067),X34066),X34068))
| ~ c_List_Olinorder__class_Osorted(X34067,hAPP(hAPP(c_List_Olist_OCons(X34067),X34066),X34065))
| ~ class_Orderings_Olinorder(X34067) )
& ( hBOOL(hAPP(hAPP(c_member(X34067),esk482_3(X34065,X34066,X34067)),hAPP(c_List_Oset(X34067),X34065)))
| ~ c_List_Olinorder__class_Osorted(X34067,X34065)
| c_List_Olinorder__class_Osorted(X34067,hAPP(hAPP(c_List_Olist_OCons(X34067),X34066),X34065))
| ~ class_Orderings_Olinorder(X34067) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34067),X34066),esk482_3(X34065,X34066,X34067)))
| ~ c_List_Olinorder__class_Osorted(X34067,X34065)
| c_List_Olinorder__class_Osorted(X34067,hAPP(hAPP(c_List_Olist_OCons(X34067),X34066),X34065))
| ~ class_Orderings_Olinorder(X34067) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__Cons])])])])]) ).
fof(i_0_8478,plain,
! [X17310,X17311,X17312] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X17312,X17311)),X17310),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17310),X17312),hAPP(X17311,X17310)))),
inference(variable_rename,[status(thm)],[fact_evalc_Oequations_I2_J]) ).
fof(i_0_8479,plain,
! [X17303,X17304,X17305] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X17305,X17304)),X17303),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17303),X17305),hAPP(X17304,X17303)))),
inference(variable_rename,[status(thm)],[fact_evalc_OAssign]) ).
fof(i_0_8480,plain,
! [X20578,X20579] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20579))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20578))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20578),X20579)),X20578) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20578),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20579),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__power__div__base])]) ).
fof(i_0_8481,plain,
! [X21605,X21606,X21607] :
( ~ class_Fields_Olinordered__field(X21607)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21607),c_Groups_Ozero__class_Ozero(X21607)),X21606))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21607),c_Groups_Ozero__class_Ozero(X21607)),X21605))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21607),c_Groups_Ozero__class_Ozero(X21607)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21607),X21606),X21605))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos])]) ).
fof(i_0_8482,plain,
! [X19363,X19364,X19365] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19365),c_Groups_Ozero__class_Ozero(X19365)),X19364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19365),c_Groups_Ozero__class_Ozero(X19365)),X19363))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19365),c_Groups_Ozero__class_Ozero(X19365)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19365),X19364),X19363)))
| ~ class_Rings_Oordered__ring(X19365) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19365),X19364),c_Groups_Ozero__class_Ozero(X19365)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19365),X19363),c_Groups_Ozero__class_Ozero(X19365)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19365),c_Groups_Ozero__class_Ozero(X19365)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19365),X19364),X19363)))
| ~ class_Rings_Oordered__ring(X19365) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).
fof(i_0_8483,plain,
! [X19408,X19409,X19410] :
( ~ class_Rings_Oordered__cancel__semiring(X19410)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19410),c_Groups_Ozero__class_Ozero(X19410)),X19409))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19410),c_Groups_Ozero__class_Ozero(X19410)),X19408))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19410),c_Groups_Ozero__class_Ozero(X19410)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19410),X19409),X19408))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).
fof(i_0_8484,plain,
! [X19343,X19344,X19345] :
( ~ class_Groups_Oordered__comm__monoid__add(X19345)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19345),c_Groups_Ozero__class_Ozero(X19345)),X19344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19345),c_Groups_Ozero__class_Ozero(X19345)),X19343))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19345),c_Groups_Ozero__class_Ozero(X19345)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19345),X19344),X19343))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_8485,plain,
! [X18635,X18636,X18637] :
( ~ class_Rings_Olinordered__semidom(X18637)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18637),c_Groups_Oone__class_Oone(X18637)),X18636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18637),c_Groups_Oone__class_Oone(X18637)),X18635))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18637),c_Groups_Oone__class_Oone(X18637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18637),X18636),X18635))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).
fof(i_0_8486,plain,
! [X21510,X21511,X21512] :
( ~ class_Fields_Olinordered__field(X21512)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21512),c_Groups_Ozero__class_Ozero(X21512)),X21511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21512),c_Groups_Ozero__class_Ozero(X21512)),X21510))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21512),c_Groups_Ozero__class_Ozero(X21512)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21512),X21511),X21510))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])]) ).
fof(i_0_8487,plain,
! [X18873,X18874,X18875] :
( ~ class_Rings_Olinordered__semiring__strict(X18875)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18875),c_Groups_Ozero__class_Ozero(X18875)),X18874))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18875),c_Groups_Ozero__class_Ozero(X18875)),X18873))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18875),c_Groups_Ozero__class_Ozero(X18875)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18875),X18874),X18873))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).
fof(i_0_8488,plain,
! [X19549,X19550,X19551] :
( ~ class_Groups_Oordered__comm__monoid__add(X19551)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19551),c_Groups_Ozero__class_Ozero(X19551)),X19550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19551),c_Groups_Ozero__class_Ozero(X19551)),X19549))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19551),c_Groups_Ozero__class_Ozero(X19551)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19551),X19550),X19549))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_8489,plain,
! [X19546,X19547,X19548] :
( ~ class_Groups_Oordered__comm__monoid__add(X19548)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19548),c_Groups_Ozero__class_Ozero(X19548)),X19547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19548),c_Groups_Ozero__class_Ozero(X19548)),X19546))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19548),c_Groups_Ozero__class_Ozero(X19548)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19548),X19547),X19546))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_8490,plain,
! [X18324,X18325,X18326] :
( ~ class_Groups_Oordered__comm__monoid__add(X18326)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18326),c_Groups_Ozero__class_Ozero(X18326)),X18325))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18326),c_Groups_Ozero__class_Ozero(X18326)),X18324))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18326),c_Groups_Ozero__class_Ozero(X18326)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18326),X18325),X18324))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_8491,plain,
! [X28067,X28068,X28069,X28070] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28070),X28069))
| hAPP(c_Finite__Set_Ocard(X28068),hAPP(c_Set_Oimage(X28070,X28068,X28067),X28069)) != hAPP(c_Finite__Set_Ocard(X28070),X28069)
| c_Fun_Oinj__on(X28070,X28068,X28067,X28069) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).
fof(i_0_8492,plain,
! [X28063,X28064,X28065,X28066] :
( ( ~ c_Fun_Oinj__on(X28066,X28064,X28063,X28065)
| hAPP(c_Finite__Set_Ocard(X28064),hAPP(c_Set_Oimage(X28066,X28064,X28063),X28065)) = hAPP(c_Finite__Set_Ocard(X28066),X28065)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28066),X28065)) )
& ( hAPP(c_Finite__Set_Ocard(X28064),hAPP(c_Set_Oimage(X28066,X28064,X28063),X28065)) != hAPP(c_Finite__Set_Ocard(X28066),X28065)
| c_Fun_Oinj__on(X28066,X28064,X28063,X28065)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28066),X28065)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).
fof(i_0_8493,plain,
! [X24086,X24087,X24088] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24088,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24088,tc_HOL_Obool)),X24087),X24086)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24088,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24088,tc_HOL_Obool)),X24087)),X24086),
inference(variable_rename,[status(thm)],[fact_Compl__Diff__eq]) ).
cnf(i_0_8494,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Relation_OId(X1)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_5714]) ).
fof(i_0_8495,plain,
! [X21002,X21003,X21004,X21005] :
( ~ class_Rings_Olinordered__semidom(X21005)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21005),X21004),X21003) != hAPP(hAPP(c_Power_Opower__class_Opower(X21005),X21002),X21003)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21005),c_Groups_Ozero__class_Ozero(X21005)),X21004))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21005),c_Groups_Ozero__class_Ozero(X21005)),X21002))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21003))
| X21004 = X21002 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).
cnf(i_0_8496,plain,
( c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X1,X2)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5715]) ).
cnf(i_0_8497,plain,
( c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X1,X2)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5716]) ).
fof(i_0_8498,plain,
! [X28653,X28654,X28655,X28656] : hAPP(c_Finite__Set_Ocard(tc_prod(X28656,X28655)),hAPP(hAPP(c_Product__Type_OSigma(X28656,X28655),X28654),hAPP(c_COMBK(tc_fun(X28655,tc_HOL_Obool),X28656),X28653))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X28656),X28654)),hAPP(c_Finite__Set_Ocard(X28655),X28653)),
inference(variable_rename,[status(thm)],[fact_card__cartesian__product]) ).
fof(i_0_8499,plain,
! [X27340,X27341,X27342,X27343] :
( ~ hBOOL(hAPP(hAPP(c_member(X27343),X27342),X27341))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27343,tc_HOL_Obool)),X27341),hAPP(hAPP(c_Set_Oinsert(X27343),X27342),X27340)) = hAPP(hAPP(c_Set_Oinsert(X27343),X27342),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27343,tc_HOL_Obool)),X27341),X27340)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1])]) ).
fof(i_0_8500,plain,
! [X27324,X27325,X27326,X27327] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27327),X27326),X27325))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27327,tc_HOL_Obool)),X27325),hAPP(hAPP(c_Set_Oinsert(X27327),X27326),X27324)) = hAPP(hAPP(c_Set_Oinsert(X27327),X27326),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27327,tc_HOL_Obool)),X27325),X27324)) )
& ( hBOOL(hAPP(hAPP(c_member(X27327),X27326),X27325))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27327,tc_HOL_Obool)),X27325),hAPP(hAPP(c_Set_Oinsert(X27327),X27326),X27324)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27327,tc_HOL_Obool)),X27325),X27324) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5717])]) ).
fof(i_0_8501,plain,
! [X32659,X32660,X32661,X32662,X32663,X32664,X32665] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32659)),X32661) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32659)),X32660)
| X32661 != X32660 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32662),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32659)),X32661)))
| hAPP(hAPP(c_List_Onth(X32659),X32661),X32662) = hAPP(hAPP(c_List_Onth(X32659),X32660),X32662)
| X32661 != X32660 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_3(X32663,X32664,X32665)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32663)),X32665)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32663)),X32665) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32663)),X32664)
| X32665 = X32664 )
& ( hAPP(hAPP(c_List_Onth(X32663),X32665),esk452_3(X32663,X32664,X32665)) != hAPP(hAPP(c_List_Onth(X32663),X32664),esk452_3(X32663,X32664,X32665))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32663)),X32665) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32663)),X32664)
| X32665 = X32664 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__eq__iff__nth__eq])])])])])]) ).
fof(i_0_8502,plain,
! [X30657,X30658,X30659,X30660,X30661,X30662] :
( ~ c_Finite__Set_Ofolding(X30662,X30661,X30660,X30659)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30662),X30658))
| hAPP(hAPP(X30659,X30658),X30657) = hAPP(hAPP(c_Finite__Set_Ofold(X30662,X30661,X30660),X30657),X30658) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oeq__fold])]) ).
fof(i_0_8503,plain,
! [X25700,X25701,X25702,X25703] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X25703,X25702,X25701)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X25703),tc_HOL_Obool)),X25700),X25701))
| c_Hoare__Mirabelle_Ohoare__derivs(X25703,X25702,X25700) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weaken])]) ).
fof(i_0_8504,plain,
! [X25280,X25281,X25282,X25283,X25284] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X25284)
| ~ hBOOL(hAPP(hAPP(c_member(X25283),X25282),X25281))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25284),hAPP(X25280,X25282)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25283,X25284),X25281),X25280))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SUPI])]) ).
fof(i_0_8505,plain,
! [X19803,X19804,X19805,X19806] :
( ~ class_Divides_Osemiring__div(X19806)
| c_Divides_Odiv__class_Omod(X19806,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19806),c_Divides_Odiv__class_Omod(X19806,X19805,X19804)),X19803),X19804) = c_Divides_Odiv__class_Omod(X19806,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19806),X19805),X19803),X19804) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J])]) ).
fof(i_0_8506,plain,
! [X19771,X19772,X19773,X19774] :
( ~ class_Divides_Osemiring__div(X19774)
| c_Divides_Odiv__class_Omod(X19774,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19774),c_Divides_Odiv__class_Omod(X19774,X19773,X19772)),X19771),X19772) = c_Divides_Odiv__class_Omod(X19774,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19774),X19773),X19771),X19772) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J])]) ).
fof(i_0_8507,plain,
! [X20275,X20276,X20277,X20278] :
( ~ class_Divides_Oring__div(X20278)
| c_Divides_Odiv__class_Omod(X20278,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20278),X20277),X20276),X20275) = c_Divides_Odiv__class_Omod(X20278,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20278),c_Divides_Odiv__class_Omod(X20278,X20277,X20275)),X20276),X20275) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])]) ).
fof(i_0_8508,plain,
! [X19819,X19820,X19821,X19822] :
( ~ class_Divides_Osemiring__div(X19822)
| c_Divides_Odiv__class_Omod(X19822,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19822),X19821),X19820),X19819) = c_Divides_Odiv__class_Omod(X19822,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19822),c_Divides_Odiv__class_Omod(X19822,X19821,X19819)),X19820),X19819) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq])]) ).
fof(i_0_8509,plain,
! [X19783,X19784,X19785,X19786] :
( ~ class_Divides_Osemiring__div(X19786)
| c_Divides_Odiv__class_Omod(X19786,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19786),X19785),X19784),X19783) = c_Divides_Odiv__class_Omod(X19786,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19786),c_Divides_Odiv__class_Omod(X19786,X19785,X19783)),X19784),X19783) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq])]) ).
fof(i_0_8510,plain,
! [X22462,X22463,X22464] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22464,tc_HOL_Obool)),X22463),X22462))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22464,tc_HOL_Obool)),X22463),X22462))
| X22463 = X22462 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22464,tc_HOL_Obool)),X22463),X22462))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22464,tc_HOL_Obool)),X22463),X22462)) )
& ( X22463 != X22462
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22464,tc_HOL_Obool)),X22463),X22462)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_8511,plain,
! [X22459,X22460,X22461] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22461,tc_HOL_Obool)),X22460),X22459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22461,tc_HOL_Obool)),X22460),X22459)) )
& ( X22460 != X22459
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22461,tc_HOL_Obool)),X22460),X22459)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22461,tc_HOL_Obool)),X22460),X22459))
| X22460 = X22459
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22461,tc_HOL_Obool)),X22460),X22459)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_8512,plain,
! [X24544,X24545,X24546] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24546),X24545))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24546),X24544))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24546),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24546,tc_HOL_Obool)),X24545),X24544))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnI])]) ).
fof(i_0_8513,plain,
! [X27268,X27269,X27270] : hAPP(c_Set_OPow(X27270),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27270,tc_HOL_Obool)),X27269),X27268)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X27270,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X27270),X27269)),hAPP(c_Set_OPow(X27270),X27268)),
inference(variable_rename,[status(thm)],[fact_Pow__Int__eq]) ).
fof(i_0_8514,plain,
! [X28152,X28153,X28154,X28155] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28154),X28153))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28154,X28155),X28152),X28153) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28155,X28154,c_Groups_Otimes__class_Otimes(X28155)),X28152),c_Groups_Oone__class_Oone(X28155)),X28153)
| ~ class_Groups_Ocomm__monoid__mult(X28155) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28154),X28153))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28154,X28155),X28152),X28153) = c_Groups_Oone__class_Oone(X28155)
| ~ class_Groups_Ocomm__monoid__mult(X28155) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5718])])]) ).
fof(i_0_8515,plain,
! [X28156,X28157,X28158,X28159] :
( ~ class_Groups_Ocomm__monoid__mult(X28159)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28158),X28157))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28158,X28159),X28156),X28157) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28159,X28158,c_Groups_Otimes__class_Otimes(X28159)),X28156),c_Groups_Oone__class_Oone(X28159)),X28157) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold])]) ).
fof(i_0_8516,plain,
! [X28148,X28149,X28150,X28151] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28150),X28149))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28150,X28151),X28148),X28149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28151,X28150,c_Groups_Oplus__class_Oplus(X28151)),X28148),c_Groups_Ozero__class_Ozero(X28151)),X28149)
| ~ class_Groups_Ocomm__monoid__add(X28151) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28150),X28149))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28150,X28151),X28148),X28149) = c_Groups_Ozero__class_Ozero(X28151)
| ~ class_Groups_Ocomm__monoid__add(X28151) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5719])])]) ).
fof(i_0_8517,plain,
! [X28144,X28145,X28146,X28147] :
( ~ class_Groups_Ocomm__monoid__add(X28147)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28146),X28145))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28146,X28147),X28144),X28145) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28147,X28146,c_Groups_Oplus__class_Oplus(X28147)),X28144),c_Groups_Ozero__class_Ozero(X28147)),X28145) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold])]) ).
fof(i_0_8518,plain,
! [X22465,X22466,X22467] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22467,tc_HOL_Obool)),X22466),X22465))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22467,tc_HOL_Obool)),X22466),X22465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_8519,plain,
! [X22227,X22228] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22227),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X22228,X22227) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22228),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22227)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg])]) ).
fof(i_0_8520,plain,
! [X33014,X33015,X33016,X33017] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33017),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33016)),X33015)))
| hAPP(hAPP(c_List_Onth(X33016),hAPP(hAPP(c_List_Oappend(X33016),X33015),X33014)),X33017) = hAPP(hAPP(c_List_Onth(X33016),X33015),X33017) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33017),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33016)),X33015)))
| hAPP(hAPP(c_List_Onth(X33016),hAPP(hAPP(c_List_Oappend(X33016),X33015),X33014)),X33017) = hAPP(hAPP(c_List_Onth(X33016),X33014),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33017),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33016)),X33015))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5720])]) ).
fof(i_0_8521,plain,
! [X25153,X25154,X25155] :
( ~ hBOOL(hAPP(hAPP(c_member(X25155),X25154),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25155,tc_HOL_Obool)),X25153)))
| ~ hBOOL(hAPP(hAPP(c_member(X25155),X25154),X25153)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5721])]) ).
fof(i_0_8522,plain,
! [X25150,X25151,X25152] :
( ~ hBOOL(hAPP(hAPP(c_member(X25152),X25151),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25152,tc_HOL_Obool)),X25150)))
| ~ hBOOL(hAPP(hAPP(c_member(X25152),X25151),X25150)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5722])]) ).
fof(i_0_8523,plain,
! [X25147,X25148,X25149] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25149),X25148),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25149,tc_HOL_Obool)),X25147)))
| ~ hBOOL(hAPP(hAPP(c_member(X25149),X25148),X25147)) )
& ( hBOOL(hAPP(hAPP(c_member(X25149),X25148),X25147))
| hBOOL(hAPP(hAPP(c_member(X25149),X25148),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25149,tc_HOL_Obool)),X25147))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5723])]) ).
fof(i_0_8524,plain,
! [X23515,X23516,X23517,X23519,X23520,X23521] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk96_2(X23515,X23516)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23516)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23517),X23516))
| ~ hBOOL(hAPP(X23515,X23517)) )
& ( hBOOL(hAPP(X23515,esk96_2(X23515,X23516)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23517),X23516))
| ~ hBOOL(hAPP(X23515,X23517)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk97_2(X23519,X23520)),X23520))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23521),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23520)))
| ~ hBOOL(hAPP(X23519,X23521)) )
& ( hBOOL(hAPP(X23519,esk97_2(X23519,X23520)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23521),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23520)))
| ~ hBOOL(hAPP(X23519,X23521)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__nat__less])])])])])]) ).
fof(i_0_8525,plain,
! [X26262,X26263,X26264,X26265] : hAPP(c_Map_Orestrict__map(X26265,X26264,hAPP(c_COMBK(tc_Option_Ooption(X26264),X26265),c_Option_Ooption_ONone(X26264)),X26263),X26262) = c_Option_Ooption_ONone(X26264),
inference(variable_rename,[status(thm)],[fact_restrict__map__empty]) ).
fof(i_0_8526,plain,
! [X33422,X33423,X33424,X33425] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33425) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Odrop(X33424),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33425)),hAPP(hAPP(c_List_Olist_OCons(X33424),X33423),X33422)) = hAPP(hAPP(c_List_Olist_OCons(X33424),X33423),X33422) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33425) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Odrop(X33424),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33425)),hAPP(hAPP(c_List_Olist_OCons(X33424),X33423),X33422)) = hAPP(hAPP(c_List_Odrop(X33424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33425)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33422) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons__number__of])]) ).
fof(i_0_8527,plain,
! [X29952,X29953] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk336_2(X29952,X29953)),c_Int_OInteg))
| hBOOL(hAPP(X29953,X29952)) )
& ( ~ hBOOL(hAPP(X29953,hAPP(c_Int_OAbs__Integ,esk336_2(X29952,X29953))))
| hBOOL(hAPP(X29953,X29952)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Abs__Integ__induct])])])]) ).
fof(i_0_8528,plain,
! [X23038,X23039] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23039),X23038)),X23039))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23038) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X23039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23038) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23039),X23038)),X23039))
| X23039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel1])])]) ).
cnf(i_0_8529,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X1)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_5724]) ).
fof(i_0_8530,plain,
! [X29652,X29653,X29654] :
( ~ c_Wellfounded_Owf(X29654,X29653)
| c_Wellfounded_Owf(X29654,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29654,X29654),tc_HOL_Obool)),X29653),X29652)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int1])]) ).
fof(i_0_8531,plain,
! [X29655,X29656,X29657] :
( ~ c_Wellfounded_Owf(X29657,X29656)
| c_Wellfounded_Owf(X29657,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29657,X29657),tc_HOL_Obool)),X29655),X29656)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int2])]) ).
fof(i_0_8532,plain,
! [X22485,X22486] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22486))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22485),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22486),X22485) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22486),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22485)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg])]) ).
fof(i_0_8533,plain,
! [X33554,X33555] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X33555)
| X33554 = c_List_Olist_ONil(X33555)
| hAPP(c_Finite__Set_Ofold1(X33555,c_Groups_Otimes__class_Otimes(X33555)),hAPP(c_List_Oset(X33555),X33554)) = hAPP(c_List_Ofoldl(X33555,X33555,c_Groups_Otimes__class_Otimes(X33555),hAPP(c_List_Ohd(X33555),X33554)),hAPP(c_List_Otl(X33555),X33554)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__set])]) ).
fof(i_0_8534,plain,
! [X33368,X33369,X33370,X33371,X33372] : hAPP(hAPP(c_List_Odrop(tc_prod(X33372,X33371)),X33370),hAPP(hAPP(c_List_Ozip(X33372,X33371),X33369),X33368)) = hAPP(hAPP(c_List_Ozip(X33372,X33371),hAPP(hAPP(c_List_Odrop(X33372),X33370),X33369)),hAPP(hAPP(c_List_Odrop(X33371),X33370),X33368)),
inference(variable_rename,[status(thm)],[fact_drop__zip]) ).
fof(i_0_8535,plain,
! [X33084,X33085,X33086,X33087,X33088] : hAPP(hAPP(c_List_Otake(tc_prod(X33088,X33087)),X33086),hAPP(hAPP(c_List_Ozip(X33088,X33087),X33085),X33084)) = hAPP(hAPP(c_List_Ozip(X33088,X33087),hAPP(hAPP(c_List_Otake(X33088),X33086),X33085)),hAPP(hAPP(c_List_Otake(X33087),X33086),X33084)),
inference(variable_rename,[status(thm)],[fact_take__zip]) ).
fof(i_0_8536,plain,
! [X24886,X24887,X24888] :
( ~ class_Orderings_Olinorder(X24888)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24888),X24887),X24886))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24888,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24888,X24887),X24886)),hAPP(hAPP(c_Set_Oinsert(X24888),X24886),c_Orderings_Obot__class_Obot(tc_fun(X24888,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X24888,X24887,X24886) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J])]) ).
fof(i_0_8537,plain,
! [X22235,X22236] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22236),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22235),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X22236,X22235) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22236),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22235)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg])]) ).
fof(i_0_8538,plain,
! [X30574,X30575,X30576,X30577,X30578] :
( ~ c_Relation_Osingle__valued(X30578,X30577,X30576)
| ~ c_Relation_Osingle__valued(X30577,X30575,X30574)
| c_Relation_Osingle__valued(X30578,X30575,hAPP(hAPP(c_Relation_Orel__comp(X30578,X30577,X30575),X30576),X30574)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__comp])]) ).
fof(i_0_8539,plain,
! [X34317,X34318] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34318),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34318))),c_List_Otranspose(X34318,X34317)))),
inference(variable_rename,[status(thm)],[fact_sorted__transpose]) ).
fof(i_0_8540,plain,
! [X27433,X27434,X27435,X27436,X27437] :
( ~ class_Orderings_Olinorder(X27437)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27437,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27437,X27436),X27435)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27437,X27434),X27433)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27437,hAPP(hAPP(c_Orderings_Oord__class_Omax(X27437),X27436),X27434)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27437),X27435),X27433)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan])]) ).
fof(i_0_8541,plain,
! [X27465,X27466,X27467,X27468,X27469] :
( ~ class_Orderings_Olinorder(X27469)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27469,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27469,X27468,X27467)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27469,X27466,X27465)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X27469,hAPP(hAPP(c_Orderings_Oord__class_Omax(X27469),X27468),X27466),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27469),X27467),X27465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan])]) ).
fof(i_0_8542,plain,
! [X27456,X27457,X27458,X27459,X27460] :
( ~ class_Orderings_Olinorder(X27460)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27460,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27460,X27459,X27458)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27460,X27457,X27456)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X27460,hAPP(hAPP(c_Orderings_Oord__class_Omax(X27460),X27459),X27457),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27460),X27458),X27456)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost])]) ).
fof(i_0_8543,plain,
! [X27428,X27429,X27430,X27431,X27432] :
( ~ class_Orderings_Olinorder(X27432)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27432,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X27432,X27431,X27430)),c_SetInterval_Oord__class_OatLeastAtMost(X27432,X27429,X27428)) = c_SetInterval_Oord__class_OatLeastAtMost(X27432,hAPP(hAPP(c_Orderings_Oord__class_Omax(X27432),X27431),X27429),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27432),X27430),X27428)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost])]) ).
fof(i_0_8544,plain,
! [X25116,X25117,X25118,X25119] :
( ~ hBOOL(hAPP(hAPP(c_member(X25119),X25118),X25117))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25119,tc_HOL_Obool)),X25117),X25116))
| hBOOL(hAPP(hAPP(c_member(X25119),X25118),X25116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_8545,plain,
! [X25120,X25121,X25122,X25123] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25123,tc_HOL_Obool)),X25122),X25121))
| ~ hBOOL(hAPP(hAPP(c_member(X25123),X25120),X25122))
| hBOOL(hAPP(hAPP(c_member(X25123),X25120),X25121)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_8546,plain,
! [X25112,X25113,X25114,X25115] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25115,tc_HOL_Obool)),X25114),X25113))
| ~ hBOOL(hAPP(hAPP(c_member(X25115),X25112),X25114))
| hBOOL(hAPP(hAPP(c_member(X25115),X25112),X25113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_8547,plain,
! [X24951,X24952,X24953,X24954] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24954,tc_HOL_Obool)),X24953),X24952))
| ~ hBOOL(hAPP(hAPP(c_member(X24954),X24951),X24953))
| hBOOL(hAPP(hAPP(c_member(X24954),X24951),X24952)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_8548,plain,
! [X25156,X25157,X25158,X25159] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25159,tc_HOL_Obool)),X25158),X25157))
| ~ hBOOL(hAPP(hAPP(c_member(X25159),X25156),X25158))
| hBOOL(hAPP(hAPP(c_member(X25159),X25156),X25157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_8549,plain,
! [X32851,X32852,X32853,X32854] : hAPP(hAPP(c_List_Onth(X32854),hAPP(hAPP(c_List_Oappend(X32854),X32853),hAPP(hAPP(c_List_Olist_OCons(X32854),X32852),X32851))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32854)),X32853)) = X32852,
inference(variable_rename,[status(thm)],[fact_nth__append__length]) ).
fof(i_0_8550,plain,
! [X22694,X22695,X22696] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22696),hAPP(c_Int_Onumber__class_Onumber__of(X22696),X22695)),hAPP(c_Int_Onumber__class_Onumber__of(X22696),X22694)))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22696),hAPP(c_Int_Onumber__class_Onumber__of(X22696),X22695)),hAPP(c_Int_Onumber__class_Onumber__of(X22696),X22694)) = hAPP(c_Int_Onumber__class_Onumber__of(X22696),X22694)
| ~ class_Int_Onumber(X22696)
| ~ class_Orderings_Oord(X22696) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22696),hAPP(c_Int_Onumber__class_Onumber__of(X22696),X22695)),hAPP(c_Int_Onumber__class_Onumber__of(X22696),X22694)))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22696),hAPP(c_Int_Onumber__class_Onumber__of(X22696),X22695)),hAPP(c_Int_Onumber__class_Onumber__of(X22696),X22694)) = hAPP(c_Int_Onumber__class_Onumber__of(X22696),X22695)
| ~ class_Int_Onumber(X22696)
| ~ class_Orderings_Oord(X22696) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5725])])]) ).
fof(i_0_8551,plain,
! [X22389,X22390,X22391] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22391),hAPP(c_Int_Onumber__class_Onumber__of(X22391),X22390)),hAPP(c_Int_Onumber__class_Onumber__of(X22391),X22389)))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22391),hAPP(c_Int_Onumber__class_Onumber__of(X22391),X22390)),hAPP(c_Int_Onumber__class_Onumber__of(X22391),X22389)) = hAPP(c_Int_Onumber__class_Onumber__of(X22391),X22390)
| ~ class_Int_Onumber(X22391)
| ~ class_Orderings_Oord(X22391) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22391),hAPP(c_Int_Onumber__class_Onumber__of(X22391),X22390)),hAPP(c_Int_Onumber__class_Onumber__of(X22391),X22389)))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22391),hAPP(c_Int_Onumber__class_Onumber__of(X22391),X22390)),hAPP(c_Int_Onumber__class_Onumber__of(X22391),X22389)) = hAPP(c_Int_Onumber__class_Onumber__of(X22391),X22389)
| ~ class_Int_Onumber(X22391)
| ~ class_Orderings_Oord(X22391) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5726])])]) ).
fof(i_0_8552,plain,
! [X22251,X22252] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22252),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22251),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22252),X22251) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22252),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22251)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg])]) ).
fof(i_0_8553,plain,
! [X28220,X28221] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X28221),X28220),
inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).
fof(i_0_8554,plain,
! [X20080,X20081] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20080),X20081)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20080))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20081)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20080))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20080),X20081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20081)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])]) ).
fof(i_0_8555,plain,
! [X21437,X21438,X21439,X21440,X21441] :
( ~ class_Fields_Ofield__inverse__zero(X21441)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21441),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21441),X21440),X21439)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21441),X21438),X21437)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21441),X21440),X21438)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21441),X21439),X21437)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq])]) ).
fof(i_0_8556,plain,
! [X18709,X18710,X18711,X18712,X18713] :
( ~ class_Rings_Ocomm__semiring__1(X18713)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18713),X18712),X18711)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18713),X18710),X18709)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18713),X18712),X18710)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18713),X18711),X18709)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).
fof(i_0_8557,plain,
! [X18165,X18166,X18167,X18168,X18169] :
( ~ class_Rings_Ocomm__semiring__1(X18169)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18169),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18169),X18168),X18167)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18169),X18166),X18165)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18169),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18169),X18168),X18166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18169),X18167),X18165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_8558,plain,
! [X18699,X18700,X18701,X18702,X18703] :
( ~ class_Rings_Ocomm__semiring__1(X18703)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18703),X18702),X18701)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18703),X18700),X18699)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18703),X18702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18703),X18701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18703),X18700),X18699))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).
fof(i_0_8559,plain,
! [X34127,X34128,X34129,X34130,X34131] :
( ~ class_Orderings_Olinorder(X34131)
| ~ c_List_Olinorder__class_Osorted(X34131,hAPP(hAPP(c_List_Omap(X34130,X34131),X34129),X34128))
| c_List_Olinorder__class_Osorted(X34131,hAPP(hAPP(c_List_Omap(X34130,X34131),X34129),c_List_Oremove1(X34130,X34127,X34128))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__remove1])]) ).
fof(i_0_8560,plain,
! [X31327,X31328,X31329] : hAPP(c_Relation_ODomain(X31329,X31328),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X31329,X31328),tc_HOL_Obool),X31327)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X31329,X31328),tc_HOL_Obool),tc_fun(X31329,tc_HOL_Obool)),X31327),c_Relation_ODomain(X31329,X31328)),
inference(variable_rename,[status(thm)],[fact_Domain__Union]) ).
fof(i_0_8561,plain,
! [X31330,X31331,X31332] : hAPP(c_Relation_ORange(X31332,X31331),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X31332,X31331),tc_HOL_Obool),X31330)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X31332,X31331),tc_HOL_Obool),tc_fun(X31331,tc_HOL_Obool)),X31330),c_Relation_ORange(X31332,X31331)),
inference(variable_rename,[status(thm)],[fact_Range__Union]) ).
fof(i_0_8562,plain,
! [X23523,X23524,X23526,X23527,X23528,X23530] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk98_2(X23523,X23524)),X23524))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23526),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23524)))
| hBOOL(hAPP(X23523,X23526)) )
& ( ~ hBOOL(hAPP(X23523,esk98_2(X23523,X23524)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23526),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23524)))
| hBOOL(hAPP(X23523,X23526)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk99_2(X23527,X23528)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23530),X23528))
| hBOOL(hAPP(X23527,X23530)) )
& ( ~ hBOOL(hAPP(X23527,esk99_2(X23527,X23528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23530),X23528))
| hBOOL(hAPP(X23527,X23530)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__nat__less])])])])])]) ).
fof(i_0_8563,plain,
! [X25760,X25761,X25762] :
( ~ class_Rings_Oring__1(X25762)
| ~ hBOOL(hAPP(hAPP(c_member(X25762),X25761),c_Int_Oring__1__class_OInts(X25762)))
| hBOOL(hAPP(hAPP(c_member(X25762),hAPP(hAPP(c_Power_Opower__class_Opower(X25762),X25761),X25760)),c_Int_Oring__1__class_OInts(X25762))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__power])]) ).
fof(i_0_8564,plain,
! [X29206,X29207] : hAPP(c_Set_OCollect(X29207),hAPP(hAPP(c_COMBC(X29207,tc_fun(X29207,tc_HOL_Obool),tc_HOL_Obool),c_member(X29207)),X29206)) = X29206,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(i_0_8565,plain,
! [X20872,X20873] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20873))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20873),X20872))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])]) ).
fof(i_0_8566,plain,
! [X23206,X23207,X23208] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23208),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23207,X23206)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23208),X23206))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23208),X23207)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zmod__imp__zdvd])]) ).
fof(i_0_8567,plain,
! [X20831,X20832,X20833] :
( ~ class_Rings_Olinordered__semidom(X20833)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20833),c_Groups_Oone__class_Oone(X20833)),X20832))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20831))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20833),c_Groups_Oone__class_Oone(X20833)),hAPP(hAPP(c_Power_Opower__class_Opower(X20833),X20832),X20831))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).
fof(i_0_8568,plain,
! [X21581,X21582,X21583] :
( ~ class_Fields_Olinordered__field(X21583)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21583),X21582),c_Groups_Ozero__class_Ozero(X21583)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21581),c_Groups_Ozero__class_Ozero(X21583)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21583),c_Groups_Ozero__class_Ozero(X21583)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21582),X21581))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg])]) ).
fof(i_0_8569,plain,
! [X19396,X19397,X19398] :
( ~ class_Rings_Oordered__ring(X19398)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19398),X19397),c_Groups_Ozero__class_Ozero(X19398)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19398),X19396),c_Groups_Ozero__class_Ozero(X19398)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19398),c_Groups_Ozero__class_Ozero(X19398)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19398),X19397),X19396))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).
fof(i_0_8570,plain,
! [X21501,X21502,X21503] :
( ~ class_Fields_Olinordered__field(X21503)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21503),X21502),c_Groups_Ozero__class_Ozero(X21503)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21503),X21501),c_Groups_Ozero__class_Ozero(X21503)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21503),c_Groups_Ozero__class_Ozero(X21503)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21503),X21502),X21501))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])]) ).
fof(i_0_8571,plain,
! [X18895,X18896,X18897] :
( ~ class_Rings_Olinordered__ring__strict(X18897)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18897),X18896),c_Groups_Ozero__class_Ozero(X18897)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18897),X18895),c_Groups_Ozero__class_Ozero(X18897)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18897),c_Groups_Ozero__class_Ozero(X18897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18897),X18896),X18895))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).
fof(i_0_8572,plain,
! [X23232,X23233,X23234] :
( ~ class_Groups_Ocomm__monoid__add(X23234)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23234),X23233),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X23232))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23234),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23234),X23233),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X23232))),hAPP(X23233,X23232)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc])]) ).
fof(i_0_8573,plain,
! [X18319,X18320] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18320),X18319)),X18320)),
inference(variable_rename,[status(thm)],[i_0_5727]) ).
fof(i_0_8574,plain,
! [X18317,X18318] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18318),X18317)),X18317)),
inference(variable_rename,[status(thm)],[i_0_5728]) ).
fof(i_0_8575,plain,
! [X32239,X32240,X32241,X32242] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32242)),X32241) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32240)),X32239)
| ~ hBOOL(hAPP(c_List_Odistinct(X32242),X32241))
| c_Map_Odom(X32242,X32240,c_Map_Omap__of(X32242,X32240,hAPP(hAPP(c_List_Ozip(X32242,X32240),X32241),X32239))) = hAPP(c_List_Oset(X32242),X32241) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__map__of__zip])]) ).
fof(i_0_8576,plain,
! [X21932,X21933] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21933))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21932))
| c_Divides_OposDivAlg(X21933,X21932) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21933),X21932)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21933,X21932)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__div__mod])]) ).
fof(i_0_8577,plain,
! [X20082,X20083] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20082),X20083)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20083),X20082))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20083)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20083),X20082))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20082),X20083)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20083)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])]) ).
fof(i_0_8578,plain,
! [X29693,X29694] : c_List_Olex(X29694,X29693) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X29694),tc_List_Olist(X29694)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X29694,X29693)),
inference(variable_rename,[status(thm)],[fact_lex__def]) ).
fof(i_0_8579,plain,
! [X32935,X32936,X32937,X32938] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32938),X32937),hAPP(c_List_Oset(X32938),X32936)))
| c_List_Oremove1(X32938,X32937,hAPP(hAPP(c_List_Oappend(X32938),X32936),X32935)) = hAPP(hAPP(c_List_Oappend(X32938),c_List_Oremove1(X32938,X32937,X32936)),X32935) )
& ( hBOOL(hAPP(hAPP(c_member(X32938),X32937),hAPP(c_List_Oset(X32938),X32936)))
| c_List_Oremove1(X32938,X32937,hAPP(hAPP(c_List_Oappend(X32938),X32936),X32935)) = hAPP(hAPP(c_List_Oappend(X32938),X32936),c_List_Oremove1(X32938,X32937,X32935)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5729])]) ).
cnf(i_0_8580,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_5730]) ).
fof(i_0_8581,plain,
! [X22586,X22587,X22588,X22589] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22589),X22588),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22589),X22587),X22586)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22589),X22588),X22587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22589),X22588),X22586))
| ~ class_Orderings_Olinorder(X22589) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22589),X22588),X22587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22589),X22588),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22589),X22587),X22586)))
| ~ class_Orderings_Olinorder(X22589) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22589),X22588),X22586))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22589),X22588),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22589),X22587),X22586)))
| ~ class_Orderings_Olinorder(X22589) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj])])]) ).
fof(i_0_8582,plain,
! [X22570,X22571,X22572,X22573] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22573),X22572),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22573),X22571),X22570)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22573),X22572),X22571))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22573),X22572),X22570))
| ~ class_Orderings_Olinorder(X22573) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22573),X22572),X22571))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22573),X22572),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22573),X22571),X22570)))
| ~ class_Orderings_Olinorder(X22573) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22573),X22572),X22570))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22573),X22572),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22573),X22571),X22570)))
| ~ class_Orderings_Olinorder(X22573) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj])])]) ).
fof(i_0_8583,plain,
! [X28589,X28590,X28591] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28591,X28590,c_Orderings_Obot__class_Obot(tc_fun(X28591,tc_HOL_Obool))),X28589)),
inference(variable_rename,[status(thm)],[i_0_5731]) ).
fof(i_0_8584,plain,
! [X20093,X20094] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20093),X20094)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20093),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20094),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20093),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20093),X20094)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20094),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff])])]) ).
fof(i_0_8585,plain,
! [X32576,X32577] :
( X32577 = c_List_Olist_ONil(X32576)
| c_Random_Oselect__weight(X32576,hAPP(hAPP(c_List_Omap(X32576,tc_prod(tc_Code__Numeral_Ocode__numeral,X32576)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X32576),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X32577)) = c_Random_Oselect(X32576,X32577) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weigth__select])]) ).
fof(i_0_8586,plain,
! [X31203,X31204,X31205] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31204,tc_HOL_Obool)),X31205),X31203))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31204),X31205))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X31204),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31204,tc_HOL_Obool),X31203))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Inter])])]) ).
fof(i_0_8587,plain,
! [X20790,X20791,X20792] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20792),c_Groups_Ozero__class_Ozero(X20792)),X20790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20792),c_Groups_Ozero__class_Ozero(X20792)),X20791))
| hAPP(c_Groups_Oabs__class_Oabs(X20792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20792),X20791),X20790)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20792),hAPP(c_Groups_Oabs__class_Oabs(X20792),X20791)),hAPP(c_Groups_Oabs__class_Oabs(X20792),X20790))
| ~ class_Rings_Oordered__ring__abs(X20792) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20792),X20790),c_Groups_Ozero__class_Ozero(X20792)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20792),c_Groups_Ozero__class_Ozero(X20792)),X20791))
| hAPP(c_Groups_Oabs__class_Oabs(X20792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20792),X20791),X20790)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20792),hAPP(c_Groups_Oabs__class_Oabs(X20792),X20791)),hAPP(c_Groups_Oabs__class_Oabs(X20792),X20790))
| ~ class_Rings_Oordered__ring__abs(X20792) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20792),c_Groups_Ozero__class_Ozero(X20792)),X20790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20792),X20791),c_Groups_Ozero__class_Ozero(X20792)))
| hAPP(c_Groups_Oabs__class_Oabs(X20792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20792),X20791),X20790)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20792),hAPP(c_Groups_Oabs__class_Oabs(X20792),X20791)),hAPP(c_Groups_Oabs__class_Oabs(X20792),X20790))
| ~ class_Rings_Oordered__ring__abs(X20792) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20792),X20790),c_Groups_Ozero__class_Ozero(X20792)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20792),X20791),c_Groups_Ozero__class_Ozero(X20792)))
| hAPP(c_Groups_Oabs__class_Oabs(X20792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20792),X20791),X20790)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20792),hAPP(c_Groups_Oabs__class_Oabs(X20792),X20791)),hAPP(c_Groups_Oabs__class_Oabs(X20792),X20790))
| ~ class_Rings_Oordered__ring__abs(X20792) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).
cnf(i_0_8588,plain,
( X1 = X2
| c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5732]) ).
fof(i_0_8589,plain,
! [X33793,X33794,X33795] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33795),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33794)),X33793)))
| c_List_Obutlast(X33794,hAPP(hAPP(c_List_Otake(X33794),X33795),X33793)) = hAPP(hAPP(c_List_Otake(X33794),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33795),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33793) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__take])]) ).
fof(i_0_8590,plain,
! [X24844,X24845] :
( ~ class_Orderings_Oorder(X24845)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24845,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24845),X24844),c_Orderings_Obot__class_Obot(tc_fun(X24845,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X24845),X24844)) = hAPP(hAPP(c_Set_Oinsert(X24845),X24844),c_Orderings_Obot__class_Obot(tc_fun(X24845,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan])]) ).
fof(i_0_8591,plain,
! [X27132,X27133,X27134,X27135,X27136,X27137,X27138,X27139] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27134,tc_HOL_Obool)),X27133),X27132) != c_Orderings_Obot__class_Obot(tc_fun(X27134,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X27134),X27135),X27133))
| ~ hBOOL(hAPP(hAPP(c_member(X27134),X27136),X27132))
| X27135 != X27136 )
& ( hBOOL(hAPP(hAPP(c_member(X27139),esk243_3(X27137,X27138,X27139)),X27138))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27139,tc_HOL_Obool)),X27138),X27137) = c_Orderings_Obot__class_Obot(tc_fun(X27139,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X27139),esk244_3(X27137,X27138,X27139)),X27137))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27139,tc_HOL_Obool)),X27138),X27137) = c_Orderings_Obot__class_Obot(tc_fun(X27139,tc_HOL_Obool)) )
& ( esk243_3(X27137,X27138,X27139) = esk244_3(X27137,X27138,X27139)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27139,tc_HOL_Obool)),X27138),X27137) = c_Orderings_Obot__class_Obot(tc_fun(X27139,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_disjoint__iff__not__equal])])])])])]) ).
fof(i_0_8592,plain,
! [X34180,X34181,X34182] :
( ~ class_Orderings_Olinorder(X34182)
| ~ hBOOL(hAPP(hAPP(c_member(X34182),X34181),hAPP(c_List_Oset(X34182),X34180)))
| ~ c_List_Olinorder__class_Osorted(X34182,X34180)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34182,X34182,c_COMBI(X34182)),X34181),c_List_Oremove1(X34182,X34181,X34180)) = X34180 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__remove1])]) ).
fof(i_0_8593,plain,
! [X21863,X21864] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21864),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21863))
| c_Divides_OnegDivAlg(X21864,X21863) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21864),X21863)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21864,X21863)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__div__mod])]) ).
fof(i_0_8594,plain,
! [X27781,X27782,X27783] :
( ~ class_Lattices_Olattice(X27783)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27783),X27782))
| X27781 = c_Orderings_Obot__class_Obot(tc_fun(X27783,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27783,tc_HOL_Obool)),X27781),X27782))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27783),c_Big__Operators_Olattice__class_OInf__fin(X27783,X27781)),c_Big__Operators_Olattice__class_OInf__fin(X27783,X27782)) = c_Big__Operators_Olattice__class_OInf__fin(X27783,X27782) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem])]) ).
fof(i_0_8595,plain,
! [X25773,X25774,X25775] :
( ~ class_Lattices_Olattice(X25775)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25775),X25774))
| X25773 = c_Orderings_Obot__class_Obot(tc_fun(X25775,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25775,tc_HOL_Obool)),X25773),X25774))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25775),c_Big__Operators_Olattice__class_OSup__fin(X25775,X25773)),c_Big__Operators_Olattice__class_OSup__fin(X25775,X25774)) = c_Big__Operators_Olattice__class_OSup__fin(X25775,X25774) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem])]) ).
fof(i_0_8596,plain,
! [X25860,X25861,X25862] :
( ~ class_Orderings_Olinorder(X25862)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25862),X25861))
| X25860 = c_Orderings_Obot__class_Obot(tc_fun(X25862,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25862,tc_HOL_Obool)),X25860),X25861))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25862),c_Big__Operators_Olinorder__class_OMax(X25862,X25860)),c_Big__Operators_Olinorder__class_OMax(X25862,X25861)) = c_Big__Operators_Olinorder__class_OMax(X25862,X25861) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem])]) ).
fof(i_0_8597,plain,
! [X25857,X25858,X25859] :
( ~ class_Orderings_Olinorder(X25859)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25859),X25858))
| X25857 = c_Orderings_Obot__class_Obot(tc_fun(X25859,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25859,tc_HOL_Obool)),X25857),X25858))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25859),c_Big__Operators_Olinorder__class_OMin(X25859,X25857)),c_Big__Operators_Olinorder__class_OMin(X25859,X25858)) = c_Big__Operators_Olinorder__class_OMin(X25859,X25858) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem])]) ).
fof(i_0_8598,plain,
! [X20655,X20656,X20657] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20657,X20656)),X20655),X20656) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20657),X20655),X20656),
inference(variable_rename,[status(thm)],[fact_zpower__zmod]) ).
fof(i_0_8599,plain,
! [X20349,X20350,X20351] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20351,X20350)),X20349),X20350) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20351),X20349),X20350),
inference(variable_rename,[status(thm)],[fact_zdiff__zmod__left]) ).
fof(i_0_8600,plain,
! [X31296,X31297,X31298,X31299] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31298),X31297),c_Complete__Lattice_OInf__class_OInf(X31298,X31296)))
| ~ hBOOL(hAPP(hAPP(c_member(X31298),X31299),X31296))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31298),X31297),X31299))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31298) )
& ( hBOOL(hAPP(hAPP(c_member(X31298),esk401_3(X31296,X31297,X31298)),X31296))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31298),X31297),c_Complete__Lattice_OInf__class_OInf(X31298,X31296)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31298) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31298),X31297),esk401_3(X31296,X31297,X31298)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31298),X31297),c_Complete__Lattice_OInf__class_OInf(X31298,X31296)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31298) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Inf__iff])])])])]) ).
fof(i_0_8601,plain,
! [X33164,X33165,X33166,X33167] :
( ( X33167 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X33166),X33167),hAPP(hAPP(c_List_Olist_OCons(X33166),X33165),X33164)) = c_List_Olist_ONil(X33166) )
& ( X33167 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X33166),X33167),hAPP(hAPP(c_List_Olist_OCons(X33166),X33165),X33164)) = hAPP(hAPP(c_List_Olist_OCons(X33166),X33165),hAPP(hAPP(c_List_Otake(X33166),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33167),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33164)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons_H])]) ).
fof(i_0_8602,plain,
! [X26977,X26978,X26979,X26980] :
( ~ hBOOL(hAPP(X26980,X26979))
| ~ hBOOL(hAPP(X26978,X26979))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26977,tc_HOL_Obool)),X26980),X26978),X26979)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])]) ).
fof(i_0_8603,plain,
! [X27737] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X27737)),c_Int_OInteg)),
inference(variable_rename,[status(thm)],[fact_Rep__Integ]) ).
fof(i_0_8604,plain,
! [X26485,X26486,X26487,X26488,X26489] :
( ~ c_Finite__Set_Ofolding__one__idem(X26489,X26488,X26487)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26489),X26486))
| X26486 = c_Orderings_Obot__class_Obot(tc_fun(X26489,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26489),X26485))
| X26485 = c_Orderings_Obot__class_Obot(tc_fun(X26489,tc_HOL_Obool))
| hAPP(X26487,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26489,tc_HOL_Obool)),X26486),X26485)) = hAPP(hAPP(X26488,hAPP(X26487,X26486)),hAPP(X26487,X26485)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem])]) ).
fof(i_0_8605,plain,
! [X19349,X19350,X19351,X19352] :
( ~ class_Groups_Oordered__comm__monoid__add(X19352)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19352),c_Groups_Ozero__class_Ozero(X19352)),X19351))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19352),X19350),X19349))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19352),X19350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19352),X19351),X19349))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_8606,plain,
! [X19353,X19354,X19355,X19356] :
( ~ class_Groups_Oordered__comm__monoid__add(X19356)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19356),c_Groups_Ozero__class_Ozero(X19356)),X19355))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19356),X19354),X19353))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19356),X19354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19356),X19353),X19355))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_8607,plain,
! [X18372,X18373,X18374,X18375] :
( ~ class_Rings_Olinordered__semidom(X18375)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18375),c_Groups_Ozero__class_Ozero(X18375)),X18374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18375),X18373),X18372))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18375),X18373),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18375),X18374),X18372))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_8608,plain,
! [X19542,X19543,X19544,X19545] :
( ~ class_Groups_Oordered__comm__monoid__add(X19545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19545),c_Groups_Ozero__class_Ozero(X19545)),X19544))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19545),X19543),X19542))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19545),X19543),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19545),X19544),X19542))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_8609,plain,
! [X19538,X19539,X19540,X19541] :
( ~ class_Groups_Oordered__comm__monoid__add(X19541)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19541),c_Groups_Ozero__class_Ozero(X19541)),X19540))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19541),X19539),X19538))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19541),X19539),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19541),X19540),X19538))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_8610,plain,
! [X20118,X20119] : X20119 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20118),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20119),X20118))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20119,X20118)),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality]) ).
fof(i_0_8611,plain,
! [X27011,X27012,X27013,X27014] :
( ~ class_Lattices_Osemilattice__inf(X27014)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27014),X27013),X27012))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27014),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27014),X27013),X27011)),X27012)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])]) ).
fof(i_0_8612,plain,
! [X27015,X27016,X27017,X27018] :
( ~ class_Lattices_Osemilattice__inf(X27018)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27018),X27017),X27016))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27018),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27018),X27015),X27017)),X27016)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])]) ).
fof(i_0_8613,plain,
! [X22288,X22289,X22290,X22291] :
( ~ class_Orderings_Olinorder(X22291)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22291),X22290),X22289))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22291),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22291),X22290),X22288)),X22289)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI1])]) ).
fof(i_0_8614,plain,
! [X22284,X22285,X22286,X22287] :
( ~ class_Orderings_Olinorder(X22287)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22287),X22286),X22285))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22287),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22287),X22284),X22286)),X22285)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI2])]) ).
fof(i_0_8615,plain,
! [X27244,X27245,X27246,X27247] :
( ~ class_Lattices_Osemilattice__inf(X27247)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27247),X27246),X27245))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27247),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27247),X27246),X27244)),X27245)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI1])]) ).
fof(i_0_8616,plain,
! [X27248,X27249,X27250,X27251] :
( ~ class_Lattices_Osemilattice__inf(X27251)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27251),X27250),X27249))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27251),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27251),X27248),X27250)),X27249)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI2])]) ).
fof(i_0_8617,plain,
! [X22345,X22346,X22347,X22348] :
( ~ class_Orderings_Olinorder(X22348)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22348),X22347),X22346))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22348),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22348),X22347),X22345)),X22346)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI1])]) ).
fof(i_0_8618,plain,
! [X22341,X22342,X22343,X22344] :
( ~ class_Orderings_Olinorder(X22344)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22344),X22343),X22342))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22344),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22344),X22341),X22343)),X22342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI2])]) ).
fof(i_0_8619,plain,
! [X32572,X32573] : hAPP(c_Relation_OImage(tc_List_Olist(X32573),tc_List_Olist(X32573),c_List_Olistrel(X32573,X32572)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32573)),c_List_Olist_ONil(X32573)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32573),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32573)),c_List_Olist_ONil(X32573)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32573),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_listrel__Nil]) ).
fof(i_0_8620,plain,
! [X26132,X26133,X26134,X26135] :
( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26134,tc_Nat_Onat),X26132),X26133) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X26134),X26135),X26133))
| hAPP(X26132,X26135) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26134),X26133)) )
& ( hBOOL(hAPP(hAPP(c_member(X26134),esk211_3(X26132,X26133,X26134)),X26133))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26134,tc_Nat_Onat),X26132),X26133) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26134),X26133)) )
& ( hAPP(X26132,esk211_3(X26132,X26133,X26134)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26134,tc_Nat_Onat),X26132),X26133) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26134),X26133)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__eq__1__iff])])])])]) ).
fof(i_0_8621,plain,
! [X24453,X24454,X24455,X24456] :
( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24455,tc_Nat_Onat),X24453),X24454) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X24455),X24456),X24454))
| hAPP(X24453,X24456) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24455),X24454)) )
& ( hBOOL(hAPP(hAPP(c_member(X24455),esk156_3(X24453,X24454,X24455)),X24454))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24455,tc_Nat_Onat),X24453),X24454) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24455),X24454)) )
& ( hAPP(X24453,esk156_3(X24453,X24454,X24455)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24455,tc_Nat_Onat),X24453),X24454) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24455),X24454)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__eq__0__iff])])])])]) ).
fof(i_0_8622,plain,
! [X26276,X26277,X26278,X26279,X26280] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X26280),X26279),X26278))
| hAPP(c_Map_Orestrict__map(X26280,X26277,X26276,X26278),X26279) = hAPP(X26276,X26279) )
& ( hBOOL(hAPP(hAPP(c_member(X26280),X26279),X26278))
| hAPP(c_Map_Orestrict__map(X26280,X26277,X26276,X26278),X26279) = c_Option_Ooption_ONone(X26277) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5733])]) ).
fof(i_0_8623,plain,
! [X26257,X26258,X26259,X26260,X26261] :
( ~ hBOOL(hAPP(hAPP(c_member(X26261),X26260),X26259))
| hAPP(c_Map_Orestrict__map(X26261,X26258,X26257,X26259),X26260) = hAPP(X26257,X26260) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrict__in])]) ).
fof(i_0_8624,plain,
! [X20502,X20503,X20504,X20505,X20506,X20507,X20508] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20503),X20502))
| hBOOL(hAPP(X20504,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X20504,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20503),X20502))) )
& ( X20503 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20502),X20505)
| hBOOL(hAPP(X20504,X20505))
| ~ hBOOL(hAPP(X20504,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20503),X20502))) )
& ( X20507 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20506),esk68_3(X20506,X20507,X20508))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20507),X20506))
| hBOOL(hAPP(X20508,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20507),X20506))) )
& ( ~ hBOOL(hAPP(X20508,esk68_3(X20506,X20507,X20508)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20507),X20506))
| hBOOL(hAPP(X20508,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20507),X20506))) )
& ( X20507 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20506),esk68_3(X20506,X20507,X20508))
| ~ hBOOL(hAPP(X20508,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20508,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20507),X20506))) )
& ( ~ hBOOL(hAPP(X20508,esk68_3(X20506,X20507,X20508)))
| ~ hBOOL(hAPP(X20508,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20508,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20507),X20506))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5734])])])])])]) ).
fof(i_0_8625,plain,
! [X20494,X20495,X20496,X20497,X20498,X20499,X20500] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20495),X20494))
| hBOOL(hAPP(X20496,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X20496,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20495),X20494))) )
& ( X20495 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20494),X20497)
| hBOOL(hAPP(X20496,X20497))
| ~ hBOOL(hAPP(X20496,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20495),X20494))) )
& ( X20499 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20498),esk67_3(X20498,X20499,X20500))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20499),X20498))
| hBOOL(hAPP(X20500,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20499),X20498))) )
& ( ~ hBOOL(hAPP(X20500,esk67_3(X20498,X20499,X20500)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20499),X20498))
| hBOOL(hAPP(X20500,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20499),X20498))) )
& ( X20499 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20498),esk67_3(X20498,X20499,X20500))
| ~ hBOOL(hAPP(X20500,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20500,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20499),X20498))) )
& ( ~ hBOOL(hAPP(X20500,esk67_3(X20498,X20499,X20500)))
| ~ hBOOL(hAPP(X20500,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20500,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20499),X20498))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__split])])])])])]) ).
fof(i_0_8626,plain,
! [X23326,X23327,X23328,X23329] :
( ~ class_Divides_Osemiring__div(X23329)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23329),X23328),X23327))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23329),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23329),X23327),X23328)),X23326) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23329),X23327),X23326)),X23328) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult])]) ).
fof(i_0_8627,plain,
! [X24572,X24573] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24573),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24573,tc_HOL_Obool)),X24572)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24573),c_Orderings_Otop__class_Otop(tc_fun(X24573,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24573),X24572)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24573),c_Orderings_Otop__class_Otop(tc_fun(X24573,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24573),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24573,tc_HOL_Obool)),X24572)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24573),X24572)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__compl])])]) ).
fof(i_0_8628,plain,
! [X21126,X21127] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21127),X21126))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21126))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21127)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21126))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21127),X21126))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21127)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21126))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21127),X21126))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21127),X21126))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21127)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21126))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21126))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21127),X21126))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21127)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21126))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__nat__number__of])])]) ).
fof(i_0_8629,plain,
! [X24394,X24395,X24396,X24397] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24397,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24397),X24396),X24395)),X24394) = hAPP(hAPP(c_Set_Oinsert(X24397),X24396),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24397,tc_HOL_Obool)),X24395),X24394)),
inference(variable_rename,[status(thm)],[fact_Un__insert__left]) ).
cnf(i_0_8630,plain,
( c_Map_Omap__comp(X3,X6,X8,X5,X1,X2) = hAPP(c_Option_Ooption_OSome(X6),X7)
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X4) != hAPP(c_Option_Ooption_OSome(X6),X7) ),
inference(split_conjunct,[status(thm)],[i_0_5271]) ).
fof(i_0_8631,plain,
! [X29115,X29116,X29117,X29118] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X29118,X29117,X29116)
| hAPP(c_Fun_Ocomp(X29117,X29117,X29117,hAPP(X29116,X29115)),hAPP(X29116,X29115)) = hAPP(X29116,X29115) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem])]) ).
fof(i_0_8632,plain,
! [X31672,X31673,X31674] : hBOOL(hAPP(c_Finite__Set_Ofinite(X31674),c_Map_Odom(X31674,X31673,c_Map_Omap__of(X31674,X31673,X31672)))),
inference(variable_rename,[status(thm)],[fact_finite__dom__map__of]) ).
fof(i_0_8633,plain,
! [X18110,X18111] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X18111,X18110)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X18111)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X18110))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_com_Osize_I12_J]) ).
fof(i_0_8634,plain,
! [X22197,X22198,X22199,X22200] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22200,X22199),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22198),X22197)))
| X22199 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X22200,X22199) = X22197 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod])]) ).
fof(i_0_8635,plain,
! [X22168,X22169,X22170] : hAPP(c_Product__Type_Osnd(X22170,X22169),X22168) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22170,X22169,X22169),hAPP(c_COMBK(tc_fun(X22169,X22169),X22170),c_COMBI(X22169))),X22168),
inference(variable_rename,[status(thm)],[fact_snd__def]) ).
fof(i_0_8636,plain,
! [X25779,X25780] :
( ~ class_Int_Oring__char__0(X25780)
| ~ hBOOL(hAPP(hAPP(c_member(X25780),X25779),c_Int_Oring__1__class_OInts(X25780)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25780),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25780),c_Groups_Oone__class_Oone(X25780)),X25779)),X25779) != c_Groups_Ozero__class_Ozero(X25780) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).
fof(i_0_8637,plain,
! [X26989,X26990,X26991] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26991),X26990))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X26991),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26991,tc_HOL_Obool)),X26990),X26989))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26991),X26989))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X26991),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26991,tc_HOL_Obool)),X26990),X26989))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Int])])]) ).
fof(i_0_8638,plain,
! [X24512,X24513,X24514] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24514),X24513))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24514),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24514,tc_HOL_Obool)),X24513),X24512))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff])]) ).
fof(i_0_8639,plain,
! [X34054,X34055,X34056,X34057] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34057),X34056),X34055))
| ~ c_List_Olinorder__class_Osorted(X34057,hAPP(hAPP(c_List_Olist_OCons(X34057),X34056),hAPP(hAPP(c_List_Olist_OCons(X34057),X34055),X34054)))
| ~ class_Orderings_Olinorder(X34057) )
& ( c_List_Olinorder__class_Osorted(X34057,hAPP(hAPP(c_List_Olist_OCons(X34057),X34055),X34054))
| ~ c_List_Olinorder__class_Osorted(X34057,hAPP(hAPP(c_List_Olist_OCons(X34057),X34056),hAPP(hAPP(c_List_Olist_OCons(X34057),X34055),X34054)))
| ~ class_Orderings_Olinorder(X34057) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34057),X34056),X34055))
| ~ c_List_Olinorder__class_Osorted(X34057,hAPP(hAPP(c_List_Olist_OCons(X34057),X34055),X34054))
| c_List_Olinorder__class_Osorted(X34057,hAPP(hAPP(c_List_Olist_OCons(X34057),X34056),hAPP(hAPP(c_List_Olist_OCons(X34057),X34055),X34054)))
| ~ class_Orderings_Olinorder(X34057) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many__eq])])]) ).
fof(i_0_8640,plain,
! [X34050,X34051,X34052,X34053] :
( ~ class_Orderings_Olinorder(X34053)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34053),X34052),X34051))
| ~ c_List_Olinorder__class_Osorted(X34053,hAPP(hAPP(c_List_Olist_OCons(X34053),X34051),X34050))
| c_List_Olinorder__class_Osorted(X34053,hAPP(hAPP(c_List_Olist_OCons(X34053),X34052),hAPP(hAPP(c_List_Olist_OCons(X34053),X34051),X34050))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many])]) ).
fof(i_0_8641,plain,
! [X22000,X22001,X22002,X22003] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22003,X22002),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22001),X22000)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22003,X22002) = X22000 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq])]) ).
fof(i_0_8642,plain,
! [X19864,X19865] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19865))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19865,X19864)),X19865)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend])]) ).
fof(i_0_8643,plain,
! [X20108,X20109] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20109))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20108,X20109)),X20109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__le__divisor])]) ).
fof(i_0_8644,plain,
! [X19890,X19891] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19890,X19891)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19891)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19890,X19891)),X19891))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19891)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__conj])])]) ).
fof(i_0_8645,plain,
! [X19870,X19871] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19871))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19870,X19871)),X19871)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])]) ).
fof(i_0_8646,plain,
! [X20015,X20016] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20016))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20015,X20016)),X20016)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less__divisor])]) ).
fof(i_0_8647,plain,
! [X32177,X32178] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X32178),hAPP(c_List_Oset(X32178),X32177))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32178)),X32177))),
inference(variable_rename,[status(thm)],[fact_card__length]) ).
fof(i_0_8648,plain,
! [X23427,X23428,X23429] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23429),hAPP(c_Int_Onumber__class_Onumber__of(X23429),X23428)),hAPP(c_Int_Onumber__class_Onumber__of(X23429),X23427)))
| c_Divides_Odiv__class_Omod(X23429,hAPP(c_Int_Onumber__class_Onumber__of(X23429),X23427),hAPP(c_Int_Onumber__class_Onumber__of(X23429),X23428)) = c_Groups_Ozero__class_Ozero(X23429)
| ~ class_Divides_Osemiring__div(X23429)
| ~ class_Int_Onumber(X23429) )
& ( c_Divides_Odiv__class_Omod(X23429,hAPP(c_Int_Onumber__class_Onumber__of(X23429),X23427),hAPP(c_Int_Onumber__class_Onumber__of(X23429),X23428)) != c_Groups_Ozero__class_Ozero(X23429)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23429),hAPP(c_Int_Onumber__class_Onumber__of(X23429),X23428)),hAPP(c_Int_Onumber__class_Onumber__of(X23429),X23427)))
| ~ class_Divides_Osemiring__div(X23429)
| ~ class_Int_Onumber(X23429) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0__number__of])])]) ).
fof(i_0_8649,plain,
! [X26523,X26524,X26525,X26526,X26527] :
( hAPP(c_Set_Oimage(X26527,X26526,X26525),X26524) != X26523
| hAPP(c_Set_Oimage(tc_fun(X26527,tc_HOL_Obool),tc_fun(X26526,tc_HOL_Obool),c_Set_Oimage(X26527,X26526,X26525)),hAPP(c_Set_OPow(X26527),X26524)) = hAPP(c_Set_OPow(X26526),X26523) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__surj])]) ).
fof(i_0_8650,plain,
! [X32344,X32345,X32346] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32346),X32345),hAPP(c_List_Oset(X32346),X32344)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32346),hAPP(hAPP(c_List_Olist_OCons(X32346),X32345),X32344))) )
& ( hBOOL(hAPP(c_List_Odistinct(X32346),X32344))
| ~ hBOOL(hAPP(c_List_Odistinct(X32346),hAPP(hAPP(c_List_Olist_OCons(X32346),X32345),X32344))) )
& ( hBOOL(hAPP(hAPP(c_member(X32346),X32345),hAPP(c_List_Oset(X32346),X32344)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32346),X32344))
| hBOOL(hAPP(c_List_Odistinct(X32346),hAPP(hAPP(c_List_Olist_OCons(X32346),X32345),X32344))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5735])])]) ).
fof(i_0_8651,plain,
! [X28288,X28289,X28290,X28291] :
( hAPP(c_Set_Oimage(X28291,X28290,X28289),c_Orderings_Otop__class_Otop(tc_fun(X28291,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28290,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X28291,X28290,X28289),hAPP(c_Set_Ovimage(X28291,X28290,X28289),X28288)) = X28288 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq])]) ).
cnf(i_0_8652,plain,
( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = X3
| c_List_Oupt(X1,X2) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_5666]) ).
fof(i_0_8653,plain,
! [X23213,X23214,X23215] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23215),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23214),X23213)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23215),X23213))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23215),X23214)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zdiffD])]) ).
fof(i_0_8654,plain,
! [X22201,X22202,X22203,X22204] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22204,X22203),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22202),X22201)))
| X22203 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22204),X22203) = X22202 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div])]) ).
fof(i_0_8655,plain,
! [X29981,X29982,X29983] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29983),c_Map_Odom(X29983,X29982,X29981)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29983),c_Orderings_Otop__class_Otop(tc_fun(X29983,tc_HOL_Obool))))
| hAPP(X29981,esk345_3(X29981,X29982,X29983)) = c_Option_Ooption_ONone(X29982) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5736])])]) ).
fof(i_0_8656,plain,
! [X20695,X20696,X20697] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20697)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20697),hAPP(c_Groups_Oabs__class_Oabs(X20697),X20696)),X20695))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20697),hAPP(c_Groups_Ouminus__class_Ouminus(X20697),X20696)),X20695)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D2])]) ).
fof(i_0_8657,plain,
! [X19233,X19234,X19235] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19235),hAPP(c_Groups_Ouminus__class_Ouminus(X19235),X19234)),X19233))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19235),hAPP(c_Groups_Ouminus__class_Ouminus(X19235),X19233)),X19234))
| ~ class_Groups_Oordered__ab__group__add(X19235) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19235),hAPP(c_Groups_Ouminus__class_Ouminus(X19235),X19233)),X19234))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19235),hAPP(c_Groups_Ouminus__class_Ouminus(X19235),X19234)),X19233))
| ~ class_Groups_Oordered__ab__group__add(X19235) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).
fof(i_0_8658,plain,
! [X18760,X18761,X18762] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18762),hAPP(c_Groups_Ouminus__class_Ouminus(X18762),X18761)),X18760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18762),hAPP(c_Groups_Ouminus__class_Ouminus(X18762),X18760)),X18761))
| ~ class_Groups_Oordered__ab__group__add(X18762) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18762),hAPP(c_Groups_Ouminus__class_Ouminus(X18762),X18760)),X18761))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18762),hAPP(c_Groups_Ouminus__class_Ouminus(X18762),X18761)),X18760))
| ~ class_Groups_Oordered__ab__group__add(X18762) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).
fof(i_0_8659,plain,
! [X19884,X19885] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19884,X19885)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19885),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19885),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19884,X19885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19885),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__conj])])]) ).
fof(i_0_8660,plain,
! [X19886,X19887] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19887),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19886,X19887)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__sign])]) ).
cnf(i_0_8661,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate(X1,X2),X3)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3),
inference(split_conjunct,[status(thm)],[i_0_5737]) ).
fof(i_0_8662,plain,
! [X29211,X29212,X29213,X29214] : hAPP(c_Set_Ovimage(X29214,X29213,X29212),hAPP(c_Set_OCollect(X29213),X29211)) = hAPP(c_Set_OCollect(X29214),hAPP(hAPP(c_COMBB(X29213,tc_HOL_Obool,X29214),X29211),X29212)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(i_0_8663,plain,
! [X22004,X22005,X22006,X22007] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22007,X22006),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22005),X22004)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22007),X22006) = X22005 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__eq])]) ).
fof(i_0_8664,plain,
! [X27902,X27903,X27904,X27905] :
( ~ c_Fun_Oinj__on(X27905,X27904,X27903,X27902)
| hAPP(c_Finite__Set_Ocard(X27904),hAPP(c_Set_Oimage(X27905,X27904,X27903),X27902)) = hAPP(c_Finite__Set_Ocard(X27905),X27902) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).
fof(i_0_8665,plain,
! [X33387,X33388,X33389,X33390] : hAPP(hAPP(c_List_Otake(X33390),X33389),hAPP(hAPP(c_List_Odrop(X33390),X33388),X33387)) = hAPP(hAPP(c_List_Odrop(X33390),X33388),hAPP(hAPP(c_List_Otake(X33390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33389),X33388)),X33387)),
inference(variable_rename,[status(thm)],[fact_take__drop]) ).
fof(i_0_8666,plain,
! [X34030,X34031,X34032,X34033,X34034] :
( ~ class_Orderings_Olinorder(X34034)
| ~ c_List_Olinorder__class_Osorted(X34034,hAPP(hAPP(c_List_Omap(X34033,X34034),X34032),X34031))
| c_List_Olinorder__class_Osorted(X34034,hAPP(hAPP(c_List_Omap(X34033,X34034),X34032),hAPP(c_List_Ofilter(X34033,X34030),X34031))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__filter])]) ).
fof(i_0_8667,plain,
! [X20591,X20592,X20593] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20593,X20592) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20591,X20592)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20591),X20593))
| X20593 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20591),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20592),esk70_3(X20591,X20592,X20593))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__eq__lemma])])]) ).
fof(i_0_8668,plain,
! [X19339,X19340] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19340),c_Groups_Ozero__class_Ozero(X19340)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19340),X19339),X19339)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19340),c_Groups_Ozero__class_Ozero(X19340)),X19339))
| ~ class_Groups_Olinordered__ab__group__add(X19340) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19340),c_Groups_Ozero__class_Ozero(X19340)),X19339))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19340),c_Groups_Ozero__class_Ozero(X19340)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19340),X19339),X19339)))
| ~ class_Groups_Olinordered__ab__group__add(X19340) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add])])]) ).
fof(i_0_8669,plain,
! [X18329,X18330] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18330),c_Groups_Ozero__class_Ozero(X18330)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18330),X18329),X18329)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18330),c_Groups_Ozero__class_Ozero(X18330)),X18329))
| ~ class_Groups_Olinordered__ab__group__add(X18330) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18330),c_Groups_Ozero__class_Ozero(X18330)),X18329))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18330),c_Groups_Ozero__class_Ozero(X18330)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18330),X18329),X18329)))
| ~ class_Groups_Olinordered__ab__group__add(X18330) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add])])]) ).
fof(i_0_8670,plain,
! [X18344,X18345] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18345),X18344)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18345))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18344)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18345))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18345),X18344))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18344))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18345),X18344))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_8671,plain,
! [X25704,X25705,X25706] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X25706),tc_HOL_Obool)),X25705),X25704))
| c_Hoare__Mirabelle_Ohoare__derivs(X25706,X25704,X25705) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_asm])]) ).
fof(i_0_8672,plain,
! [X20265,X20266,X20267,X20268,X20269,X20270] :
( ~ class_Divides_Oring__div(X20270)
| c_Divides_Odiv__class_Omod(X20270,X20269,X20268) != c_Divides_Odiv__class_Omod(X20270,X20267,X20268)
| c_Divides_Odiv__class_Omod(X20270,X20266,X20268) != c_Divides_Odiv__class_Omod(X20270,X20265,X20268)
| c_Divides_Odiv__class_Omod(X20270,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20270),X20269),X20266),X20268) = c_Divides_Odiv__class_Omod(X20270,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20270),X20267),X20265),X20268) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__cong])]) ).
fof(i_0_8673,plain,
! [X19797,X19798,X19799,X19800,X19801,X19802] :
( ~ class_Divides_Osemiring__div(X19802)
| c_Divides_Odiv__class_Omod(X19802,X19801,X19800) != c_Divides_Odiv__class_Omod(X19802,X19799,X19800)
| c_Divides_Odiv__class_Omod(X19802,X19798,X19800) != c_Divides_Odiv__class_Omod(X19802,X19797,X19800)
| c_Divides_Odiv__class_Omod(X19802,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19802),X19801),X19798),X19800) = c_Divides_Odiv__class_Omod(X19802,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19802),X19799),X19797),X19800) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__cong])]) ).
fof(i_0_8674,plain,
! [X19765,X19766,X19767,X19768,X19769,X19770] :
( ~ class_Divides_Osemiring__div(X19770)
| c_Divides_Odiv__class_Omod(X19770,X19769,X19768) != c_Divides_Odiv__class_Omod(X19770,X19767,X19768)
| c_Divides_Odiv__class_Omod(X19770,X19766,X19768) != c_Divides_Odiv__class_Omod(X19770,X19765,X19768)
| c_Divides_Odiv__class_Omod(X19770,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19770),X19769),X19766),X19768) = c_Divides_Odiv__class_Omod(X19770,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19770),X19767),X19765),X19768) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__cong])]) ).
fof(i_0_8675,plain,
! [X23148,X23149,X23150,X23151] :
( ~ class_Divides_Osemiring__div(X23151)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23151),X23150),X23149))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23151),X23150),X23148))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23151),X23150),c_Divides_Odiv__class_Omod(X23151,X23149,X23148))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod])]) ).
fof(i_0_8676,plain,
! [X21772,X21773,X21774,X21775] :
( ~ class_Fields_Ofield(X21775)
| X21774 = c_Groups_Ozero__class_Ozero(X21775)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21773),X21772))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21775),X21774),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21772),X21773)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21775),hAPP(hAPP(c_Power_Opower__class_Opower(X21775),X21774),X21772)),hAPP(hAPP(c_Power_Opower__class_Opower(X21775),X21774),X21773)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__diff])]) ).
fof(i_0_8677,plain,
! [X25329,X25330,X25331] :
( hBOOL(hAPP(hAPP(c_member(X25331),X25330),X25329))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25331,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25331),X25330),X25329)),hAPP(hAPP(c_Set_Oinsert(X25331),X25330),c_Orderings_Obot__class_Obot(tc_fun(X25331,tc_HOL_Obool)))) = X25329 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5738])]) ).
fof(i_0_8678,plain,
! [X26184,X26185,X26186,X26187,X26188] :
( ~ class_Groups_Ocomm__monoid__mult(X26188)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26187),X26186))
| hBOOL(hAPP(hAPP(c_member(X26187),X26185),X26186))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26187,X26188),X26184),hAPP(hAPP(c_Set_Oinsert(X26187),X26185),X26186)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26188),hAPP(X26184,X26185)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26187,X26188),X26184),X26186)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5739])]) ).
fof(i_0_8679,plain,
! [X26179,X26180,X26181,X26182,X26183] :
( ~ class_Groups_Ocomm__monoid__mult(X26183)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26182),X26181))
| hBOOL(hAPP(hAPP(c_member(X26182),X26180),X26181))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26182,X26183),X26179),hAPP(hAPP(c_Set_Oinsert(X26182),X26180),X26181)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26183),hAPP(X26179,X26180)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26182,X26183),X26179),X26181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5740])]) ).
fof(i_0_8680,plain,
! [X25358,X25359,X25360,X25361,X25362] :
( ~ class_Groups_Ocomm__monoid__add(X25362)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25361),X25360))
| hBOOL(hAPP(hAPP(c_member(X25361),X25359),X25360))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25361,X25362),X25358),hAPP(hAPP(c_Set_Oinsert(X25361),X25359),X25360)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25362),hAPP(X25358,X25359)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25361,X25362),X25358),X25360)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5741])]) ).
fof(i_0_8681,plain,
! [X25353,X25354,X25355,X25356,X25357] :
( ~ class_Groups_Ocomm__monoid__add(X25357)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25356),X25355))
| hBOOL(hAPP(hAPP(c_member(X25356),X25354),X25355))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25356,X25357),X25353),hAPP(hAPP(c_Set_Oinsert(X25356),X25354),X25355)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25357),hAPP(X25353,X25354)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25356,X25357),X25353),X25355)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5742])]) ).
fof(i_0_8682,plain,
! [X22189,X22190,X22191] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22191),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22190)),X22189))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22191,X22190),hAPP(c_Divides_OnegateSnd,X22189))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__neg])]) ).
fof(i_0_8683,plain,
! [X17919,X17920,X17921,X17922] :
( ~ c_Natural_Oevaln(X17922,X17921,X17920,X17919)
| c_Natural_Oevaln(X17922,X17921,hAPP(c_Nat_OSuc,X17920),X17919) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__Suc])]) ).
fof(i_0_8684,plain,
! [X25255,X25256,X25257,X25258] :
( ~ hBOOL(hAPP(hAPP(c_member(X25258),X25257),X25256))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25258,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25258),X25257),X25255)),X25256) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25258,tc_HOL_Obool)),X25255),X25256) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff1])]) ).
fof(i_0_8685,plain,
! [X28482,X28483,X28484] : c_Map_Odom(X28484,X28483,hAPP(hAPP(c_COMBB(X28483,tc_Option_Ooption(X28483),X28484),c_Option_Ooption_OSome(X28483)),X28482)) = c_Orderings_Otop__class_Otop(tc_fun(X28484,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_dom__const]) ).
fof(i_0_8686,plain,
! [X20329,X20330,X20331] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20331),X20330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20331),X20329))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20330),X20331)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20329),X20331)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20330),X20329) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).
fof(i_0_8687,plain,
! [X23538,X23539,X23540,X23542,X23543,X23544] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk101_2(X23538,X23539)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23539)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23540),X23539))
| ~ hBOOL(hAPP(X23538,X23540)) )
& ( hBOOL(hAPP(X23538,esk101_2(X23538,X23539)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23540),X23539))
| ~ hBOOL(hAPP(X23538,X23540)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk102_2(X23542,X23543)),X23543))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23544),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23543)))
| ~ hBOOL(hAPP(X23542,X23544)) )
& ( hBOOL(hAPP(X23542,esk102_2(X23542,X23543)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23544),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23543)))
| ~ hBOOL(hAPP(X23542,X23544)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__nat__less__eq])])])])])]) ).
fof(i_0_8688,plain,
! [X20290,X20291,X20292] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20292)),X20291)),hAPP(c_Nat_OSuc,X20290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20292),X20291)),X20290),
inference(variable_rename,[status(thm)],[fact_Suc__diff__diff]) ).
fof(i_0_8689,plain,
! [X20958,X20959,X20960,X20961] :
( ~ class_Rings_Olinordered__semidom(X20961)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20961),X20960),hAPP(c_Nat_OSuc,X20959)) != hAPP(hAPP(c_Power_Opower__class_Opower(X20961),X20958),hAPP(c_Nat_OSuc,X20959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20961),c_Groups_Ozero__class_Ozero(X20961)),X20960))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20961),c_Groups_Ozero__class_Ozero(X20961)),X20958))
| X20960 = X20958 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__base])]) ).
cnf(i_0_8690,plain,
hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X1),c_List_Oupt(X2,X3)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),X3),
inference(split_conjunct,[status(thm)],[i_0_5743]) ).
fof(i_0_8691,plain,
! [X19640,X19641] :
( ( X19641 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19641)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19640)))) )
& ( X19640 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19641)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19640)))) )
& ( X19641 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19640 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19641)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19640)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__zle__neg])])]) ).
fof(i_0_8692,plain,
! [X29673] :
( ~ class_Orderings_Owellorder(X29673)
| c_Wellfounded_Owf(X29673,hAPP(c_Set_OCollect(tc_prod(X29673,X29673)),hAPP(c_Product__Type_Oprod_Oprod__case(X29673,X29673,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X29673)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf])]) ).
fof(i_0_8693,plain,
! [X33910,X33911,X33912,X33913,X33914,X33915,X33916] :
( ( hAPP(c_List_Ofilter(X33912,X33911),X33910) != c_List_Olist_ONil(X33912)
| ~ hBOOL(hAPP(hAPP(c_member(X33912),X33913),hAPP(c_List_Oset(X33912),X33910)))
| ~ hBOOL(hAPP(X33911,X33913)) )
& ( hBOOL(hAPP(hAPP(c_member(X33916),esk480_3(X33914,X33915,X33916)),hAPP(c_List_Oset(X33916),X33914)))
| hAPP(c_List_Ofilter(X33916,X33915),X33914) = c_List_Olist_ONil(X33916) )
& ( hBOOL(hAPP(X33915,esk480_3(X33914,X33915,X33916)))
| hAPP(c_List_Ofilter(X33916,X33915),X33914) = c_List_Olist_ONil(X33916) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5744])])])])])]) ).
fof(i_0_8694,plain,
! [X23222,X23223,X23224,X23225] :
( ~ class_Rings_Ocomm__ring__1(X23225)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23225),X23224),X23223))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23225),X23224),X23222))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23225),X23224),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23225),X23223),X23222))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff])]) ).
fof(i_0_8695,plain,
! [X23061,X23062,X23063,X23064] :
( ~ class_Rings_Ocomm__semiring__1(X23064)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23064),X23063),X23062))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23064),X23063),X23061))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23064),X23063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23064),X23062),X23061))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__add])]) ).
fof(i_0_8696,plain,
! [X27029,X27030,X27031,X27032] :
( ~ class_Lattices_Osemilattice__inf(X27032)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27032),X27031),X27030))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27032),X27031),X27029))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27032),X27031),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27032),X27030),X27029))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__greatest])]) ).
fof(i_0_8697,plain,
! [X27025,X27026,X27027,X27028] :
( ~ class_Lattices_Osemilattice__inf(X27028)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27028),X27027),X27026))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27028),X27027),X27025))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27028),X27027),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27028),X27026),X27025))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI])]) ).
fof(i_0_8698,plain,
! [X27007,X27008,X27009,X27010] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27010),X27009),X27008))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27010),X27009),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27010),X27008),X27007)))
| ~ class_Lattices_Osemilattice__inf(X27010) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27010),X27009),X27007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27010),X27009),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27010),X27008),X27007)))
| ~ class_Lattices_Osemilattice__inf(X27010) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27010),X27009),X27008))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27010),X27009),X27007))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27010),X27009),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27010),X27008),X27007)))
| ~ class_Lattices_Osemilattice__inf(X27010) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__inf__iff])])]) ).
fof(i_0_8699,plain,
! [X22292,X22293,X22294,X22295] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),X22294),X22293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),X22294),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22295),X22293),X22292)))
| ~ class_Orderings_Olinorder(X22295) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),X22294),X22292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),X22294),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22295),X22293),X22292)))
| ~ class_Orderings_Olinorder(X22295) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),X22294),X22293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),X22294),X22292))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),X22294),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22295),X22293),X22292)))
| ~ class_Orderings_Olinorder(X22295) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff])])]) ).
fof(i_0_8700,plain,
! [X22274,X22275,X22276,X22277] :
( ~ class_Orderings_Olinorder(X22277)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22277),X22276),X22275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22277),X22276),X22274))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22277),X22276),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22277),X22275),X22274))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI])]) ).
fof(i_0_8701,plain,
! [X22270,X22271,X22272,X22273] :
( ~ class_Orderings_Olinorder(X22273)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22273),X22272),X22271))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22273),X22272),X22270))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22273),X22272),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22273),X22271),X22270))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__greatest])]) ).
fof(i_0_8702,plain,
! [X22349,X22350,X22351,X22352] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22352),X22351),X22350))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22352),X22351),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22352),X22350),X22349)))
| ~ class_Orderings_Olinorder(X22352) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22352),X22351),X22349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22352),X22351),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22352),X22350),X22349)))
| ~ class_Orderings_Olinorder(X22352) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22352),X22351),X22350))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22352),X22351),X22349))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22352),X22351),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22352),X22350),X22349)))
| ~ class_Orderings_Olinorder(X22352) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj])])]) ).
fof(i_0_8703,plain,
! [X18934,X18935] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18935)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18934)))),
inference(variable_rename,[status(thm)],[i_0_5745]) ).
fof(i_0_8704,plain,
! [X19670,X19671,X19672] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19672))
| X19672 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19672),X19670))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19671))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19670),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2])]) ).
fof(i_0_8705,plain,
! [X33878,X33879,X33880,X33881,X33882,X33883,X33884] :
( ( hAPP(c_List_Ofilter(X33880,X33879),X33878) != X33878
| ~ hBOOL(hAPP(hAPP(c_member(X33880),X33881),hAPP(c_List_Oset(X33880),X33878)))
| hBOOL(hAPP(X33879,X33881)) )
& ( hBOOL(hAPP(hAPP(c_member(X33884),esk479_3(X33882,X33883,X33884)),hAPP(c_List_Oset(X33884),X33882)))
| hAPP(c_List_Ofilter(X33884,X33883),X33882) = X33882 )
& ( ~ hBOOL(hAPP(X33883,esk479_3(X33882,X33883,X33884)))
| hAPP(c_List_Ofilter(X33884,X33883),X33882) = X33882 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__id__conv])])])])])]) ).
fof(i_0_8706,plain,
! [X19866,X19867] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19866))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19867,X19866))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_8707,plain,
! [X17383,X17384,X17385,X17386,X17387] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17387),X17386),X17385))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17384),X17385),X17383))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17387,X17384)),X17386),X17383)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OSemi])]) ).
fof(i_0_8708,plain,
! [X32855,X32856,X32857,X32858] : hAPP(hAPP(c_List_Onth(X32858),hAPP(hAPP(c_List_Oappend(X32858),X32857),X32856)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32858)),X32857)),X32855)) = hAPP(hAPP(c_List_Onth(X32858),X32856),X32855),
inference(variable_rename,[status(thm)],[fact_nth__append__length__plus]) ).
cnf(i_0_8709,plain,
hAPP(c_List_Oset(X1),hAPP(c_List_Orotate(X1,X2),X3)) = hAPP(c_List_Oset(X1),X3),
inference(split_conjunct,[status(thm)],[i_0_5746]) ).
fof(i_0_8710,plain,
! [X32606,X32607,X32608,X32609,X32610,X32611] : hAPP(c_List_Olist_Olist__case(X32611,X32610,X32609,X32608),hAPP(hAPP(c_List_Olist_OCons(X32610),X32607),X32606)) = hAPP(hAPP(X32608,X32607),X32606),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J]) ).
fof(i_0_8711,plain,
! [X23860,X23861,X23862,X23863] :
( ~ hBOOL(hAPP(X23863,X23862))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23861,tc_HOL_Obool)),X23863),X23860),X23862)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I1])]) ).
fof(i_0_8712,plain,
! [X23838,X23839,X23840,X23841] :
( ( ~ hBOOL(hAPP(X23841,X23840))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23838,tc_HOL_Obool)),X23839),X23841),X23840)) )
& ( ~ hBOOL(hAPP(X23839,X23840))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23838,tc_HOL_Obool)),X23839),X23841),X23840)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5747])])]) ).
fof(i_0_8713,plain,
! [X23856,X23857,X23858,X23859] :
( ~ hBOOL(hAPP(X23859,X23858))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23857,tc_HOL_Obool)),X23856),X23859),X23858)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I2])]) ).
fof(i_0_8714,plain,
! [X20989,X20990,X20991] :
( ~ class_Rings_Olinordered__idom(X20991)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20991),c_Groups_Ozero__class_Ozero(X20991)),hAPP(hAPP(c_Power_Opower__class_Opower(X20991),hAPP(c_Groups_Oabs__class_Oabs(X20991),X20990)),X20989))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).
fof(i_0_8715,plain,
! [X20515,X20516,X20517] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20517),X20516))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20515),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20516),X20517))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20515),X20517)),hAPP(c_Nat_OSuc,X20516)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1])]) ).
fof(i_0_8716,plain,
! [X24638,X24639] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24639,tc_HOL_Obool)),X24638),c_Orderings_Obot__class_Obot(tc_fun(X24639,tc_HOL_Obool))))
| X24638 = c_Orderings_Obot__class_Obot(tc_fun(X24639,tc_HOL_Obool)) )
& ( X24638 != c_Orderings_Obot__class_Obot(tc_fun(X24639,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24639,tc_HOL_Obool)),X24638),c_Orderings_Obot__class_Obot(tc_fun(X24639,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])]) ).
fof(i_0_8717,plain,
! [X29877,X29878] :
( ~ c_Wellfounded_OwfP(X29878,X29877)
| c_Wellfounded_Oacyclic(X29878,hAPP(c_Set_OCollect(tc_prod(X29878,X29878)),hAPP(c_Product__Type_Oprod_Oprod__case(X29878,X29878,tc_HOL_Obool),X29877))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__acyclicP])]) ).
fof(i_0_8718,plain,
! [X23295,X23296] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23296)),X23295))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23296),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23295)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23296),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23295))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23296)),X23295)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__dvd__iff])]) ).
cnf(i_0_8719,plain,
( c_Map_Omap__comp(X3,X6,X7,X5,X1,X2) = c_Option_Ooption_ONone(X6)
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X4) != c_Option_Ooption_ONone(X6) ),
inference(split_conjunct,[status(thm)],[i_0_5368]) ).
fof(i_0_8720,plain,
! [X29521,X29522,X29523,X29524] : hAPP(hAPP(c_Relation_Orel__comp(X29524,X29523,X29522),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29524,X29523),tc_HOL_Obool))),X29521) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29524,X29522),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_rel__comp__empty1]) ).
fof(i_0_8721,plain,
! [X20195,X20196] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20195,X20196) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20195)),X20196) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20195),X20196))
| X20196 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20195,X20196) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20195)),X20196) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20195),X20196))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X20196 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zminus1__eq__if])])]) ).
fof(i_0_8722,plain,
! [X33941,X33942,X33943,X33944,X33945,X33946,X33947] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X33945),X33946),hAPP(c_List_Oset(X33945),X33942)))
| hBOOL(hAPP(X33944,X33946))
| c_List_Opartition(X33945,X33944,X33943) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33945),tc_List_Olist(X33945)),X33942),X33941) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X33945),X33947),hAPP(c_List_Oset(X33945),X33941)))
| ~ hBOOL(hAPP(X33944,X33947))
| c_List_Opartition(X33945,X33944,X33943) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33945),tc_List_Olist(X33945)),X33942),X33941) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5748])])])]) ).
fof(i_0_8723,plain,
! [X19734,X19735,X19736] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19736),hAPP(c_Groups_Ouminus__class_Ouminus(X19736),X19735)),hAPP(c_Groups_Ouminus__class_Ouminus(X19736),X19734)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19736),X19734),X19735))
| ~ class_Lattices_Oboolean__algebra(X19736) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19736),X19734),X19735))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19736),hAPP(c_Groups_Ouminus__class_Ouminus(X19736),X19735)),hAPP(c_Groups_Ouminus__class_Ouminus(X19736),X19734)))
| ~ class_Lattices_Oboolean__algebra(X19736) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).
fof(i_0_8724,plain,
! [X19230,X19231,X19232] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19232),hAPP(c_Groups_Ouminus__class_Ouminus(X19232),X19231)),hAPP(c_Groups_Ouminus__class_Ouminus(X19232),X19230)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19232),X19230),X19231))
| ~ class_Groups_Oordered__ab__group__add(X19232) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19232),X19230),X19231))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19232),hAPP(c_Groups_Ouminus__class_Ouminus(X19232),X19231)),hAPP(c_Groups_Ouminus__class_Ouminus(X19232),X19230)))
| ~ class_Groups_Oordered__ab__group__add(X19232) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).
fof(i_0_8725,plain,
! [X18763,X18764,X18765] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18765),hAPP(c_Groups_Ouminus__class_Ouminus(X18765),X18764)),hAPP(c_Groups_Ouminus__class_Ouminus(X18765),X18763)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18765),X18763),X18764))
| ~ class_Groups_Oordered__ab__group__add(X18765) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18765),X18763),X18764))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18765),hAPP(c_Groups_Ouminus__class_Ouminus(X18765),X18764)),hAPP(c_Groups_Ouminus__class_Ouminus(X18765),X18763)))
| ~ class_Groups_Oordered__ab__group__add(X18765) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).
fof(i_0_8726,plain,
! [X23546,X23547,X23549,X23550,X23551,X23553] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk103_2(X23546,X23547)),X23547))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23549),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23547)))
| hBOOL(hAPP(X23546,X23549)) )
& ( ~ hBOOL(hAPP(X23546,esk103_2(X23546,X23547)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23549),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23547)))
| hBOOL(hAPP(X23546,X23549)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk104_2(X23550,X23551)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23551)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23553),X23551))
| hBOOL(hAPP(X23550,X23553)) )
& ( ~ hBOOL(hAPP(X23550,esk104_2(X23550,X23551)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23553),X23551))
| hBOOL(hAPP(X23550,X23553)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__nat__less__eq])])])])])]) ).
fof(i_0_8727,plain,
! [X20974,X20975,X20976] :
( ~ class_Rings_Olinordered__semidom(X20976)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20976),c_Groups_Oone__class_Oone(X20976)),X20975))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20976),c_Groups_Oone__class_Oone(X20976)),hAPP(hAPP(c_Power_Opower__class_Opower(X20976),X20975),hAPP(c_Nat_OSuc,X20974)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).
fof(i_0_8728,plain,
! [X19667,X19668,X19669] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19669))
| X19669 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19668),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19669),X19667))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19668),X19669))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19667)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).
cnf(i_0_8729,plain,
hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Otrancl(X1,X2)) = hAPP(c_Relation_ODomain(X1,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_5749]) ).
cnf(i_0_8730,plain,
hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Otrancl(X1,X2)) = hAPP(c_Relation_ORange(X1,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_5750]) ).
fof(i_0_8731,plain,
! [X21128,X21129] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21129)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21128)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21129),X21128))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21129),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21129),X21128))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21129)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21128))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21129),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21129)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21128))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5751])])]) ).
fof(i_0_8732,plain,
! [X20737,X20738,X20739] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20739),hAPP(c_Int_Onumber__class_Onumber__of(X20739),X20738)),hAPP(c_Int_Onumber__class_Onumber__of(X20739),X20737)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20738),X20737))
| ~ class_Int_Onumber__ring(X20739)
| ~ class_Rings_Olinordered__idom(X20739) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20738),X20737))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20739),hAPP(c_Int_Onumber__class_Onumber__of(X20739),X20738)),hAPP(c_Int_Onumber__class_Onumber__of(X20739),X20737)))
| ~ class_Int_Onumber__ring(X20739)
| ~ class_Rings_Olinordered__idom(X20739) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of])])]) ).
fof(i_0_8733,plain,
! [X20746,X20747,X20748] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20748),hAPP(c_Int_Onumber__class_Onumber__of(X20748),X20747)),hAPP(c_Int_Onumber__class_Onumber__of(X20748),X20746)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20747),X20746))
| ~ class_Int_Onumber__ring(X20748)
| ~ class_Rings_Olinordered__idom(X20748) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20747),X20746))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20748),hAPP(c_Int_Onumber__class_Onumber__of(X20748),X20747)),hAPP(c_Int_Onumber__class_Onumber__of(X20748),X20746)))
| ~ class_Int_Onumber__ring(X20748)
| ~ class_Rings_Olinordered__idom(X20748) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])]) ).
fof(i_0_8734,plain,
! [X23364,X23365] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23364))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23365),X23364))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23364),X23365))
| X23365 = X23364 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__nonneg])]) ).
fof(i_0_8735,plain,
! [X23069,X23070,X23071] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23071),X23069))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23070),X23069))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23069),X23070))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23071),X23070))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23070),X23071)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23069),X23071))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23070),X23069))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23069),X23070))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23071),X23070))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23070),X23071)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5752])])]) ).
fof(i_0_8736,plain,
! [X32774,X32775,X32776,X32777] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32777)),X32776)),X32775))
| hAPP(hAPP(c_List_Olist__update(X32777,X32776),X32775),X32774) = X32776 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__beyond])]) ).
fof(i_0_8737,plain,
! [X19003] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19003),X19003)))),
inference(variable_rename,[status(thm)],[fact_le__cube]) ).
fof(i_0_8738,plain,
! [X33808,X33809,X33810] :
( ~ hBOOL(hAPP(hAPP(c_member(X33810),X33809),hAPP(c_List_Oset(X33810),c_List_Obutlast(X33810,X33808))))
| hBOOL(hAPP(hAPP(c_member(X33810),X33809),hAPP(c_List_Oset(X33810),X33808))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlastD])]) ).
fof(i_0_8739,plain,
! [X25237,X25238,X25239,X25240,X25241] :
( ~ hBOOL(hAPP(hAPP(c_member(X25241),X25240),X25239))
| hAPP(hAPP(c_Set_Oinsert(X25238),hAPP(X25237,X25240)),hAPP(c_Set_Oimage(X25241,X25238,X25237),X25239)) = hAPP(c_Set_Oimage(X25241,X25238,X25237),X25239) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).
cnf(i_0_8740,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_5753]) ).
cnf(i_0_8741,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_5754]) ).
fof(i_0_8742,plain,
! [X22194,X22195,X22196] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22196,X22196),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22195),X22194)))
| X22196 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X22195 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient])]) ).
fof(i_0_8743,plain,
! [X22174,X22175,X22176] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22176,X22176),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22175),X22174)))
| X22176 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X22174 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__remainder])]) ).
fof(i_0_8744,plain,
! [X30753,X30754,X30755,X30756,X30757] :
( ~ c_Finite__Set_Ofolding__one(X30757,X30756,X30755)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30757),X30754))
| hBOOL(hAPP(hAPP(c_member(X30757),X30753),X30754))
| hAPP(X30755,hAPP(hAPP(c_Set_Oinsert(X30757),X30753),X30754)) = hAPP(hAPP(c_Finite__Set_Ofold(X30757,X30757,X30756),X30753),X30754) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5755])]) ).
fof(i_0_8745,plain,
! [X30476,X30477,X30478] :
( ~ c_Wellfounded_Owf(X30478,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30478,X30478),tc_HOL_Obool),X30477),X30476))
| c_Wellfounded_Owf(X30478,X30476) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__exp])]) ).
fof(i_0_8746,plain,
! [X19103,X19104,X19105] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19105),hAPP(c_Int_Oring__1__class_Oof__int(X19105),X19104)),hAPP(c_Int_Oring__1__class_Oof__int(X19105),X19103)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19104),X19103))
| ~ class_Rings_Olinordered__idom(X19105) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19104),X19103))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19105),hAPP(c_Int_Oring__1__class_Oof__int(X19105),X19104)),hAPP(c_Int_Oring__1__class_Oof__int(X19105),X19103)))
| ~ class_Rings_Olinordered__idom(X19105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__iff])])]) ).
fof(i_0_8747,plain,
! [X19096,X19097,X19098] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19098),X19097)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19098),X19096)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19097),X19096))
| ~ class_Rings_Olinordered__semidom(X19098) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19097),X19096))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19098),X19097)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19098),X19096)))
| ~ class_Rings_Olinordered__semidom(X19098) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff])])]) ).
fof(i_0_8748,plain,
! [X18947,X18948,X18949] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18949),hAPP(c_Int_Oring__1__class_Oof__int(X18949),X18948)),hAPP(c_Int_Oring__1__class_Oof__int(X18949),X18947)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18948),X18947))
| ~ class_Rings_Olinordered__idom(X18949) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18948),X18947))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18949),hAPP(c_Int_Oring__1__class_Oof__int(X18949),X18948)),hAPP(c_Int_Oring__1__class_Oof__int(X18949),X18947)))
| ~ class_Rings_Olinordered__idom(X18949) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__iff])])]) ).
fof(i_0_8749,plain,
! [X18498,X18499,X18500] :
( ~ class_Rings_Olinordered__semidom(X18500)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18500),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18500),X18499)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18500),X18498)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18499),X18498)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less])]) ).
fof(i_0_8750,plain,
! [X18492,X18493,X18494] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18494),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18494),X18493)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18494),X18492)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18493),X18492))
| ~ class_Rings_Olinordered__semidom(X18494) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18493),X18492))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18494),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18494),X18493)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18494),X18492)))
| ~ class_Rings_Olinordered__semidom(X18494) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff])])]) ).
fof(i_0_8751,plain,
! [X29950] :
( X29950 = hAPP(c_Int_OAbs__Integ,esk335_1(X29950))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk335_1(X29950)),c_Int_OInteg)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5756])])]) ).
cnf(i_0_8752,plain,
( c_List_Oupt(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Oupt(hAPP(c_Nat_OSuc,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5757]) ).
cnf(i_0_8753,plain,
( c_List_Oupt(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Oupt(hAPP(c_Nat_OSuc,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5758]) ).
fof(i_0_8754,plain,
! [X21569,X21570,X21571,X21572] :
( ~ class_Fields_Ofield(X21572)
| X21571 = c_Groups_Ozero__class_Ozero(X21572)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21572),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21572),X21570),X21571)),X21569) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21572),hAPP(hAPP(c_Power_Opower__class_Opower(X21572),X21570),X21569)),hAPP(hAPP(c_Power_Opower__class_Opower(X21572),X21571),X21569)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide])]) ).
fof(i_0_8755,plain,
! [X19638,X19639] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19639),X19638))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19639),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19638)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).
fof(i_0_8756,plain,
! [X27784,X27785,X27786] :
( ~ class_Lattices_Olattice(X27786)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27786),X27785))
| X27785 = c_Orderings_Obot__class_Obot(tc_fun(X27786,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27786),X27784))
| X27784 = c_Orderings_Obot__class_Obot(tc_fun(X27786,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X27786,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27786,tc_HOL_Obool)),X27785),X27784)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27786),c_Big__Operators_Olattice__class_OInf__fin(X27786,X27785)),c_Big__Operators_Olattice__class_OInf__fin(X27786,X27784)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem])]) ).
fof(i_0_8757,plain,
! [X25863,X25864,X25865] :
( ~ class_Orderings_Olinorder(X25865)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25865),X25864))
| X25864 = c_Orderings_Obot__class_Obot(tc_fun(X25865,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25865),X25863))
| X25863 = c_Orderings_Obot__class_Obot(tc_fun(X25865,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25865,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25865,tc_HOL_Obool)),X25864),X25863)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25865),c_Big__Operators_Olinorder__class_OMin(X25865,X25864)),c_Big__Operators_Olinorder__class_OMin(X25865,X25863)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__Un])]) ).
fof(i_0_8758,plain,
! [X25866,X25867,X25868] :
( ~ class_Orderings_Olinorder(X25868)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25868),X25867))
| X25867 = c_Orderings_Obot__class_Obot(tc_fun(X25868,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25868),X25866))
| X25866 = c_Orderings_Obot__class_Obot(tc_fun(X25868,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25868,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25868,tc_HOL_Obool)),X25867),X25866)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25868),c_Big__Operators_Olinorder__class_OMax(X25868,X25867)),c_Big__Operators_Olinorder__class_OMax(X25868,X25866)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__Un])]) ).
fof(i_0_8759,plain,
! [X25776,X25777,X25778] :
( ~ class_Lattices_Olattice(X25778)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25778),X25777))
| X25777 = c_Orderings_Obot__class_Obot(tc_fun(X25778,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25778),X25776))
| X25776 = c_Orderings_Obot__class_Obot(tc_fun(X25778,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25778,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25778,tc_HOL_Obool)),X25777),X25776)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25778),c_Big__Operators_Olattice__class_OSup__fin(X25778,X25777)),c_Big__Operators_Olattice__class_OSup__fin(X25778,X25776)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem])]) ).
fof(i_0_8760,plain,
! [X25278,X25279] :
( ( hAPP(c_Code__Numeral_Oof__nat,X25279) != hAPP(c_Code__Numeral_Oof__nat,X25278)
| X25279 = X25278
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25278),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25279),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) )
& ( X25279 != X25278
| hAPP(c_Code__Numeral_Oof__nat,X25279) = hAPP(c_Code__Numeral_Oof__nat,X25278)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25278),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25279),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oof__nat__inject])])]) ).
fof(i_0_8761,plain,
! [X19321,X19322] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19322)),hAPP(c_Int_Onat,X19321)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19322),X19321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19322)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19322),X19321))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19322)),hAPP(c_Int_Onat,X19321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19322)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19322)),hAPP(c_Int_Onat,X19321)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19322),X19321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19321)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19322),X19321))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19322)),hAPP(c_Int_Onat,X19321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19321)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__eq__zle])])]) ).
fof(i_0_8762,plain,
! [X19651,X19652] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19652)),hAPP(c_Int_Onat,X19651)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19652),X19651))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19652)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19652),X19651))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19652)),hAPP(c_Int_Onat,X19651)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19652)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless])])]) ).
fof(i_0_8763,plain,
! [X18955,X18956] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18955)),hAPP(c_Int_Onat,X18956)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18955),X18956))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18956)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18955),X18956))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18955)),hAPP(c_Int_Onat,X18956)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18956)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mono__iff])])]) ).
cnf(i_0_8764,plain,
( c_Map_Omap__comp(X3,X5,X6,X7,X1,X2) = hAPP(X7,X4)
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_5759]) ).
fof(i_0_8765,plain,
! [X30479,X30480,X30481,X30482] : hAPP(X30482,hAPP(hAPP(hAPP(c_Nat_Ocompow(X30481,X30481),X30480),X30482),X30479)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X30481,X30481),X30480),X30482),hAPP(X30482,X30479)),
inference(variable_rename,[status(thm)],[fact_funpow__swap1]) ).
fof(i_0_8766,plain,
! [X33886,X33887,X33888,X33889,X33890,X33891] :
( ~ class_Orderings_Olinorder(X33891)
| hBOOL(hAPP(X33890,X33889))
| hAPP(c_List_Ofilter(X33888,X33890),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X33888,X33891,X33887),X33889),X33886)) = hAPP(c_List_Ofilter(X33888,X33890),X33886) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5760])]) ).
fof(i_0_8767,plain,
! [X18803,X18804,X18805,X18806] :
( ~ class_Rings_Ocomm__semiring__1(X18806)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18806),X18805),X18804)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18806),X18803),X18804)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18806),X18805),X18803)),X18804) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).
fof(i_0_8768,plain,
! [X27114,X27115,X27116,X27117] :
( ~ class_Lattices_Odistrib__lattice(X27117)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27117),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27117),X27116),X27115)),X27114) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27117),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27117),X27116),X27114)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27117),X27115),X27114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2])]) ).
fof(i_0_8769,plain,
! [X27110,X27111,X27112,X27113] :
( ~ class_Lattices_Odistrib__lattice(X27113)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27113),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27113),X27112),X27111)),X27110) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27113),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27113),X27112),X27110)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27113),X27111),X27110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2])]) ).
fof(i_0_8770,plain,
! [X22558,X22559,X22560,X22561] :
( ~ class_Orderings_Olinorder(X22561)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22561),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22561),X22560),X22559)),X22558) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22561),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22561),X22560),X22558)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22561),X22559),X22558)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib2])]) ).
fof(i_0_8771,plain,
! [X22562,X22563,X22564,X22565] :
( ~ class_Orderings_Olinorder(X22565)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22565),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22565),X22564),X22563)),X22562) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22565),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22565),X22564),X22562)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22565),X22563),X22562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2])]) ).
fof(i_0_8772,plain,
! [X21446,X21447,X21448,X21449] :
( ~ class_Rings_Odivision__ring(X21449)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21449),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21449),X21448),X21447)),X21446) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21449),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21449),X21448),X21446)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21449),X21447),X21446)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib])]) ).
fof(i_0_8773,plain,
! [X21433,X21434,X21435,X21436] :
( ~ class_Rings_Odivision__ring(X21436)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21436),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21436),X21435),X21434)),X21433) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21436),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21436),X21435),X21433)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21436),X21434),X21433)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])]) ).
fof(i_0_8774,plain,
! [X21461,X21462,X21463,X21464] :
( ~ class_Fields_Ofield__inverse__zero(X21464)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21464),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21464),X21463),X21462)),X21461) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21464),hAPP(hAPP(c_Power_Opower__class_Opower(X21464),X21463),X21461)),hAPP(hAPP(c_Power_Opower__class_Opower(X21464),X21462),X21461)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])]) ).
fof(i_0_8775,plain,
! [X20895,X20896,X20897,X20898] :
( ~ class_Groups_Ocomm__monoid__mult(X20898)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20898),X20897),X20896)),X20895) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20898),hAPP(hAPP(c_Power_Opower__class_Opower(X20898),X20897),X20895)),hAPP(hAPP(c_Power_Opower__class_Opower(X20898),X20896),X20895)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).
fof(i_0_8776,plain,
! [X20639,X20640,X20641,X20642] :
( ~ class_Rings_Ocomm__semiring__1(X20642)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20642),X20641),X20640)),X20639) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20642),hAPP(hAPP(c_Power_Opower__class_Opower(X20642),X20641),X20639)),hAPP(hAPP(c_Power_Opower__class_Opower(X20642),X20640),X20639)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).
fof(i_0_8777,plain,
! [X22582,X22583,X22584,X22585] :
( ~ class_Groups_Oordered__ab__group__add(X22585)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22585),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22585),X22584),X22583)),X22582) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22585),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22585),X22584),X22582)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22585),X22583),X22582)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__diff__distrib__left])]) ).
fof(i_0_8778,plain,
! [X22357,X22358,X22359,X22360] :
( ~ class_Groups_Oordered__ab__group__add(X22360)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22360),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22360),X22359),X22358)),X22357) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22360),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22360),X22359),X22357)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22360),X22358),X22357)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left])]) ).
fof(i_0_8779,plain,
! [X18825,X18826,X18827,X18828] :
( ~ class_Rings_Ocomm__semiring(X18828)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18828),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18828),X18827),X18826)),X18825) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18828),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18828),X18827),X18825)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18828),X18826),X18825)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).
fof(i_0_8780,plain,
! [X18807,X18808,X18809,X18810] :
( ~ class_Rings_Ocomm__semiring__1(X18810)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18810),X18809),X18808)),X18807) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18810),X18809),X18807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18810),X18808),X18807)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
fof(i_0_8781,plain,
! [X22636,X22637,X22638,X22639] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22639)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22639),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22639),X22638),X22637)),X22636) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22639),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22639),X22638),X22636)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22639),X22637),X22636)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__add__distrib__left])]) ).
fof(i_0_8782,plain,
! [X22307,X22308,X22309,X22310] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22310)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22310),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22310),X22309),X22308)),X22307) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22310),X22309),X22307)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22310),X22308),X22307)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__add__distrib__left])]) ).
fof(i_0_8783,plain,
! [X32134,X32135,X32136,X32137,X32138] :
( ~ class_Orderings_Olinorder(X32138)
| hAPP(c_List_Oset(X32137),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32137,X32138,X32136),X32135),X32134)) = hAPP(hAPP(c_Set_Oinsert(X32137),X32135),hAPP(c_List_Oset(X32137),X32134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort])]) ).
fof(i_0_8784,plain,
! [X20013,X20014] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20014))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20013))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20014),X20013))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_8785,plain,
! [X19518,X19519] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19518))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19519),X19518))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_8786,plain,
! [X19482,X19483] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19482))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19483),X19482))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_8787,plain,
! [X19457,X19458] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19458),X19457))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19457))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19458),X19457))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19457))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19458),X19457))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).
fof(i_0_8788,plain,
! [X23430,X23431,X23432,X23433,X23434] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23434),X23431),X23433) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23434),X23430),X23432)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23434),X23431),X23432) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23434),X23433),X23430)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23434),X23432),X23430))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23434),X23433),X23431))
| X23432 = c_Groups_Ozero__class_Ozero(X23434)
| X23433 = c_Groups_Ozero__class_Ozero(X23434)
| ~ class_Divides_Osemiring__div(X23434) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23434),X23431),X23432) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23434),X23433),X23430)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23434),X23431),X23433) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23434),X23430),X23432)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23434),X23432),X23430))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23434),X23433),X23431))
| X23432 = c_Groups_Ozero__class_Ozero(X23434)
| X23433 = c_Groups_Ozero__class_Ozero(X23434)
| ~ class_Divides_Osemiring__div(X23434) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__div__eq__mult])])]) ).
fof(i_0_8789,plain,
! [X30777,X30778,X30779] :
( ~ class_Orderings_Olinorder(X30779)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30779),X30778))
| hBOOL(hAPP(hAPP(c_member(X30779),X30777),X30778))
| c_Big__Operators_Olattice_OInf__fin(X30779,c_Orderings_Oord__class_Omin(X30779),hAPP(hAPP(c_Set_Oinsert(X30779),X30777),X30778)) = hAPP(hAPP(c_Finite__Set_Ofold(X30779,X30779,c_Orderings_Oord__class_Omin(X30779)),X30777),X30778) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5761])]) ).
fof(i_0_8790,plain,
! [X30650,X30651,X30652] :
( ~ class_Orderings_Olinorder(X30652)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30652),X30651))
| hBOOL(hAPP(hAPP(c_member(X30652),X30650),X30651))
| c_Big__Operators_Olattice_OSup__fin(X30652,c_Orderings_Oord__class_Omax(X30652),hAPP(hAPP(c_Set_Oinsert(X30652),X30650),X30651)) = hAPP(hAPP(c_Finite__Set_Ofold(X30652,X30652,c_Orderings_Oord__class_Omax(X30652)),X30650),X30651) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5762])]) ).
fof(i_0_8791,plain,
! [X24869,X24870] :
( ~ class_Orderings_Olinorder(X24870)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24870,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24870),X24869),c_Orderings_Obot__class_Obot(tc_fun(X24870,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24870),X24869)) = hAPP(c_SetInterval_Oord__class_OatLeast(X24870),X24869) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J])]) ).
fof(i_0_8792,plain,
! [X30355,X30356,X30357] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30357,X30356)),hAPP(c_Relation_Oconverse(X30356,X30357),X30355)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30356,X30357)),X30355)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30356,X30357)),X30355))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30357,X30356)),hAPP(c_Relation_Oconverse(X30356,X30357),X30355))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__converse])]) ).
fof(i_0_8793,plain,
! [X24597] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24597),c_Orderings_Otop__class_Otop(tc_fun(X24597,tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24597),c_Orderings_Otop__class_Otop(tc_fun(X24597,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).
fof(i_0_8794,plain,
! [X32016,X32017,X32018] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32018),X32017))
| hAPP(c_List_Oset(X32018),c_List_Oremove1(X32018,X32016,X32017)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32018,tc_HOL_Obool)),hAPP(c_List_Oset(X32018),X32017)),hAPP(hAPP(c_Set_Oinsert(X32018),X32016),c_Orderings_Obot__class_Obot(tc_fun(X32018,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__remove1__eq])]) ).
fof(i_0_8795,plain,
! [X31344,X31345,X31346] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31346,tc_HOL_Obool)),X31345),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31346,tc_HOL_Obool),X31344)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31346,tc_HOL_Obool),tc_fun(X31346,tc_HOL_Obool)),X31344),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31346,tc_HOL_Obool)),X31345)),
inference(variable_rename,[status(thm)],[fact_Int__Union]) ).
fof(i_0_8796,plain,
! [X31262,X31263,X31264] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31264,tc_HOL_Obool)),X31263),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31264,tc_HOL_Obool),X31262)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X31264,tc_HOL_Obool),tc_fun(X31264,tc_HOL_Obool)),X31262),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31264,tc_HOL_Obool)),X31263)),
inference(variable_rename,[status(thm)],[fact_Un__Inter]) ).
fof(i_0_8797,plain,
! [X32149,X32150,X32151,X32152,X32153] :
( ~ class_Orderings_Olinorder(X32153)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32152)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32152,X32153,X32151),X32150),X32149)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32152)),X32149)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__insort])]) ).
fof(i_0_8798,plain,
! [X23402,X23403] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23403))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23403),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23402)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23403)),X23402)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23403))
| X23402 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23403)),X23402)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23403))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23403))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23403)),X23402)) )
& ( X23402 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23403))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23403)),X23402)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23403))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23403),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23402)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23403)),X23402)) )
& ( X23402 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23403),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23402)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23403)),X23402)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5763])])]) ).
fof(i_0_8799,plain,
! [X18982,X18983] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18983)),X18982))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18983),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18982)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18983)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18983),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18982)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18983)),X18982))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18983)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__iff])])]) ).
cnf(i_0_8800,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_5695]) ).
fof(i_0_8801,plain,
! [X24667,X24668] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24668,tc_HOL_Obool)),X24667),c_Orderings_Obot__class_Obot(tc_fun(X24668,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_5764]) ).
fof(i_0_8802,plain,
! [X26266,X26267,X26268,X26269,X26270] :
( hBOOL(hAPP(hAPP(c_member(X26270),X26269),X26268))
| hAPP(c_Map_Orestrict__map(X26270,X26267,X26266,X26268),X26269) = c_Option_Ooption_ONone(X26267) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5765])]) ).
fof(i_0_8803,plain,
! [X32174,X32175,X32176] :
( ~ class_Orderings_Olinorder(X32176)
| c_List_Oremove1(X32176,X32175,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32176,X32176,c_COMBI(X32176)),X32175),X32174)) = X32174 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1__insort])]) ).
fof(i_0_8804,plain,
! [X29929,X29930,X29931,X29932,X29933,X29934,X29935] :
( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X29931,X29930),X29929))
| ~ hBOOL(hAPP(hAPP(c_member(X29931),X29932),X29929))
| hBOOL(hAPP(X29930,X29932)) )
& ( hBOOL(hAPP(hAPP(c_member(X29935),esk333_3(X29933,X29934,X29935)),X29933))
| hBOOL(hAPP(c_Predicate_OPowp(X29935,X29934),X29933)) )
& ( ~ hBOOL(hAPP(X29934,esk333_3(X29933,X29934,X29935)))
| hBOOL(hAPP(c_Predicate_OPowp(X29935,X29934),X29933)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__def])])])])])]) ).
fof(i_0_8805,plain,
! [X26281,X26282,X26283,X26284] : hAPP(c_Map_Orestrict__map(X26284,X26283,X26282,c_Orderings_Obot__class_Obot(tc_fun(X26284,tc_HOL_Obool))),X26281) = c_Option_Ooption_ONone(X26283),
inference(variable_rename,[status(thm)],[fact_restrict__map__to__empty]) ).
fof(i_0_8806,plain,
! [X23023,X23024,X23025,X23026] : hAPP(c_Product__Type_Oprod_Oprod__case(X23026,X23025,X23024),c_Product__Type_Ocurry(X23026,X23025,X23024,X23023)) = X23023,
inference(variable_rename,[status(thm)],[fact_split__curry]) ).
fof(i_0_8807,plain,
! [X21062,X21063,X21064] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X21064),X21063) != hAPP(c_Int_Onumber__class_Onumber__of(X21064),X21062)
| c_Int_Oiszero(X21064,hAPP(c_Int_Onumber__class_Onumber__of(X21064),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21063),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21062))))
| ~ class_Int_Onumber__ring(X21064) )
& ( ~ c_Int_Oiszero(X21064,hAPP(c_Int_Onumber__class_Onumber__of(X21064),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21063),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21062))))
| hAPP(c_Int_Onumber__class_Onumber__of(X21064),X21063) = hAPP(c_Int_Onumber__class_Onumber__of(X21064),X21062)
| ~ class_Int_Onumber__ring(X21064) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq])])]) ).
fof(i_0_8808,plain,
! [X33318,X33319,X33320,X33321] :
( ( X33320 = hAPP(hAPP(c_List_Otake(X33321),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33321)),X33320)),X33318)
| hAPP(hAPP(c_List_Oappend(X33321),X33320),X33319) != X33318 )
& ( X33319 = hAPP(hAPP(c_List_Odrop(X33321),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33321)),X33320)),X33318)
| hAPP(hAPP(c_List_Oappend(X33321),X33320),X33319) != X33318 )
& ( X33320 != hAPP(hAPP(c_List_Otake(X33321),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33321)),X33320)),X33318)
| X33319 != hAPP(hAPP(c_List_Odrop(X33321),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33321)),X33320)),X33318)
| hAPP(hAPP(c_List_Oappend(X33321),X33320),X33319) = X33318 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj])])]) ).
fof(i_0_8809,plain,
! [X30762,X30763,X30764] :
( ~ class_Groups_Oab__semigroup__mult(X30764)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30764),X30763))
| hBOOL(hAPP(hAPP(c_member(X30764),X30762),X30763))
| hAPP(c_Finite__Set_Ofold1(X30764,c_Groups_Otimes__class_Otimes(X30764)),hAPP(hAPP(c_Set_Oinsert(X30764),X30762),X30763)) = hAPP(hAPP(c_Finite__Set_Ofold(X30764,X30764,c_Groups_Otimes__class_Otimes(X30764)),X30762),X30763) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5766])]) ).
cnf(i_0_8810,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5767]) ).
fof(i_0_8811,plain,
! [X20197,X20198] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20197,X20198) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20197),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20198)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20197),X20198))
| X20198 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20197,X20198) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20197),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20198)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20197),X20198))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X20198 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2__eq__if])])]) ).
fof(i_0_8812,plain,
! [X29160,X29161] : hAPP(c_Set_OCollect(X29161),hAPP(hAPP(c_COMBC(X29161,X29161,tc_HOL_Obool),c_fequal),X29160)) = hAPP(hAPP(c_Set_Oinsert(X29161),X29160),c_Orderings_Obot__class_Obot(tc_fun(X29161,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv]) ).
cnf(i_0_8813,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5542]) ).
fof(i_0_8814,plain,
! [X24737,X24738,X24739] : hAPP(hAPP(c_Set_Oinsert(X24739),X24738),X24737) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24739,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24739),X24738),c_Orderings_Obot__class_Obot(tc_fun(X24739,tc_HOL_Obool)))),X24737),
inference(variable_rename,[status(thm)],[fact_insert__is__Un]) ).
fof(i_0_8815,plain,
! [X17306,X17307,X17308,X17309] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X17309,X17308)),X17307),X17306))
| X17306 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X17307),X17309),hAPP(X17308,X17307)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I2_J])]) ).
cnf(i_0_8816,plain,
hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) = X2,
inference(split_conjunct,[status(thm)],[i_0_5768]) ).
fof(i_0_8817,plain,
! [X20296,X20297,X20298] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20298),X20297))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20298),X20296)),X20297)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).
fof(i_0_8818,plain,
! [X27038,X27039,X27040,X27041] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27041),X27040),X27039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27041),X27040),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27041),X27039),X27038)))
| ~ class_Lattices_Osemilattice__inf(X27041) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27041),X27040),X27038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27041),X27040),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27041),X27039),X27038)))
| ~ class_Lattices_Osemilattice__inf(X27041) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5769])])]) ).
fof(i_0_8819,plain,
! [X22261,X22262,X22263,X22264] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22264),X22263),X22262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22264),X22263),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22264),X22262),X22261)))
| ~ class_Orderings_Olinorder(X22264) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22264),X22263),X22261))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22264),X22263),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22264),X22262),X22261)))
| ~ class_Orderings_Olinorder(X22264) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5770])])]) ).
fof(i_0_8820,plain,
! [X32236,X32237,X32238] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32238),X32237),hAPP(c_List_Oset(X32238),X32236)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32238)),c_List_Oremove1(X32238,X32237,X32236)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32238)),X32236)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ( hBOOL(hAPP(hAPP(c_member(X32238),X32237),hAPP(c_List_Oset(X32238),X32236)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32238)),c_List_Oremove1(X32238,X32237,X32236)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32238)),X32236) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5771])]) ).
fof(i_0_8821,plain,
! [X20422,X20423,X20424] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20424),X20423))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20423),X20424)),X20422) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20423),X20422)),X20424) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).
fof(i_0_8822,plain,
! [X20419,X20420,X20421] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20421),X20420))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20420),X20419)),X20421) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20420),X20421)),X20419) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).
fof(i_0_8823,plain,
! [X27054,X27055,X27056] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27056,tc_HOL_Obool)),X27055),X27054))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27056,tc_HOL_Obool)),X27055),X27054) = X27055 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])]) ).
fof(i_0_8824,plain,
! [X27051,X27052,X27053] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27053,tc_HOL_Obool)),X27052),X27051))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27053,tc_HOL_Obool)),X27051),X27052) = X27052 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])]) ).
fof(i_0_8825,plain,
! [X23997,X23998,X23999] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23999,tc_HOL_Obool)),X23998),X23997))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23999,tc_HOL_Obool)),X23998),X23997) = X23997 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb1])]) ).
fof(i_0_8826,plain,
! [X23994,X23995,X23996] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23996,tc_HOL_Obool)),X23995),X23994))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23996,tc_HOL_Obool)),X23995),X23994) = X23994 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23996,tc_HOL_Obool)),X23995),X23994) != X23994
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23996,tc_HOL_Obool)),X23995),X23994)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Un__eq])]) ).
fof(i_0_8827,plain,
! [X24000,X24001,X24002] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24002,tc_HOL_Obool)),X24001),X24000))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24002,tc_HOL_Obool)),X24000),X24001) = X24000 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb2])]) ).
fof(i_0_8828,plain,
! [X23203,X23204,X23205] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23205),X23204))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23205),X23203))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23205),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23204,X23203))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zmod])]) ).
fof(i_0_8829,plain,
! [X27336,X27337,X27338,X27339] :
( hBOOL(hAPP(hAPP(c_member(X27339),X27338),X27337))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27339,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X27339),X27338),X27336)),X27337) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27339,tc_HOL_Obool)),X27336),X27337) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5772])]) ).
fof(i_0_8830,plain,
! [X29208,X29209] : hAPP(c_Set_OCollect(X29209),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29209),c_fNot),X29208)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29209,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29209),X29208)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(i_0_8831,plain,
! [X18446,X18447,X18448,X18449,X18450] : hAPP(c_Sum__Type_OSumr(X18450,X18449,X18448,X18447),hAPP(c_Sum__Type_OInr(X18450,X18448),X18446)) = hAPP(X18447,X18446),
inference(variable_rename,[status(thm)],[fact_Sumr_Osimps]) ).
fof(i_0_8832,plain,
! [X18441,X18442,X18443,X18444,X18445] : hAPP(c_Sum__Type_OSuml(X18445,X18444,X18443,X18442),hAPP(c_Sum__Type_OInl(X18445,X18443),X18441)) = hAPP(X18442,X18441),
inference(variable_rename,[status(thm)],[fact_Suml_Osimps]) ).
fof(i_0_8833,plain,
! [X33380,X33381,X33382] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33382)),X33381)),X33380))
| hAPP(hAPP(c_List_Odrop(X33382),X33380),X33381) = c_List_Olist_ONil(X33382) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__all])]) ).
fof(i_0_8834,plain,
! [X33377,X33378,X33379] :
( ( hAPP(hAPP(c_List_Odrop(X33379),X33378),X33377) != c_List_Olist_ONil(X33379)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33379)),X33377)),X33378)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33379)),X33377)),X33378))
| hAPP(hAPP(c_List_Odrop(X33379),X33378),X33377) = c_List_Olist_ONil(X33379) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil])]) ).
fof(i_0_8835,plain,
! [X25190,X25191,X25192,X25193] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25193),X25192),hAPP(hAPP(c_Set_Oinsert(X25193),X25191),X25190)))
| X25192 = X25191
| hBOOL(hAPP(hAPP(c_member(X25193),X25192),X25190)) )
& ( X25192 != X25191
| hBOOL(hAPP(hAPP(c_member(X25193),X25192),hAPP(hAPP(c_Set_Oinsert(X25193),X25191),X25190))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25193),X25192),X25190))
| hBOOL(hAPP(hAPP(c_member(X25193),X25192),hAPP(hAPP(c_Set_Oinsert(X25193),X25191),X25190))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).
fof(i_0_8836,plain,
! [X24947,X24948,X24949,X24950] :
( ~ hBOOL(hAPP(hAPP(c_member(X24950),X24949),hAPP(hAPP(c_Set_Oinsert(X24950),X24948),X24947)))
| X24949 = X24948
| hBOOL(hAPP(hAPP(c_member(X24950),X24949),X24947)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).
cnf(i_0_8837,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_5698]) ).
cnf(i_0_8838,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
inference(split_conjunct,[status(thm)],[i_0_5699]) ).
cnf(i_0_8839,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_5701]) ).
cnf(i_0_8840,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
inference(split_conjunct,[status(thm)],[i_0_5700]) ).
cnf(i_0_8841,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5702]) ).
fof(i_0_8842,plain,
! [X33143,X33144,X33145] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33145)),X33144)),X33143))
| hAPP(hAPP(c_List_Otake(X33145),X33143),X33144) = X33144 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__all])]) ).
cnf(i_0_8843,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| c_Code__Numeral_Onat__of__aux(X1,X2) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5773]) ).
cnf(i_0_8844,plain,
c_Code__Numeral_Onat__of__aux(X1,X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_5774]) ).
cnf(i_0_8845,plain,
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_5775]) ).
fof(i_0_8846,plain,
! [X23586,X23587,X23588,X23589] :
( ~ class_Orderings_Olinorder(X23589)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23589),X23588),X23587))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23589,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23589,X23588),X23586)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23589,X23588),X23587)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23589,X23587),X23586) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__diff])]) ).
fof(i_0_8847,plain,
! [X21969,X21970,X21971,X21972,X21973,X21974,X21975] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X21971,X21970),X21969))
| ~ hBOOL(hAPP(hAPP(X21970,X21972),X21969))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X21971,X21970),X21972)) )
& ( hBOOL(hAPP(hAPP(X21974,esk80_3(X21973,X21974,X21975)),X21973))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X21975,X21974),X21973)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X21975,X21974),esk80_3(X21973,X21974,X21975)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X21975,X21974),X21973)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp_Oequations])])])])])]) ).
fof(i_0_8848,plain,
! [X21961,X21962,X21963,X21964,X21965,X21966,X21967] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X21963,X21962),X21961))
| ~ hBOOL(hAPP(hAPP(X21962,X21964),X21961))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X21963,X21962),X21964)) )
& ( hBOOL(hAPP(hAPP(X21966,esk79_3(X21965,X21966,X21967)),X21965))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X21967,X21966),X21965)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X21967,X21966),esk79_3(X21965,X21966,X21967)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X21967,X21966),X21965)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp_Osimps])])])])])]) ).
cnf(i_0_8849,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Relation_OId(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_5776]) ).
fof(i_0_8850,plain,
! [X28666,X28667,X28668,X28669] :
( ( hAPP(hAPP(c_Product__Type_OSigma(X28669,X28668),X28667),hAPP(c_COMBK(tc_fun(X28668,tc_HOL_Obool),X28669),X28666)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28669,X28668),tc_HOL_Obool))
| X28667 = c_Orderings_Obot__class_Obot(tc_fun(X28669,tc_HOL_Obool))
| X28666 = c_Orderings_Obot__class_Obot(tc_fun(X28668,tc_HOL_Obool)) )
& ( X28667 != c_Orderings_Obot__class_Obot(tc_fun(X28669,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(X28669,X28668),X28667),hAPP(c_COMBK(tc_fun(X28668,tc_HOL_Obool),X28669),X28666)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28669,X28668),tc_HOL_Obool)) )
& ( X28666 != c_Orderings_Obot__class_Obot(tc_fun(X28668,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(X28669,X28668),X28667),hAPP(c_COMBK(tc_fun(X28668,tc_HOL_Obool),X28669),X28666)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28669,X28668),tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__empty])])]) ).
cnf(i_0_8851,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5707]) ).
fof(i_0_8852,plain,
! [X24132,X24133,X24134] :
( ~ class_Orderings_Olinorder(X24134)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24134),X24133),X24132))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24134,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24134,X24133,X24132)),hAPP(c_SetInterval_Oord__class_OatLeast(X24134),X24132)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X24134),X24133) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J])]) ).
fof(i_0_8853,plain,
! [X24114,X24115,X24116] :
( ~ class_Orderings_Olinorder(X24116)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24116),X24115),X24114))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24116,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24116,X24115,X24114)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24116),X24114)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X24116),X24115) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J])]) ).
fof(i_0_8854,plain,
! [X24135,X24136,X24137] :
( ~ class_Orderings_Olinorder(X24137)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24137),X24136),X24135))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24137,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24137,X24136,X24135)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24137),X24135)) = hAPP(c_SetInterval_Oord__class_OatLeast(X24137),X24136) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J])]) ).
fof(i_0_8855,plain,
! [X33620,X33621] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33621)
| c_Complete__Lattice_OSup__class_OSup(X33621,hAPP(c_List_Oset(X33621),X33620)) = hAPP(c_List_Ofoldl(X33621,X33621,c_Lattices_Osemilattice__sup__class_Osup(X33621),c_Orderings_Obot__class_Obot(X33621)),X33620) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__set__fold])]) ).
fof(i_0_8856,plain,
! [X33622,X33623] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33623)
| c_Complete__Lattice_OInf__class_OInf(X33623,hAPP(c_List_Oset(X33623),X33622)) = hAPP(c_List_Ofoldl(X33623,X33623,c_Lattices_Osemilattice__inf__class_Oinf(X33623),c_Orderings_Otop__class_Otop(X33623)),X33622) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__set__fold])]) ).
cnf(i_0_8857,plain,
( c_Map_Omap__comp(X3,X4,X5,X6,X1,X2) = c_Option_Ooption_ONone(X4)
| hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[i_0_5368]) ).
cnf(i_0_8858,plain,
( c_Map_Omap__comp(X3,X4,X5,X6,X1,X2) = c_Option_Ooption_ONone(X4)
| hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[i_0_5777]) ).
fof(i_0_8859,plain,
! [X23746,X23747] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X23747,X23746)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23746),X23747)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost__int]) ).
fof(i_0_8860,plain,
! [X24518,X24519,X24520,X24521] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24521),X24520))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24519),hAPP(c_Set_Oimage(X24521,X24519,X24518),X24520))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
cnf(i_0_8861,plain,
( c_List_Oconcat(X2,X1) = c_List_Olist_ONil(X2)
| esk490_2(X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5619]) ).
cnf(i_0_8862,plain,
( c_List_Olist_ONil(X2) = c_List_Oconcat(X2,X1)
| esk489_2(X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5620]) ).
fof(i_0_8863,plain,
! [X25551,X25552] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25552),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25551)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25552),X25551)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25552),X25551))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25552),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25551))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatMost__iff])]) ).
fof(i_0_8864,plain,
! [X25549,X25550] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25550),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25549)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25549),X25550)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25549),X25550))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25550),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25549))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeast__iff])]) ).
fof(i_0_8865,plain,
! [X31420,X31421,X31422] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31422)
| c_Complete__Lattice_OSup__class_OSup(X31422,hAPP(hAPP(c_Set_Oinsert(X31422),X31421),hAPP(hAPP(c_Set_Oinsert(X31422),X31420),c_Orderings_Obot__class_Obot(tc_fun(X31422,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X31422),X31421),X31420) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__binary])]) ).
fof(i_0_8866,plain,
! [X31423,X31424,X31425] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31425)
| c_Complete__Lattice_OInf__class_OInf(X31425,hAPP(hAPP(c_Set_Oinsert(X31425),X31424),hAPP(hAPP(c_Set_Oinsert(X31425),X31423),c_Orderings_Obot__class_Obot(tc_fun(X31425,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31425),X31424),X31423) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__binary])]) ).
fof(i_0_8867,plain,
! [X23333,X23334,X23335,X23336] :
( ~ class_Divides_Osemiring__div(X23336)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23336),X23335),X23334))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23336),X23333),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23336),X23334),X23335)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23336),X23333),X23334)),X23335) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__swap])]) ).
fof(i_0_8868,plain,
! [X25557,X25558,X25559,X25560] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25560),X25559),c_SetInterval_Oord_OatMost(X25560,X25558,X25557)))
| hBOOL(hAPP(hAPP(X25558,X25559),X25557)) )
& ( ~ hBOOL(hAPP(hAPP(X25558,X25559),X25557))
| hBOOL(hAPP(hAPP(c_member(X25560),X25559),c_SetInterval_Oord_OatMost(X25560,X25558,X25557))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff])]) ).
fof(i_0_8869,plain,
! [X25503,X25504,X25505,X25506] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25506),X25505),c_SetInterval_Oord_OlessThan(X25506,X25504,X25503)))
| hBOOL(hAPP(hAPP(X25504,X25505),X25503)) )
& ( ~ hBOOL(hAPP(hAPP(X25504,X25505),X25503))
| hBOOL(hAPP(hAPP(c_member(X25506),X25505),c_SetInterval_Oord_OlessThan(X25506,X25504,X25503))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff])]) ).
fof(i_0_8870,plain,
! [X25553,X25554,X25555,X25556] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25556),X25555),c_SetInterval_Oord_OatLeast(X25556,X25554,X25553)))
| hBOOL(hAPP(hAPP(X25554,X25553),X25555)) )
& ( ~ hBOOL(hAPP(hAPP(X25554,X25553),X25555))
| hBOOL(hAPP(hAPP(c_member(X25556),X25555),c_SetInterval_Oord_OatLeast(X25556,X25554,X25553))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff])]) ).
fof(i_0_8871,plain,
! [X25507,X25508,X25509,X25510] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25510),X25509),c_SetInterval_Oord_OgreaterThan(X25510,X25508,X25507)))
| hBOOL(hAPP(hAPP(X25508,X25507),X25509)) )
& ( ~ hBOOL(hAPP(hAPP(X25508,X25507),X25509))
| hBOOL(hAPP(hAPP(c_member(X25510),X25509),c_SetInterval_Oord_OgreaterThan(X25510,X25508,X25507))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff])]) ).
fof(i_0_8872,plain,
! [X33851,X33852,X33853,X33854,X33855] :
( c_List_Opartition(X33855,X33854,X33853) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33855),tc_List_Olist(X33855)),X33852),X33851)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33855,tc_HOL_Obool)),hAPP(c_List_Oset(X33855),X33852)),hAPP(c_List_Oset(X33855),X33851)) = hAPP(c_List_Oset(X33855),X33853) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_partition__set])]) ).
fof(i_0_8873,plain,
! [X32691,X32692,X32693,X32694] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32694) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Onth(X32693),hAPP(hAPP(c_List_Olist_OCons(X32693),X32692),X32691)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32694)) = X32692 )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32694) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Onth(X32693),hAPP(hAPP(c_List_Olist_OCons(X32693),X32692),X32691)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32694)) = hAPP(hAPP(c_List_Onth(X32693),X32691),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32694)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__Cons__number__of])]) ).
fof(i_0_8874,plain,
! [X30207,X30208] : hAPP(hAPP(c_Relation_Orel__comp(X30208,X30208,X30208),X30207),c_Transitive__Closure_Ortrancl(X30208,X30207)) = hAPP(hAPP(c_Relation_Orel__comp(X30208,X30208,X30208),c_Transitive__Closure_Ortrancl(X30208,X30207)),X30207),
inference(variable_rename,[status(thm)],[fact_r__comp__rtrancl__eq]) ).
cnf(i_0_8875,plain,
c_Transitive__Closure_Otrancl(X1,X2) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2),
inference(split_conjunct,[status(thm)],[i_0_5778]) ).
fof(i_0_8876,plain,
! [X34439,X34440,X34441,X34442,X34443,X34444] : hAPP(hAPP(hAPP(c_COMBS(X34444,X34443,X34442),X34441),X34440),X34439) = hAPP(hAPP(X34441,X34439),hAPP(X34440,X34439)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
cnf(i_0_8877,plain,
c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_5779]) ).
fof(i_0_8878,plain,
! [X20803,X20804] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20804)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20804),hAPP(c_Groups_Ouminus__class_Ouminus(X20804),hAPP(c_Groups_Oabs__class_Oabs(X20804),X20803))),c_Groups_Ozero__class_Ozero(X20804))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])]) ).
fof(i_0_8879,plain,
! [X24398,X24399,X24400,X24401] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24401,tc_HOL_Obool)),X24400),hAPP(hAPP(c_Set_Oinsert(X24401),X24399),X24398)) = hAPP(hAPP(c_Set_Oinsert(X24401),X24399),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24401,tc_HOL_Obool)),X24400),X24398)),
inference(variable_rename,[status(thm)],[fact_Un__insert__right]) ).
fof(i_0_8880,plain,
! [X18920,X18921,X18922] :
( ( X18921 = c_Groups_Ozero__class_Ozero(X18922)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18922),X18921),X18921)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18922),X18920),X18920)) != c_Groups_Ozero__class_Ozero(X18922)
| ~ class_Rings_Olinordered__ring__strict(X18922) )
& ( X18920 = c_Groups_Ozero__class_Ozero(X18922)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18922),X18921),X18921)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18922),X18920),X18920)) != c_Groups_Ozero__class_Ozero(X18922)
| ~ class_Rings_Olinordered__ring__strict(X18922) )
& ( X18921 != c_Groups_Ozero__class_Ozero(X18922)
| X18920 != c_Groups_Ozero__class_Ozero(X18922)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18922),X18921),X18921)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18922),X18920),X18920)) = c_Groups_Ozero__class_Ozero(X18922)
| ~ class_Rings_Olinordered__ring__strict(X18922) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).
fof(i_0_8881,plain,
! [X31629,X31630,X31631,X31632,X31633,X31634] :
( hAPP(X31634,X31633) != hAPP(c_Option_Ooption_OSome(X31632),X31631)
| hAPP(c_Map_Omap__add(X31630,X31632,X31629,X31634),X31633) = hAPP(c_Option_Ooption_OSome(X31632),X31631) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__find__right])]) ).
fof(i_0_8882,plain,
! [X30672,X30673,X30674] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30674),X30673))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30674,tc_HOL_Obool)),X30673),X30672) = hAPP(hAPP(c_Finite__Set_Ofold(X30674,tc_fun(X30674,tc_HOL_Obool),c_Set_Oinsert(X30674)),X30672),X30673) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__fold__insert])]) ).
fof(i_0_8883,plain,
! [X21096,X21097] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X21097),X21096) != c_Groups_Ozero__class_Ozero(X21097)
| c_Int_Oiszero(X21097,hAPP(c_Int_Onumber__class_Onumber__of(X21097),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21096),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| ~ class_Int_Onumber__ring(X21097) )
& ( ~ c_Int_Oiszero(X21097,hAPP(c_Int_Onumber__class_Onumber__of(X21097),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21096),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(X21097),X21096) = c_Groups_Ozero__class_Ozero(X21097)
| ~ class_Int_Onumber__ring(X21097) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J])])]) ).
fof(i_0_8884,plain,
! [X21094,X21095] :
( ( c_Groups_Ozero__class_Ozero(X21095) != hAPP(c_Int_Onumber__class_Onumber__of(X21095),X21094)
| c_Int_Oiszero(X21095,hAPP(c_Int_Onumber__class_Onumber__of(X21095),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21094))))
| ~ class_Int_Onumber__ring(X21095) )
& ( ~ c_Int_Oiszero(X21095,hAPP(c_Int_Onumber__class_Onumber__of(X21095),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21094))))
| c_Groups_Ozero__class_Ozero(X21095) = hAPP(c_Int_Onumber__class_Onumber__of(X21095),X21094)
| ~ class_Int_Onumber__ring(X21095) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J])])]) ).
fof(i_0_8885,plain,
! [X29588,X29589,X29590,X29591] :
( ~ c_Wellfounded_Owf(X29591,X29590)
| ~ c_Wellfounded_Owf(X29589,X29588)
| c_Wellfounded_Owf(tc_prod(X29591,X29589),c_Wellfounded_Olex__prod(X29591,X29589,X29590,X29588)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex__prod])]) ).
cnf(i_0_8886,plain,
c_List_Oconcat(X1,c_List_Olist_ONil(tc_List_Olist(X1))) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_5780]) ).
fof(i_0_8887,plain,
! [X24816,X24817] :
( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24817,X24816) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24817),X24816)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24817),X24816))
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24817,X24816) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5781])]) ).
fof(i_0_8888,plain,
! [X24818,X24819] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24819,X24818)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24819),X24818)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24819),X24818))
| c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24819,X24818) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5782])]) ).
fof(i_0_8889,plain,
! [X32048,X32049,X32050,X32051] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32051),X32050))
| hBOOL(hAPP(c_List_Odistinct(tc_prod(X32051,X32049)),hAPP(hAPP(c_List_Ozip(X32051,X32049),X32050),X32048))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI1])]) ).
fof(i_0_8890,plain,
! [X32052,X32053,X32054,X32055] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32055),X32054))
| hBOOL(hAPP(c_List_Odistinct(tc_prod(X32053,X32055)),hAPP(hAPP(c_List_Ozip(X32053,X32055),X32052),X32054))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI2])]) ).
fof(i_0_8891,plain,
! [X30768,X30769,X30770] :
( ~ class_Lattices_Olattice(X30770)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30770),X30769))
| hBOOL(hAPP(hAPP(c_member(X30770),X30768),X30769))
| c_Big__Operators_Olattice__class_OInf__fin(X30770,hAPP(hAPP(c_Set_Oinsert(X30770),X30768),X30769)) = hAPP(hAPP(c_Finite__Set_Ofold(X30770,X30770,c_Lattices_Osemilattice__inf__class_Oinf(X30770)),X30768),X30769) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5783])]) ).
fof(i_0_8892,plain,
! [X30771,X30772,X30773] :
( ~ class_Orderings_Olinorder(X30773)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30773),X30772))
| hBOOL(hAPP(hAPP(c_member(X30773),X30771),X30772))
| c_Big__Operators_Olinorder__class_OMin(X30773,hAPP(hAPP(c_Set_Oinsert(X30773),X30771),X30772)) = hAPP(hAPP(c_Finite__Set_Ofold(X30773,X30773,c_Orderings_Oord__class_Omin(X30773)),X30771),X30772) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5784])]) ).
fof(i_0_8893,plain,
! [X30774,X30775,X30776] :
( ~ class_Orderings_Olinorder(X30776)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30776),X30775))
| hBOOL(hAPP(hAPP(c_member(X30776),X30774),X30775))
| c_Big__Operators_Olinorder__class_OMax(X30776,hAPP(hAPP(c_Set_Oinsert(X30776),X30774),X30775)) = hAPP(hAPP(c_Finite__Set_Ofold(X30776,X30776,c_Orderings_Oord__class_Omax(X30776)),X30774),X30775) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5785])]) ).
fof(i_0_8894,plain,
! [X30765,X30766,X30767] :
( ~ class_Lattices_Olattice(X30767)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30767),X30766))
| hBOOL(hAPP(hAPP(c_member(X30767),X30765),X30766))
| c_Big__Operators_Olattice__class_OSup__fin(X30767,hAPP(hAPP(c_Set_Oinsert(X30767),X30765),X30766)) = hAPP(hAPP(c_Finite__Set_Ofold(X30767,X30767,c_Lattices_Osemilattice__sup__class_Osup(X30767)),X30765),X30766) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5786])]) ).
fof(i_0_8895,plain,
! [X31337,X31338,X31339,X31340] : hAPP(c_Set_Ovimage(X31340,X31339,X31338),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31339,tc_HOL_Obool),X31337)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31339,tc_HOL_Obool),tc_fun(X31340,tc_HOL_Obool)),X31337),c_Set_Ovimage(X31340,X31339,X31338)),
inference(variable_rename,[status(thm)],[fact_vimage__Union]) ).
fof(i_0_8896,plain,
! [X31355,X31356,X31357,X31358] : hAPP(c_Set_Oimage(X31358,X31357,X31356),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31358,tc_HOL_Obool),X31355)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31358,tc_HOL_Obool),tc_fun(X31357,tc_HOL_Obool)),X31355),c_Set_Oimage(X31358,X31357,X31356)),
inference(variable_rename,[status(thm)],[fact_image__Union]) ).
fof(i_0_8897,plain,
! [X26497,X26498] : hBOOL(hAPP(hAPP(c_member(tc_fun(X26498,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X26498,tc_HOL_Obool))),hAPP(c_Set_OPow(X26498),X26497))),
inference(variable_rename,[status(thm)],[fact_Pow__bottom]) ).
fof(i_0_8898,plain,
! [X32443,X32444,X32445] :
( ~ class_Groups_Omonoid__add(X32445)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32445),hAPP(hAPP(c_List_Omap(X32444,X32445),hAPP(c_COMBK(X32445,X32444),c_Groups_Ozero__class_Ozero(X32445))),X32443)) = c_Groups_Ozero__class_Ozero(X32445) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__0])]) ).
fof(i_0_8899,plain,
! [X27177,X27178,X27179] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27179,tc_HOL_Obool)),X27178),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27179,tc_HOL_Obool)),X27178),X27177)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27179,tc_HOL_Obool)),X27178),X27177),
inference(variable_rename,[status(thm)],[fact_Int__left__absorb]) ).
fof(i_0_8900,plain,
! [X23900,X23901,X23902] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23902,tc_HOL_Obool)),X23901),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23902,tc_HOL_Obool)),X23901),X23900)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23902,tc_HOL_Obool)),X23901),X23900),
inference(variable_rename,[status(thm)],[fact_Un__left__absorb]) ).
fof(i_0_8901,plain,
! [X23971,X23972,X23973] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23973,tc_HOL_Obool)),X23972),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23973,tc_HOL_Obool)),X23971),X23972)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23973,tc_HOL_Obool)),X23972),X23971),
inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel]) ).
fof(i_0_8902,plain,
! [X33430,X33431] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33431)),X33430)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| hAPP(c_List_Orotate1(X33431),X33430) = X33430 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__length01])]) ).
fof(i_0_8903,plain,
! [X27938,X27939,X27940,X27941,X27942] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27942,X27941,X27940),X27939),X27938),c_Orderings_Obot__class_Obot(tc_fun(X27941,tc_HOL_Obool))) = X27938,
inference(variable_rename,[status(thm)],[fact_fold__image__empty]) ).
fof(i_0_8904,plain,
! [X23200,X23201,X23202] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23202),X23201))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23202),X23200))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23201),X23200))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat])]) ).
fof(i_0_8905,plain,
! [X20576,X20577] :
( ( X20577 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20577),X20576) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X20577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20577),X20576) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20577),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20576)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).
fof(i_0_8906,plain,
! [X23441,X23442] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23442)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23441)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23441),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23442)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23441),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23442)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23442)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23441))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__iff__zmod__eq__0__number__of])]) ).
fof(i_0_8907,plain,
! [X25803,X25804,X25805,X25806,X25807,X25808] : c_Hoare__Mirabelle_Otriple_Otriple__case(X25808,X25807,X25806,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25808),X25805),X25804),X25803)) = hAPP(hAPP(hAPP(X25806,X25805),X25804),X25803),
inference(variable_rename,[status(thm)],[fact_triple_Osimps_I2_J]) ).
fof(i_0_8908,plain,
! [X25797,X25798,X25799,X25800,X25801,X25802] : c_Hoare__Mirabelle_Otriple_Otriple__rec(X25802,X25801,X25800,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25802),X25799),X25798),X25797)) = hAPP(hAPP(hAPP(X25800,X25799),X25798),X25797),
inference(variable_rename,[status(thm)],[fact_triple_Orecs]) ).
fof(i_0_8909,plain,
! [X29767,X29768,X29769,X29770,X29772,X29773,X29774,X29775,X29776] :
( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X29770,X29769,X29768),X29767))
| hBOOL(hAPP(hAPP(X29768,esk325_2(X29767,X29768)),X29767)) )
& ( ~ hBOOL(hAPP(hAPP(X29773,X29774),X29772))
| hBOOL(hAPP(c_Predicate_ORangeP(X29776,X29775,X29773),X29772)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Oequations])])])])]) ).
fof(i_0_8910,plain,
! [X21034,X21035] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)))
| X21035 = X21034
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( X21035 != X21034
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( X21035 != X21034
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( X21035 != X21034
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) )
& ( X21035 != X21034
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21035) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21034)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21034) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5787])])]) ).
fof(i_0_8911,plain,
! [X19337,X19338] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19338),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19338),X19337)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19338))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19337))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib__neg])]) ).
fof(i_0_8912,plain,
! [X18356,X18357,X18358,X18359] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X18359,X18358)),c_Nitpick_Opair__box_OPairBox(X18359,X18358,X18357,X18356)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I2_J]) ).
fof(i_0_8913,plain,
! [X33837,X33838,X33839,X33840] :
( ( X33840 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33839)),X33838)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_List_Obutlast(X33839,hAPP(hAPP(c_List_Olist__update(X33839,X33838),X33840),X33837)) = c_List_Obutlast(X33839,X33838) )
& ( X33840 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33839)),X33838)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_List_Obutlast(X33839,hAPP(hAPP(c_List_Olist__update(X33839,X33838),X33840),X33837)) = hAPP(hAPP(c_List_Olist__update(X33839,c_List_Obutlast(X33839,X33838)),X33840),X33837) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__list__update])]) ).
fof(i_0_8914,plain,
! [X24436,X24437,X24438,X24439,X24440] : hAPP(c_Set_Oimage(X24440,X24439,X24438),hAPP(hAPP(c_Set_Oinsert(X24440),X24437),X24436)) = hAPP(hAPP(c_Set_Oinsert(X24439),hAPP(X24438,X24437)),hAPP(c_Set_Oimage(X24440,X24439,X24438),X24436)),
inference(variable_rename,[status(thm)],[fact_image__insert]) ).
cnf(i_0_8915,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))
| c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_List_Olist_ONil(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_5561]) ).
fof(i_0_8916,plain,
! [X24530,X24531,X24532] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24532,tc_HOL_Obool)),X24531),X24530))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24532),X24530))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24532),X24531)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).
fof(i_0_8917,plain,
! [X24533,X24534,X24535] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24535),X24534))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24535,tc_HOL_Obool)),X24533),X24534))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24535),X24533)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).
fof(i_0_8918,plain,
! [X19435,X19436] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19436),hAPP(c_Groups_Ouminus__class_Ouminus(X19436),X19435)),c_Groups_Ozero__class_Ozero(X19436)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19436),c_Groups_Ozero__class_Ozero(X19436)),X19435))
| ~ class_Groups_Oordered__ab__group__add(X19436) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19436),c_Groups_Ozero__class_Ozero(X19436)),X19435))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19436),hAPP(c_Groups_Ouminus__class_Ouminus(X19436),X19435)),c_Groups_Ozero__class_Ozero(X19436)))
| ~ class_Groups_Oordered__ab__group__add(X19436) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).
fof(i_0_8919,plain,
! [X18841,X18842] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18842),hAPP(c_Groups_Ouminus__class_Ouminus(X18842),X18841)),c_Groups_Ozero__class_Ozero(X18842)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18842),c_Groups_Ozero__class_Ozero(X18842)),X18841))
| ~ class_Groups_Oordered__ab__group__add(X18842) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18842),c_Groups_Ozero__class_Ozero(X18842)),X18841))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18842),hAPP(c_Groups_Ouminus__class_Ouminus(X18842),X18841)),c_Groups_Ozero__class_Ozero(X18842)))
| ~ class_Groups_Oordered__ab__group__add(X18842) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).
fof(i_0_8920,plain,
! [X34306,X34307,X34308,X34309] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34309)),X34308) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34307)),X34306)
| hAPP(hAPP(c_List_Ozip(X34309,X34307),hAPP(c_List_Orev(X34309),X34308)),hAPP(c_List_Orev(X34307),X34306)) = hAPP(c_List_Orev(tc_prod(X34309,X34307)),hAPP(hAPP(c_List_Ozip(X34309,X34307),X34308),X34306)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__rev])]) ).
fof(i_0_8921,plain,
! [X20869,X20870] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20870),X20869)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20870))
| X20869 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20870))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20870),X20869))) )
& ( X20869 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20870),X20869))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).
fof(i_0_8922,plain,
! [X27488,X27489,X27490,X27491] :
( ~ class_Orderings_Olinorder(X27491)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27491,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X27491,X27490,X27489)),hAPP(c_SetInterval_Oord__class_OatLeast(X27491),X27488)) = c_SetInterval_Oord__class_OatLeastAtMost(X27491,hAPP(hAPP(c_Orderings_Oord__class_Omax(X27491),X27490),X27488),X27489) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2])]) ).
fof(i_0_8923,plain,
! [X27474,X27475,X27476,X27477] :
( ~ class_Orderings_Olinorder(X27477)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27477,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X27477,X27476,X27475)),hAPP(c_SetInterval_Oord__class_OatMost(X27477),X27474)) = c_SetInterval_Oord__class_OatLeastAtMost(X27477,X27476,hAPP(hAPP(c_Orderings_Oord__class_Omin(X27477),X27475),X27474)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1])]) ).
fof(i_0_8924,plain,
! [X32789,X32790,X32791,X32792] : hAPP(hAPP(c_List_Olist__update(X32792,hAPP(hAPP(c_List_Olist_OCons(X32792),X32791),X32790)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32789) = hAPP(hAPP(c_List_Olist_OCons(X32792),X32789),X32790),
inference(variable_rename,[status(thm)],[fact_list__update__code_I2_J]) ).
fof(i_0_8925,plain,
! [X34433,X34434,X34435,X34436,X34437,X34438] : hAPP(hAPP(hAPP(c_COMBC(X34438,X34437,X34436),X34435),X34434),X34433) = hAPP(hAPP(X34435,X34433),X34434),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_8926,plain,
! [X34427,X34428,X34429,X34430,X34431,X34432] : hAPP(hAPP(hAPP(c_COMBB(X34432,X34431,X34430),X34429),X34428),X34427) = hAPP(X34429,hAPP(X34428,X34427)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_8927,plain,
! [X18123,X18124,X18125,X18126,X18127] : hAPP(c_Option_Ooption_Ooption__case(X18127,X18126,X18125,X18124),hAPP(c_Option_Ooption_OSome(X18126),X18123)) = hAPP(X18124,X18123),
inference(variable_rename,[status(thm)],[fact_option_Osimps_I5_J]) ).
fof(i_0_8928,plain,
! [X20662,X20663] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20663),hAPP(c_Int_Onumber__class_Onumber__of(X20663),X20662)),c_Groups_Ozero__class_Ozero(X20663)))
| hAPP(c_Groups_Oabs__class_Oabs(X20663),hAPP(c_Int_Onumber__class_Onumber__of(X20663),X20662)) = hAPP(c_Groups_Ouminus__class_Ouminus(X20663),hAPP(c_Int_Onumber__class_Onumber__of(X20663),X20662))
| ~ class_Int_Onumber__ring(X20663)
| ~ class_Rings_Olinordered__idom(X20663) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20663),hAPP(c_Int_Onumber__class_Onumber__of(X20663),X20662)),c_Groups_Ozero__class_Ozero(X20663)))
| hAPP(c_Groups_Oabs__class_Oabs(X20663),hAPP(c_Int_Onumber__class_Onumber__of(X20663),X20662)) = hAPP(c_Int_Onumber__class_Onumber__of(X20663),X20662)
| ~ class_Int_Onumber__ring(X20663)
| ~ class_Rings_Olinordered__idom(X20663) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5788])])]) ).
fof(i_0_8929,plain,
! [X28322,X28323,X28324,X28325] : hAPP(c_Set_Ovimage(X28325,X28324,X28323),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28324,tc_HOL_Obool)),X28322)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28325,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28325,X28324,X28323),X28322)),
inference(variable_rename,[status(thm)],[fact_vimage__Compl]) ).
fof(i_0_8930,plain,
! [X20033,X20034,X20035] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20035),X20034)),X20033),X20034) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20033,X20034),
inference(variable_rename,[status(thm)],[fact_mod__mult__self3]) ).
fof(i_0_8931,plain,
! [X20002,X20003] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20003))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20002))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X20003)),hAPP(c_Int_Onat,X20002)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20003),X20002)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I1_J])]) ).
fof(i_0_8932,plain,
! [X19325,X19326] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19325))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X19326)),hAPP(c_Int_Onat,X19325)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19326),X19325)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J])]) ).
fof(i_0_8933,plain,
! [X19657,X19658] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19658))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19657))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X19658)),hAPP(c_Int_Onat,X19657)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19658),X19657)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J])]) ).
fof(i_0_8934,plain,
! [X19659,X19660] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19659))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19660),X19659)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X19660)),hAPP(c_Int_Onat,X19659)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__distrib])]) ).
fof(i_0_8935,plain,
! [X32130,X32131,X32132,X32133] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X32133,X32132))),hAPP(hAPP(c_List_Ozip(X32133,X32132),X32131),X32130)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32133)),X32131)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32132)),X32130)),
inference(variable_rename,[status(thm)],[fact_length__zip]) ).
fof(i_0_8936,plain,
! [X31366,X31367,X31368,X31369] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31369,tc_HOL_Obool),hAPP(c_Set_Oimage(X31368,tc_fun(X31369,tc_HOL_Obool),X31367),X31366)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31368,tc_fun(X31369,tc_HOL_Obool)),X31366),X31367),
inference(variable_rename,[status(thm)],[fact_Union__image__eq]) ).
fof(i_0_8937,plain,
! [X31222,X31223,X31224,X31225] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31225,tc_HOL_Obool),hAPP(c_Set_Oimage(X31224,tc_fun(X31225,tc_HOL_Obool),X31223),X31222)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31224,tc_fun(X31225,tc_HOL_Obool)),X31222),X31223),
inference(variable_rename,[status(thm)],[fact_Inter__image__eq]) ).
fof(i_0_8938,plain,
! [X31218,X31219,X31220,X31221] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31221,tc_fun(X31220,tc_HOL_Obool)),X31219),X31218) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X31220,tc_HOL_Obool),hAPP(c_Set_Oimage(X31221,tc_fun(X31220,tc_HOL_Obool),X31218),X31219)),
inference(variable_rename,[status(thm)],[fact_INTER__eq__Inter__image]) ).
fof(i_0_8939,plain,
! [X31370,X31371,X31372,X31373] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31373,tc_fun(X31372,tc_HOL_Obool)),X31371),X31370) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X31372,tc_HOL_Obool),hAPP(c_Set_Oimage(X31373,tc_fun(X31372,tc_HOL_Obool),X31370),X31371)),
inference(variable_rename,[status(thm)],[fact_UNION__eq__Union__image]) ).
fof(i_0_8940,plain,
! [X18170,X18171,X18172,X18173] :
( ~ class_Rings_Osemiring__1(X18173)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X18173,X18172,hAPP(c_Nat_OSuc,X18171),X18170) = c_Nat_Osemiring__1__class_Oof__nat__aux(X18173,X18172,X18171,hAPP(X18172,X18170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J])]) ).
fof(i_0_8941,plain,
! [X20188,X20189] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20189))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20188))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X20189),hAPP(c_Int_Onat,X20188)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X20189,X20188)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I2_J])]) ).
fof(i_0_8942,plain,
! [X20186,X20187] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20187))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20186))
| hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X20187,X20186)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X20187),hAPP(c_Int_Onat,X20186)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__distrib])]) ).
fof(i_0_8943,plain,
! [X20554,X20555] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X20555,X20554) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20555),X20554)),X20554)),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality_H]) ).
fof(i_0_8944,plain,
! [X20457,X20458] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20458,X20457) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20458),X20457)),X20457)),
inference(variable_rename,[status(thm)],[fact_Divides_Omod__div__equality_H]) ).
fof(i_0_8945,plain,
! [X20930,X20931,X20932] :
( ~ class_Rings_Olinordered__semidom(X20932)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20932),c_Groups_Oone__class_Oone(X20932)),X20931))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20932),c_Groups_Oone__class_Oone(X20932)),hAPP(hAPP(c_Power_Opower__class_Opower(X20932),X20931),X20930))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).
fof(i_0_8946,plain,
! [X20917,X20918,X20919] :
( ~ class_Rings_Olinordered__semidom(X20919)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20919),c_Groups_Ozero__class_Ozero(X20919)),X20918))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20919),c_Groups_Ozero__class_Ozero(X20919)),hAPP(hAPP(c_Power_Opower__class_Opower(X20919),X20918),X20917))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).
fof(i_0_8947,plain,
! [X20924,X20925,X20926] :
( ~ class_Rings_Olinordered__semidom(X20926)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20926),c_Groups_Ozero__class_Ozero(X20926)),X20925))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20926),c_Groups_Ozero__class_Ozero(X20926)),hAPP(hAPP(c_Power_Opower__class_Opower(X20926),X20925),X20924))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
fof(i_0_8948,plain,
! [X25347,X25348,X25349,X25350,X25351] :
( ~ hBOOL(hAPP(hAPP(c_member(X25351),X25350),X25349))
| hAPP(c_Set_Oimage(X25351,X25348,hAPP(c_COMBK(X25348,X25351),X25347)),X25349) = hAPP(hAPP(c_Set_Oinsert(X25348),X25347),c_Orderings_Obot__class_Obot(tc_fun(X25348,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant])]) ).
fof(i_0_8949,plain,
! [X18957,X18958] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18957))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18958)),hAPP(c_Int_Onat,X18957))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18958),X18957))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18958)),hAPP(c_Int_Onat,X18957))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18957))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18958),X18957))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18958)),hAPP(c_Int_Onat,X18957))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__conj])])]) ).
fof(i_0_8950,plain,
! [X28725,X28726] : hAPP(hAPP(c_Product__Type_OSigma(X28726,X28725),c_Orderings_Otop__class_Otop(tc_fun(X28726,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X28725,tc_HOL_Obool),X28726),c_Orderings_Otop__class_Otop(tc_fun(X28725,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X28726,X28725),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__Times__UNIV]) ).
fof(i_0_8951,plain,
! [X18940,X18941] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18940),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18941),X18940))
| X18941 = X18940 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18941),X18940))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18940),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
& ( X18941 != X18940
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18940),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])]) ).
cnf(i_0_8952,plain,
hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId(X1)) = c_Relation_OId(X1),
inference(split_conjunct,[status(thm)],[i_0_5789]) ).
fof(i_0_8953,plain,
! [X19437,X19438] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19438),hAPP(c_Groups_Ouminus__class_Ouminus(X19438),X19437)),X19437))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19438),c_Groups_Ozero__class_Ozero(X19438)),X19437))
| ~ class_Groups_Olinordered__ab__group__add(X19438) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19438),c_Groups_Ozero__class_Ozero(X19438)),X19437))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19438),hAPP(c_Groups_Ouminus__class_Ouminus(X19438),X19437)),X19437))
| ~ class_Groups_Olinordered__ab__group__add(X19438) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).
fof(i_0_8954,plain,
! [X18843,X18844] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18844),hAPP(c_Groups_Ouminus__class_Ouminus(X18844),X18843)),X18843))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18844),c_Groups_Ozero__class_Ozero(X18844)),X18843))
| ~ class_Groups_Olinordered__ab__group__add(X18844) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18844),c_Groups_Ozero__class_Ozero(X18844)),X18843))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18844),hAPP(c_Groups_Ouminus__class_Ouminus(X18844),X18843)),X18843))
| ~ class_Groups_Olinordered__ab__group__add(X18844) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).
fof(i_0_8955,plain,
! [X30483,X30484,X30485,X30486] : hAPP(hAPP(c_Nat_Ocompow(X30486,X30486),X30485),hAPP(hAPP(c_Nat_Ocompow(X30486,X30486),X30484),X30483)) = hAPP(hAPP(c_Nat_Ocompow(X30486,X30486),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30484),X30485)),X30483),
inference(variable_rename,[status(thm)],[fact_funpow__mult]) ).
fof(i_0_8956,plain,
! [X23158,X23159] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23159)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23158)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23159),X23158)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23159),X23158))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23159)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23158))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I4_J])]) ).
fof(i_0_8957,plain,
! [X23156,X23157] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23157),X23156))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23157)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23156))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23157)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23156)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23157),X23156)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__int])]) ).
fof(i_0_8958,plain,
! [X20854,X20855] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20855)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20854)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20855),X20854)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20855),X20854))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20855)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20854))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code])]) ).
fof(i_0_8959,plain,
! [X19101,X19102] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19102)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19101)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19102),X19101)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19102),X19101))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19102)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19101))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I3_J])]) ).
fof(i_0_8960,plain,
! [X19099,X19100] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19100)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19099)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19100),X19099)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19100),X19099))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19100)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19099))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__int])]) ).
fof(i_0_8961,plain,
! [X20856,X20857] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20857)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20856)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20857),X20856)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20857),X20856))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20857)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20856))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code])]) ).
fof(i_0_8962,plain,
! [X18516,X18517] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18517)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18516)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18517),X18516)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18517),X18516))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18517)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18516))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I2_J])]) ).
fof(i_0_8963,plain,
! [X18481,X18482] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18482)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18481)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18482),X18481)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18482),X18481))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18482)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18481))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__int])]) ).
fof(i_0_8964,plain,
! [X20396,X20397] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20397),X20396)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20396),X20397)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20396),X20397))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20397),X20396))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).
fof(i_0_8965,plain,
! [X19634,X19635] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19635),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19634),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19635),X19634)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19635),X19634))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19635),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19634),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le])]) ).
fof(i_0_8966,plain,
! [X20510,X20511] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20511),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20510),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20511),X20510)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20511),X20510))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20511),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20510),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq])]) ).
fof(i_0_8967,plain,
! [X20815,X20816,X20817] :
( ~ class_Int_Onumber__ring(X20817)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20817),hAPP(c_Groups_Ouminus__class_Ouminus(X20817),hAPP(c_Int_Onumber__class_Onumber__of(X20817),X20816))),X20815) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20817),hAPP(c_Int_Onumber__class_Onumber__of(X20817),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20816))),X20815) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult])]) ).
fof(i_0_8968,plain,
! [X18632,X18633,X18634] :
( ~ class_Rings_Ocomm__semiring__1(X18634)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18634),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18634),X18633),X18632)),X18632) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18634),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18634),X18633),c_Groups_Oone__class_Oone(X18634))),X18632) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).
fof(i_0_8969,plain,
! [X32812,X32813,X32814,X32815] :
( ( hAPP(hAPP(c_List_Olist__update(X32814,X32813),X32815),X32812) != X32813
| hAPP(hAPP(c_List_Onth(X32814),X32813),X32815) = X32812
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32815),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32814)),X32813))) )
& ( hAPP(hAPP(c_List_Onth(X32814),X32813),X32815) != X32812
| hAPP(hAPP(c_List_Olist__update(X32814,X32813),X32815),X32812) = X32813
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32815),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32814)),X32813))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__same__conv])])]) ).
fof(i_0_8970,plain,
! [X21014,X21015] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21015)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21015),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21014)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21014)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21015),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21014)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21015)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21015))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21014)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21015),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21014)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21015),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21014)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21015))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5790])])]) ).
fof(i_0_8971,plain,
! [X25983,X25984,X25985] :
( ~ class_Orderings_Olinorder(X25985)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25985),X25984))
| hBOOL(hAPP(hAPP(c_member(X25985),X25983),X25984))
| X25984 = c_Orderings_Obot__class_Obot(tc_fun(X25985,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25985,c_Orderings_Oord__class_Omin(X25985),hAPP(hAPP(c_Set_Oinsert(X25985),X25983),X25984)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25985),X25983),c_Big__Operators_Olattice_OInf__fin(X25985,c_Orderings_Oord__class_Omin(X25985),X25984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5791])]) ).
fof(i_0_8972,plain,
! [X25986,X25987,X25988] :
( ~ class_Orderings_Olinorder(X25988)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25988),X25987))
| hBOOL(hAPP(hAPP(c_member(X25988),X25986),X25987))
| X25987 = c_Orderings_Obot__class_Obot(tc_fun(X25988,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25988,c_Orderings_Oord__class_Omax(X25988),hAPP(hAPP(c_Set_Oinsert(X25988),X25986),X25987)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25988),X25986),c_Big__Operators_Olattice_OSup__fin(X25988,c_Orderings_Oord__class_Omax(X25988),X25987)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5792])]) ).
fof(i_0_8973,plain,
! [X17248,X17249,X17250,X17251,X17252] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OAss(X17252,X17251),X17250,X17249,X17248)
| X17248 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X17250),X17252),hAPP(X17251,X17250)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I2_J])]) ).
fof(i_0_8974,plain,
! [X18995,X18996] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18996))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18995))),
inference(variable_rename,[status(thm)],[fact_negative__zle]) ).
fof(i_0_8975,plain,
! [X20615,X20616] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20616)),X20615))),
inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs]) ).
fof(i_0_8976,plain,
! [X22361,X22362,X22363] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22363),X22362)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22361),X22362)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22363),X22361)),X22362),
inference(variable_rename,[status(thm)],[fact_min__diff]) ).
fof(i_0_8977,plain,
! [X20337,X20338,X20339] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20339),X20338)),X20337) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20339),X20337)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20338),X20337)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).
cnf(i_0_8978,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X1)),X2) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_5793]) ).
fof(i_0_8979,plain,
! [X18831,X18832,X18833] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18833),X18832)),X18831) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18833),X18831)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18832),X18831)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(i_0_8980,plain,
! [X20346,X20347,X20348] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20348),X20347)),X20346) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20348),X20346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20347),X20346)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).
fof(i_0_8981,plain,
! [X19242,X19243,X19244] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19244),X19243)),X19242) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19244),X19242)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19243),X19242)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
fof(i_0_8982,plain,
! [X32621,X32622,X32623,X32624] : hAPP(hAPP(c_List_Onth(X32624),hAPP(hAPP(c_List_Olist_OCons(X32624),X32623),X32622)),X32621) = c_Nat_Onat_Onat__case(X32624,X32623,hAPP(c_List_Onth(X32624),X32622),X32621),
inference(variable_rename,[status(thm)],[fact_nth_Osimps]) ).
fof(i_0_8983,plain,
! [X24646,X24647,X24648,X24649] :
( ( X24647 = c_Orderings_Obot__class_Obot(tc_fun(X24649,tc_HOL_Obool))
| c_Sum__Type_OPlus(X24649,X24648,X24647,X24646) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X24649,X24648),tc_HOL_Obool)) )
& ( X24646 = c_Orderings_Obot__class_Obot(tc_fun(X24648,tc_HOL_Obool))
| c_Sum__Type_OPlus(X24649,X24648,X24647,X24646) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X24649,X24648),tc_HOL_Obool)) )
& ( X24647 != c_Orderings_Obot__class_Obot(tc_fun(X24649,tc_HOL_Obool))
| X24646 != c_Orderings_Obot__class_Obot(tc_fun(X24648,tc_HOL_Obool))
| c_Sum__Type_OPlus(X24649,X24648,X24647,X24646) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X24649,X24648),tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv])])]) ).
fof(i_0_8984,plain,
! [X23092,X23093,X23094] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23094),X23092))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23093),X23092))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23092),X23093))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23094),X23093)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23092),X23094))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23093),X23092))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23092),X23093))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23094),X23093)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5794])])]) ).
fof(i_0_8985,plain,
! [X23074,X23075,X23076] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23076),X23074))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23075),X23074))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23076),X23075))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23075),X23076)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23074),X23076))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23075),X23074))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23076),X23075))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23075),X23076)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5795])])]) ).
fof(i_0_8986,plain,
! [X24851,X24852,X24853] :
( ( X24853 = X24852
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24853,X24852) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24851),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
& ( X24852 = X24851
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24853,X24852) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24851),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
& ( X24853 != X24852
| X24852 != X24851
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24853,X24852) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24851),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton__iff])])]) ).
fof(i_0_8987,plain,
! [X31268,X31269,X31270] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31270,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31270,tc_HOL_Obool)),X31269),X31268)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31270,tc_HOL_Obool)),X31269),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31270,tc_HOL_Obool),X31268)),
inference(variable_rename,[status(thm)],[fact_Union__insert]) ).
fof(i_0_8988,plain,
! [X31363,X31364,X31365] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31365,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31365,tc_HOL_Obool)),X31364),X31363)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31365,tc_HOL_Obool)),X31364),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31365,tc_HOL_Obool),X31363)),
inference(variable_rename,[status(thm)],[fact_Inter__insert]) ).
fof(i_0_8989,plain,
! [X23390,X23391,X23392] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23392,X23391) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X23390,X23391)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23391),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23392),X23390))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23391),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23392),X23390)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X23392,X23391) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X23390,X23391) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__eq__dvd__iff])]) ).
fof(i_0_8990,plain,
! [X29596,X29597] :
( hAPP(hAPP(c_Relation_Orel__comp(X29597,X29597,X29597),X29596),X29596) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29597,X29597),tc_HOL_Obool))
| c_Wellfounded_Owf(X29597,X29596) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__loop])]) ).
fof(i_0_8991,plain,
! [X20570,X20571] :
( ( X20571 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20571),X20570) = X20570 )
& ( X20571 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20571),X20570) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20571),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20570)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])]) ).
fof(i_0_8992,plain,
! [X26215,X26216,X26217,X26218,X26219] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26219,tc_Option_Ooption(X26218)),X26217),X26216),hAPP(c_Option_Ooption_OSome(X26218),X26215)) != hAPP(c_COMBK(tc_Option_Ooption(X26218),X26219),c_Option_Ooption_ONone(X26218)),
inference(variable_rename,[status(thm)],[fact_map__upd__nonempty]) ).
fof(i_0_8993,plain,
! [X23771,X23772,X23773,X23774] :
( ~ class_Rings_Osemiring__1(X23774)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23773,X23774),hAPP(c_COMBK(X23774,X23773),X23772)),X23771) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23774),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23774),hAPP(c_Finite__Set_Ocard(X23773),X23771))),X23772) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__constant])]) ).
fof(i_0_8994,plain,
! [X19329,X19330] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19330),hAPP(c_Int_Oring__1__class_Oof__int(X19330),X19329)),c_Groups_Ozero__class_Ozero(X19330)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19329),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(X19330) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19329),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19330),hAPP(c_Int_Oring__1__class_Oof__int(X19330),X19329)),c_Groups_Ozero__class_Ozero(X19330)))
| ~ class_Rings_Olinordered__idom(X19330) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff])])]) ).
fof(i_0_8995,plain,
! [X18610,X18611] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18611),hAPP(c_Int_Oring__1__class_Oof__int(X18611),X18610)),c_Groups_Ozero__class_Ozero(X18611)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18610),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(X18611) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18610),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18611),hAPP(c_Int_Oring__1__class_Oof__int(X18611),X18610)),c_Groups_Ozero__class_Ozero(X18611)))
| ~ class_Rings_Olinordered__idom(X18611) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff])])]) ).
fof(i_0_8996,plain,
! [X19775,X19776,X19777,X19778] :
( ~ class_Divides_Osemiring__div(X19778)
| c_Divides_Odiv__class_Omod(X19778,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19778),X19777),c_Divides_Odiv__class_Omod(X19778,X19776,X19775)),X19775) = c_Divides_Odiv__class_Omod(X19778,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19778),X19777),X19776),X19775) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J])]) ).
fof(i_0_8997,plain,
! [X20279,X20280,X20281,X20282] :
( ~ class_Divides_Oring__div(X20282)
| c_Divides_Odiv__class_Omod(X20282,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20282),X20281),X20280),X20279) = c_Divides_Odiv__class_Omod(X20282,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20282),X20281),c_Divides_Odiv__class_Omod(X20282,X20280,X20279)),X20279) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq])]) ).
fof(i_0_8998,plain,
! [X19823,X19824,X19825,X19826] :
( ~ class_Divides_Osemiring__div(X19826)
| c_Divides_Odiv__class_Omod(X19826,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19826),X19825),X19824),X19823) = c_Divides_Odiv__class_Omod(X19826,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19826),X19825),c_Divides_Odiv__class_Omod(X19826,X19824,X19823)),X19823) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])]) ).
fof(i_0_8999,plain,
! [X19787,X19788,X19789,X19790] :
( ~ class_Divides_Osemiring__div(X19790)
| c_Divides_Odiv__class_Omod(X19790,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19790),X19789),X19788),X19787) = c_Divides_Odiv__class_Omod(X19790,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19790),X19789),c_Divides_Odiv__class_Omod(X19790,X19788,X19787)),X19787) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])]) ).
fof(i_0_9000,plain,
! [X22946,X22947,X22948,X22949] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22949,tc_HOL_Obool)),X22948),X22947))
| ~ hBOOL(hAPP(X22948,X22946))
| hBOOL(hAPP(X22947,X22946)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_9001,plain,
! [X22942,X22943,X22944,X22945] :
( ~ hBOOL(hAPP(X22945,X22944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22943,tc_HOL_Obool)),X22945),X22942))
| hBOOL(hAPP(X22942,X22944)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_9002,plain,
! [X20355,X20356] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20356))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20356),X20355))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20355),X20356)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X20355)),hAPP(c_Int_Onat,X20356)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__distrib])]) ).
fof(i_0_9003,plain,
! [X24172,X24173,X24174] :
( ~ class_Orderings_Olinorder(X24174)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24174),X24173),X24172))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24174,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24174,X24173),X24172)),hAPP(c_SetInterval_Oord__class_OatLeast(X24174),X24172)) = hAPP(c_SetInterval_Oord__class_OatLeast(X24174),X24173) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J])]) ).
fof(i_0_9004,plain,
! [X21132,X21133] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21133),hAPP(c_Int_Onumber__class_Onumber__of(X21133),X21132)),c_Groups_Ozero__class_Ozero(X21133)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21132),c_Int_OPls))
| ~ class_Int_Onumber__ring(X21133)
| ~ class_Rings_Olinordered__idom(X21133) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21132),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21133),hAPP(c_Int_Onumber__class_Onumber__of(X21133),X21132)),c_Groups_Ozero__class_Ozero(X21133)))
| ~ class_Int_Onumber__ring(X21133)
| ~ class_Rings_Olinordered__idom(X21133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])]) ).
fof(i_0_9005,plain,
! [X21134,X21135] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21135),hAPP(c_Int_Onumber__class_Onumber__of(X21135),X21134)),c_Groups_Ozero__class_Ozero(X21135)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21134),c_Int_OPls))
| ~ class_Int_Onumber__ring(X21135)
| ~ class_Rings_Olinordered__idom(X21135) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21134),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21135),hAPP(c_Int_Onumber__class_Onumber__of(X21135),X21134)),c_Groups_Ozero__class_Ozero(X21135)))
| ~ class_Int_Onumber__ring(X21135)
| ~ class_Rings_Olinordered__idom(X21135) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).
fof(i_0_9006,plain,
! [X28459,X28460,X28461,X28462] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28462),X28461),c_Map_Odom(X28462,X28460,X28459)))
| hAPP(X28459,X28461) != c_Option_Ooption_ONone(X28460) )
& ( hAPP(X28459,X28461) = c_Option_Ooption_ONone(X28460)
| hBOOL(hAPP(hAPP(c_member(X28462),X28461),c_Map_Odom(X28462,X28460,X28459))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_domIff])]) ).
fof(i_0_9007,plain,
! [X32188,X32189,X32190,X32191] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32191)),X32190) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32189)),X32188)
| hAPP(hAPP(c_List_Omap(tc_prod(X32191,X32189),X32191),c_Product__Type_Ofst(X32191,X32189)),hAPP(hAPP(c_List_Ozip(X32191,X32189),X32190),X32188)) = X32190 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__fst__zip])]) ).
fof(i_0_9008,plain,
! [X32192,X32193,X32194,X32195] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32195)),X32194) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32193)),X32192)
| hAPP(hAPP(c_List_Omap(tc_prod(X32195,X32193),X32193),c_Product__Type_Osnd(X32195,X32193)),hAPP(hAPP(c_List_Ozip(X32195,X32193),X32194),X32192)) = X32192 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__snd__zip])]) ).
fof(i_0_9009,plain,
! [X20140,X20141,X20142] :
( ~ class_Divides_Osemiring__div(X20142)
| X20141 = c_Groups_Ozero__class_Ozero(X20142)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20142),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20142),X20141),X20140)),X20141) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20142),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20142),X20140),X20141)),c_Groups_Oone__class_Oone(X20142)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self1])]) ).
fof(i_0_9010,plain,
! [X20137,X20138,X20139] :
( ~ class_Divides_Osemiring__div(X20139)
| X20138 = c_Groups_Ozero__class_Ozero(X20139)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20139),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20139),X20137),X20138)),X20138) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20139),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20139),X20137),X20138)),c_Groups_Oone__class_Oone(X20139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self2])]) ).
fof(i_0_9011,plain,
! [X19807,X19808,X19809,X19810] :
( ~ class_Divides_Osemiring__div(X19810)
| c_Divides_Odiv__class_Omod(X19810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19810),X19809),X19808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19810),X19807),X19808)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19810),c_Divides_Odiv__class_Omod(X19810,X19809,X19807)),X19808) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2])]) ).
fof(i_0_9012,plain,
! [X20818,X20819] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20819),X20818))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20819))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20818))),
inference(variable_rename,[status(thm)],[fact_nat__abs__mult__distrib]) ).
fof(i_0_9013,plain,
! [X20073,X20074,X20075] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20075))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20075),X20074)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20075),X20073)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20074),X20073) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])]) ).
fof(i_0_9014,plain,
! [X20112,X20113,X20114] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20114))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20112),X20114)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20113),X20112)),X20114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])]) ).
fof(i_0_9015,plain,
! [X21042,X21043] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21043)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21043)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21042)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21042)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21043)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21043)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21042)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21043)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21042))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5796])]) ).
fof(i_0_9016,plain,
! [X21012,X21013] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21013)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21013)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21012)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21013)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21013)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21012)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21013)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21012))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5797])]) ).
fof(i_0_9017,plain,
! [X31952,X31953,X31954] : c_Map_Odom(X31954,X31953,c_Map_Omap__of(X31954,X31953,X31952)) = hAPP(c_Set_Oimage(tc_prod(X31954,X31953),X31954,c_Product__Type_Ofst(X31954,X31953)),hAPP(c_List_Oset(tc_prod(X31954,X31953)),X31952)),
inference(variable_rename,[status(thm)],[fact_dom__map__of__conv__image__fst]) ).
fof(i_0_9018,plain,
! [X22418,X22419,X22420,X22421,X22422] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22422,X22421,X22420),X22419),X22418) = hAPP(hAPP(X22419,hAPP(c_Product__Type_Ofst(X22422,X22421),X22418)),hAPP(c_Product__Type_Osnd(X22422,X22421),X22418)),
inference(variable_rename,[status(thm)],[fact_split__def]) ).
fof(i_0_9019,plain,
! [X22413,X22414,X22415,X22416,X22417] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22417,X22416,X22415),X22414),X22413) = hAPP(hAPP(X22414,hAPP(c_Product__Type_Ofst(X22417,X22416),X22413)),hAPP(c_Product__Type_Osnd(X22417,X22416),X22413)),
inference(variable_rename,[status(thm)],[fact_split__beta]) ).
fof(i_0_9020,plain,
! [X22398,X22399,X22400,X22401,X22402] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22402,X22401,X22400),X22399),X22398) = hAPP(hAPP(X22399,hAPP(c_Product__Type_Ofst(X22402,X22401),X22398)),hAPP(c_Product__Type_Osnd(X22402,X22401),X22398)),
inference(variable_rename,[status(thm)],[fact_prod__case__beta]) ).
fof(i_0_9021,plain,
! [X32878,X32879,X32880,X32881,X32882] :
( ( X32881 = X32879
| hAPP(hAPP(c_List_Oappend(X32882),X32881),hAPP(hAPP(c_List_Olist_OCons(X32882),X32880),c_List_Olist_ONil(X32882))) != hAPP(hAPP(c_List_Oappend(X32882),X32879),hAPP(hAPP(c_List_Olist_OCons(X32882),X32878),c_List_Olist_ONil(X32882))) )
& ( X32880 = X32878
| hAPP(hAPP(c_List_Oappend(X32882),X32881),hAPP(hAPP(c_List_Olist_OCons(X32882),X32880),c_List_Olist_ONil(X32882))) != hAPP(hAPP(c_List_Oappend(X32882),X32879),hAPP(hAPP(c_List_Olist_OCons(X32882),X32878),c_List_Olist_ONil(X32882))) )
& ( X32881 != X32879
| X32880 != X32878
| hAPP(hAPP(c_List_Oappend(X32882),X32881),hAPP(hAPP(c_List_Olist_OCons(X32882),X32880),c_List_Olist_ONil(X32882))) = hAPP(hAPP(c_List_Oappend(X32882),X32879),hAPP(hAPP(c_List_Olist_OCons(X32882),X32878),c_List_Olist_ONil(X32882))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])]) ).
fof(i_0_9022,plain,
! [X23216,X23217] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23216),X23217)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23217),X23216)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23217),X23216))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23216),X23217))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__reduce])]) ).
fof(i_0_9023,plain,
! [X33448,X33449,X33450] :
( X33450 = c_List_Olist_ONil(X33449)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33448),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33449)),X33450)))
| hAPP(c_List_Ohd(X33449),hAPP(hAPP(c_List_Odrop(X33449),X33448),X33450)) = hAPP(hAPP(c_List_Onth(X33449),X33450),X33448) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__drop__conv__nth])]) ).
fof(i_0_9024,plain,
! [X20625,X20626,X20627] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20627)
| hAPP(c_Groups_Oabs__class_Oabs(X20627),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20627),hAPP(c_Groups_Oabs__class_Oabs(X20627),X20626)),hAPP(c_Groups_Oabs__class_Oabs(X20627),X20625))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20627),hAPP(c_Groups_Oabs__class_Oabs(X20627),X20626)),hAPP(c_Groups_Oabs__class_Oabs(X20627),X20625)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).
fof(i_0_9025,plain,
! [X30708,X30709,X30710,X30711,X30712] :
( ~ c_Finite__Set_Ofolding__one__idem(X30712,X30711,X30710)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30712),X30709))
| hAPP(X30710,hAPP(hAPP(c_Set_Oinsert(X30712),X30708),X30709)) = hAPP(hAPP(c_Finite__Set_Ofold(X30712,X30712,X30711),X30708),X30709) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H])]) ).
fof(i_0_9026,plain,
! [X26995,X26996,X26997] :
( ~ class_Lattices_Osemilattice__inf(X26997)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26997),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26997),X26996),X26995)),X26996)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])]) ).
fof(i_0_9027,plain,
! [X26992,X26993,X26994] :
( ~ class_Lattices_Olattice(X26994)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26994),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26994),X26993),X26992)),X26993)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J])]) ).
fof(i_0_9028,plain,
! [X27001,X27002,X27003] :
( ~ class_Lattices_Osemilattice__inf(X27003)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27003),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27003),X27002),X27001)),X27001)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])]) ).
fof(i_0_9029,plain,
! [X26998,X26999,X27000] :
( ~ class_Lattices_Olattice(X27000)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27000),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27000),X26999),X26998)),X26998)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])]) ).
fof(i_0_9030,plain,
! [X22302,X22303,X22304] :
( ~ class_Orderings_Olinorder(X22304)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22304),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22304),X22303),X22302)),X22303)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le1])]) ).
fof(i_0_9031,plain,
! [X22299,X22300,X22301] :
( ~ class_Orderings_Olinorder(X22301)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22301),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22301),X22300),X22299)),X22299)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2])]) ).
fof(i_0_9032,plain,
! [X20599] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20599)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20599) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20599)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_expand__Suc])]) ).
fof(i_0_9033,plain,
! [X17674,X17675,X17676] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17676),X17675),X17674))
| c_Natural_Oevaln(X17676,X17675,esk7_3(X17674,X17675,X17676),X17674) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__evaln])])]) ).
fof(i_0_9034,plain,
! [X17463,X17464,X17465,X17467,X17468,X17469,X17470] :
( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17465),X17464),X17463))
| c_Natural_Oevaln(X17465,X17464,esk3_3(X17463,X17464,X17465),X17463) )
& ( ~ c_Natural_Oevaln(X17469,X17468,X17470,X17467)
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17469),X17468),X17467)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eval__eq])])])])]) ).
fof(i_0_9035,plain,
! [X24066,X24067,X24068] :
( ~ class_Orderings_Olinorder(X24068)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24068),X24067),X24066))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24068,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24068),X24067)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24068,X24067,X24066)) = hAPP(c_SetInterval_Oord__class_OlessThan(X24068),X24066) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J])]) ).
fof(i_0_9036,plain,
! [X23846,X23847,X23848] :
( ~ class_Orderings_Olinorder(X23848)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23848),X23847),X23846))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23848,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X23848),X23847)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23848,X23847,X23846)) = hAPP(c_SetInterval_Oord__class_OatMost(X23848),X23846) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J])]) ).
fof(i_0_9037,plain,
! [X24063,X24064,X24065] :
( ~ class_Orderings_Olinorder(X24065)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24065),X24064),X24063))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24065,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24065),X24064)),c_SetInterval_Oord__class_OatLeastAtMost(X24065,X24064,X24063)) = hAPP(c_SetInterval_Oord__class_OatMost(X24065),X24063) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J])]) ).
fof(i_0_9038,plain,
! [X23226,X23227,X23228] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23228),hAPP(c_Groups_Ouminus__class_Ouminus(X23228),X23227)),X23226))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23228),X23227),X23226))
| ~ class_Rings_Ocomm__ring__1(X23228) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23228),X23227),X23226))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23228),hAPP(c_Groups_Ouminus__class_Ouminus(X23228),X23227)),X23226))
| ~ class_Rings_Ocomm__ring__1(X23228) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff])])]) ).
fof(i_0_9039,plain,
! [X23194,X23195,X23196] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23196),hAPP(c_Groups_Oabs__class_Oabs(X23196),X23195)),X23194))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23196),X23195),X23194))
| ~ class_Rings_Olinordered__idom(X23196) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23196),X23195),X23194))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23196),hAPP(c_Groups_Oabs__class_Oabs(X23196),X23195)),X23194))
| ~ class_Rings_Olinordered__idom(X23196) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__dvd__iff])])]) ).
fof(i_0_9040,plain,
! [X20619,X20620,X20621] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20621)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20621),hAPP(c_Groups_Oabs__class_Oabs(X20621),X20620)),X20619))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20621),X20620),X20619)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).
fof(i_0_9041,plain,
! [X27122,X27123,X27124,X27125] :
( ~ class_Lattices_Odistrib__lattice(X27125)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27125),X27124),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27125),X27123),X27122)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27125),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27125),X27124),X27123)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27125),X27124),X27122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1])]) ).
fof(i_0_9042,plain,
! [X27118,X27119,X27120,X27121] :
( ~ class_Lattices_Odistrib__lattice(X27121)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27121),X27120),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27121),X27119),X27118)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27121),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27121),X27120),X27119)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27121),X27120),X27118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1])]) ).
fof(i_0_9043,plain,
! [X22550,X22551,X22552,X22553] :
( ~ class_Orderings_Olinorder(X22553)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22553),X22552),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22553),X22551),X22550)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22553),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22553),X22552),X22551)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22553),X22552),X22550)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib1])]) ).
fof(i_0_9044,plain,
! [X22554,X22555,X22556,X22557] :
( ~ class_Orderings_Olinorder(X22557)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22557),X22556),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22557),X22555),X22554)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22557),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22557),X22556),X22555)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22557),X22556),X22554)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib1])]) ).
fof(i_0_9045,plain,
! [X18816,X18817,X18818,X18819] :
( ~ class_Rings_Ocomm__semiring__1(X18819)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18819),X18818),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18819),X18817),X18816)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18819),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18819),X18818),X18817)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18819),X18818),X18816)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).
fof(i_0_9046,plain,
! [X18695,X18696,X18697,X18698] :
( ~ class_Rings_Ocomm__semiring__1(X18698)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18698),X18697),X18696)),X18695) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18698),X18697),X18695)),X18696) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).
fof(i_0_9047,plain,
! [X18161,X18162,X18163,X18164] :
( ~ class_Rings_Ocomm__semiring__1(X18164)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18164),X18163),X18162)),X18161) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18164),X18163),X18161)),X18162) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_9048,plain,
! [X24522] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X24522),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X24522)),c_Option_Ooption_ONone(X24522)),hAPP(c_Set_Oimage(X24522,tc_Option_Ooption(X24522),c_Option_Ooption_OSome(X24522)),c_Orderings_Otop__class_Otop(tc_fun(X24522,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__option__conv]) ).
fof(i_0_9049,plain,
! [X29425,X29426,X29427] : hAPP(c_Fun_Ocomp(X29427,X29427,X29426,c_Fun_Oid(X29427)),X29425) = X29425,
inference(variable_rename,[status(thm)],[fact_id__o]) ).
fof(i_0_9050,plain,
! [X32201,X32202,X32203] :
( ~ hBOOL(hAPP(hAPP(c_member(X32203),X32202),hAPP(c_List_Oset(X32203),X32201)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32203)),X32201))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__pos__if__in__set])]) ).
fof(i_0_9051,plain,
! [X29079,X29080,X29081] :
( ~ class_Groups_Oab__semigroup__mult(X29081)
| X29080 = c_Orderings_Obot__class_Obot(tc_fun(X29081,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29081),X29080))
| hBOOL(hAPP(hAPP(c_member(X29081),X29079),X29080))
| hAPP(c_Finite__Set_Ofold1(X29081,c_Groups_Otimes__class_Otimes(X29081)),hAPP(hAPP(c_Set_Oinsert(X29081),X29079),X29080)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29081),X29079),hAPP(c_Finite__Set_Ofold1(X29081,c_Groups_Otimes__class_Otimes(X29081)),X29080)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5798])]) ).
fof(i_0_9052,plain,
! [X30586,X30587,X30588] :
( ~ c_Relation_Osingle__valued(X30588,X30588,X30587)
| c_Relation_Osingle__valued(X30588,X30588,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30588,X30588),tc_HOL_Obool),X30586),X30587)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__pow])]) ).
fof(i_0_9053,plain,
! [X22988,X22989,X22990,X22991] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X22991),X22990),X22989),X22988) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22991)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X22991),X22990)),
inference(variable_rename,[status(thm)],[fact_Random__Sequence_Osingle__def]) ).
fof(i_0_9054,plain,
! [X29867,X29868,X29869,X29870,X29872,X29873,X29874,X29875,X29876] :
( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X29870,X29869,X29868),X29867))
| hBOOL(hAPP(hAPP(X29868,X29867),esk329_2(X29867,X29868))) )
& ( ~ hBOOL(hAPP(hAPP(X29873,X29872),X29874))
| hBOOL(hAPP(c_Predicate_ODomainP(X29876,X29875,X29873),X29872)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Oequations])])])])]) ).
fof(i_0_9055,plain,
! [X27980,X27981,X27982,X27983,X27984] :
( ( hAPP(X27982,X27981) != hAPP(X27982,X27980)
| X27981 = X27980
| ~ c_Fun_Oinj__on(X27984,X27983,X27982,c_Orderings_Otop__class_Otop(tc_fun(X27984,tc_HOL_Obool))) )
& ( X27981 != X27980
| hAPP(X27982,X27981) = hAPP(X27982,X27980)
| ~ c_Fun_Oinj__on(X27984,X27983,X27982,c_Orderings_Otop__class_Otop(tc_fun(X27984,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).
fof(i_0_9056,plain,
! [X27985,X27986,X27987,X27988,X27989] :
( ~ c_Fun_Oinj__on(X27989,X27988,X27987,c_Orderings_Otop__class_Otop(tc_fun(X27989,tc_HOL_Obool)))
| hAPP(X27987,X27986) != hAPP(X27987,X27985)
| X27986 = X27985 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).
fof(i_0_9057,plain,
! [X24814,X24815] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24815),X24814))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24814),X24815))
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24814,X24815) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5799])]) ).
fof(i_0_9058,plain,
! [X30744,X30745,X30746] :
( ~ class_Orderings_Olinorder(X30746)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30746),X30745))
| c_Big__Operators_Olattice_OInf__fin(X30746,c_Orderings_Oord__class_Omin(X30746),hAPP(hAPP(c_Set_Oinsert(X30746),X30744),X30745)) = hAPP(hAPP(c_Finite__Set_Ofold(X30746,X30746,c_Orderings_Oord__class_Omin(X30746)),X30744),X30745) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H])]) ).
fof(i_0_9059,plain,
! [X30747,X30748,X30749] :
( ~ class_Orderings_Olinorder(X30749)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30749),X30748))
| c_Big__Operators_Olattice_OSup__fin(X30749,c_Orderings_Oord__class_Omax(X30749),hAPP(hAPP(c_Set_Oinsert(X30749),X30747),X30748)) = hAPP(hAPP(c_Finite__Set_Ofold(X30749,X30749,c_Orderings_Oord__class_Omax(X30749)),X30747),X30748) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H])]) ).
cnf(i_0_9060,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5800]) ).
fof(i_0_9061,plain,
! [X19737,X19738,X19740] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk53_2(X19737,X19738)),X19737))
| ~ hBOOL(hAPP(X19738,X19737))
| hBOOL(hAPP(X19738,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19740),esk53_2(X19737,X19738)))
| ~ hBOOL(hAPP(X19738,X19740))
| ~ hBOOL(hAPP(X19738,X19737))
| hBOOL(hAPP(X19738,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X19738,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk53_2(X19737,X19738)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X19738,X19737))
| hBOOL(hAPP(X19738,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5801])])])])]) ).
fof(i_0_9062,plain,
! [X33560,X33561,X33562,X33563] : hAPP(c_List_Ofoldl(X33563,X33562,X33561,X33560),c_List_Olist_ONil(X33562)) = X33560,
inference(variable_rename,[status(thm)],[fact_foldl__Nil]) ).
fof(i_0_9063,plain,
! [X32612,X32613,X32614,X32615] : hAPP(c_List_Olist_Olist__case(X32615,X32614,X32613,X32612),c_List_Olist_ONil(X32614)) = X32613,
inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J]) ).
fof(i_0_9064,plain,
! [X29422,X29423,X29424] : hAPP(c_Fun_Ocomp(X29424,X29423,X29424,X29422),c_Fun_Oid(X29424)) = X29422,
inference(variable_rename,[status(thm)],[fact_o__id]) ).
fof(i_0_9065,plain,
! [X18133,X18134,X18135,X18136] : hAPP(c_Option_Ooption_Ooption__case(X18136,X18135,X18134,X18133),c_Option_Ooption_ONone(X18135)) = X18134,
inference(variable_rename,[status(thm)],[fact_option_Osimps_I4_J]) ).
fof(i_0_9066,plain,
! [X19346,X19347,X19348] :
( ( X19347 = c_Groups_Ozero__class_Ozero(X19348)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19348),X19347),X19346) != c_Groups_Ozero__class_Ozero(X19348)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19348),c_Groups_Ozero__class_Ozero(X19348)),X19346))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19348),c_Groups_Ozero__class_Ozero(X19348)),X19347))
| ~ class_Groups_Oordered__comm__monoid__add(X19348) )
& ( X19346 = c_Groups_Ozero__class_Ozero(X19348)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19348),X19347),X19346) != c_Groups_Ozero__class_Ozero(X19348)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19348),c_Groups_Ozero__class_Ozero(X19348)),X19346))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19348),c_Groups_Ozero__class_Ozero(X19348)),X19347))
| ~ class_Groups_Oordered__comm__monoid__add(X19348) )
& ( X19347 != c_Groups_Ozero__class_Ozero(X19348)
| X19346 != c_Groups_Ozero__class_Ozero(X19348)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19348),X19347),X19346) = c_Groups_Ozero__class_Ozero(X19348)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19348),c_Groups_Ozero__class_Ozero(X19348)),X19346))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19348),c_Groups_Ozero__class_Ozero(X19348)),X19347))
| ~ class_Groups_Oordered__comm__monoid__add(X19348) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
cnf(i_0_9067,plain,
c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))),
inference(split_conjunct,[status(thm)],[i_0_5802]) ).
fof(i_0_9068,plain,
! [X20425,X20426,X20427] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20427),X20426))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20425),X20426)),X20427) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20426),X20427)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).
fof(i_0_9069,plain,
! [X20447,X20448,X20449] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20449),X20448))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20448),X20449)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20447),X20449)),X20448) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).
fof(i_0_9070,plain,
! [X20436,X20437,X20438] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20438),X20437))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20436),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20437),X20438)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20436),X20437)),X20438) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).
fof(i_0_9071,plain,
! [X19731,X19732,X19733] :
( ~ class_Lattices_Oboolean__algebra(X19733)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19733),X19732),X19731))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19733),hAPP(c_Groups_Ouminus__class_Ouminus(X19733),X19731)),hAPP(c_Groups_Ouminus__class_Ouminus(X19733),X19732))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).
fof(i_0_9072,plain,
! [X19227,X19228,X19229] :
( ~ class_Groups_Oordered__ab__group__add(X19229)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19229),X19228),X19227))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19229),hAPP(c_Groups_Ouminus__class_Ouminus(X19229),X19227)),hAPP(c_Groups_Ouminus__class_Ouminus(X19229),X19228))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).
cnf(i_0_9073,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5803]) ).
cnf(i_0_9074,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5804]) ).
cnf(i_0_9075,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5805]) ).
cnf(i_0_9076,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5806]) ).
fof(i_0_9077,plain,
! [X18838] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X18838)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18838)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18838))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X18838))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq])]) ).
fof(i_0_9078,plain,
! [X19982,X19983] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19983,X19982)),X19983)),
inference(variable_rename,[status(thm)],[fact_mod__less__eq__dividend]) ).
fof(i_0_9079,plain,
! [X24862] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24862)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X24862)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24862)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_greaterThan__Suc]) ).
fof(i_0_9080,plain,
! [X20742,X20743,X20744,X20745] :
( ~ class_Rings_Ocomm__semiring__1(X20745)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20745),hAPP(hAPP(c_Power_Opower__class_Opower(X20745),X20744),X20743)),hAPP(hAPP(c_Power_Opower__class_Opower(X20745),X20744),X20742)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20745),X20744),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20743),X20742)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).
fof(i_0_9081,plain,
! [X20947,X20948,X20949,X20950] :
( ~ class_Groups_Omonoid__mult(X20950)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20950),X20949),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20948),X20947)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20950),hAPP(hAPP(c_Power_Opower__class_Opower(X20950),X20949),X20948)),hAPP(hAPP(c_Power_Opower__class_Opower(X20950),X20949),X20947)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).
fof(i_0_9082,plain,
! [X30729,X30730,X30731] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X30731)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30731),X30730))
| hAPP(c_Finite__Set_Ofold1(X30731,c_Groups_Otimes__class_Otimes(X30731)),hAPP(hAPP(c_Set_Oinsert(X30731),X30729),X30730)) = hAPP(hAPP(c_Finite__Set_Ofold(X30731,X30731,c_Groups_Otimes__class_Otimes(X30731)),X30729),X30730) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem])]) ).
fof(i_0_9083,plain,
! [X18923,X18924,X18925,X18926,X18927,X18928] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18928)
| X18927 = c_Groups_Ozero__class_Ozero(X18928)
| X18926 != X18925
| X18924 = X18923
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18928),X18926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18928),X18927),X18924)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18928),X18925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18928),X18927),X18923)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).
fof(i_0_9084,plain,
! [X30016,X30017] : c_Hilbert__Choice_OEps(X30017,hAPP(hAPP(c_COMBC(X30017,X30017,tc_HOL_Obool),c_fequal),X30016)) = X30016,
inference(variable_rename,[status(thm)],[fact_some__eq__trivial]) ).
fof(i_0_9085,plain,
! [X22994,X22995] : c_HOL_OThe(X22995,hAPP(hAPP(c_COMBC(X22995,X22995,tc_HOL_Obool),c_fequal),X22994)) = X22994,
inference(variable_rename,[status(thm)],[fact_the__eq__trivial]) ).
fof(i_0_9086,plain,
! [X20398,X20399] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20399),X20398)),hAPP(c_Nat_OSuc,X20399))),
inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).
fof(i_0_9087,plain,
! [X18346,X18347] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18347),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18347),X18346)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_9088,plain,
! [X18348,X18349] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18349),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18348),X18349)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_9089,plain,
! [X27448,X27449,X27450,X27451] :
( ~ class_Orderings_Oorder(X27451)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27451,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27451,X27450,X27449)),c_SetInterval_Oord__class_OatLeastAtMost(X27451,X27449,X27448)) = c_Orderings_Obot__class_Obot(tc_fun(X27451,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J])]) ).
fof(i_0_9090,plain,
! [X27495,X27496,X27497,X27498] :
( ~ class_Orderings_Oorder(X27498)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27498,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27498,X27497,X27496)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27498,X27496,X27495)) = c_Orderings_Obot__class_Obot(tc_fun(X27498,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J])]) ).
fof(i_0_9091,plain,
! [X27401,X27402,X27403,X27404] :
( ~ class_Orderings_Oorder(X27404)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27404,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27404,X27403,X27402)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27404,X27402,X27401)) = c_Orderings_Obot__class_Obot(tc_fun(X27404,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J])]) ).
fof(i_0_9092,plain,
! [X27452,X27453,X27454,X27455] :
( ~ class_Orderings_Oorder(X27455)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27455,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X27455,X27454,X27453)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27455,X27453,X27452)) = c_Orderings_Obot__class_Obot(tc_fun(X27455,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J])]) ).
fof(i_0_9093,plain,
! [X27444,X27445,X27446,X27447] :
( ~ class_Orderings_Oorder(X27447)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27447,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X27447,X27446,X27445)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27447,X27445,X27444)) = c_Orderings_Obot__class_Obot(tc_fun(X27447,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J])]) ).
fof(i_0_9094,plain,
! [X24614,X24615] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24615,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X24615,tc_HOL_Obool))),X24614)),
inference(variable_rename,[status(thm)],[fact_empty__subsetI]) ).
fof(i_0_9095,plain,
! [X30396,X30397,X30398] :
( ~ c_Equiv__Relations_Oequiv(X30398,X30397,X30396)
| hAPP(hAPP(c_Relation_Orel__comp(X30398,X30398,X30398),hAPP(c_Relation_Oconverse(X30398,X30398),X30396)),X30396) = X30396 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__comp__eq])]) ).
fof(i_0_9096,plain,
! [X27332,X27333,X27334,X27335] :
( hBOOL(hAPP(hAPP(c_member(X27335),X27334),X27333))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27335,tc_HOL_Obool)),X27333),hAPP(hAPP(c_Set_Oinsert(X27335),X27334),X27332)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27335,tc_HOL_Obool)),X27333),X27332) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5807])]) ).
fof(i_0_9097,plain,
! [X17471,X17472,X17473,X17474] :
( ~ c_Natural_Oevaln(X17474,X17473,X17472,X17471)
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17474),X17473),X17471)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__evalc])]) ).
fof(i_0_9098,plain,
! [X17278,X17279,X17280,X17281] : c_Natural_Oevaln(c_Com_Ocom_OAss(X17281,X17280),X17279,X17278,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17279),X17281),hAPP(X17280,X17279))),
inference(variable_rename,[status(thm)],[fact_evaln_Oequations_I2_J]) ).
fof(i_0_9099,plain,
! [X17244,X17245,X17246,X17247] : c_Natural_Oevaln(c_Com_Ocom_OAss(X17247,X17246),X17245,X17244,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17245),X17247),hAPP(X17246,X17245))),
inference(variable_rename,[status(thm)],[fact_evaln_OAssign]) ).
fof(i_0_9100,plain,
! [X19939,X19940] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19940))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19939))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X19940,X19939))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).
fof(i_0_9101,plain,
! [X24416,X24417,X24418] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24418,tc_HOL_Obool)),X24417),hAPP(hAPP(c_Set_Oinsert(X24418),X24416),X24417))),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
fof(i_0_9102,plain,
! [X20352,X20353,X20354] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20354),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20353,X20352)),X20352) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20354),X20353),X20352),
inference(variable_rename,[status(thm)],[fact_zdiff__zmod__right]) ).
fof(i_0_9103,plain,
! [X19839,X19840,X19841] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19841),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19840,X19839)),X19839) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19841),X19840),X19839),
inference(variable_rename,[status(thm)],[fact_zmod__simps_I3_J]) ).
fof(i_0_9104,plain,
! [X19836,X19837,X19838] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19838),X19837),X19836) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19838),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19837,X19836)),X19836),
inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq]) ).
fof(i_0_9105,plain,
! [X24107,X24108,X24109] :
( ~ class_Orderings_Olinorder(X24109)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24109),X24108),X24107))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24109,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24109),X24108)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24109,X24108),X24107)) = hAPP(c_SetInterval_Oord__class_OlessThan(X24109),X24107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J])]) ).
cnf(i_0_9106,plain,
( hAPP(c_List_Orotate(X2,X1),X3) = X3
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_5808]) ).
fof(i_0_9107,plain,
! [X24469,X24470] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24470),hAPP(c_Nat_OSuc,X24469)))
| c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24470,hAPP(c_Nat_OSuc,X24469)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24469)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24470,X24469)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv])]) ).
cnf(i_0_9108,plain,
( X3 = c_List_Olist_ONil(X1)
| hAPP(c_List_Orotate(X1,X2),X3) != c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5809]) ).
fof(i_0_9109,plain,
! [X24537] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X24537)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X24537),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24537),c_Orderings_Otop__class_Otop(tc_fun(X24537,tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24537),c_Orderings_Otop__class_Otop(tc_fun(X24537,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X24537)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X24537),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).
fof(i_0_9110,plain,
! [X18495,X18496,X18497] :
( ~ class_Rings_Olinordered__semidom(X18497)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18496),X18495))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18497),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18497),X18496)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18497),X18495))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less])]) ).
fof(i_0_9111,plain,
! [X27484,X27485,X27486,X27487] :
( ~ class_Orderings_Olinorder(X27487)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27487,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X27487),X27486)),c_SetInterval_Oord__class_OatLeastAtMost(X27487,X27485,X27484)) = c_SetInterval_Oord__class_OatLeastAtMost(X27487,hAPP(hAPP(c_Orderings_Oord__class_Omax(X27487),X27486),X27485),X27484) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2])]) ).
fof(i_0_9112,plain,
! [X27470,X27471,X27472,X27473] :
( ~ class_Orderings_Olinorder(X27473)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27473,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X27473),X27472)),c_SetInterval_Oord__class_OatLeastAtMost(X27473,X27471,X27470)) = c_SetInterval_Oord__class_OatLeastAtMost(X27473,X27471,hAPP(hAPP(c_Orderings_Oord__class_Omin(X27473),X27472),X27470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1])]) ).
fof(i_0_9113,plain,
! [X18959,X18960] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18960),hAPP(c_Int_Onat,X18959)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18960)),X18959)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18960)),X18959))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18960),hAPP(c_Int_Onat,X18959))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless])]) ).
fof(i_0_9114,plain,
! [X24909,X24910] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24910),X24909))
| c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24909,X24910) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24910),X24909))
| c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24909,X24910) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X24909),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24909),c_Groups_Oone__class_Oone(tc_Int_Oint)),X24910)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5810])]) ).
fof(i_0_9115,plain,
! [X20204,X20205] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20204))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X20205)),hAPP(c_Int_Onat,X20204)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X20205,X20204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J])]) ).
fof(i_0_9116,plain,
! [X33391,X33392,X33393,X33394] : hAPP(hAPP(c_List_Odrop(X33394),X33393),hAPP(hAPP(c_List_Otake(X33394),X33392),X33391)) = hAPP(hAPP(c_List_Otake(X33394),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33392),X33393)),hAPP(hAPP(c_List_Odrop(X33394),X33393),X33391)),
inference(variable_rename,[status(thm)],[fact_drop__take]) ).
fof(i_0_9117,plain,
! [X29525,X29526,X29527,X29528] : hAPP(hAPP(c_Relation_Orel__comp(X29528,X29527,X29526),X29525),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29527,X29526),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29528,X29526),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_rel__comp__empty2]) ).
fof(i_0_9118,plain,
! [X23027,X23028,X23029,X23030] : c_Product__Type_Ocurry(X23030,X23029,X23028,hAPP(c_Product__Type_Oprod_Oprod__case(X23030,X23029,X23028),X23027)) = X23027,
inference(variable_rename,[status(thm)],[fact_curry__split]) ).
fof(i_0_9119,plain,
! [X22215] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22215)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22215)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22215))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__1__number__of])]) ).
fof(i_0_9120,plain,
! [X19987,X19988,X19989] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19989,X19988)),X19987) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19989),X19987),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19988),X19987)),
inference(variable_rename,[status(thm)],[fact_mod__mult__distrib]) ).
fof(i_0_9121,plain,
! [X23453,X23454,X23455] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23454))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23455),X23453),hAPP(hAPP(c_Power_Opower__class_Opower(X23455),X23453),X23454)))
| ~ class_Rings_Ocomm__semiring__1(X23455) )
& ( X23453 != c_Groups_Oone__class_Oone(X23455)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23455),X23453),hAPP(hAPP(c_Power_Opower__class_Opower(X23455),X23453),X23454)))
| ~ class_Rings_Ocomm__semiring__1(X23455) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power])])]) ).
fof(i_0_9122,plain,
! [X23181,X23182,X23183,X23184] :
( ~ class_Rings_Ocomm__semiring__1(X23184)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23184),X23183),X23182))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23184),X23183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23184),X23182),X23181))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult2])]) ).
fof(i_0_9123,plain,
! [X23177,X23178,X23179,X23180] :
( ~ class_Rings_Ocomm__semiring__1(X23180)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23180),X23179),X23178))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23180),X23179),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23180),X23177),X23178))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult])]) ).
fof(i_0_9124,plain,
! [X24039,X24040,X24041,X24042] :
( ~ class_Lattices_Osemilattice__sup(X24042)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24042),X24041),X24040))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24042),X24041),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24042),X24040),X24039))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI1])]) ).
fof(i_0_9125,plain,
! [X24035,X24036,X24037,X24038] :
( ~ class_Lattices_Osemilattice__sup(X24038)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24038),X24037),X24036))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24038),X24037),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24038),X24035),X24036))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI2])]) ).
fof(i_0_9126,plain,
! [X22617,X22618,X22619,X22620] :
( ~ class_Orderings_Olinorder(X22620)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22620),X22619),X22618))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22620),X22619),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22620),X22618),X22617))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI1])]) ).
fof(i_0_9127,plain,
! [X22613,X22614,X22615,X22616] :
( ~ class_Orderings_Olinorder(X22616)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22616),X22615),X22614))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22616),X22615),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22616),X22613),X22614))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI2])]) ).
fof(i_0_9128,plain,
! [X23980,X23981,X23982,X23983] :
( ~ class_Lattices_Osemilattice__sup(X23983)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23983),X23982),X23981))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23983),X23982),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23983),X23981),X23980))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI1])]) ).
fof(i_0_9129,plain,
! [X23984,X23985,X23986,X23987] :
( ~ class_Lattices_Osemilattice__sup(X23987)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23987),X23986),X23985))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23987),X23986),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23987),X23984),X23985))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI2])]) ).
fof(i_0_9130,plain,
! [X22574,X22575,X22576,X22577] :
( ~ class_Orderings_Olinorder(X22577)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22577),X22576),X22575))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22577),X22576),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22577),X22575),X22574))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI1])]) ).
fof(i_0_9131,plain,
! [X22578,X22579,X22580,X22581] :
( ~ class_Orderings_Olinorder(X22581)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22581),X22580),X22579))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22581),X22580),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22581),X22578),X22579))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI2])]) ).
cnf(i_0_9132,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5811]) ).
fof(i_0_9133,plain,
! [X19642] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19642))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_negative__zle__0]) ).
fof(i_0_9134,plain,
! [X33985,X33986,X33987,X33988,X33989] :
( ( c_List_Otranspose(X33986,X33985) != c_List_Olist_ONil(tc_List_Olist(X33986))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33986)),X33987),hAPP(c_List_Oset(tc_List_Olist(X33986)),X33985)))
| X33987 = c_List_Olist_ONil(X33986) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33989)),esk481_2(X33988,X33989)),hAPP(c_List_Oset(tc_List_Olist(X33989)),X33988)))
| c_List_Otranspose(X33989,X33988) = c_List_Olist_ONil(tc_List_Olist(X33989)) )
& ( esk481_2(X33988,X33989) != c_List_Olist_ONil(X33989)
| c_List_Otranspose(X33989,X33988) = c_List_Olist_ONil(tc_List_Olist(X33989)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__empty])])])])])]) ).
fof(i_0_9135,plain,
! [X23600,X23601,X23602] :
( ~ class_Groups_Ocomm__monoid__add(X23602)
| hAPP(X23601,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X23602)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23602),X23601),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X23600)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X23602),X23601),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23600)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt])]) ).
fof(i_0_9136,plain,
! [X24686,X24687,X24688] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24688,tc_fun(X24687,tc_HOL_Obool)),X24686),hAPP(c_COMBK(tc_fun(X24687,tc_HOL_Obool),X24688),c_Orderings_Obot__class_Obot(tc_fun(X24687,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24687,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UN__empty2]) ).
fof(i_0_9137,plain,
! [X18277,X18278,X18279] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18279),X18278))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18278),X18277))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18279)),X18277)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_9138,plain,
! [X22484] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22484)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22484)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22484))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of])]) ).
fof(i_0_9139,plain,
! [X19892,X19893] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19893))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19892,X19893))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__sign])]) ).
fof(i_0_9140,plain,
! [X31997,X31998] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X31998,X31997) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X31998),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X31997),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upto]) ).
fof(i_0_9141,plain,
! [X32329,X32330,X32331,X32332,X32333] : hAPP(hAPP(c_List_Omap(X32333,X32332),X32331),hAPP(hAPP(c_List_Olist_OCons(X32333),X32330),X32329)) = hAPP(hAPP(c_List_Olist_OCons(X32332),hAPP(X32331,X32330)),hAPP(hAPP(c_List_Omap(X32333,X32332),X32331),X32329)),
inference(variable_rename,[status(thm)],[fact_map_Osimps_I2_J]) ).
fof(i_0_9142,plain,
! [X21576,X21577,X21578] :
( ~ class_Fields_Ofield__inverse__zero(X21578)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21578),c_Groups_Oone__class_Oone(X21578)),hAPP(hAPP(c_Power_Opower__class_Opower(X21578),X21577),X21576)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21578),c_Groups_Oone__class_Oone(X21578)),X21577)),X21576) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])]) ).
fof(i_0_9143,plain,
! [X19661] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19661))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19661))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).
fof(i_0_9144,plain,
! [X25182,X25183,X25184,X25185] :
( ~ hBOOL(hAPP(hAPP(c_member(X25185),X25184),X25183))
| hBOOL(hAPP(hAPP(c_member(X25185),X25184),hAPP(hAPP(c_Set_Oinsert(X25185),X25182),X25183))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).
fof(i_0_9145,plain,
! [X24943,X24944,X24945,X24946] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X24946),X24945),X24944))
| hBOOL(hAPP(hAPP(c_member(X24946),X24945),hAPP(hAPP(c_Set_Oinsert(X24946),X24943),X24944))) )
& ( X24945 != X24943
| hBOOL(hAPP(hAPP(c_member(X24946),X24945),hAPP(hAPP(c_Set_Oinsert(X24946),X24943),X24944))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5812])])]) ).
fof(i_0_9146,plain,
! [X19236,X19237,X19238] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19238),X19237),hAPP(c_Groups_Ouminus__class_Ouminus(X19238),X19236)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19238),X19236),hAPP(c_Groups_Ouminus__class_Ouminus(X19238),X19237)))
| ~ class_Groups_Oordered__ab__group__add(X19238) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19238),X19236),hAPP(c_Groups_Ouminus__class_Ouminus(X19238),X19237)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19238),X19237),hAPP(c_Groups_Ouminus__class_Ouminus(X19238),X19236)))
| ~ class_Groups_Oordered__ab__group__add(X19238) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).
fof(i_0_9147,plain,
! [X18757,X18758,X18759] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18759),X18758),hAPP(c_Groups_Ouminus__class_Ouminus(X18759),X18757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18759),X18757),hAPP(c_Groups_Ouminus__class_Ouminus(X18759),X18758)))
| ~ class_Groups_Oordered__ab__group__add(X18759) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18759),X18757),hAPP(c_Groups_Ouminus__class_Ouminus(X18759),X18758)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18759),X18758),hAPP(c_Groups_Ouminus__class_Ouminus(X18759),X18757)))
| ~ class_Groups_Oordered__ab__group__add(X18759) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).
fof(i_0_9148,plain,
! [X33726,X33727,X33728,X33729] :
( ( X33727 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33728)),X33729)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_List_Olast(X33728,hAPP(hAPP(c_List_Olist__update(X33728,X33729),X33727),X33726)) = X33726
| X33729 = c_List_Olist_ONil(X33728) )
& ( X33727 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33728)),X33729)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_List_Olast(X33728,hAPP(hAPP(c_List_Olist__update(X33728,X33729),X33727),X33726)) = c_List_Olast(X33728,X33729)
| X33729 = c_List_Olist_ONil(X33728) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__list__update])])]) ).
fof(i_0_9149,plain,
! [X19616,X19617] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19617),c_Groups_Osgn__class_Osgn(X19617,X19616)),c_Groups_Ozero__class_Ozero(X19617)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19617),X19616),c_Groups_Ozero__class_Ozero(X19617)))
| ~ class_Rings_Olinordered__idom(X19617) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19617),X19616),c_Groups_Ozero__class_Ozero(X19617)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19617),c_Groups_Osgn__class_Osgn(X19617,X19616)),c_Groups_Ozero__class_Ozero(X19617)))
| ~ class_Rings_Olinordered__idom(X19617) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])]) ).
fof(i_0_9150,plain,
! [X33830,X33831,X33832] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33832),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33831)),X33830)))
| hAPP(hAPP(c_List_Otake(X33831),X33832),c_List_Obutlast(X33831,X33830)) = hAPP(hAPP(c_List_Otake(X33831),X33832),X33830) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__butlast])]) ).
fof(i_0_9151,plain,
! [X33763,X33764,X33765] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33765),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33764)),X33763)))
| c_List_Olast(X33764,hAPP(hAPP(c_List_Odrop(X33764),X33765),X33763)) = c_List_Olast(X33764,X33763) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__drop])]) ).
cnf(i_0_9152,plain,
c_Int_OBit1(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1),
inference(split_conjunct,[status(thm)],[i_0_5813]) ).
cnf(i_0_9153,plain,
hAPP(hAPP(c_Product__Type_Ointernal__split(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_5814]) ).
cnf(i_0_9154,plain,
c_Product__Type_Ointernal__split(X1,X2,X3) = c_Product__Type_Oprod_Oprod__case(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_5815]) ).
fof(i_0_9155,plain,
! [X22097,X22098,X22099,X22100,X22101,X22102] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22102,X22101,X22100),X22099),hAPP(hAPP(c_Product__Type_OPair(X22102,X22101),X22098),X22097)) = hAPP(hAPP(X22099,X22098),X22097),
inference(variable_rename,[status(thm)],[fact_prod_Osimps_I2_J]) ).
fof(i_0_9156,plain,
! [X22091,X22092,X22093,X22094,X22095,X22096] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22096,X22095,X22094),X22093),hAPP(hAPP(c_Product__Type_OPair(X22096,X22095),X22092),X22091)) = hAPP(hAPP(X22093,X22092),X22091),
inference(variable_rename,[status(thm)],[fact_split__conv]) ).
fof(i_0_9157,plain,
! [X25952,X25953,X25954] :
( ~ class_Orderings_Olinorder(X25954)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25954),X25953))
| ~ hBOOL(hAPP(hAPP(c_member(X25954),X25952),X25953))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25954),X25952),c_Big__Operators_Olattice_OSup__fin(X25954,c_Orderings_Oord__class_Omax(X25954),X25953)) = c_Big__Operators_Olattice_OSup__fin(X25954,c_Orderings_Oord__class_Omax(X25954),X25953) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem])]) ).
fof(i_0_9158,plain,
! [X25949,X25950,X25951] :
( ~ class_Orderings_Olinorder(X25951)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25951),X25950))
| ~ hBOOL(hAPP(hAPP(c_member(X25951),X25949),X25950))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25951),X25949),c_Big__Operators_Olattice_OInf__fin(X25951,c_Orderings_Oord__class_Omin(X25951),X25950)) = c_Big__Operators_Olattice_OInf__fin(X25951,c_Orderings_Oord__class_Omin(X25951),X25950) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem])]) ).
fof(i_0_9159,plain,
! [X24979,X24980,X24981] :
( hBOOL(hAPP(hAPP(c_member(X24981),X24980),X24979))
| hBOOL(hAPP(hAPP(c_member(X24981),X24980),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24981,tc_HOL_Obool)),X24979))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5816])]) ).
fof(i_0_9160,plain,
! [X28382,X28383,X28384,X28385] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28385),X28384),X28383))
| hAPP(c_Set_Ovimage(X28382,X28385,hAPP(c_COMBK(X28385,X28382),X28384)),X28383) = c_Orderings_Otop__class_Otop(tc_fun(X28382,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X28385),X28384),X28383))
| hAPP(c_Set_Ovimage(X28382,X28385,hAPP(c_COMBK(X28385,X28382),X28384)),X28383) = c_Orderings_Obot__class_Obot(tc_fun(X28382,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5817])]) ).
fof(i_0_9161,plain,
! [X23554,X23555,X23556,X23557,X23558] :
( ( X23557 = X23555
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23558,X23557),X23556) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23558,X23555),X23554)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23558),X23555),X23554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23558),X23557),X23556))
| ~ class_Orderings_Olinorder(X23558) )
& ( X23556 = X23554
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23558,X23557),X23556) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23558,X23555),X23554)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23558),X23555),X23554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23558),X23557),X23556))
| ~ class_Orderings_Olinorder(X23558) )
& ( X23557 != X23555
| X23556 != X23554
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23558,X23557),X23556) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23558,X23555),X23554)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23558),X23555),X23554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23558),X23557),X23556))
| ~ class_Orderings_Olinorder(X23558) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).
fof(i_0_9162,plain,
! [X23559,X23560,X23561,X23562,X23563] :
( ~ class_Orderings_Olinorder(X23563)
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23563,X23562),X23561) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23563,X23560),X23559)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23563),X23562),X23561))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23563),X23560),X23559))
| X23562 = X23560 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).
fof(i_0_9163,plain,
! [X23564,X23565,X23566,X23567,X23568] :
( ~ class_Orderings_Olinorder(X23568)
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23568,X23567),X23566) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23568,X23565),X23564)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23568),X23567),X23566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23568),X23565),X23564))
| X23566 = X23564 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).
fof(i_0_9164,plain,
! [X25591,X25592,X25593,X25594,X25595] :
( ~ c_Finite__Set_Ofolding__one(X25595,X25594,X25593)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25595),X25592))
| hBOOL(hAPP(hAPP(c_member(X25595),X25591),X25592))
| X25592 = c_Orderings_Obot__class_Obot(tc_fun(X25595,tc_HOL_Obool))
| hAPP(X25593,hAPP(hAPP(c_Set_Oinsert(X25595),X25591),X25592)) = hAPP(hAPP(X25594,X25591),hAPP(X25593,X25592)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5818])]) ).
cnf(i_0_9165,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_5730]) ).
fof(i_0_9166,plain,
! [X22211,X22212] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22211))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22212,X22211),c_Divides_OposDivAlg(X22212,X22211))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__correct])]) ).
fof(i_0_9167,plain,
! [X32726,X32727,X32728,X32729,X32730] :
( X32730 = X32729
| hAPP(hAPP(c_List_Onth(X32728),hAPP(hAPP(c_List_Olist__update(X32728,X32727),X32730),X32726)),X32729) = hAPP(hAPP(c_List_Onth(X32728),X32727),X32729) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__neq])]) ).
fof(i_0_9168,plain,
! [X27461,X27462,X27463,X27464] :
( ~ class_Orderings_Oorder(X27464)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27464,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27464,X27463,X27462)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27464,X27462),X27461)) = c_Orderings_Obot__class_Obot(tc_fun(X27464,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J])]) ).
fof(i_0_9169,plain,
! [X30369,X30370,X30371,X30372] : hAPP(c_Relation_Oconverse(X30372,X30372),hAPP(hAPP(c_Relation_Oinv__image(X30371,X30372),X30370),X30369)) = hAPP(hAPP(c_Relation_Oinv__image(X30371,X30372),hAPP(c_Relation_Oconverse(X30371,X30371),X30370)),X30369),
inference(variable_rename,[status(thm)],[fact_converse__inv__image]) ).
fof(i_0_9170,plain,
! [X30735,X30736,X30737] :
( ~ class_Lattices_Olattice(X30737)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30737),X30736))
| c_Big__Operators_Olattice__class_OInf__fin(X30737,hAPP(hAPP(c_Set_Oinsert(X30737),X30735),X30736)) = hAPP(hAPP(c_Finite__Set_Ofold(X30737,X30737,c_Lattices_Osemilattice__inf__class_Oinf(X30737)),X30735),X30736) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H])]) ).
fof(i_0_9171,plain,
! [X30738,X30739,X30740] :
( ~ class_Orderings_Olinorder(X30740)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30740),X30739))
| c_Big__Operators_Olinorder__class_OMin(X30740,hAPP(hAPP(c_Set_Oinsert(X30740),X30738),X30739)) = hAPP(hAPP(c_Finite__Set_Ofold(X30740,X30740,c_Orderings_Oord__class_Omin(X30740)),X30738),X30739) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H])]) ).
fof(i_0_9172,plain,
! [X30741,X30742,X30743] :
( ~ class_Orderings_Olinorder(X30743)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30743),X30742))
| c_Big__Operators_Olinorder__class_OMax(X30743,hAPP(hAPP(c_Set_Oinsert(X30743),X30741),X30742)) = hAPP(hAPP(c_Finite__Set_Ofold(X30743,X30743,c_Orderings_Oord__class_Omax(X30743)),X30741),X30742) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H])]) ).
fof(i_0_9173,plain,
! [X30732,X30733,X30734] :
( ~ class_Lattices_Olattice(X30734)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30734),X30733))
| c_Big__Operators_Olattice__class_OSup__fin(X30734,hAPP(hAPP(c_Set_Oinsert(X30734),X30732),X30733)) = hAPP(hAPP(c_Finite__Set_Ofold(X30734,X30734,c_Lattices_Osemilattice__sup__class_Osup(X30734)),X30732),X30733) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H])]) ).
fof(i_0_9174,plain,
! [X21799,X21800] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X21800),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| c_Random_Olog(X21800,X21799) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21799),X21800))
| c_Random_Olog(X21800,X21799) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X21800),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21799),X21800))
| c_Random_Olog(X21800,X21799) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X21800,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X21799),X21800))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_log_Osimps])])]) ).
fof(i_0_9175,plain,
! [X25748,X25749] :
( ~ class_Rings_Oring__1(X25749)
| ~ hBOOL(hAPP(hAPP(c_member(X25749),X25748),c_Int_Oring__1__class_OInts(X25749)))
| hBOOL(hAPP(hAPP(c_member(X25749),hAPP(c_Groups_Ouminus__class_Ouminus(X25749),X25748)),c_Int_Oring__1__class_OInts(X25749))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__minus])]) ).
fof(i_0_9176,plain,
! [X23366,X23367] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23367))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23367),X23366))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23366),X23367)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5819])]) ).
fof(i_0_9177,plain,
! [X23383,X23384] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23384),X23383))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23383),X23384)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5820])]) ).
fof(i_0_9178,plain,
! [X25088,X25089] :
( ( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X25089,tc_HOL_Obool)),X25088))
| hBOOL(hAPP(hAPP(c_member(X25089),X25088),c_Orderings_Obot__class_Obot(tc_fun(X25089,tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25089),X25088),c_Orderings_Obot__class_Obot(tc_fun(X25089,tc_HOL_Obool))))
| hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X25089,tc_HOL_Obool)),X25088)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq])]) ).
cnf(i_0_9179,plain,
hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X1,X2)) = c_List_Oupt(hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2)),
inference(split_conjunct,[status(thm)],[i_0_5821]) ).
fof(i_0_9180,plain,
! [X21707,X21708,X21709] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21709)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21709),c_Groups_Ozero__class_Ozero(X21709)),X21708))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21709),hAPP(c_Groups_Oabs__class_Oabs(X21709),X21707)),X21708) = hAPP(c_Groups_Oabs__class_Oabs(X21709),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21709),X21707),X21708)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div__pos])]) ).
fof(i_0_9181,plain,
! [X20787,X20788,X20789] :
( ~ class_Rings_Olinordered__idom(X20789)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20789),c_Groups_Ozero__class_Ozero(X20789)),X20788))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20789),hAPP(c_Groups_Oabs__class_Oabs(X20789),X20787)),X20788) = hAPP(c_Groups_Oabs__class_Oabs(X20789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20789),X20787),X20788)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).
fof(i_0_9182,plain,
! [X26496] : hAPP(c_Set_OPow(X26496),c_Orderings_Obot__class_Obot(tc_fun(X26496,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X26496,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X26496,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26496,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_Pow__empty]) ).
fof(i_0_9183,plain,
! [X23473,X23474] :
( hAPP(X23474,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X23474),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23473)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X23474),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23473)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0])]) ).
fof(i_0_9184,plain,
! [X27236,X27237,X27238,X27239,X27240] :
( ~ class_Lattices_Olattice(X27240)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27239,X27240)),X27238),X27237),X27236) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27240),hAPP(X27238,X27236)),hAPP(X27237,X27236)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])]) ).
fof(i_0_9185,plain,
! [X27185,X27186,X27187,X27188,X27189] :
( ~ class_Lattices_Olattice(X27189)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27188,X27189)),X27187),X27186),X27185) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27189),hAPP(X27187,X27185)),hAPP(X27186,X27185)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])]) ).
fof(i_0_9186,plain,
! [X23959,X23960,X23961,X23962,X23963] :
( ~ class_Lattices_Olattice(X23963)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23962,X23963)),X23961),X23960),X23959) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23963),hAPP(X23961,X23959)),hAPP(X23960,X23959)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__fun__def])]) ).
fof(i_0_9187,plain,
! [X23908,X23909,X23910,X23911,X23912] :
( ~ class_Lattices_Olattice(X23912)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23911,X23912)),X23910),X23909),X23908) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23912),hAPP(X23910,X23908)),hAPP(X23909,X23908)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__apply])]) ).
fof(i_0_9188,plain,
! [X21840,X21841,X21842,X21843,X21844] :
( ~ class_Groups_Ominus(X21844)
| hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21843,X21844)),X21842),X21841),X21840) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21844),hAPP(X21842,X21840)),hAPP(X21841,X21840)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__diff__def])]) ).
fof(i_0_9189,plain,
! [X20226,X20227,X20228,X20229,X20230] :
( ~ class_Groups_Ominus(X20230)
| hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20229,X20230)),X20228),X20227),X20226) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20230),hAPP(X20228,X20226)),hAPP(X20227,X20226)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).
fof(i_0_9190,plain,
! [X22205,X22206] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22206),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22205))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22206,X22205),c_Divides_OnegDivAlg(X22206,X22205))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__correct])]) ).
fof(i_0_9191,plain,
! [X19868,X19869] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19869),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19869),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19868,X19869))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__bound])]) ).
fof(i_0_9192,plain,
! [X29452,X29453,X29454,X29455] :
( ~ c_Finite__Set_Ofolding(X29455,X29454,X29453,X29452)
| hAPP(X29452,c_Orderings_Obot__class_Obot(tc_fun(X29455,tc_HOL_Obool))) = c_Fun_Oid(X29454) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oempty])]) ).
fof(i_0_9193,plain,
! [X22027,X22028] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22027))
| c_Divides_Odivmod__int(X22028,X22027) = c_Divides_OposDivAlg(X22028,X22027)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22028)) )
& ( X22028 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22028,X22027) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22027))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22028)) )
& ( X22028 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22028,X22027) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22028),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22027)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22027))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22028)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22027))
| c_Divides_Odivmod__int(X22028,X22027) = c_Divides_OnegDivAlg(X22028,X22027)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22028)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22027))
| c_Divides_Odivmod__int(X22028,X22027) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22028),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22027)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22028)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5822])])]) ).
fof(i_0_9194,plain,
! [X22749,X22750] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X22750),X22749))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22750)),hAPP(c_Code__Numeral_Onat__of,X22749))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22750)),hAPP(c_Code__Numeral_Onat__of,X22749)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X22750),X22749)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def])]) ).
fof(i_0_9195,plain,
! [X21879,X21880] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21880)),hAPP(c_Code__Numeral_Oof__nat,X21879)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21880),X21879)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21880),X21879))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21880)),hAPP(c_Code__Numeral_Oof__nat,X21879))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code])]) ).
fof(i_0_9196,plain,
! [X19250,X19251] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19251)),hAPP(c_Nat_OSuc,X19250)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19251),X19250)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19251),X19250))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19251)),hAPP(c_Nat_OSuc,X19250))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_9197,plain,
! [X22746,X22747] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X22747),X22746))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22747)),hAPP(c_Code__Numeral_Onat__of,X22746))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22747)),hAPP(c_Code__Numeral_Onat__of,X22746)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X22747),X22746)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def])]) ).
fof(i_0_9198,plain,
! [X21871,X21872] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21872)),hAPP(c_Code__Numeral_Oof__nat,X21871)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21872),X21871)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21872),X21871))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21872)),hAPP(c_Code__Numeral_Oof__nat,X21871))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code])]) ).
fof(i_0_9199,plain,
! [X18288,X18289] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18289)),hAPP(c_Nat_OSuc,X18288)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18289),X18288)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18289),X18288))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18289)),hAPP(c_Nat_OSuc,X18288))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_9200,plain,
! [X18271,X18272] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18272)),hAPP(c_Nat_OSuc,X18271)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18272),X18271)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_9201,plain,
! [X33149,X33150,X33151,X33152] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33152),X33151))
| hAPP(hAPP(c_List_Onth(X33150),hAPP(hAPP(c_List_Otake(X33150),X33151),X33149)),X33152) = hAPP(hAPP(c_List_Onth(X33150),X33149),X33152) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take])]) ).
fof(i_0_9202,plain,
! [X27356,X27357,X27358] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27358,tc_HOL_Obool)),X27357),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27358,tc_HOL_Obool)),X27356),X27357)) = c_Orderings_Obot__class_Obot(tc_fun(X27358,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__disjoint]) ).
fof(i_0_9203,plain,
! [X34224,X34225,X34226,X34227] :
( ( hAPP(c_List_Orev(X34227),X34226) != hAPP(hAPP(c_List_Olist_OCons(X34227),X34225),X34224)
| X34226 = hAPP(hAPP(c_List_Oappend(X34227),hAPP(c_List_Orev(X34227),X34224)),hAPP(hAPP(c_List_Olist_OCons(X34227),X34225),c_List_Olist_ONil(X34227))) )
& ( X34226 != hAPP(hAPP(c_List_Oappend(X34227),hAPP(c_List_Orev(X34227),X34224)),hAPP(hAPP(c_List_Olist_OCons(X34227),X34225),c_List_Olist_ONil(X34227)))
| hAPP(c_List_Orev(X34227),X34226) = hAPP(hAPP(c_List_Olist_OCons(X34227),X34225),X34224) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff])]) ).
fof(i_0_9204,plain,
! [X20759,X20760] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20760),X20759))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).
fof(i_0_9205,plain,
! [X20316,X20317] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20317),X20316)),X20317)),
inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).
fof(i_0_9206,plain,
! [X19969,X19970] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19970),X19969)),X19970)),
inference(variable_rename,[status(thm)],[fact_div__le__dividend]) ).
fof(i_0_9207,plain,
! [X24865,X24866] :
( ~ class_Orderings_Olinorder(X24866)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24866,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24866),X24865)),hAPP(hAPP(c_Set_Oinsert(X24866),X24865),c_Orderings_Obot__class_Obot(tc_fun(X24866,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X24866),X24865) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J])]) ).
fof(i_0_9208,plain,
! [X25829,X25830,X25831] :
( ~ class_Orderings_Olinorder(X25831)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25831),X25830))
| ~ hBOOL(hAPP(hAPP(c_member(X25831),X25829),X25830))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25831),c_Big__Operators_Olinorder__class_OMin(X25831,X25830)),X25829)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__le])]) ).
fof(i_0_9209,plain,
! [X20776,X20777,X20778] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20778),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20777),X20776)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20778),X20777)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20778),X20776)),
inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(i_0_9210,plain,
! [X20340,X20341,X20342] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20342),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20341),X20340)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20342),X20341)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20342),X20340)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).
fof(i_0_9211,plain,
! [X18834,X18835,X18836] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18836),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18835),X18834)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18836),X18835)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18836),X18834)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(i_0_9212,plain,
! [X20343,X20344,X20345] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20345),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20344),X20343)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20345),X20344)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20345),X20343)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).
fof(i_0_9213,plain,
! [X19239,X19240,X19241] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19241),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19240),X19239)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19241),X19240)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19241),X19239)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).
fof(i_0_9214,plain,
! [X20215,X20216,X20217] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20217),X20216)),X20215) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20217),X20215)),X20216),
inference(variable_rename,[status(thm)],[fact_diff__commute]) ).
fof(i_0_9215,plain,
! [X19431,X19432] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19432),c_Groups_Ozero__class_Ozero(X19432)),hAPP(c_Groups_Ouminus__class_Ouminus(X19432),X19431)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19432),X19431),c_Groups_Ozero__class_Ozero(X19432)))
| ~ class_Groups_Oordered__ab__group__add(X19432) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19432),X19431),c_Groups_Ozero__class_Ozero(X19432)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19432),c_Groups_Ozero__class_Ozero(X19432)),hAPP(c_Groups_Ouminus__class_Ouminus(X19432),X19431)))
| ~ class_Groups_Oordered__ab__group__add(X19432) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).
fof(i_0_9216,plain,
! [X18839,X18840] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18840),c_Groups_Ozero__class_Ozero(X18840)),hAPP(c_Groups_Ouminus__class_Ouminus(X18840),X18839)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18840),X18839),c_Groups_Ozero__class_Ozero(X18840)))
| ~ class_Groups_Oordered__ab__group__add(X18840) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18840),X18839),c_Groups_Ozero__class_Ozero(X18840)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18840),c_Groups_Ozero__class_Ozero(X18840)),hAPP(c_Groups_Ouminus__class_Ouminus(X18840),X18839)))
| ~ class_Groups_Oordered__ab__group__add(X18840) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).
fof(i_0_9217,plain,
! [X17241,X17242,X17243] :
( ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X17243,X17242,X17241)))
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17242))) )
& ( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17242)))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X17243,X17242,X17241))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I8_J])]) ).
fof(i_0_9218,plain,
! [X17235,X17236,X17237] :
( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X17237,X17236,X17235)))
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17236))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I8_J])]) ).
fof(i_0_9219,plain,
! [X23130,X23131,X23132,X23133] :
( ~ class_Rings_Ocomm__semiring__1(X23133)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23133),X23132),X23131))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23133),X23131),X23130))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23133),X23132),X23130)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__trans])]) ).
fof(i_0_9220,plain,
! [X19050,X19051,X19052,X19053] :
( ~ class_Orderings_Opreorder(X19053)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19053),X19052),X19051))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19053),X19051),X19050))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19053),X19052),X19050)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_9221,plain,
! [X19043,X19044,X19045,X19046] :
( ~ class_Orderings_Oorder(X19046)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19046),X19045),X19044))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19046),X19043),X19045))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19046),X19043),X19044)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_9222,plain,
! [X19167,X19168,X19169,X19170] :
( ~ class_Orderings_Opreorder(X19170)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19170),X19169),X19168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19170),X19168),X19167))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19170),X19169),X19167)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_9223,plain,
! [X19175,X19176,X19177,X19178] :
( ~ class_Orderings_Opreorder(X19178)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19178),X19177),X19176))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19178),X19176),X19175))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19178),X19177),X19175)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_9224,plain,
! [X18528,X18529,X18530,X18531] :
( ~ class_Orderings_Opreorder(X18531)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18531),X18530),X18529))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18531),X18529),X18528))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18531),X18530),X18528)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_9225,plain,
! [X19171,X19172,X19173,X19174] :
( ~ class_Orderings_Oorder(X19174)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19174),X19173),X19172))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19174),X19171),X19173))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19174),X19171),X19172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_9226,plain,
! [X19179,X19180,X19181,X19182] :
( ~ class_Orderings_Oorder(X19182)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19182),X19181),X19180))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19182),X19179),X19181))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19182),X19179),X19180)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_9227,plain,
! [X18524,X18525,X18526,X18527] :
( ~ class_Orderings_Oorder(X18527)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18527),X18526),X18525))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18527),X18524),X18526))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18527),X18524),X18525)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_9228,plain,
! [X22173] :
( X22173 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22173),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__0])]) ).
fof(i_0_9229,plain,
! [X22213,X22214] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22214))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22213))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X22214,X22213) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X22214,X22213)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos])]) ).
fof(i_0_9230,plain,
! [X20236,X20237,X20238,X20239,X20240] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20240),X20239),X20238))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20240),X20237),X20236))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20240),X20239),X20238) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20240),X20237),X20236)
| ~ class_Groups_Oordered__ab__group__add(X20240) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20240),X20237),X20236))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20240),X20239),X20238))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20240),X20239),X20238) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20240),X20237),X20236)
| ~ class_Groups_Oordered__ab__group__add(X20240) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).
fof(i_0_9231,plain,
! [X20251,X20252,X20253,X20254,X20255] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20255),X20254),X20253))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20255),X20252),X20251))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20255),X20254),X20253) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20255),X20252),X20251)
| ~ class_Groups_Oordered__ab__group__add(X20255) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20255),X20252),X20251))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20255),X20254),X20253))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20255),X20254),X20253) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20255),X20252),X20251)
| ~ class_Groups_Oordered__ab__group__add(X20255) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).
fof(i_0_9232,plain,
! [X20326,X20327,X20328] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20327),X20328) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20326),X20328)
| X20327 = X20326
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20328),X20326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20328),X20327)) )
& ( X20327 != X20326
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20327),X20328) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20326),X20328)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20328),X20326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20328),X20327)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).
fof(i_0_9233,plain,
! [X23209,X23210] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23210),X23209))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23210)),X23209)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23210)),X23209))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23210),X23209)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I1_J])]) ).
fof(i_0_9234,plain,
! [X28663,X28664,X28665] : hAPP(hAPP(c_Product__Type_OSigma(X28665,X28664),X28663),hAPP(c_COMBK(tc_fun(X28664,tc_HOL_Obool),X28665),c_Orderings_Obot__class_Obot(tc_fun(X28664,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28665,X28664),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Sigma__empty2]) ).
cnf(i_0_9235,plain,
c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Relation_OId(X1)),
inference(split_conjunct,[status(thm)],[i_0_5823]) ).
cnf(i_0_9236,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_numeral__1__eq__Suc__0]) ).
fof(i_0_9237,plain,
! [X18629,X18630,X18631] :
( ~ class_Rings_Ocomm__semiring__1(X18631)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18631),X18630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18631),X18629),X18630)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18631),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18631),X18629),c_Groups_Oone__class_Oone(X18631))),X18630) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
cnf(i_0_9238,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5824]) ).
cnf(i_0_9239,plain,
( c_Groups_Oone__class_Oone(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5825]) ).
fof(i_0_9240,plain,
! [X22482,X22483] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22482))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22483),X22482) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X22483,X22482)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos])]) ).
fof(i_0_9241,plain,
! [X19246,X19247] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19247),X19246))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19246)),X19247)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19246)),X19247))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19247),X19246)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5826])]) ).
fof(i_0_9242,plain,
! [X27424,X27425,X27426,X27427] :
( ~ class_Orderings_Oorder(X27427)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27427,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27427,X27426),X27425)),c_SetInterval_Oord__class_OatLeastAtMost(X27427,X27425,X27424)) = c_Orderings_Obot__class_Obot(tc_fun(X27427,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J])]) ).
fof(i_0_9243,plain,
! [X19327,X19328] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19328),c_Groups_Ozero__class_Ozero(X19328)),hAPP(c_Int_Oring__1__class_Oof__int(X19328),X19327)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19327))
| ~ class_Rings_Olinordered__idom(X19328) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19327))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19328),c_Groups_Ozero__class_Ozero(X19328)),hAPP(c_Int_Oring__1__class_Oof__int(X19328),X19327)))
| ~ class_Rings_Olinordered__idom(X19328) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff])])]) ).
fof(i_0_9244,plain,
! [X18608,X18609] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18609),c_Groups_Ozero__class_Ozero(X18609)),hAPP(c_Int_Oring__1__class_Oof__int(X18609),X18608)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18608))
| ~ class_Rings_Olinordered__idom(X18609) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18608))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18609),c_Groups_Ozero__class_Ozero(X18609)),hAPP(c_Int_Oring__1__class_Oof__int(X18609),X18608)))
| ~ class_Rings_Olinordered__idom(X18609) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff])])]) ).
fof(i_0_9245,plain,
! [X18451,X18452] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18452),c_Groups_Ozero__class_Ozero(X18452)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18452),X18451)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18451))
| ~ class_Rings_Olinordered__semidom(X18452) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18451))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18452),c_Groups_Ozero__class_Ozero(X18452)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18452),X18451)))
| ~ class_Rings_Olinordered__semidom(X18452) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff])])]) ).
fof(i_0_9246,plain,
! [X18101,X18102,X18103] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X18103,X18102,X18101)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X18102)),c_Com_Ocom_Ocom__size(X18101))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_com_Osize_I5_J]) ).
fof(i_0_9247,plain,
! [X20668,X20669] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20669),hAPP(c_Groups_Oabs__class_Oabs(X20669),X20668)),c_Groups_Ozero__class_Ozero(X20669)))
| X20668 = c_Groups_Ozero__class_Ozero(X20669)
| ~ class_Groups_Oordered__ab__group__add__abs(X20669) )
& ( X20668 != c_Groups_Ozero__class_Ozero(X20669)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20669),hAPP(c_Groups_Oabs__class_Oabs(X20669),X20668)),c_Groups_Ozero__class_Ozero(X20669)))
| ~ class_Groups_Oordered__ab__group__add__abs(X20669) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).
fof(i_0_9248,plain,
! [X23451,X23452] :
( X23452 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23451),X23452))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23451)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23452))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__le__int])]) ).
fof(i_0_9249,plain,
! [X22207,X22208] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22208),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22207))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X22208,X22207) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X22208,X22207)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__pos])]) ).
fof(i_0_9250,plain,
! [X25959,X25960,X25961] :
( ~ class_Orderings_Olinorder(X25961)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25961),X25960))
| X25960 = c_Orderings_Obot__class_Obot(tc_fun(X25961,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25961,c_Orderings_Oord__class_Omin(X25961),hAPP(hAPP(c_Set_Oinsert(X25961),X25959),X25960)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25961),X25959),c_Big__Operators_Olattice_OInf__fin(X25961,c_Orderings_Oord__class_Omin(X25961),X25960)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem])]) ).
fof(i_0_9251,plain,
! [X25962,X25963,X25964] :
( ~ class_Orderings_Olinorder(X25964)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25964),X25963))
| X25963 = c_Orderings_Obot__class_Obot(tc_fun(X25964,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25964,c_Orderings_Oord__class_Omax(X25964),hAPP(hAPP(c_Set_Oinsert(X25964),X25962),X25963)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25964),X25962),c_Big__Operators_Olattice_OSup__fin(X25964,c_Orderings_Oord__class_Omax(X25964),X25963)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem])]) ).
fof(i_0_9252,plain,
! [X20672,X20673] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20673)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20673),hAPP(c_Groups_Oabs__class_Oabs(X20673),X20672)),c_Groups_Ozero__class_Ozero(X20673))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5827])]) ).
fof(i_0_9253,plain,
! [X18489,X18490] :
( ~ class_Rings_Olinordered__semidom(X18490)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18490),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18490),X18489)),c_Groups_Ozero__class_Ozero(X18490))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5828])]) ).
fof(i_0_9254,plain,
! [X23330,X23331,X23332] :
( ~ class_Divides_Osemiring__div(X23332)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23332),X23331),X23330))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23332),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23332),X23330),X23331)),X23331) = X23330 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult__self])]) ).
fof(i_0_9255,plain,
! [X20231,X20232,X20233] :
( ~ class_Rings_Oring__1(X20233)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20232),X20231))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20233),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20231),X20232)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20233),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20233),X20231)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20233),X20232)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__diff])]) ).
cnf(i_0_9256,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5829]) ).
fof(i_0_9257,plain,
! [X21139,X21140] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21140),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21140)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21139)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21139) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21139),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21140)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21139)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21140)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21140),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21139),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21140)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21139)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21140),X21139))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21140),c_Int_OPls)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5830])])]) ).
fof(i_0_9258,plain,
! [X21044,X21045] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21045)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21045)),X21044) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21044) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21045)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21045)),X21044) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21045)),X21044)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5831])]) ).
fof(i_0_9259,plain,
! [X22480,X22481] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22481),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22480))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22481),X22480) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X22481,X22480)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos])]) ).
fof(i_0_9260,plain,
! [X24527,X24528,X24529] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24529),hAPP(hAPP(c_Set_Oinsert(X24529),X24528),X24527)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24529),X24527)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24529),X24527))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24529),hAPP(hAPP(c_Set_Oinsert(X24529),X24528),X24527))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).
cnf(i_0_9261,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1)),
inference(split_conjunct,[status(thm)],[i_0_5832]) ).
fof(i_0_9262,plain,
! [X31431,X31432,X31433] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31433)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31433),X31432))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31433),X31431),c_Complete__Lattice_OInf__class_OInf(X31433,X31432)) = hAPP(hAPP(c_Finite__Set_Ofold(X31433,X31433,c_Lattices_Osemilattice__inf__class_Oinf(X31433)),X31431),X31432) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf])]) ).
fof(i_0_9263,plain,
! [X31426,X31427,X31428] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31428)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31428),X31427))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X31428),X31426),c_Complete__Lattice_OSup__class_OSup(X31428,X31427)) = hAPP(hAPP(c_Finite__Set_Ofold(X31428,X31428,c_Lattices_Osemilattice__sup__class_Osup(X31428)),X31426),X31427) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup])]) ).
cnf(i_0_9264,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_nat__numeral__1__eq__1]) ).
cnf(i_0_9265,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_one__code__numeral__code]) ).
cnf(i_0_9266,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_one__is__num__one]) ).
cnf(i_0_9267,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_Numeral1__eq1__nat]) ).
fof(i_0_9268,plain,
! [X27380,X27381] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27381,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27381,tc_HOL_Obool)),X27380)),X27380) = c_Orderings_Obot__class_Obot(tc_fun(X27381,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__disjoint2]) ).
fof(i_0_9269,plain,
! [X24337,X24338] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24338,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24338,tc_HOL_Obool)),X24337)),X24337) = c_Orderings_Otop__class_Otop(tc_fun(X24338,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__partition2]) ).
fof(i_0_9270,plain,
! [X24726,X24727] : c_Sum__Type_OPlus(X24727,X24726,c_Orderings_Otop__class_Otop(tc_fun(X24727,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X24726,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X24727,X24726),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(i_0_9271,plain,
! [X27502,X27503,X27504] :
( ~ class_Orderings_Oorder(X27504)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27504,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27504,X27503,X27502)),hAPP(c_SetInterval_Oord__class_OatLeast(X27504),X27502)) = c_Orderings_Obot__class_Obot(tc_fun(X27504,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J])]) ).
fof(i_0_9272,plain,
! [X27505,X27506,X27507] :
( ~ class_Orderings_Oorder(X27507)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27507,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27507,X27506,X27505)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27507),X27505)) = c_Orderings_Obot__class_Obot(tc_fun(X27507,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J])]) ).
fof(i_0_9273,plain,
! [X27481,X27482,X27483] :
( ~ class_Orderings_Oorder(X27483)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27483,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X27483,X27482,X27481)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27483),X27481)) = c_Orderings_Obot__class_Obot(tc_fun(X27483,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J])]) ).
fof(i_0_9274,plain,
! [X21805,X21806,X21807] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21807),X21806))
| c_Random_Ominus__shift(X21805,X21807,X21806) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X21805),X21807)),X21806) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21807),X21806))
| c_Random_Ominus__shift(X21805,X21807,X21806) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X21807),X21806) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5833])]) ).
fof(i_0_9275,plain,
! [X21130,X21131] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21131),c_Groups_Ozero__class_Ozero(X21131)),hAPP(c_Int_Onumber__class_Onumber__of(X21131),X21130)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21130))
| ~ class_Int_Onumber__ring(X21131)
| ~ class_Rings_Olinordered__idom(X21131) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21130))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21131),c_Groups_Ozero__class_Ozero(X21131)),hAPP(c_Int_Onumber__class_Onumber__of(X21131),X21130)))
| ~ class_Int_Onumber__ring(X21131)
| ~ class_Rings_Olinordered__idom(X21131) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])]) ).
fof(i_0_9276,plain,
! [X21136,X21137] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21137),c_Groups_Ozero__class_Ozero(X21137)),hAPP(c_Int_Onumber__class_Onumber__of(X21137),X21136)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21136))
| ~ class_Int_Onumber__ring(X21137)
| ~ class_Rings_Olinordered__idom(X21137) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21136))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21137),c_Groups_Ozero__class_Ozero(X21137)),hAPP(c_Int_Onumber__class_Onumber__of(X21137),X21136)))
| ~ class_Int_Onumber__ring(X21137)
| ~ class_Rings_Olinordered__idom(X21137) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I1_J])])]) ).
fof(i_0_9277,plain,
! [X19741,X19742,X19743] :
( ( ~ hBOOL(hAPP(X19743,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19742,X19741)))
| epred1_3(X19743,X19742,X19741) )
& ( ~ epred1_3(X19743,X19742,X19741)
| hBOOL(hAPP(X19743,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19742,X19741))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5834])]) ).
fof(i_0_9278,plain,
! [X29815,X29816,X29817] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29817,X29816)),X29815))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29817),hAPP(c_Relation_ODomain(X29817,X29816),X29815))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Domain])]) ).
fof(i_0_9279,plain,
! [X29724,X29725,X29726] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29726,X29725)),X29724))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29725),hAPP(c_Relation_ORange(X29726,X29725),X29724))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Range])]) ).
fof(i_0_9280,plain,
! [X28585,X28586,X28587,X28588] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28588,X28587,X28586),X28585))
| X28586 != c_Orderings_Obot__class_Obot(tc_fun(X28588,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty])]) ).
fof(i_0_9281,plain,
! [X21008,X21009] : hAPP(hAPP(c_Nitpick_Oint__gcd,X21009),X21008) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21009)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21008)))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__gcd__def]) ).
fof(i_0_9282,plain,
! [X33343,X33344,X33345,X33346,X33347] : hAPP(hAPP(c_List_Odrop(X33347),X33346),hAPP(hAPP(c_List_Omap(X33345,X33347),X33344),X33343)) = hAPP(hAPP(c_List_Omap(X33345,X33347),X33344),hAPP(hAPP(c_List_Odrop(X33345),X33346),X33343)),
inference(variable_rename,[status(thm)],[fact_drop__map]) ).
fof(i_0_9283,plain,
! [X33119,X33120,X33121,X33122,X33123] : hAPP(hAPP(c_List_Otake(X33123),X33122),hAPP(hAPP(c_List_Omap(X33121,X33123),X33120),X33119)) = hAPP(hAPP(c_List_Omap(X33121,X33123),X33120),hAPP(hAPP(c_List_Otake(X33121),X33122),X33119)),
inference(variable_rename,[status(thm)],[fact_take__map]) ).
fof(i_0_9284,plain,
! [X33867,X33868,X33869,X33870] : hAPP(c_List_Ofilter(X33870,X33869),hAPP(hAPP(c_List_Oappend(X33870),X33868),X33867)) = hAPP(hAPP(c_List_Oappend(X33870),hAPP(c_List_Ofilter(X33870,X33869),X33868)),hAPP(c_List_Ofilter(X33870,X33869),X33867)),
inference(variable_rename,[status(thm)],[fact_filter__append]) ).
fof(i_0_9285,plain,
! [X32565,X32566] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32566),X32565))
| c_List_Oupto(X32566,X32565) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X32566),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32566),c_Groups_Oone__class_Oone(tc_Int_Oint)),X32565)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32566),X32565))
| c_List_Oupto(X32566,X32565) = c_List_Olist_ONil(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5835])]) ).
fof(i_0_9286,plain,
! [X29605,X29606,X29607,X29608,X29609] :
( ( ~ c_Wellfounded_Owf(X29606,X29605)
| hBOOL(hAPP(hAPP(c_member(X29606),X29607),c_Wellfounded_Oacc(X29606,X29605))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29609),esk317_2(X29608,X29609)),c_Wellfounded_Oacc(X29609,X29608)))
| c_Wellfounded_Owf(X29609,X29608) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acc__iff])])])])]) ).
fof(i_0_9287,plain,
! [X25823,X25824] :
( ~ class_Groups_Olinordered__ab__group__add(X25824)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25824),X25823))
| X25823 = c_Orderings_Obot__class_Obot(tc_fun(X25824,tc_HOL_Obool))
| hAPP(c_Groups_Ouminus__class_Ouminus(X25824),c_Big__Operators_Olinorder__class_OMin(X25824,X25823)) = c_Big__Operators_Olinorder__class_OMax(X25824,hAPP(c_Set_Oimage(X25824,X25824,c_Groups_Ouminus__class_Ouminus(X25824)),X25823)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max])]) ).
fof(i_0_9288,plain,
! [X25821,X25822] :
( ~ class_Groups_Olinordered__ab__group__add(X25822)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25822),X25821))
| X25821 = c_Orderings_Obot__class_Obot(tc_fun(X25822,tc_HOL_Obool))
| hAPP(c_Groups_Ouminus__class_Ouminus(X25822),c_Big__Operators_Olinorder__class_OMax(X25822,X25821)) = c_Big__Operators_Olinorder__class_OMin(X25822,hAPP(c_Set_Oimage(X25822,X25822,c_Groups_Ouminus__class_Ouminus(X25822)),X25821)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min])]) ).
fof(i_0_9289,plain,
! [X31316,X31317] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31317),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31317,tc_HOL_Obool),X31316)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31317,tc_HOL_Obool)),X31316)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnionD])]) ).
fof(i_0_9290,plain,
! [X20184,X20185] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20185))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20185),X20184)),X20185) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__times__mod__eq])]) ).
fof(i_0_9291,plain,
! [X19618,X19619] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19619),c_Groups_Ozero__class_Ozero(X19619)),c_Groups_Osgn__class_Osgn(X19619,X19618)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19619),c_Groups_Ozero__class_Ozero(X19619)),X19618))
| ~ class_Rings_Olinordered__idom(X19619) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19619),c_Groups_Ozero__class_Ozero(X19619)),X19618))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19619),c_Groups_Ozero__class_Ozero(X19619)),c_Groups_Osgn__class_Osgn(X19619,X19618)))
| ~ class_Rings_Olinordered__idom(X19619) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])]) ).
fof(i_0_9292,plain,
! [X23340,X23341,X23342] :
( ~ class_Divides_Oring__div(X23342)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23342),X23341),X23340))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23342),hAPP(c_Groups_Ouminus__class_Ouminus(X23342),X23340)),X23341) = hAPP(c_Groups_Ouminus__class_Ouminus(X23342),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23342),X23340),X23341)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__neg__div])]) ).
cnf(i_0_9293,plain,
c_Int_OBit0(X1) != c_Int_OBit1(X2),
inference(split_conjunct,[status(thm)],[i_0_5836]) ).
cnf(i_0_9294,plain,
c_Int_OBit1(X1) != c_Int_OBit0(X2),
inference(split_conjunct,[status(thm)],[i_0_5837]) ).
fof(i_0_9295,plain,
! [X19811,X19812,X19813,X19814] :
( ~ class_Divides_Osemiring__div(X19814)
| c_Divides_Odiv__class_Omod(X19814,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19814),X19813),X19812),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19814),X19813),X19811)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19814),X19813),c_Divides_Odiv__class_Omod(X19814,X19812,X19811)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1])]) ).
fof(i_0_9296,plain,
! [X30951,X30952,X30953,X30954] :
( ( X30954 != c_Orderings_Obot__class_Obot(tc_fun(X30953,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30953,tc_fun(X30952,tc_HOL_Obool)),X30954),hAPP(c_COMBK(tc_fun(X30952,tc_HOL_Obool),X30953),X30951)) = c_Orderings_Otop__class_Otop(tc_fun(X30952,tc_HOL_Obool)) )
& ( X30954 = c_Orderings_Obot__class_Obot(tc_fun(X30953,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30953,tc_fun(X30952,tc_HOL_Obool)),X30954),hAPP(c_COMBK(tc_fun(X30952,tc_HOL_Obool),X30953),X30951)) = X30951 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__constant])]) ).
fof(i_0_9297,plain,
! [X24689,X24690,X24691,X24692] :
( ( X24692 != c_Orderings_Obot__class_Obot(tc_fun(X24691,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24691,tc_fun(X24690,tc_HOL_Obool)),X24692),hAPP(c_COMBK(tc_fun(X24690,tc_HOL_Obool),X24691),X24689)) = c_Orderings_Obot__class_Obot(tc_fun(X24690,tc_HOL_Obool)) )
& ( X24692 = c_Orderings_Obot__class_Obot(tc_fun(X24691,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24691,tc_fun(X24690,tc_HOL_Obool)),X24692),hAPP(c_COMBK(tc_fun(X24690,tc_HOL_Obool),X24691),X24689)) = X24689 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__constant])]) ).
fof(i_0_9298,plain,
! [X22985,X22986,X22987] : c_Random__Sequence_Oempty(X22987,X22986,X22985) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22987)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X22987)),
inference(variable_rename,[status(thm)],[fact_Random__Sequence_Oempty__def]) ).
fof(i_0_9299,plain,
! [X20057,X20058,X20059,X20060] :
( ( X20059 != c_Groups_Ozero__class_Ozero(X20060)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20060),X20059),X20058)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20060),X20059),X20057)) = c_Groups_Ozero__class_Ozero(X20060)
| ~ class_Divides_Osemiring__div(X20060) )
& ( X20059 = c_Groups_Ozero__class_Ozero(X20060)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20060),X20059),X20058)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20060),X20059),X20057)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20060),X20058),X20057)
| ~ class_Divides_Osemiring__div(X20060) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if])])]) ).
fof(i_0_9300,plain,
! [X21531,X21532,X21533,X21534] :
( ~ class_Fields_Ofield__inverse__zero(X21534)
| X21533 = c_Groups_Ozero__class_Ozero(X21534)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21534),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21534),X21533),X21532)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21534),X21533),X21531)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21534),X21532),X21531) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left])]) ).
fof(i_0_9301,plain,
! [X21527,X21528,X21529,X21530] :
( ~ class_Fields_Ofield__inverse__zero(X21530)
| X21529 = c_Groups_Ozero__class_Ozero(X21530)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21530),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21530),X21528),X21529)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21530),X21527),X21529)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21530),X21528),X21527) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])]) ).
fof(i_0_9302,plain,
! [X20043,X20044,X20045,X20046] :
( ~ class_Divides_Osemiring__div(X20046)
| X20045 = c_Groups_Ozero__class_Ozero(X20046)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20046),X20045),X20044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20046),X20045),X20043)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20046),X20044),X20043) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1])]) ).
fof(i_0_9303,plain,
! [X20047,X20048,X20049,X20050] :
( ~ class_Divides_Osemiring__div(X20050)
| X20049 = c_Groups_Ozero__class_Ozero(X20050)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20050),X20048),X20049)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20050),X20047),X20049)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20050),X20048),X20047) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult2])]) ).
cnf(i_0_9304,plain,
c_Divides_Odivmod__nat(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_5838]) ).
fof(i_0_9305,plain,
! [X21991,X21992,X21993,X21994] : hAPP(c_Nat_Onat_Onat__rec(X21994,X21993,X21992),hAPP(c_Nat_OSuc,X21991)) = hAPP(hAPP(X21992,X21991),hAPP(c_Nat_Onat_Onat__rec(X21994,X21993,X21992),X21991)),
inference(variable_rename,[status(thm)],[fact_nat__rec__Suc]) ).
fof(i_0_9306,plain,
! [X19289,X19290,X19291] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19291),X19290))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19291),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19290),X19289))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_9307,plain,
! [X19270,X19271,X19272] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19272),X19271))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19272),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19271),X19270))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_9308,plain,
! [X19292,X19293,X19294] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19294),X19293))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19294),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19292),X19293))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_9309,plain,
! [X19273,X19274,X19275] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19275),X19274))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19275),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19273),X19274))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_9310,plain,
! [X18420,X18421,X18422] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18422),X18421))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18422),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18421),X18420))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_9311,plain,
! [X18311,X18312,X18313] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18313),X18312))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18313),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18312),X18311))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_9312,plain,
! [X18398,X18399,X18400] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18400),X18399))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18400),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18398),X18399))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_9313,plain,
! [X18308,X18309,X18310] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18310),X18309))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18308),X18309))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_9314,plain,
! [X19858,X19859,X19860,X19861] :
( ~ class_Divides_Osemiring__div(X19861)
| c_Divides_Odiv__class_Omod(X19861,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19861),X19860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19861),X19859),X19858)),X19859) = c_Divides_Odiv__class_Omod(X19861,X19860,X19859) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2])]) ).
fof(i_0_9315,plain,
! [X19854,X19855,X19856,X19857] :
( ~ class_Divides_Osemiring__div(X19857)
| c_Divides_Odiv__class_Omod(X19857,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19857),X19856),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19857),X19855),X19854)),X19854) = c_Divides_Odiv__class_Omod(X19857,X19856,X19854) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])]) ).
fof(i_0_9316,plain,
! [X18338,X18339,X18341,X18342,X18343] :
( ( X18339 = hAPP(c_Nat_OSuc,esk31_2(X18338,X18339))
| X18339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18339),hAPP(c_Nat_OSuc,X18338))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk31_2(X18338,X18339)),X18338))
| X18339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18339),hAPP(c_Nat_OSuc,X18338))) )
& ( X18342 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18342),hAPP(c_Nat_OSuc,X18341))) )
& ( X18342 != hAPP(c_Nat_OSuc,X18343)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18343),X18341))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18342),hAPP(c_Nat_OSuc,X18341))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj])])])])])]) ).
cnf(i_0_9317,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,c_Code__Numeral_OSuc__code__numeral(X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_5839]) ).
fof(i_0_9318,plain,
! [X33468,X33469] :
( X33469 = c_List_Olist_ONil(X33468)
| hAPP(c_List_Orotate1(X33468),X33469) = hAPP(hAPP(c_List_Oappend(X33468),hAPP(c_List_Otl(X33468),X33469)),hAPP(hAPP(c_List_Olist_OCons(X33468),hAPP(c_List_Ohd(X33468),X33469)),c_List_Olist_ONil(X33468))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__hd__tl])]) ).
fof(i_0_9319,plain,
! [X26101,X26102,X26103,X26104,X26105,X26106] :
( ( X26106 != X26105
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26104,X26103),X26102),X26105),X26101),X26106) = X26101 )
& ( X26106 = X26105
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26104,X26103),X26102),X26105),X26101),X26106) = hAPP(X26102,X26106) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__def])]) ).
fof(i_0_9320,plain,
! [X26090,X26091,X26092,X26093,X26094,X26095] :
( X26095 = X26094
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26093,X26092),X26091),X26094),X26090),X26095) = hAPP(X26091,X26095) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__other])]) ).
fof(i_0_9321,plain,
! [X26077,X26078,X26079,X26080,X26081,X26082] :
( ( X26082 != X26081
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26080,X26079),X26078),X26081),X26077),X26082) = X26077 )
& ( X26082 = X26081
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26080,X26079),X26078),X26081),X26077),X26082) = hAPP(X26078,X26082) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__apply])]) ).
cnf(i_0_9322,plain,
c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_5840]) ).
fof(i_0_9323,plain,
! [X32460,X32461,X32462,X32463] :
( ~ class_Groups_Ocomm__monoid__add(X32463)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X32463),X32462),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X32461,X32460))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32463),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X32463),X32462),c_List_Oupto(X32461,X32460))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upto__conv__listsum__int])]) ).
fof(i_0_9324,plain,
! [X32464,X32465,X32466,X32467] :
( ~ class_Groups_Ocomm__monoid__add(X32467)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32467),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X32467),X32466),c_List_Oupto(X32465,X32464))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X32467),X32466),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X32465,X32464))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__int])]) ).
fof(i_0_9325,plain,
! [X27198,X27199,X27200,X27201] :
( ~ class_Lattices_Osemilattice__inf(X27201)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27201),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27201),X27200),X27199)),X27198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27201),X27200),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27201),X27199),X27198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])]) ).
fof(i_0_9326,plain,
! [X27190,X27191,X27192,X27193] :
( ~ class_Lattices_Osemilattice__inf(X27193)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27193),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27193),X27192),X27191)),X27190) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27193),X27192),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27193),X27191),X27190)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])]) ).
fof(i_0_9327,plain,
! [X27194,X27195,X27196,X27197] :
( ~ class_Lattices_Olattice(X27197)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27197),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27197),X27196),X27195)),X27194) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27197),X27196),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27197),X27195),X27194)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J])]) ).
fof(i_0_9328,plain,
! [X23921,X23922,X23923,X23924] :
( ~ class_Lattices_Osemilattice__sup(X23924)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23924),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23924),X23923),X23922)),X23921) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23924),X23923),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23924),X23922),X23921)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oassoc])]) ).
fof(i_0_9329,plain,
! [X23913,X23914,X23915,X23916] :
( ~ class_Lattices_Osemilattice__sup(X23916)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23916),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23916),X23915),X23914)),X23913) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23916),X23915),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23916),X23914),X23913)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__assoc])]) ).
fof(i_0_9330,plain,
! [X23917,X23918,X23919,X23920] :
( ~ class_Lattices_Olattice(X23920)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23920),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23920),X23919),X23918)),X23917) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23920),X23919),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23920),X23918),X23917)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I6_J])]) ).
fof(i_0_9331,plain,
! [X22666,X22667,X22668,X22669] :
( ~ class_Orderings_Olinorder(X22669)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22669),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22669),X22668),X22667)),X22666) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22669),X22668),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22669),X22667),X22666)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__assoc])]) ).
fof(i_0_9332,plain,
! [X22662,X22663,X22664,X22665] :
( ~ class_Orderings_Olinorder(X22665)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22665),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22665),X22664),X22663)),X22662) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22665),X22664),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22665),X22663),X22662)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oassoc])]) ).
fof(i_0_9333,plain,
! [X22337,X22338,X22339,X22340] :
( ~ class_Orderings_Olinorder(X22340)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22340),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22340),X22339),X22338)),X22337) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22340),X22339),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22340),X22338),X22337)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__assoc])]) ).
fof(i_0_9334,plain,
! [X22333,X22334,X22335,X22336] :
( ~ class_Orderings_Olinorder(X22336)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22336),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22336),X22335),X22334)),X22333) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22336),X22335),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22336),X22334),X22333)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oassoc])]) ).
fof(i_0_9335,plain,
! [X20899,X20900,X20901] :
( ~ class_Groups_Omonoid__mult(X20901)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20901),hAPP(hAPP(c_Power_Opower__class_Opower(X20901),X20900),X20899)),X20900) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20901),X20900),hAPP(hAPP(c_Power_Opower__class_Opower(X20901),X20900),X20899)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).
fof(i_0_9336,plain,
! [X18735,X18736,X18737,X18738] :
( ~ class_Groups_Oab__semigroup__mult(X18738)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18738),X18737),X18736)),X18735) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18738),X18737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18738),X18736),X18735)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).
fof(i_0_9337,plain,
! [X18688,X18689,X18690,X18691] :
( ~ class_Rings_Ocomm__semiring__1(X18691)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18691),X18690),X18689)),X18688) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18691),X18690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18691),X18689),X18688)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).
fof(i_0_9338,plain,
! [X18157,X18158,X18159,X18160] :
( ~ class_Rings_Ocomm__semiring__1(X18160)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18160),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18160),X18159),X18158)),X18157) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18160),X18159),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18160),X18158),X18157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_9339,plain,
! [X18008,X18009,X18010,X18011] :
( ~ class_Groups_Oab__semigroup__add(X18011)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18011),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18011),X18010),X18009)),X18008) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18011),X18010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18011),X18009),X18008)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_9340,plain,
! [X21442,X21443,X21444,X21445] :
( ~ class_Rings_Odivision__ring(X21445)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21445),X21444),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21445),X21443),X21442)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21445),X21444),X21443)),X21442) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right])]) ).
fof(i_0_9341,plain,
! [X18679,X18680,X18681,X18682] :
( ~ class_Rings_Ocomm__semiring__1(X18682)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18682),X18681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18682),X18680),X18679)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18682),X18681),X18680)),X18679) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).
fof(i_0_9342,plain,
! [X18153,X18154,X18155,X18156] :
( ~ class_Rings_Ocomm__semiring__1(X18156)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18156),X18155),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18156),X18154),X18153)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18156),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18156),X18155),X18154)),X18153) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_9343,plain,
! [X33766,X33767] :
( X33767 = c_List_Olist_ONil(X33766)
| c_List_Olast(X33766,X33767) = hAPP(hAPP(c_List_Onth(X33766),X33767),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33766)),X33767)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__conv__nth])]) ).
fof(i_0_9344,plain,
! [X18743,X18744] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18743),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Oring__1__class_Oof__int(X18744),X18743) = hAPP(c_Groups_Ouminus__class_Ouminus(X18744),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18744),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18743))))
| ~ class_Rings_Oring__1(X18744) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18743),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Oring__1__class_Oof__int(X18744),X18743) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18744),hAPP(c_Int_Onat,X18743))
| ~ class_Rings_Oring__1(X18744) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5841])])]) ).
fof(i_0_9345,plain,
! [X25648,X25649] :
( ~ class_Int_Onumber__ring(X25649)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X25648))
| hBOOL(hAPP(hAPP(c_member(X25649),hAPP(c_Int_Onumber__class_Onumber__of(X25649),X25648)),c_Nat_Osemiring__1__class_ONats(X25649))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__number__of])]) ).
fof(i_0_9346,plain,
! [X26478,X26479] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26479),X26478))
| hAPP(c_Finite__Set_Ocard(tc_fun(X26479,tc_HOL_Obool)),hAPP(c_Set_OPow(X26479),X26478)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X26479),X26478)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Pow])]) ).
fof(i_0_9347,plain,
! [X24861] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24861)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X24861)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24861),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_atLeast__Suc]) ).
fof(i_0_9348,plain,
! [X27395,X27396,X27397] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27397,tc_HOL_Obool)),X27396),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27397,tc_HOL_Obool)),X27395)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27397,tc_HOL_Obool)),X27396),X27395),
inference(variable_rename,[status(thm)],[fact_Diff__Compl]) ).
fof(i_0_9349,plain,
! [X27398,X27399,X27400] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27400,tc_HOL_Obool)),X27399),X27398) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27400,tc_HOL_Obool)),X27399),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27400,tc_HOL_Obool)),X27398)),
inference(variable_rename,[status(thm)],[fact_Diff__eq]) ).
fof(i_0_9350,plain,
! [X18967] :
( ~ class_Rings_Olinordered__semidom(X18967)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18967),c_Groups_Ozero__class_Ozero(X18967)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18967),c_Groups_Oone__class_Oone(X18967)),c_Groups_Oone__class_Oone(X18967)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_9351,plain,
! [X23786,X23787] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X23787,X23786)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23786),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23787),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan__int]) ).
fof(i_0_9352,plain,
! [X25974,X25975,X25976] :
( ~ class_Orderings_Olinorder(X25976)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25976),X25975))
| ~ hBOOL(hAPP(hAPP(c_member(X25976),X25974),X25975))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25976),X25974),c_Big__Operators_Olattice_OInf__fin(X25976,c_Orderings_Oord__class_Omin(X25976),X25975)) = X25974 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb])]) ).
fof(i_0_9353,plain,
! [X25971,X25972,X25973] :
( ~ class_Orderings_Olinorder(X25973)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25973),X25972))
| ~ hBOOL(hAPP(hAPP(c_member(X25973),X25971),X25972))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25973),X25971),c_Big__Operators_Olattice_OSup__fin(X25973,c_Orderings_Oord__class_Omax(X25973),X25972)) = X25971 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb])]) ).
fof(i_0_9354,plain,
! [X19433,X19434] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19434),X19433),hAPP(c_Groups_Ouminus__class_Ouminus(X19434),X19433)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19434),X19433),c_Groups_Ozero__class_Ozero(X19434)))
| ~ class_Groups_Olinordered__ab__group__add(X19434) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19434),X19433),c_Groups_Ozero__class_Ozero(X19434)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19434),X19433),hAPP(c_Groups_Ouminus__class_Ouminus(X19434),X19433)))
| ~ class_Groups_Olinordered__ab__group__add(X19434) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).
fof(i_0_9355,plain,
! [X18845,X18846] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18846),X18845),hAPP(c_Groups_Ouminus__class_Ouminus(X18846),X18845)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18846),X18845),c_Groups_Ozero__class_Ozero(X18846)))
| ~ class_Rings_Olinordered__idom(X18846) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18846),X18845),c_Groups_Ozero__class_Ozero(X18846)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18846),X18845),hAPP(c_Groups_Ouminus__class_Ouminus(X18846),X18845)))
| ~ class_Rings_Olinordered__idom(X18846) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).
fof(i_0_9356,plain,
! [X27353,X27354,X27355] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27355,tc_HOL_Obool)),X27354),X27353) != c_Orderings_Obot__class_Obot(tc_fun(X27355,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27355,tc_HOL_Obool)),X27354),X27353) = X27354 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__triv])]) ).
fof(i_0_9357,plain,
! [X32512,X32513,X32514,X32515,X32516] :
( ~ class_Orderings_Olinorder(X32516)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32515,X32516,X32514),X32513),X32512) != c_List_Olist_ONil(X32515) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__not__Nil])]) ).
fof(i_0_9358,plain,
! [X26175,X26176,X26177,X26178] :
( ~ class_Groups_Ocomm__monoid__mult(X26178)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26177),X26176))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26177,X26178),hAPP(c_COMBK(X26178,X26177),X26175)),X26176) = hAPP(hAPP(c_Power_Opower__class_Opower(X26178),X26175),hAPP(c_Finite__Set_Ocard(X26177),X26176)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__constant])]) ).
fof(i_0_9359,plain,
! [X29053,X29054,X29055] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X29055)
| X29054 = c_Orderings_Obot__class_Obot(tc_fun(X29055,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29055),X29054))
| hAPP(c_Finite__Set_Ofold1(X29055,c_Groups_Otimes__class_Otimes(X29055)),hAPP(hAPP(c_Set_Oinsert(X29055),X29053),X29054)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29055),X29053),hAPP(c_Finite__Set_Ofold1(X29055,c_Groups_Otimes__class_Otimes(X29055)),X29054)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem])]) ).
fof(i_0_9360,plain,
! [X27374,X27375,X27376,X27377] :
( ~ class_Orderings_Oorder(X27377)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27377,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27377,X27376),X27375)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27377,X27375),X27374)) = c_Orderings_Obot__class_Obot(tc_fun(X27377,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J])]) ).
fof(i_0_9361,plain,
! [X21930,X21931] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21931),hAPP(c_Nat_OSuc,X21930)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21931),X21930)),
inference(variable_rename,[status(thm)],[fact_diff__Suc]) ).
fof(i_0_9362,plain,
! [X32939,X32940,X32941,X32942] : hAPP(hAPP(c_List_Oappend(X32942),hAPP(hAPP(c_List_Oappend(X32942),X32941),X32940)),X32939) = hAPP(hAPP(c_List_Oappend(X32942),X32941),hAPP(hAPP(c_List_Oappend(X32942),X32940),X32939)),
inference(variable_rename,[status(thm)],[fact_append__assoc]) ).
fof(i_0_9363,plain,
! [X32920,X32921,X32922,X32923] : hAPP(hAPP(c_List_Oappend(X32923),hAPP(hAPP(c_List_Olist_OCons(X32923),X32922),X32921)),X32920) = hAPP(hAPP(c_List_Olist_OCons(X32923),X32922),hAPP(hAPP(c_List_Oappend(X32923),X32921),X32920)),
inference(variable_rename,[status(thm)],[fact_append__Cons]) ).
fof(i_0_9364,plain,
! [X23439,X23440] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23440),X23439))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23439))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23440),X23439)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__imp__le])]) ).
fof(i_0_9365,plain,
! [X23443,X23444] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23444),X23443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23443))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23444),X23443)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__le])]) ).
fof(i_0_9366,plain,
! [X33548,X33549,X33550] :
( X33550 = c_List_Olist_ONil(X33549)
| hAPP(hAPP(c_List_Otake(X33549),hAPP(c_Nat_OSuc,X33548)),X33550) = hAPP(hAPP(c_List_Olist_OCons(X33549),hAPP(c_List_Ohd(X33549),X33550)),hAPP(hAPP(c_List_Otake(X33549),X33548),hAPP(c_List_Otl(X33549),X33550))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc])]) ).
fof(i_0_9367,plain,
! [X23673] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23673))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23673) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,X23673))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int])]) ).
fof(i_0_9368,plain,
! [X32685,X32686,X32687,X32688] :
( ( X32688 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Onth(X32687),hAPP(hAPP(c_List_Olist_OCons(X32687),X32686),X32685)),X32688) = X32686 )
& ( X32688 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Onth(X32687),hAPP(hAPP(c_List_Olist_OCons(X32687),X32686),X32685)),X32688) = hAPP(hAPP(c_List_Onth(X32687),X32685),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32688),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__Cons_H])]) ).
fof(i_0_9369,plain,
! [X24798,X24799,X24800,X24801] :
( ( X24801 != c_Orderings_Obot__class_Obot(tc_fun(X24800,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X24800,X24799,hAPP(c_COMBK(X24799,X24800),X24798)),X24801) = c_Orderings_Obot__class_Obot(tc_fun(X24799,tc_HOL_Obool)) )
& ( X24801 = c_Orderings_Obot__class_Obot(tc_fun(X24800,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X24800,X24799,hAPP(c_COMBK(X24799,X24800),X24798)),X24801) = hAPP(hAPP(c_Set_Oinsert(X24799),X24798),c_Orderings_Obot__class_Obot(tc_fun(X24799,tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant__conv])]) ).
cnf(i_0_9370,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5803]) ).
cnf(i_0_9371,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5805]) ).
cnf(i_0_9372,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5804]) ).
cnf(i_0_9373,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5806]) ).
fof(i_0_9374,plain,
! [X17502,X17503,X17504] :
( ( hBOOL(hAPP(c_Com_OWT,X17503))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17504,X17503,X17502))) )
& ( hBOOL(hAPP(c_Com_OWT,X17502))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17504,X17503,X17502))) )
& ( ~ hBOOL(hAPP(c_Com_OWT,X17503))
| ~ hBOOL(hAPP(c_Com_OWT,X17502))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17504,X17503,X17502))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I5_J])])]) ).
fof(i_0_9375,plain,
! [X17332,X17333,X17334] :
( ( hBOOL(hAPP(c_Com_OWT,X17333))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17334,X17333,X17332))) )
& ( hBOOL(hAPP(c_Com_OWT,X17332))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17334,X17333,X17332))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5842])])]) ).
fof(i_0_9376,plain,
! [X17476,X17477,X17478] :
( ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X17478,X17477,X17476)))
| hBOOL(hAPP(c_Com_OWT,X17476)) )
& ( ~ hBOOL(hAPP(c_Com_OWT,X17476))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X17478,X17477,X17476))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I3_J])]) ).
fof(i_0_9377,plain,
! [X17353,X17354,X17355] :
( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X17355,X17354,X17353)))
| hBOOL(hAPP(c_Com_OWT,X17353)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I3_J])]) ).
fof(i_0_9378,plain,
! [X32456,X32457,X32458,X32459] :
( ~ class_Groups_Ocomm__monoid__add(X32459)
| ~ hBOOL(hAPP(c_List_Odistinct(X32458),X32457))
| hAPP(c_List_Omonoid__add__class_Olistsum(X32459),hAPP(hAPP(c_List_Omap(X32458,X32459),X32456),X32457)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32458,X32459),X32456),hAPP(c_List_Oset(X32458),X32457)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__distinct__conv__setsum__set])]) ).
fof(i_0_9379,plain,
! [X20907,X20908,X20909,X20910] :
( ~ class_Groups_Omonoid__mult(X20910)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20910),X20909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20908),X20907)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20910),hAPP(hAPP(c_Power_Opower__class_Opower(X20910),X20909),X20908)),X20907) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).
fof(i_0_9380,plain,
! [X20646,X20647,X20648,X20649] :
( ~ class_Rings_Ocomm__semiring__1(X20649)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20649),hAPP(hAPP(c_Power_Opower__class_Opower(X20649),X20648),X20647)),X20646) = hAPP(hAPP(c_Power_Opower__class_Opower(X20649),X20648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20647),X20646)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).
fof(i_0_9381,plain,
! [X19831,X19832,X19833] :
( ~ class_Divides_Oring__div(X19833)
| c_Divides_Odiv__class_Omod(X19833,hAPP(c_Groups_Ouminus__class_Ouminus(X19833),X19832),X19831) = c_Divides_Odiv__class_Omod(X19833,hAPP(c_Groups_Ouminus__class_Ouminus(X19833),c_Divides_Odiv__class_Omod(X19833,X19832,X19831)),X19831) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__eq])]) ).
fof(i_0_9382,plain,
! [X33545,X33546,X33547] : hAPP(c_List_Otl(X33547),hAPP(hAPP(c_List_Otake(X33547),X33546),X33545)) = hAPP(hAPP(c_List_Otake(X33547),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33546),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X33547),X33545)),
inference(variable_rename,[status(thm)],[fact_tl__take]) ).
fof(i_0_9383,plain,
! [X20951,X20952,X20953] :
( ~ class_Rings_Olinordered__idom(X20953)
| hAPP(c_Groups_Oabs__class_Oabs(X20953),hAPP(hAPP(c_Power_Opower__class_Opower(X20953),hAPP(c_Groups_Ouminus__class_Ouminus(X20953),X20952)),X20951)) = hAPP(c_Groups_Oabs__class_Oabs(X20953),hAPP(hAPP(c_Power_Opower__class_Opower(X20953),X20952),X20951)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])]) ).
cnf(i_0_9384,plain,
hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId(X1)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_5843]) ).
cnf(i_0_9385,plain,
hAPP(c_Relation_ORange(X1,X1),c_Relation_OId(X1)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_5844]) ).
fof(i_0_9386,plain,
! [X26072,X26073,X26074,X26075,X26076] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26076,X26075),X26074),X26073),X26072),X26073) = X26072,
inference(variable_rename,[status(thm)],[fact_fun__upd__same]) ).
fof(i_0_9387,plain,
! [X27789,X27790,X27791] :
( ~ class_Lattices_Olattice(X27791)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27791),X27790))
| hBOOL(hAPP(hAPP(c_member(X27791),X27789),X27790))
| X27790 = c_Orderings_Obot__class_Obot(tc_fun(X27791,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X27791,hAPP(hAPP(c_Set_Oinsert(X27791),X27789),X27790)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27791),X27789),c_Big__Operators_Olattice__class_OInf__fin(X27791,X27790)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5845])]) ).
fof(i_0_9388,plain,
! [X25869,X25870,X25871] :
( ~ class_Orderings_Olinorder(X25871)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25871),X25870))
| hBOOL(hAPP(hAPP(c_member(X25871),X25869),X25870))
| X25870 = c_Orderings_Obot__class_Obot(tc_fun(X25871,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25871,hAPP(hAPP(c_Set_Oinsert(X25871),X25869),X25870)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25871),X25869),c_Big__Operators_Olinorder__class_OMin(X25871,X25870)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5846])]) ).
fof(i_0_9389,plain,
! [X25872,X25873,X25874] :
( ~ class_Orderings_Olinorder(X25874)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25874),X25873))
| hBOOL(hAPP(hAPP(c_member(X25874),X25872),X25873))
| X25873 = c_Orderings_Obot__class_Obot(tc_fun(X25874,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25874,hAPP(hAPP(c_Set_Oinsert(X25874),X25872),X25873)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25874),X25872),c_Big__Operators_Olinorder__class_OMax(X25874,X25873)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5847])]) ).
fof(i_0_9390,plain,
! [X25781,X25782,X25783] :
( ~ class_Lattices_Olattice(X25783)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25783),X25782))
| hBOOL(hAPP(hAPP(c_member(X25783),X25781),X25782))
| X25782 = c_Orderings_Obot__class_Obot(tc_fun(X25783,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25783,hAPP(hAPP(c_Set_Oinsert(X25783),X25781),X25782)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25783),X25781),c_Big__Operators_Olattice__class_OSup__fin(X25783,X25782)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5848])]) ).
fof(i_0_9391,plain,
! [X24570,X24571] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24571),c_Orderings_Otop__class_Otop(tc_fun(X24571,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(X24571),X24570) != hAPP(c_Finite__Set_Ocard(X24571),c_Orderings_Otop__class_Otop(tc_fun(X24571,tc_HOL_Obool)))
| X24570 = c_Orderings_Otop__class_Otop(tc_fun(X24571,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).
fof(i_0_9392,plain,
! [X33402,X33403,X33404,X33405] :
( ( X33405 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Odrop(X33404),X33405),hAPP(hAPP(c_List_Olist_OCons(X33404),X33403),X33402)) = hAPP(hAPP(c_List_Olist_OCons(X33404),X33403),X33402) )
& ( X33405 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Odrop(X33404),X33405),hAPP(hAPP(c_List_Olist_OCons(X33404),X33403),X33402)) = hAPP(hAPP(c_List_Odrop(X33404),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33405),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33402) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons_H])]) ).
fof(i_0_9393,plain,
! [X21033] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X21033))))),
inference(variable_rename,[status(thm)],[fact_neg__zminus__int]) ).
fof(i_0_9394,plain,
! [X24432,X24433,X24434,X24435] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X24435),X24434),X24433),X24432))
| X24434 = X24432
| hBOOL(hAPP(X24433,X24432)) )
& ( X24434 != X24432
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X24435),X24434),X24433),X24432)) )
& ( ~ hBOOL(hAPP(X24433,X24432))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X24435),X24434),X24433),X24432)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
fof(i_0_9395,plain,
! [X23229,X23230,X23231] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23231),X23230),hAPP(c_Groups_Ouminus__class_Ouminus(X23231),X23229)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23231),X23230),X23229))
| ~ class_Rings_Ocomm__ring__1(X23231) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23231),X23230),X23229))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23231),X23230),hAPP(c_Groups_Ouminus__class_Ouminus(X23231),X23229)))
| ~ class_Rings_Ocomm__ring__1(X23231) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff])])]) ).
fof(i_0_9396,plain,
! [X23191,X23192,X23193] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23193),X23192),hAPP(c_Groups_Oabs__class_Oabs(X23193),X23191)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23193),X23192),X23191))
| ~ class_Rings_Olinordered__idom(X23193) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23193),X23192),X23191))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23193),X23192),hAPP(c_Groups_Oabs__class_Oabs(X23193),X23191)))
| ~ class_Rings_Olinordered__idom(X23193) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__abs__iff])])]) ).
fof(i_0_9397,plain,
! [X25269,X25270,X25271] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25271),X25270),hAPP(c_SetInterval_Oord__class_OatMost(X25271),X25269)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25271),X25270),X25269))
| ~ class_Orderings_Oord(X25271) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25271),X25270),X25269))
| hBOOL(hAPP(hAPP(c_member(X25271),X25270),hAPP(c_SetInterval_Oord__class_OatMost(X25271),X25269)))
| ~ class_Orderings_Oord(X25271) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__iff])])]) ).
fof(i_0_9398,plain,
! [X25272,X25273,X25274] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25274),X25273),hAPP(c_SetInterval_Oord__class_OatLeast(X25274),X25272)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25274),X25272),X25273))
| ~ class_Orderings_Oord(X25274) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25274),X25272),X25273))
| hBOOL(hAPP(hAPP(c_member(X25274),X25273),hAPP(c_SetInterval_Oord__class_OatLeast(X25274),X25272)))
| ~ class_Orderings_Oord(X25274) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__iff])])]) ).
fof(i_0_9399,plain,
! [X25259,X25260,X25261] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25261),X25260),hAPP(c_SetInterval_Oord__class_OlessThan(X25261),X25259)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25261),X25260),X25259))
| ~ class_Orderings_Oord(X25261) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25261),X25260),X25259))
| hBOOL(hAPP(hAPP(c_member(X25261),X25260),hAPP(c_SetInterval_Oord__class_OlessThan(X25261),X25259)))
| ~ class_Orderings_Oord(X25261) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__iff])])]) ).
fof(i_0_9400,plain,
! [X25275,X25276,X25277] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25277),X25276),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25277),X25275)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25277),X25275),X25276))
| ~ class_Orderings_Oord(X25277) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25277),X25275),X25276))
| hBOOL(hAPP(hAPP(c_member(X25277),X25276),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25277),X25275)))
| ~ class_Orderings_Oord(X25277) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__iff])])]) ).
fof(i_0_9401,plain,
! [X23682,X23683,X23684] :
( ~ class_Groups_Oordered__ab__group__add(X23684)
| hAPP(c_Set_Oimage(X23684,X23684,c_Groups_Ouminus__class_Ouminus(X23684)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23684,X23683,X23682)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23684,hAPP(c_Groups_Ouminus__class_Ouminus(X23684),X23682)),hAPP(c_Groups_Ouminus__class_Ouminus(X23684),X23683)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost])]) ).
fof(i_0_9402,plain,
! [X26539,X26540,X26541,X26542,X26543] :
( ~ c_Finite__Set_Ofolding__one__idem(X26543,X26542,X26541)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26543),X26540))
| ~ hBOOL(hAPP(hAPP(c_member(X26543),X26539),X26540))
| hAPP(hAPP(X26542,X26539),hAPP(X26541,X26540)) = hAPP(X26541,X26540) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem])]) ).
fof(i_0_9403,plain,
! [X25832,X25833,X25834] :
( ~ class_Orderings_Olinorder(X25834)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25834),X25833))
| ~ hBOOL(hAPP(hAPP(c_member(X25834),X25832),X25833))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25834),X25832),c_Big__Operators_Olinorder__class_OMax(X25834,X25833))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__ge])]) ).
fof(i_0_9404,plain,
! [X32695,X32696] :
( ~ class_Groups_Ocomm__monoid__add(X32696)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32696),X32695) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X32696),hAPP(c_List_Onth(X32696),X32695)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32696)),X32695))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__setsum__nth])]) ).
fof(i_0_9405,plain,
! [X20234,X20235] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20235),X20234))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20234)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20235)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20234),X20235)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int])]) ).
fof(i_0_9406,plain,
! [X23400,X23401] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23401),X23400))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23400),X23401)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23400)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23401)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div])]) ).
fof(i_0_9407,plain,
! [X18939] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18939)),X18939) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).
fof(i_0_9408,plain,
! [X29844,X29845] : hAPP(c_Relation_OField(X29845),X29844) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29845,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29845,X29845),X29844)),hAPP(c_Relation_ORange(X29845,X29845),X29844)),
inference(variable_rename,[status(thm)],[fact_Field__def]) ).
cnf(i_0_9409,plain,
c_Transitive__Closure_Otrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_5849]) ).
fof(i_0_9410,plain,
! [X23778,X23779] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23779,X23778) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23779),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23778))),
inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J]) ).
fof(i_0_9411,plain,
! [X32567,X32568,X32569] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32569))
| c_List_Osublist(X32568,hAPP(hAPP(c_List_Olist_OCons(X32568),X32567),c_List_Olist_ONil(X32568)),X32569) = hAPP(hAPP(c_List_Olist_OCons(X32568),X32567),c_List_Olist_ONil(X32568)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32569))
| c_List_Osublist(X32568,hAPP(hAPP(c_List_Olist_OCons(X32568),X32567),c_List_Olist_ONil(X32568)),X32569) = c_List_Olist_ONil(X32568) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5850])]) ).
fof(i_0_9412,plain,
! [X20071,X20072] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20072))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20072),X20071)),X20072) = X20071 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m])]) ).
fof(i_0_9413,plain,
! [X20069,X20070] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20070))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20069),X20070)),X20070) = X20069 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m])]) ).
fof(i_0_9414,plain,
! [X20548,X20549] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20549,X20548) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X20549,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20548)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20549,X20548) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X20549,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20548)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20549,X20548)),X20548) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__eq__if])]) ).
fof(i_0_9415,plain,
! [X24315,X24316] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24316,tc_HOL_Obool)),X24315),c_Orderings_Otop__class_Otop(tc_fun(X24316,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
fof(i_0_9416,plain,
! [X21010] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21010)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21010)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21010)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21010)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21010))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5851])]) ).
cnf(i_0_9417,plain,
c_Relation_Osingle__valued(X1,X1,c_Relation_OId(X1)),
inference(split_conjunct,[status(thm)],[i_0_5852]) ).
fof(i_0_9418,plain,
! [X23098,X23099,X23100] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23100),X23099))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23099),X23098))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23100),X23098)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans])]) ).
fof(i_0_9419,plain,
! [X19027,X19028,X19029] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19029),X19028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19028),X19027))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19029),X19027)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).
fof(i_0_9420,plain,
! [X19706,X19707,X19708] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19708),X19707))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19707),X19706))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19708),X19706)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_9421,plain,
! [X23144,X23145,X23146,X23147] :
( ~ class_Divides_Osemiring__div(X23147)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23147),X23146),X23145))
| c_Divides_Odiv__class_Omod(X23147,c_Divides_Odiv__class_Omod(X23147,X23144,X23145),X23146) = c_Divides_Odiv__class_Omod(X23147,X23144,X23146) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__cancel])]) ).
fof(i_0_9422,plain,
! [X17222,X17223,X17224] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X17224,X17223,X17222)
| X17222 = X17224 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I1_J])]) ).
fof(i_0_9423,plain,
! [X18627,X18628] :
( ~ class_Rings_Ocomm__semiring__1(X18628)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18628),X18627),X18627) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18628),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18628),c_Groups_Oone__class_Oone(X18628)),c_Groups_Oone__class_Oone(X18628))),X18627) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).
fof(i_0_9424,plain,
! [X19128,X19129,X19130] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19130),X19129),X19128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19130),X19129),X19128))
| ~ class_Orderings_Opreorder(X19130) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19130),X19128),X19129))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19130),X19129),X19128))
| ~ class_Orderings_Opreorder(X19130) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19130),X19129),X19128))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19130),X19128),X19129))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19130),X19129),X19128))
| ~ class_Orderings_Opreorder(X19130) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5853])])]) ).
fof(i_0_9425,plain,
! [X18297,X18298,X18299,X18300] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18300),X18299))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18298),X18299) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18300),X18297)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18298),X18297)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_9426,plain,
! [X23343,X23344,X23345] :
( ~ class_Divides_Oring__div(X23345)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23345),X23344),X23343))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23345),X23343),hAPP(c_Groups_Ouminus__class_Ouminus(X23345),X23344)) = hAPP(c_Groups_Ouminus__class_Ouminus(X23345),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23345),X23343),X23344)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__neg])]) ).
fof(i_0_9427,plain,
! [X19256,X19257] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19257)),X19256))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19257),X19256)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_9428,plain,
! [X19478,X19479] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19479),X19478))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19479)),X19478)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19479)),X19478))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19479),X19478)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_9429,plain,
! [X19474,X19475] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19475)),X19474))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19475),X19474)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19475),X19474))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19475)),X19474)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_9430,plain,
! [X19466,X19467] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19467)),X19466))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19467),X19466)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_9431,plain,
! [X18273,X18274] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18274)),X18273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18274),X18273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_9432,plain,
! [X25377,X25378,X25379] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25379),X25378))
| hBOOL(hAPP(hAPP(c_member(X25379),X25377),X25378))
| hAPP(c_Finite__Set_Ocard(X25379),hAPP(hAPP(c_Set_Oinsert(X25379),X25377),X25378)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X25379),X25378)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5854])]) ).
fof(i_0_9433,plain,
! [X33362,X33363,X33364,X33365] : hAPP(hAPP(c_List_Odrop(X33365),X33364),hAPP(hAPP(c_List_Odrop(X33365),X33363),X33362)) = hAPP(hAPP(c_List_Odrop(X33365),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33364),X33363)),X33362),
inference(variable_rename,[status(thm)],[fact_drop__drop]) ).
fof(i_0_9434,plain,
! [X33089,X33090,X33091,X33092] : hAPP(hAPP(c_List_Otake(X33092),X33091),hAPP(hAPP(c_List_Otake(X33092),X33090),X33089)) = hAPP(hAPP(c_List_Otake(X33092),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X33091),X33090)),X33089),
inference(variable_rename,[status(thm)],[fact_take__take]) ).
fof(i_0_9435,plain,
! [X19945,X19946,X19947] :
( ( ~ hBOOL(hAPP(X19947,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19946),X19945)))
| epred2_3(X19947,X19946,X19945) )
& ( ~ epred2_3(X19947,X19946,X19945)
| hBOOL(hAPP(X19947,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19946),X19945))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5855])]) ).
fof(i_0_9436,plain,
! [X31378,X31379,X31380] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31380)
| ~ hBOOL(hAPP(hAPP(c_member(X31380),X31379),X31378))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31380),c_Complete__Lattice_OInf__class_OInf(X31380,X31378)),X31379)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__lower])]) ).
fof(i_0_9437,plain,
! [X19492,X19494,X19495,X19497] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk46_1(X19492)))
| hBOOL(hAPP(X19492,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19494))) )
& ( ~ hBOOL(hAPP(X19492,esk46_1(X19492)))
| hBOOL(hAPP(X19492,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19494))) )
& ( ~ hBOOL(hAPP(X19495,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk47_1(X19495))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19497))
| hBOOL(hAPP(X19495,X19497)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I1_J])])])])])]) ).
fof(i_0_9438,plain,
! [X20000,X20001] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20001))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20001),X20000)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X20001)),hAPP(c_Int_Onat,X20000)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__div__distrib])]) ).
fof(i_0_9439,plain,
! [X19323,X19324] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19324))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19324),X19323)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X19324)),hAPP(c_Int_Onat,X19323)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib])]) ).
fof(i_0_9440,plain,
! [X23730,X23731] :
( ~ c_Nat__Transfer_Ois__nat(X23731)
| ~ c_Nat__Transfer_Ois__nat(X23730)
| c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X23731,X23730) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,X23731),hAPP(c_Int_Onat,X23730))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions])]) ).
fof(i_0_9441,plain,
! [X34208] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X34208)),c_List_Otranspose__rel(X34208)),c_List_Olist_ONil(tc_List_Olist(X34208))))
| c_List_Otranspose(X34208,c_List_Olist_ONil(tc_List_Olist(X34208))) = c_List_Olist_ONil(tc_List_Olist(X34208)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I1_J])]) ).
fof(i_0_9442,plain,
! [X19984,X19985,X19986] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19986),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19985,X19984)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19986),X19985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19986),X19984)),
inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2]) ).
fof(i_0_9443,plain,
! [X23698,X23699] :
( ( X23699 != X23698
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23699) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23698) )
& ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23699) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23698)
| X23699 = X23698 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J])]) ).
fof(i_0_9444,plain,
! [X32932,X32933,X32934] : hAPP(c_List_Oset(X32934),hAPP(hAPP(c_List_Oappend(X32934),X32933),X32932)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X32934,tc_HOL_Obool)),hAPP(c_List_Oset(X32934),X32933)),hAPP(c_List_Oset(X32934),X32932)),
inference(variable_rename,[status(thm)],[fact_set__append]) ).
fof(i_0_9445,plain,
! [X18214,X18215] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18215),X18214))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18215)),hAPP(c_Nat_OSuc,X18214))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_9446,plain,
! [X25186,X25187,X25188,X25189] :
( ( hAPP(hAPP(c_Set_Oinsert(X25189),X25188),X25187) != hAPP(hAPP(c_Set_Oinsert(X25189),X25188),X25186)
| X25187 = X25186
| hBOOL(hAPP(hAPP(c_member(X25189),X25188),X25186))
| hBOOL(hAPP(hAPP(c_member(X25189),X25188),X25187)) )
& ( X25187 != X25186
| hAPP(hAPP(c_Set_Oinsert(X25189),X25188),X25187) = hAPP(hAPP(c_Set_Oinsert(X25189),X25188),X25186)
| hBOOL(hAPP(hAPP(c_member(X25189),X25188),X25186))
| hBOOL(hAPP(hAPP(c_member(X25189),X25188),X25187)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5856])])]) ).
fof(i_0_9447,plain,
! [X20935,X20936,X20937,X20938] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X20938),X20937),X20936) != hAPP(hAPP(c_Power_Opower__class_Opower(X20938),X20937),X20935)
| X20936 = X20935
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20938),c_Groups_Oone__class_Oone(X20938)),X20937))
| ~ class_Rings_Olinordered__semidom(X20938) )
& ( X20936 != X20935
| hAPP(hAPP(c_Power_Opower__class_Opower(X20938),X20937),X20936) = hAPP(hAPP(c_Power_Opower__class_Opower(X20938),X20937),X20935)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20938),c_Groups_Oone__class_Oone(X20938)),X20937))
| ~ class_Rings_Olinordered__semidom(X20938) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).
fof(i_0_9448,plain,
! [X32593,X32594,X32595] : c_List_Olistset(X32595,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32595,tc_HOL_Obool)),X32594),X32593)) = c_List_Oset__Cons(X32595,X32594,c_List_Olistset(X32595,X32593)),
inference(variable_rename,[status(thm)],[fact_listset_Osimps_I2_J]) ).
fof(i_0_9449,plain,
! [X31201,X31202] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31202)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31202),X31201))
| c_Complete__Lattice_OSup__class_OSup(X31202,X31201) = hAPP(hAPP(c_Finite__Set_Ofold(X31202,X31202,c_Lattices_Osemilattice__sup__class_Osup(X31202)),c_Orderings_Obot__class_Obot(X31202)),X31201) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup])]) ).
fof(i_0_9450,plain,
! [X31199,X31200] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31200)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31200),X31199))
| c_Complete__Lattice_OInf__class_OInf(X31200,X31199) = hAPP(hAPP(c_Finite__Set_Ofold(X31200,X31200,c_Lattices_Osemilattice__inf__class_Oinf(X31200)),c_Orderings_Otop__class_Otop(X31200)),X31199) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf])]) ).
fof(i_0_9451,plain,
! [X20884,X20885] :
( ( X20885 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20884),X20885) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X20885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20884),X20885) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20884),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20884),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20885),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__if])]) ).
fof(i_0_9452,plain,
! [X23807,X23808,X23809] :
( ~ class_Groups_Oordered__ab__group__add(X23809)
| hAPP(c_Set_Oimage(X23809,X23809,c_Groups_Ouminus__class_Ouminus(X23809)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23809,X23808,X23807)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X23809,hAPP(c_Groups_Ouminus__class_Ouminus(X23809),X23807),hAPP(c_Groups_Ouminus__class_Ouminus(X23809),X23808)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan])]) ).
fof(i_0_9453,plain,
! [X23722,X23723,X23724] :
( ~ class_Groups_Oordered__ab__group__add(X23724)
| hAPP(c_Set_Oimage(X23724,X23724,c_Groups_Ouminus__class_Ouminus(X23724)),c_SetInterval_Oord__class_OatLeastAtMost(X23724,X23723,X23722)) = c_SetInterval_Oord__class_OatLeastAtMost(X23724,hAPP(c_Groups_Ouminus__class_Ouminus(X23724),X23722),hAPP(c_Groups_Ouminus__class_Ouminus(X23724),X23723)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost])]) ).
fof(i_0_9454,plain,
! [X25374,X25375,X25376] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25376),X25374),X25375))
| hAPP(c_Finite__Set_Ocard(X25376),hAPP(hAPP(c_Set_Oinsert(X25376),X25374),X25375)) = hAPP(c_Finite__Set_Ocard(X25376),X25375)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25376),X25375)) )
& ( hBOOL(hAPP(hAPP(c_member(X25376),X25374),X25375))
| hAPP(c_Finite__Set_Ocard(X25376),hAPP(hAPP(c_Set_Oinsert(X25376),X25374),X25375)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X25376),X25375))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25376),X25375)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5857])])]) ).
fof(i_0_9455,plain,
! [X24371] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24371)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24371))),
inference(variable_rename,[status(thm)],[fact_lessThan__Suc__eq__insert__0]) ).
fof(i_0_9456,plain,
! [X22126,X22127] : c_Code__Numeral_Odiv__mod__code__numeral(X22127,X22126) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X22127),X22126)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X22127,X22126)),
inference(variable_rename,[status(thm)],[fact_div__mod__code__numeral__def]) ).
fof(i_0_9457,plain,
! [X22010,X22011] : c_Divides_Odivmod__int(X22011,X22010) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22011),X22010)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22011,X22010)),
inference(variable_rename,[status(thm)],[fact_divmod__int__mod__div]) ).
fof(i_0_9458,plain,
! [X19846,X19847] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19847,X19846)),X19846) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19847),X19846),
inference(variable_rename,[status(thm)],[fact_zminus__zmod]) ).
fof(i_0_9459,plain,
! [X19512,X19513] :
( ( hAPP(c_Int_Onat,X19513) != hAPP(c_Int_Onat,X19512)
| X19513 = X19512
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19512))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19513)) )
& ( X19513 != X19512
| hAPP(c_Int_Onat,X19513) = hAPP(c_Int_Onat,X19512)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19512))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19513)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I1_J])])]) ).
fof(i_0_9460,plain,
! [X19498,X19499] :
( ( hAPP(c_Int_Onat,X19499) != hAPP(c_Int_Onat,X19498)
| X19499 = X19498
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19498))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19499)) )
& ( X19499 != X19498
| hAPP(c_Int_Onat,X19499) = hAPP(c_Int_Onat,X19498)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19498))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19499)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__nat__nat__iff])])]) ).
fof(i_0_9461,plain,
! [X18475,X18476,X18478,X18479,X18480] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18476),X18475))
| X18475 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18476),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk36_2(X18475,X18476)))) )
& ( X18478 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18479),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X18480)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18479),X18478)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__iff__Suc__zadd])])])])]) ).
cnf(i_0_9462,plain,
( c_List_Olast(tc_Nat_Onat,c_List_Oupt(X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5858]) ).
fof(i_0_9463,plain,
! [X20461,X20462] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20462),X20461)),X20461) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20462),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20462,X20461)),
inference(variable_rename,[status(thm)],[fact_div__mod__equality_H]) ).
fof(i_0_9464,plain,
! [X20431,X20432] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20432),X20431))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20431),X20432)),X20432) = X20431 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).
fof(i_0_9465,plain,
! [X18488] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18488)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18488)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18488))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18488))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv])]) ).
fof(i_0_9466,plain,
! [X20886,X20887] :
( ( X20887 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20886))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20887) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20886) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20886)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20887) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20886) )
& ( X20887 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20886)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20887) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20886) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff__number__of])])]) ).
fof(i_0_9467,plain,
! [X26285,X26286,X26287,X26288,X26289] :
( hAPP(X26289,X26288) != hAPP(c_Option_Ooption_OSome(X26287),X26286)
| hBOOL(hAPP(hAPP(c_member(X26287),X26286),c_Map_Oran(X26285,X26287,X26289))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ranI])]) ).
fof(i_0_9468,plain,
! [X28463,X28464,X28465,X28466,X28467] :
( hAPP(X28467,X28466) != hAPP(c_Option_Ooption_OSome(X28465),X28464)
| hBOOL(hAPP(hAPP(c_member(X28463),X28466),c_Map_Odom(X28463,X28465,X28467))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_domI])]) ).
fof(i_0_9469,plain,
! [X26528,X26529] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X26529,tc_HOL_Obool)),hAPP(c_Set_OPow(X26529),X26528)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X26529),X26528)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26529),X26528))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X26529,tc_HOL_Obool)),hAPP(c_Set_OPow(X26529),X26528))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff])]) ).
fof(i_0_9470,plain,
! [X29862,X29863,X29864,X29865,X29866] :
( ~ hBOOL(hAPP(hAPP(X29866,X29865),X29864))
| hBOOL(hAPP(c_Predicate_ODomainP(X29863,X29862,X29866),X29865)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros])]) ).
fof(i_0_9471,plain,
! [X29762,X29763,X29764,X29765,X29766] :
( ~ hBOOL(hAPP(hAPP(X29766,X29765),X29764))
| hBOOL(hAPP(c_Predicate_ORangeP(X29763,X29762,X29766),X29764)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros])]) ).
fof(i_0_9472,plain,
! [X32555,X32556] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32556)),X32555)))
| X32555 != c_List_Olist_ONil(X32556) )
& ( X32555 = c_List_Olist_ONil(X32556)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32556)),X32555))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv])]) ).
fof(i_0_9473,plain,
! [X27478,X27479,X27480] :
( ~ class_Orderings_Oorder(X27480)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27480,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27480,X27479),X27478)),hAPP(c_SetInterval_Oord__class_OatLeast(X27480),X27478)) = c_Orderings_Obot__class_Obot(tc_fun(X27480,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J])]) ).
fof(i_0_9474,plain,
! [X19468,X19469] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19468),hAPP(c_Nat_OSuc,X19469)))
| X19468 = X19469
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19469),X19468)) )
& ( X19468 != X19469
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19468),hAPP(c_Nat_OSuc,X19469)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19469),X19468)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
cnf(i_0_9475,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X1)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X1,
inference(split_conjunct,[status(thm)],[i_0_5859]) ).
fof(i_0_9476,plain,
! [X19888,X19889] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19889))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19889),X19888))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19889,X19888) = X19889 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial])]) ).
fof(i_0_9477,plain,
! [X27559,X27560] :
( ~ class_Orderings_Oorder(X27560)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27560,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X27560),X27559)),hAPP(c_SetInterval_Oord__class_OatLeast(X27560),X27559)) = hAPP(hAPP(c_Set_Oinsert(X27560),X27559),c_Orderings_Obot__class_Obot(tc_fun(X27560,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast])]) ).
fof(i_0_9478,plain,
! [X18292,X18293] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18293),X18292))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18292),hAPP(c_Nat_OSuc,X18293))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18292),hAPP(c_Nat_OSuc,X18293)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18293),X18292)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5860])]) ).
cnf(i_0_9479,plain,
hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_5861]) ).
fof(i_0_9480,plain,
! [X32870,X32871,X32872] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32872)),hAPP(hAPP(c_List_Oappend(X32872),X32871),X32870)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32872)),X32871)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32872)),X32870)),
inference(variable_rename,[status(thm)],[fact_length__append]) ).
fof(i_0_9481,plain,
! [X23797,X23798] :
( ( X23798 != X23797
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23798) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23797)
| ~ c_Nat__Transfer_Onat__set(X23797)
| ~ c_Nat__Transfer_Onat__set(X23798) )
& ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23798) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23797)
| X23798 = X23797
| ~ c_Nat__Transfer_Onat__set(X23797)
| ~ c_Nat__Transfer_Onat__set(X23798) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I3_J])])]) ).
fof(i_0_9482,plain,
! [X25721,X25722,X25723,X25724,X25725,X25726,X25727] :
( ( X25726 = X25723
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25727),X25726),X25725),X25724) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25727),X25723),X25722),X25721) )
& ( X25725 = X25722
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25727),X25726),X25725),X25724) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25727),X25723),X25722),X25721) )
& ( X25724 = X25721
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25727),X25726),X25725),X25724) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25727),X25723),X25722),X25721) )
& ( X25726 != X25723
| X25725 != X25722
| X25724 != X25721
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25727),X25726),X25725),X25724) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25727),X25723),X25722),X25721) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triple_Oinject])])]) ).
fof(i_0_9483,plain,
! [X26107,X26108,X26109,X26110,X26111] :
( ~ class_Rings_Ocomm__semiring__1(X26110)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26109),X26108))
| ~ hBOOL(hAPP(hAPP(c_member(X26109),X26111),X26108))
| hAPP(X26107,X26111) != c_Groups_Ozero__class_Ozero(X26110)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26109,X26110),X26107),X26108) = c_Groups_Ozero__class_Ozero(X26110) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__zero])])]) ).
fof(i_0_9484,plain,
! [X20007,X20008,X20009] :
( ( X20009 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20009),X20008)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20009),X20007)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X20009 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20009),X20008)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20009),X20007)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20008),X20007) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj])]) ).
fof(i_0_9485,plain,
! [X26510,X26511] : hBOOL(hAPP(hAPP(c_member(tc_fun(X26511,tc_HOL_Obool)),X26510),hAPP(c_Set_OPow(X26511),X26510))),
inference(variable_rename,[status(thm)],[fact_Pow__top]) ).
fof(i_0_9486,plain,
! [X34221,X34222,X34223] : hAPP(c_List_Orev(X34223),hAPP(hAPP(c_List_Olist_OCons(X34223),X34222),X34221)) = hAPP(hAPP(c_List_Oappend(X34223),hAPP(c_List_Orev(X34223),X34221)),hAPP(hAPP(c_List_Olist_OCons(X34223),X34222),c_List_Olist_ONil(X34223))),
inference(variable_rename,[status(thm)],[fact_rev_Osimps_I2_J]) ).
cnf(i_0_9487,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_Relation_OId(X1),
inference(split_conjunct,[status(thm)],[i_0_5862]) ).
fof(i_0_9488,plain,
! [X20091,X20092] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20092),X20091))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20092),X20091) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial])]) ).
fof(i_0_9489,plain,
! [X20078,X20079] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20079),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20079))
| X20078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20079),X20078) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20078),X20079))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20079))
| X20078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20079),X20078) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20079),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20079),X20078))
| X20078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20079),X20078) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20078),X20079))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20079),X20078))
| X20078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20079),X20078) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X20078 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20079),X20078) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20079),X20078))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20079),X20078) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20079),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20078),X20079))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20079),X20078) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff])])]) ).
fof(i_0_9490,plain,
! [X27787,X27788] :
( ~ class_Lattices_Olattice(X27788)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27788),X27787))
| X27787 = c_Orderings_Obot__class_Obot(tc_fun(X27788,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27788),c_Big__Operators_Olattice__class_OInf__fin(X27788,X27787)),c_Big__Operators_Olattice__class_OSup__fin(X27788,X27787))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup])]) ).
fof(i_0_9491,plain,
! [X27831,X27832,X27833,X27834,X27835] :
( ~ c_Equiv__Relations_Oequivp(X27835,X27834)
| ~ hBOOL(hAPP(hAPP(X27834,X27833),X27832))
| ~ hBOOL(hAPP(hAPP(X27834,X27832),X27831))
| hBOOL(hAPP(hAPP(X27834,X27833),X27831)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__transp])]) ).
fof(i_0_9492,plain,
! [X26544,X26545,X26546,X26547,X26548] :
( ~ c_Finite__Set_Ofolding__one__idem(X26548,X26547,X26546)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26548),X26545))
| X26545 = c_Orderings_Obot__class_Obot(tc_fun(X26548,tc_HOL_Obool))
| hAPP(X26546,hAPP(hAPP(c_Set_Oinsert(X26548),X26544),X26545)) = hAPP(hAPP(X26547,X26544),hAPP(X26546,X26545)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem])]) ).
fof(i_0_9493,plain,
! [X19827,X19828,X19829,X19830] :
( ~ class_Divides_Oring__div(X19830)
| c_Divides_Odiv__class_Omod(X19830,X19829,X19828) != c_Divides_Odiv__class_Omod(X19830,X19827,X19828)
| c_Divides_Odiv__class_Omod(X19830,hAPP(c_Groups_Ouminus__class_Ouminus(X19830),X19829),X19828) = c_Divides_Odiv__class_Omod(X19830,hAPP(c_Groups_Ouminus__class_Ouminus(X19830),X19827),X19828) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__cong])]) ).
fof(i_0_9494,plain,
! [X31453,X31454] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31454,tc_HOL_Obool),X31453) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31454,tc_HOL_Obool),tc_fun(X31454,tc_HOL_Obool)),X31453),c_COMBI(tc_fun(X31454,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_Union__def]) ).
fof(i_0_9495,plain,
! [X31451,X31452] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31452,tc_HOL_Obool),X31451) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X31452,tc_HOL_Obool),tc_fun(X31452,tc_HOL_Obool)),X31451),c_COMBI(tc_fun(X31452,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_Inter__def]) ).
fof(i_0_9496,plain,
! [X20809] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20809)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X20809 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X20809 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20809)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff])]) ).
fof(i_0_9497,plain,
! [X19626] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19626)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X19626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19626 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19626)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__le__0__conv])]) ).
fof(i_0_9498,plain,
! [X31618,X31619,X31620] : c_Map_Omap__add(X31620,X31619,hAPP(c_COMBK(tc_Option_Ooption(X31619),X31620),c_Option_Ooption_ONone(X31619)),X31618) = X31618,
inference(variable_rename,[status(thm)],[fact_empty__map__add]) ).
fof(i_0_9499,plain,
! [X31621,X31622,X31623] : c_Map_Omap__add(X31623,X31622,X31621,hAPP(c_COMBK(tc_Option_Ooption(X31622),X31623),c_Option_Ooption_ONone(X31622))) = X31621,
inference(variable_rename,[status(thm)],[fact_map__add__empty]) ).
fof(i_0_9500,plain,
! [X20890,X20891] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20891))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X20891)),X20890) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20891),X20890)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J])]) ).
fof(i_0_9501,plain,
! [X20888,X20889] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20889))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20889),X20888)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X20889)),X20888) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq])]) ).
fof(i_0_9502,plain,
! [X20310,X20311,X20312] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20312),X20311)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20312),X20310)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20311),X20310),
inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).
fof(i_0_9503,plain,
! [X20313,X20314,X20315] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20315),X20314)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20313),X20314)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20315),X20313),
inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).
fof(i_0_9504,plain,
! [X20650,X20651,X20652] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20652),X20651)),X20650) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20651),X20650)),
inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).
fof(i_0_9505,plain,
! [X20307,X20308,X20309] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20309),X20308)),X20307) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20309),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20308),X20307)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(i_0_9506,plain,
! [X18692,X18693,X18694] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18694),X18693)),X18692) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18694),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18693),X18692)),
inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).
fof(i_0_9507,plain,
! [X19012,X19013,X19014] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19014),X19013)),X19012) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19013),X19012)),
inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).
fof(i_0_9508,plain,
! [X18546,X18547,X18548] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18548),X18547)),X18546) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18547),X18546)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(i_0_9509,plain,
! [X18038,X18039,X18040] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18040),X18039)),X18038) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18040),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18039),X18038)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_9510,plain,
! [X19977,X19978,X19979] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19979),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19978),X19977)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19979),X19978)),X19977),
inference(variable_rename,[status(thm)],[fact_div__mult2__eq]) ).
fof(i_0_9511,plain,
! [X29937,X29938,X29939] :
( ~ hBOOL(hAPP(hAPP(c_member(X29938),X29939),c_Orderings_Obot__class_Obot(tc_fun(X29938,tc_HOL_Obool))))
| hBOOL(hAPP(X29937,X29939)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ball__empty])]) ).
fof(i_0_9512,plain,
! [X27499,X27500,X27501] :
( ~ class_Orderings_Oorder(X27501)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27501,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X27501),X27500)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27501,X27500,X27499)) = c_Orderings_Obot__class_Obot(tc_fun(X27501,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J])]) ).
fof(i_0_9513,plain,
! [X27492,X27493,X27494] :
( ~ class_Orderings_Oorder(X27494)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27494,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X27494),X27493)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27494,X27493,X27492)) = c_Orderings_Obot__class_Obot(tc_fun(X27494,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J])]) ).
fof(i_0_9514,plain,
! [X27438,X27439,X27440] :
( ~ class_Orderings_Oorder(X27440)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27440,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27440),X27439)),c_SetInterval_Oord__class_OatLeastAtMost(X27440,X27439,X27438)) = c_Orderings_Obot__class_Obot(tc_fun(X27440,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J])]) ).
fof(i_0_9515,plain,
! [X19882,X19883] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19883),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19882),X19883))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19883,X19882) = X19883 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial])]) ).
fof(i_0_9516,plain,
! [X31835,X31836,X31837,X31838] : hAPP(c_List_Oset(X31838),hAPP(hAPP(c_List_Omap(X31837,X31838),X31836),X31835)) = hAPP(c_Set_Oimage(X31837,X31838,X31836),hAPP(c_List_Oset(X31837),X31835)),
inference(variable_rename,[status(thm)],[fact_set__map]) ).
fof(i_0_9517,plain,
! [X33395,X33396,X33397] : hAPP(hAPP(c_List_Oappend(X33397),hAPP(hAPP(c_List_Otake(X33397),X33396),X33395)),hAPP(hAPP(c_List_Odrop(X33397),X33396),X33395)) = X33395,
inference(variable_rename,[status(thm)],[fact_append__take__drop__id]) ).
fof(i_0_9518,plain,
! [X18536] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18536)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[i_0_5863]) ).
fof(i_0_9519,plain,
! [X19975,X19976] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19976),X19975) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19976,X19975)),X19975),
inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).
fof(i_0_9520,plain,
! [X18112,X18113] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X18113,X18112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X18113)),c_Com_Ocom_Ocom__size(X18112))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_com_Osize_I4_J]) ).
fof(i_0_9521,plain,
! [X21138] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21138)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21138)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21138))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21138))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__0__number__of])]) ).
fof(i_0_9522,plain,
! [X17238,X17239,X17240] :
( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17240)))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X17239,X17240,X17238))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OCall])]) ).
fof(i_0_9523,plain,
! [X20100,X20101] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20100),X20101))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20101),X20100) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg__trivial])]) ).
cnf(i_0_9524,plain,
( c_Int_OMin = X1
| c_Int_OMin != c_Int_OBit1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5864]) ).
cnf(i_0_9525,plain,
( X1 = c_Int_OMin
| c_Int_OBit1(X1) != c_Int_OMin ),
inference(split_conjunct,[status(thm)],[i_0_5865]) ).
fof(i_0_9526,plain,
! [X33124,X33125,X33126,X33127] : hAPP(hAPP(c_List_Otake(X33127),hAPP(c_Nat_OSuc,X33126)),hAPP(hAPP(c_List_Olist_OCons(X33127),X33125),X33124)) = hAPP(hAPP(c_List_Olist_OCons(X33127),X33125),hAPP(hAPP(c_List_Otake(X33127),X33126),X33124)),
inference(variable_rename,[status(thm)],[fact_take__Suc__Cons]) ).
fof(i_0_9527,plain,
! [X32163,X32164,X32165,X32166,X32167,X32168,X32169] :
( hAPP(hAPP(c_List_Omap(X32169,X32168),X32167),X32166) != hAPP(hAPP(c_List_Omap(X32165,X32168),X32164),X32163)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32169)),X32166) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32165)),X32163) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__eq__imp__length__eq])]) ).
cnf(i_0_9528,plain,
c_Int_OBit1(X1) != c_Int_OPls,
inference(split_conjunct,[status(thm)],[i_0_5866]) ).
cnf(i_0_9529,plain,
c_Int_OPls != c_Int_OBit1(X1),
inference(split_conjunct,[status(thm)],[i_0_5867]) ).
fof(i_0_9530,plain,
! [X23767] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23767)) = X23767,
inference(variable_rename,[status(thm)],[fact_transfer__int__nat__set__return__embed]) ).
fof(i_0_9531,plain,
! [X22368,X22369,X22370,X22371,X22372] :
( hAPP(c_Product__Type_Ofst(X22372,X22371),hAPP(hAPP(c_Product__Type_OPair(X22372,X22371),X22370),X22369)) != X22368
| X22370 = X22368 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__eqD])]) ).
fof(i_0_9532,plain,
! [X22148,X22149,X22150,X22151,X22152] :
( hAPP(c_Product__Type_Osnd(X22152,X22151),hAPP(hAPP(c_Product__Type_OPair(X22152,X22151),X22150),X22149)) != X22148
| X22149 = X22148 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__eqD])]) ).
fof(i_0_9533,plain,
! [X23820] :
( ~ c_Nat__Transfer_Onat__set(X23820)
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23820)) = X23820 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__return__embed])]) ).
fof(i_0_9534,plain,
! [X26435,X26436] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X26436,X26436)),X26435))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X26436),hAPP(c_Relation_OField(X26436),X26435))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Field])]) ).
fof(i_0_9535,plain,
! [X23685,X23686,X23687] :
( ~ class_Groups_Oordered__ab__group__add(X23687)
| hAPP(c_Set_Oimage(X23687,X23687,c_Groups_Ouminus__class_Ouminus(X23687)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23687,X23686),X23685)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X23687,hAPP(c_Groups_Ouminus__class_Ouminus(X23687),X23685),hAPP(c_Groups_Ouminus__class_Ouminus(X23687),X23686)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan])]) ).
fof(i_0_9536,plain,
! [X18280,X18281] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18281),X18280))
| hAPP(c_Nat_OSuc,X18281) = X18280
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18281)),X18280)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_9537,plain,
! [X24402,X24404,X24405,X24406] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24402))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24404),X24402))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24404),esk152_1(X24402))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk153_2(X24405,X24406)),X24405))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24405)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk153_2(X24405,X24406)),X24406))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24405)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded__le])])])])])]) ).
fof(i_0_9538,plain,
! [X24419,X24421,X24422,X24423] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24419))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24421),X24419))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24421),esk154_1(X24419))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk155_2(X24422,X24423)),X24422))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24422)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk155_2(X24422,X24423)),X24423))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24422)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded])])])])])]) ).
fof(i_0_9539,plain,
! [X20658,X20659] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20658)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20658)) = hAPP(c_Int_Onumber__class_Onumber__of(X20659),X20658)
| ~ class_Int_Onumber__ring(X20659) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20658)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20658)) = c_Groups_Ozero__class_Ozero(X20659)
| ~ class_Int_Onumber__ring(X20659) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5868])])]) ).
fof(i_0_9540,plain,
! [X20820,X20821,X20822] :
( ~ class_Int_Onumber__ring(X20822)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20822),hAPP(c_Int_Onumber__class_Onumber__of(X20822),X20821)),hAPP(c_Int_Onumber__class_Onumber__of(X20822),X20820)) = hAPP(c_Int_Onumber__class_Onumber__of(X20822),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20821),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20820))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__number__of__eq])]) ).
fof(i_0_9541,plain,
! [X25371,X25372,X25373] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25373),X25372))
| hBOOL(hAPP(hAPP(c_member(X25373),X25371),X25372))
| hAPP(c_Finite__Set_Ocard(X25373),hAPP(hAPP(c_Set_Oinsert(X25373),X25371),X25372)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X25373),X25372)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5869])]) ).
fof(i_0_9542,plain,
! [X18622] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X18622)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18622)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18622))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X18622))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq])]) ).
fof(i_0_9543,plain,
! [X19155,X19156,X19157] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19157),X19156),X19155))
| X19156 = X19155
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19157),X19156),X19155))
| ~ class_Orderings_Olinorder(X19157) )
& ( X19156 != X19155
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19157),X19156),X19155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19157),X19156),X19155))
| ~ class_Orderings_Olinorder(X19157) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5870])])]) ).
fof(i_0_9544,plain,
! [X33827,X33828,X33829] : c_List_Obutlast(X33829,hAPP(hAPP(c_List_Oappend(X33829),X33828),hAPP(hAPP(c_List_Olist_OCons(X33829),X33827),c_List_Olist_ONil(X33829)))) = X33828,
inference(variable_rename,[status(thm)],[fact_butlast__snoc]) ).
fof(i_0_9545,plain,
! [X33760,X33761,X33762] : c_List_Olast(X33762,hAPP(hAPP(c_List_Oappend(X33762),X33761),hAPP(hAPP(c_List_Olist_OCons(X33762),X33760),c_List_Olist_ONil(X33762)))) = X33760,
inference(variable_rename,[status(thm)],[fact_last__snoc]) ).
fof(i_0_9546,plain,
! [X30205,X30206] : hAPP(hAPP(c_Relation_Orel__comp(X30206,X30206,X30206),c_Transitive__Closure_Ortrancl(X30206,X30205)),c_Transitive__Closure_Ortrancl(X30206,X30205)) = c_Transitive__Closure_Ortrancl(X30206,X30205),
inference(variable_rename,[status(thm)],[fact_rtrancl__idemp__self__comp]) ).
fof(i_0_9547,plain,
! [X22386,X22387,X22388] : hAPP(c_Product__Type_Ofst(X22388,X22387),X22386) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22388,X22387,X22388),c_COMBK(X22388,X22387)),X22386),
inference(variable_rename,[status(thm)],[fact_fst__def]) ).
fof(i_0_9548,plain,
! [X31880] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X31880)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31880),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_5871]) ).
fof(i_0_9549,plain,
! [X30439,X30440] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30440,X30440)),X30439))
| ~ c_Wellfounded_Oacyclic(X30440,X30439)
| c_Wellfounded_Owf(X30440,hAPP(c_Relation_Oconverse(X30440,X30440),X30439)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf__converse])]) ).
fof(i_0_9550,plain,
! [X19084,X19085,X19086] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19086),X19085),X19084))
| X19085 != X19084
| ~ class_Orderings_Oorder(X19086) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19086),X19084),X19085))
| X19085 != X19084
| ~ class_Orderings_Oorder(X19086) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19086),X19085),X19084))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19086),X19084),X19085))
| X19085 = X19084
| ~ class_Orderings_Oorder(X19086) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_9551,plain,
! [X19073,X19074,X19075] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19075),X19073),X19074))
| X19073 = X19074
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19075),X19074),X19073))
| ~ class_Orderings_Oorder(X19075) )
& ( X19073 != X19074
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19075),X19073),X19074))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19075),X19074),X19073))
| ~ class_Orderings_Oorder(X19075) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_9552,plain,
! [X19054,X19055,X19056] :
( ~ class_Orderings_Oorder(X19056)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19056),X19055),X19054))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19056),X19054),X19055))
| X19055 = X19054 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_9553,plain,
! [X19047,X19048,X19049] :
( ~ class_Orderings_Oorder(X19049)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19049),X19048),X19047))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19049),X19047),X19048))
| X19047 = X19048 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_9554,plain,
! [X17723,X17724,X17725] :
( hBOOL(hAPP(X17725,X17724))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17725,X17723)),X17724),X17724)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5872])]) ).
fof(i_0_9555,plain,
! [X20335,X20336] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20336),X20335))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20335,X20336) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20335),X20336),X20336) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mod__geq])]) ).
fof(i_0_9556,plain,
! [X24855,X24856] :
( X24856 != X24855
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24856,X24855) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24856),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton_H])]) ).
fof(i_0_9557,plain,
! [X23211,X23212] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23212),X23211))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23212),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23211))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23212),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23211)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23212),X23211)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I2_J])]) ).
fof(i_0_9558,plain,
! [X20411,X20412] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20412),X20411))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20411)),X20412) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20411),X20412)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])]) ).
fof(i_0_9559,plain,
! [X18588,X18589,X18590] :
( ~ class_Orderings_Opreorder(X18590)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18590),X18589),X18588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18590),X18588),X18589)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5873])]) ).
fof(i_0_9560,plain,
! [X18579,X18580,X18581] :
( ~ class_Orderings_Opreorder(X18581)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18581),X18580),X18579))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18581),X18579),X18580)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5874])]) ).
fof(i_0_9561,plain,
! [X18576,X18577,X18578] :
( ~ class_Orderings_Opreorder(X18578)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18578),X18577),X18576))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18578),X18576),X18577)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5875])]) ).
fof(i_0_9562,plain,
! [X18521,X18522,X18523] :
( ~ class_Orderings_Opreorder(X18523)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18523),X18522),X18521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18523),X18521),X18522)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5876])]) ).
fof(i_0_9563,plain,
! [X19119,X19120,X19121] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19121),X19120),X19119))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19121),X19119),X19120))
| ~ class_Orderings_Olinorder(X19121) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19121),X19119),X19120))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19121),X19120),X19119))
| ~ class_Orderings_Olinorder(X19121) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5877])])]) ).
fof(i_0_9564,plain,
! [X19149,X19150,X19151] :
( ~ class_Orderings_Olinorder(X19151)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19151),X19150),X19149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19151),X19149),X19150)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5878])]) ).
fof(i_0_9565,plain,
! [X19116,X19117,X19118] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19118),X19117),X19116))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19118),X19116),X19117))
| ~ class_Orderings_Olinorder(X19118) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19118),X19116),X19117))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19118),X19117),X19116))
| ~ class_Orderings_Olinorder(X19118) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5879])])]) ).
fof(i_0_9566,plain,
! [X18561,X18562,X18563] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18563),X18562),X18561))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18563),X18561),X18562))
| X18562 = X18561
| ~ class_Orderings_Olinorder(X18563) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18563),X18561),X18562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18563),X18562),X18561))
| ~ class_Orderings_Olinorder(X18563) )
& ( X18562 != X18561
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18563),X18562),X18561))
| ~ class_Orderings_Olinorder(X18563) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5880])])]) ).
fof(i_0_9567,plain,
! [X18591,X18592,X18593] :
( ~ class_Orderings_Oorder(X18593)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18593),X18592),X18591))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18593),X18591),X18592)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5881])]) ).
fof(i_0_9568,plain,
! [X20704,X20705] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20705)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20705),hAPP(c_Groups_Ouminus__class_Ouminus(X20705),X20704)),hAPP(c_Groups_Oabs__class_Oabs(X20705),X20704))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self])]) ).
fof(i_0_9569,plain,
! [X19417,X19418] :
( ~ class_Rings_Olinordered__ring(X19418)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19418),c_Groups_Ozero__class_Ozero(X19418)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19418),X19417),X19417))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).
fof(i_0_9570,plain,
! [X18929,X18930] :
( ~ class_Rings_Olinordered__semidom(X18930)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18930),X18929),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18930),X18929),c_Groups_Oone__class_Oone(X18930)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_9571,plain,
! [X20674,X20675] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20675),c_Groups_Ozero__class_Ozero(X20675)),hAPP(c_Groups_Oabs__class_Oabs(X20675),X20674)))
| X20674 != c_Groups_Ozero__class_Ozero(X20675)
| ~ class_Groups_Oordered__ab__group__add__abs(X20675) )
& ( X20674 = c_Groups_Ozero__class_Ozero(X20675)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20675),c_Groups_Ozero__class_Ozero(X20675)),hAPP(c_Groups_Oabs__class_Oabs(X20675),X20674)))
| ~ class_Groups_Oordered__ab__group__add__abs(X20675) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).
fof(i_0_9572,plain,
! [X21977,X21978,X21979,X21980] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X21980,X21979),X21978))
| ~ hBOOL(hAPP(hAPP(X21979,X21977),X21978))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X21980,X21979),X21977)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__downward])]) ).
fof(i_0_9573,plain,
! [X21102,X21103] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21103),c_Int_OPls))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21103)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21102)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21103),c_Int_OPls))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21103)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21102)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21103),X21102)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5882])]) ).
fof(i_0_9574,plain,
! [X33464,X33465] :
( X33465 = c_List_Olist_ONil(X33464)
| hBOOL(hAPP(hAPP(c_member(X33464),hAPP(c_List_Ohd(X33464),X33465)),hAPP(c_List_Oset(X33464),X33465))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__in__set])]) ).
fof(i_0_9575,plain,
! [X24854] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24854,X24854) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24854),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_dvd_OatLeastAtMost__singleton]) ).
fof(i_0_9576,plain,
! [X20720,X20721,X20722] :
( ~ class_Rings_Ocomm__semiring__1(X20722)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20722),hAPP(hAPP(c_Power_Opower__class_Opower(X20722),X20721),X20720)),X20721) = hAPP(hAPP(c_Power_Opower__class_Opower(X20722),X20721),hAPP(c_Nat_OSuc,X20720)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).
fof(i_0_9577,plain,
! [X20939,X20940,X20941] :
( ~ class_Groups_Omonoid__mult(X20941)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20941),X20940),hAPP(c_Nat_OSuc,X20939)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20941),hAPP(hAPP(c_Power_Opower__class_Opower(X20941),X20940),X20939)),X20940) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).
fof(i_0_9578,plain,
! [X17411,X17412,X17413,X17414] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17414),X17413),X17412))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17414),X17413),X17411))
| X17411 = X17412 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com__det])]) ).
fof(i_0_9579,plain,
! [X26227,X26228,X26229,X26230,X26231] :
( hAPP(X26231,X26230) != hAPP(c_Option_Ooption_OSome(X26229),X26228)
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26227,tc_Option_Ooption(X26229)),X26231),X26230),hAPP(c_Option_Ooption_OSome(X26229),X26228)) = X26231 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__triv])]) ).
fof(i_0_9580,plain,
! [X17126,X17127,X17128,X17129,X17130] :
( ~ c_Groups_Osemigroup(X17130,X17129)
| hAPP(hAPP(X17129,hAPP(hAPP(X17129,X17128),X17127)),X17126) = hAPP(hAPP(X17129,X17128),hAPP(hAPP(X17129,X17127),X17126)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semigroup_Oassoc])]) ).
fof(i_0_9581,plain,
! [X32353,X32354,X32355] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32355)),hAPP(hAPP(c_List_Olist_OCons(X32355),X32354),X32353)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32355)),X32353)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_list_Osize_I4_J]) ).
fof(i_0_9582,plain,
! [X19486,X19487,X19489,X19490] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19487))
| ~ hBOOL(hAPP(X19486,X19487))
| hBOOL(hAPP(X19486,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk44_1(X19486)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk45_1(X19489)))
| ~ hBOOL(hAPP(X19489,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19490))) )
& ( hBOOL(hAPP(X19489,esk45_1(X19489)))
| ~ hBOOL(hAPP(X19489,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19490))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I2_J])])])])])]) ).
fof(i_0_9583,plain,
! [X19470,X19471] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19471),X19470))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19471)),X19470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_9584,plain,
! [X27775,X27776,X27777] :
( ~ class_Lattices_Olattice(X27777)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27777),X27776))
| ~ hBOOL(hAPP(hAPP(c_member(X27777),X27775),X27776))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27777),X27775),c_Big__Operators_Olattice__class_OInf__fin(X27777,X27776)) = c_Big__Operators_Olattice__class_OInf__fin(X27777,X27776) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem])]) ).
fof(i_0_9585,plain,
! [X25765,X25766,X25767] :
( ~ class_Lattices_Olattice(X25767)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25767),X25766))
| ~ hBOOL(hAPP(hAPP(c_member(X25767),X25765),X25766))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25767),X25765),c_Big__Operators_Olattice__class_OSup__fin(X25767,X25766)) = c_Big__Operators_Olattice__class_OSup__fin(X25767,X25766) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem])]) ).
fof(i_0_9586,plain,
! [X25842,X25843,X25844] :
( ~ class_Orderings_Olinorder(X25844)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25844),X25843))
| ~ hBOOL(hAPP(hAPP(c_member(X25844),X25842),X25843))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25844),X25842),c_Big__Operators_Olinorder__class_OMax(X25844,X25843)) = c_Big__Operators_Olinorder__class_OMax(X25844,X25843) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem])]) ).
fof(i_0_9587,plain,
! [X25839,X25840,X25841] :
( ~ class_Orderings_Olinorder(X25841)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25841),X25840))
| ~ hBOOL(hAPP(hAPP(c_member(X25841),X25839),X25840))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25841),X25839),c_Big__Operators_Olinorder__class_OMin(X25841,X25840)) = c_Big__Operators_Olinorder__class_OMin(X25841,X25840) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem])]) ).
fof(i_0_9588,plain,
! [X31374,X31375,X31376] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31376)
| ~ hBOOL(hAPP(hAPP(c_member(X31376),X31375),X31374))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31376),X31375),c_Complete__Lattice_OSup__class_OSup(X31376,X31374))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__upper])]) ).
cnf(i_0_9589,plain,
( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X1,X2)) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5883]) ).
fof(i_0_9590,plain,
! [X27441,X27442,X27443] :
( ~ class_Orderings_Oorder(X27443)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27443,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27443),X27442)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27443,X27442),X27441)) = c_Orderings_Obot__class_Obot(tc_fun(X27443,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J])]) ).
fof(i_0_9591,plain,
! [X24863,X24864] :
( ( X24863 != c_Orderings_Obot__class_Obot(tc_fun(X24864,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24864),X24863))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24864),X24863))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24864),X24863))) )
& ( X24863 = c_Orderings_Obot__class_Obot(tc_fun(X24864,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24864),X24863))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24864),X24863))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])]) ).
fof(i_0_9592,plain,
! [X32628,X32629,X32630,X32631] : hAPP(hAPP(c_List_Onth(X32631),hAPP(hAPP(c_List_Olist_OCons(X32631),X32630),X32629)),hAPP(c_Nat_OSuc,X32628)) = hAPP(hAPP(c_List_Onth(X32631),X32629),X32628),
inference(variable_rename,[status(thm)],[fact_nth__Cons__Suc]) ).
fof(i_0_9593,plain,
! [X33494,X33495,X33496,X33497] : hAPP(hAPP(c_List_Omap(X33497,X33496),X33495),hAPP(c_List_Otl(X33497),X33494)) = hAPP(c_List_Otl(X33496),hAPP(hAPP(c_List_Omap(X33497,X33496),X33495),X33494)),
inference(variable_rename,[status(thm)],[fact_map__tl]) ).
fof(i_0_9594,plain,
! [X34259,X34260,X34261,X34262] : hAPP(c_List_Orev(X34262),hAPP(hAPP(c_List_Omap(X34261,X34262),X34260),X34259)) = hAPP(hAPP(c_List_Omap(X34261,X34262),X34260),hAPP(c_List_Orev(X34261),X34259)),
inference(variable_rename,[status(thm)],[fact_rev__map]) ).
fof(i_0_9595,plain,
! [X23246,X23247] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23247),X23246))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23246),X23247))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23247) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23246) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__abs])]) ).
fof(i_0_9596,plain,
! [X25034,X25035] : ~ hBOOL(hAPP(hAPP(c_member(X25035),X25034),c_Orderings_Obot__class_Obot(tc_fun(X25035,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_5884]) ).
fof(i_0_9597,plain,
! [X24941,X24942] : ~ hBOOL(hAPP(hAPP(c_member(X24942),X24941),c_Orderings_Obot__class_Obot(tc_fun(X24942,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_5885]) ).
fof(i_0_9598,plain,
! [X23337,X23338,X23339] :
( ~ class_Divides_Osemiring__div(X23339)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23339),X23338),X23337))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23339),X23338),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23339),X23337),X23338)) = X23337 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__div__cancel])]) ).
fof(i_0_9599,plain,
! [X19500,X19501,X19503,X19504] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk48_1(X19500)))
| ~ hBOOL(hAPP(X19500,X19501)) )
& ( hBOOL(hAPP(X19500,hAPP(c_Int_Onat,esk48_1(X19500))))
| ~ hBOOL(hAPP(X19500,X19501)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19504))
| ~ hBOOL(hAPP(X19503,hAPP(c_Int_Onat,X19504)))
| hBOOL(hAPP(X19503,esk49_1(X19503))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__nat])])])])])]) ).
fof(i_0_9600,plain,
! [X24579,X24580] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24580),X24579)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24580),X24579)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).
cnf(i_0_9601,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2)))
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5829]) ).
fof(i_0_9602,plain,
! [X20493] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20493))
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20493),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X20493 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred])]) ).
fof(i_0_9603,plain,
! [X24628,X24629,X24630] :
( hAPP(hAPP(c_Set_Oinsert(X24630),X24629),c_Orderings_Obot__class_Obot(tc_fun(X24630,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(X24630),X24628),c_Orderings_Obot__class_Obot(tc_fun(X24630,tc_HOL_Obool)))
| X24629 = X24628 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__inject])]) ).
fof(i_0_9604,plain,
! [X25352] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25352),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X25352)) = X25352 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__inverse])]) ).
fof(i_0_9605,plain,
! [X21687,X21688,X21689,X21690] :
( ( X21688 = c_Groups_Ozero__class_Ozero(X21690)
| X21689 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21690),hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687)),X21688)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21690),X21689),X21688) != hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687)
| ~ class_Fields_Ofield__inverse__zero(X21690)
| ~ class_Int_Onumber(X21690) )
& ( X21688 != c_Groups_Ozero__class_Ozero(X21690)
| hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687) = c_Groups_Ozero__class_Ozero(X21690)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21690),X21689),X21688) != hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687)
| ~ class_Fields_Ofield__inverse__zero(X21690)
| ~ class_Int_Onumber(X21690) )
& ( X21688 = c_Groups_Ozero__class_Ozero(X21690)
| X21688 != c_Groups_Ozero__class_Ozero(X21690)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21690),X21689),X21688) = hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687)
| ~ class_Fields_Ofield__inverse__zero(X21690)
| ~ class_Int_Onumber(X21690) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687) != c_Groups_Ozero__class_Ozero(X21690)
| X21688 != c_Groups_Ozero__class_Ozero(X21690)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21690),X21689),X21688) = hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687)
| ~ class_Fields_Ofield__inverse__zero(X21690)
| ~ class_Int_Onumber(X21690) )
& ( X21688 = c_Groups_Ozero__class_Ozero(X21690)
| X21689 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21690),hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687)),X21688)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21690),X21689),X21688) = hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687)
| ~ class_Fields_Ofield__inverse__zero(X21690)
| ~ class_Int_Onumber(X21690) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687) != c_Groups_Ozero__class_Ozero(X21690)
| X21689 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21690),hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687)),X21688)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21690),X21689),X21688) = hAPP(c_Int_Onumber__class_Onumber__of(X21690),X21687)
| ~ class_Fields_Ofield__inverse__zero(X21690)
| ~ class_Int_Onumber(X21690) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of])])]) ).
fof(i_0_9606,plain,
! [X21691,X21692,X21693,X21694] :
( ( X21691 = c_Groups_Ozero__class_Ozero(X21694)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21694),hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693)),X21691) = X21692
| hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21694),X21692),X21691)
| ~ class_Fields_Ofield__inverse__zero(X21694)
| ~ class_Int_Onumber(X21694) )
& ( X21691 != c_Groups_Ozero__class_Ozero(X21694)
| hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693) = c_Groups_Ozero__class_Ozero(X21694)
| hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21694),X21692),X21691)
| ~ class_Fields_Ofield__inverse__zero(X21694)
| ~ class_Int_Onumber(X21694) )
& ( X21691 = c_Groups_Ozero__class_Ozero(X21694)
| X21691 != c_Groups_Ozero__class_Ozero(X21694)
| hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21694),X21692),X21691)
| ~ class_Fields_Ofield__inverse__zero(X21694)
| ~ class_Int_Onumber(X21694) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693) != c_Groups_Ozero__class_Ozero(X21694)
| X21691 != c_Groups_Ozero__class_Ozero(X21694)
| hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21694),X21692),X21691)
| ~ class_Fields_Ofield__inverse__zero(X21694)
| ~ class_Int_Onumber(X21694) )
& ( X21691 = c_Groups_Ozero__class_Ozero(X21694)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21694),hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693)),X21691) != X21692
| hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21694),X21692),X21691)
| ~ class_Fields_Ofield__inverse__zero(X21694)
| ~ class_Int_Onumber(X21694) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693) != c_Groups_Ozero__class_Ozero(X21694)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21694),hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693)),X21691) != X21692
| hAPP(c_Int_Onumber__class_Onumber__of(X21694),X21693) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21694),X21692),X21691)
| ~ class_Fields_Ofield__inverse__zero(X21694)
| ~ class_Int_Onumber(X21694) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of])])]) ).
fof(i_0_9607,plain,
! [X19254,X19255] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19255),hAPP(c_Nat_OSuc,X19254)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19255),X19254))
| X19255 = hAPP(c_Nat_OSuc,X19254) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5886])]) ).
fof(i_0_9608,plain,
! [X19248,X19249] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19249),hAPP(c_Nat_OSuc,X19248)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19249),X19248))
| X19249 = hAPP(c_Nat_OSuc,X19248) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19249),X19248))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19249),hAPP(c_Nat_OSuc,X19248))) )
& ( X19249 != hAPP(c_Nat_OSuc,X19248)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19249),hAPP(c_Nat_OSuc,X19248))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_9609,plain,
! [X33845,X33846] :
( X33846 = c_List_Olist_ONil(X33845)
| hAPP(hAPP(c_List_Oappend(X33845),c_List_Obutlast(X33845,X33846)),hAPP(hAPP(c_List_Olist_OCons(X33845),c_List_Olast(X33845,X33846)),c_List_Olist_ONil(X33845))) = X33846 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__butlast__last__id])]) ).
cnf(i_0_9610,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2))),
inference(split_conjunct,[status(thm)],[i_0_5887]) ).
fof(i_0_9611,plain,
! [X17505,X17506,X17507] :
( ~ hBOOL(hAPP(c_Com_OWT,X17507))
| ~ hBOOL(hAPP(c_Com_OWT,X17506))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17505,X17507,X17506))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OIf])]) ).
fof(i_0_9612,plain,
! [X22392,X22393,X22394] : hAPP(hAPP(c_Product__Type_OPair(X22394,X22393),hAPP(c_Product__Type_Ofst(X22394,X22393),X22392)),hAPP(c_Product__Type_Osnd(X22394,X22393),X22392)) = X22392,
inference(variable_rename,[status(thm)],[fact_pair__collapse]) ).
fof(i_0_9613,plain,
! [X22395,X22396,X22397] : X22397 = hAPP(hAPP(c_Product__Type_OPair(X22396,X22395),hAPP(c_Product__Type_Ofst(X22396,X22395),X22397)),hAPP(c_Product__Type_Osnd(X22396,X22395),X22397)),
inference(variable_rename,[status(thm)],[fact_surjective__pairing]) ).
fof(i_0_9614,plain,
! [X24867,X24868] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24868),X24867))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24868),hAPP(c_Nat_OSuc,X24867)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24867),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24868),X24867)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24868),X24867))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24868),hAPP(c_Nat_OSuc,X24867)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5888])]) ).
fof(i_0_9615,plain,
! [X32547,X32548,X32549,X32550] :
( ~ class_Orderings_Olinorder(X32550)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32549,X32550,X32548),X32547),c_List_Olist_ONil(X32549)) = hAPP(hAPP(c_List_Olist_OCons(X32549),X32547),c_List_Olist_ONil(X32549)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I1_J])]) ).
fof(i_0_9616,plain,
! [X26061,X26062,X26063,X26064,X26065] :
( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26065,X26064),X26063),X26062),X26061) != X26063
| hAPP(X26063,X26062) = X26061 )
& ( hAPP(X26063,X26062) != X26061
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26065,X26064),X26063),X26062),X26061) = X26063 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff])]) ).
fof(i_0_9617,plain,
! [X32400,X32401,X32402] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32402),X32401))
| hBOOL(hAPP(c_List_Odistinct(X32402),c_List_Osublist(X32402,X32401,X32400))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sublistI])]) ).
fof(i_0_9618,plain,
! [X32037,X32038,X32039] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32039),X32038))
| hBOOL(hAPP(c_List_Odistinct(X32039),c_List_Oremove1(X32039,X32037,X32038))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1])]) ).
fof(i_0_9619,plain,
! [X32033,X32034,X32035,X32036] : c_List_Oremove1(X32036,X32035,c_List_Oremove1(X32036,X32034,X32033)) = c_List_Oremove1(X32036,X32034,c_List_Oremove1(X32036,X32035,X32033)),
inference(variable_rename,[status(thm)],[fact_remove1__commute]) ).
fof(i_0_9620,plain,
! [X30797,X30798,X30799,X30800,X30801,X30802] :
( ~ c_Finite__Set_Ofun__left__comm(X30802,X30801,X30800)
| hAPP(hAPP(X30800,X30799),hAPP(hAPP(X30800,X30798),X30797)) = hAPP(hAPP(X30800,X30798),hAPP(hAPP(X30800,X30799),X30797)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm])]) ).
fof(i_0_9621,plain,
! [X27418,X27419,X27420] :
( ~ class_Lattices_Olattice(X27420)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27420),X27419))
| ~ hBOOL(hAPP(hAPP(c_member(X27420),X27418),X27419))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27420),X27418),c_Big__Operators_Olattice__class_OSup__fin(X27420,X27419)) = X27418 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb])]) ).
fof(i_0_9622,plain,
! [X27772,X27773,X27774] :
( ~ class_Lattices_Olattice(X27774)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27774),X27773))
| ~ hBOOL(hAPP(hAPP(c_member(X27774),X27772),X27773))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27774),X27772),c_Big__Operators_Olattice__class_OInf__fin(X27774,X27773)) = X27772 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb])]) ).
fof(i_0_9623,plain,
! [X29782] : c_Wellfounded_OwfP(X29782,hAPP(c_COMBK(tc_fun(X29782,tc_HOL_Obool),X29782),hAPP(c_COMBK(tc_HOL_Obool,X29782),c_fFalse))),
inference(variable_rename,[status(thm)],[fact_wfP__empty]) ).
fof(i_0_9624,plain,
! [X33874,X33875,X33876,X33877] :
( ( ~ hBOOL(hAPP(X33877,X33876))
| hAPP(c_List_Ofilter(X33875,X33877),hAPP(hAPP(c_List_Olist_OCons(X33875),X33876),X33874)) = hAPP(hAPP(c_List_Olist_OCons(X33875),X33876),hAPP(c_List_Ofilter(X33875,X33877),X33874)) )
& ( hBOOL(hAPP(X33877,X33876))
| hAPP(c_List_Ofilter(X33875,X33877),hAPP(hAPP(c_List_Olist_OCons(X33875),X33876),X33874)) = hAPP(c_List_Ofilter(X33875,X33877),X33874) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5889])]) ).
fof(i_0_9625,plain,
! [X23188,X23189,X23190] :
( ~ class_Rings_Ocomm__semiring__1(X23190)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23190),X23189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23190),X23189),X23188))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__left])]) ).
fof(i_0_9626,plain,
! [X23185,X23186,X23187] :
( ~ class_Rings_Ocomm__semiring__1(X23187)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23187),X23186),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23187),X23185),X23186))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__right])]) ).
fof(i_0_9627,plain,
! [X24056,X24057,X24058] :
( ~ class_Lattices_Osemilattice__sup(X24058)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24058),X24057),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24058),X24057),X24056))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge1])]) ).
fof(i_0_9628,plain,
! [X24059,X24060,X24061] :
( ~ class_Lattices_Olattice(X24061)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24061),X24060),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24061),X24060),X24059))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J])]) ).
fof(i_0_9629,plain,
! [X24050,X24051,X24052] :
( ~ class_Lattices_Osemilattice__sup(X24052)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24052),X24051),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24052),X24050),X24051))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge2])]) ).
fof(i_0_9630,plain,
! [X24053,X24054,X24055] :
( ~ class_Lattices_Olattice(X24055)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24055),X24054),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24055),X24053),X24054))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J])]) ).
fof(i_0_9631,plain,
! [X22631,X22632,X22633] :
( ~ class_Orderings_Olinorder(X22633)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22633),X22632),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22633),X22632),X22631))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI1])]) ).
fof(i_0_9632,plain,
! [X22628,X22629,X22630] :
( ~ class_Orderings_Olinorder(X22630)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22630),X22629),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22630),X22628),X22629))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI2])]) ).
fof(i_0_9633,plain,
! [X29203,X29204,X29205] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X29205),X29204),hAPP(c_Set_OCollect(X29205),X29203)))
| hBOOL(hAPP(X29203,X29204)) )
& ( ~ hBOOL(hAPP(X29203,X29204))
| hBOOL(hAPP(hAPP(c_member(X29205),X29204),hAPP(c_Set_OCollect(X29205),X29203))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq])]) ).
fof(i_0_9634,plain,
! [X29200,X29201,X29202] :
( ~ hBOOL(hAPP(hAPP(c_member(X29202),X29201),hAPP(c_Set_OCollect(X29202),X29200)))
| hBOOL(hAPP(X29200,X29201)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectD])]) ).
fof(i_0_9635,plain,
! [X29197,X29198,X29199] :
( ~ hBOOL(hAPP(hAPP(c_member(X29199),X29198),hAPP(c_Set_OCollect(X29199),X29197)))
| hBOOL(hAPP(X29197,X29198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectE])]) ).
fof(i_0_9636,plain,
! [X18981] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18981))
| hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X18981)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18981)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__nat__eq__nat__zadd1])]) ).
cnf(i_0_9637,plain,
( hAPP(c_List_Orotate(X2,X3),X1) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5809]) ).
fof(i_0_9638,plain,
! [X32334,X32335,X32336,X32337] :
( ( X32337 != X32336
| c_List_Oremove1(X32335,X32337,hAPP(hAPP(c_List_Olist_OCons(X32335),X32336),X32334)) = X32334 )
& ( X32337 = X32336
| c_List_Oremove1(X32335,X32337,hAPP(hAPP(c_List_Olist_OCons(X32335),X32336),X32334)) = hAPP(hAPP(c_List_Olist_OCons(X32335),X32336),c_List_Oremove1(X32335,X32337,X32334)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I2_J])]) ).
fof(i_0_9639,plain,
! [X23435,X23436,X23437,X23438] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23438),X23436),X23437) != X23435
| X23436 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23438),X23435),X23437)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23438),X23437),X23436))
| X23437 = c_Groups_Ozero__class_Ozero(X23438)
| ~ class_Divides_Osemiring__div(X23438) )
& ( X23436 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23438),X23435),X23437)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23438),X23436),X23437) = X23435
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23438),X23437),X23436))
| X23437 = c_Groups_Ozero__class_Ozero(X23438)
| ~ class_Divides_Osemiring__div(X23438) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__eq__mult])])]) ).
fof(i_0_9640,plain,
! [X18290,X18291] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18291),hAPP(c_Nat_OSuc,X18290)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18291),X18290))
| X18291 = X18290 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18291),X18290))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18291),hAPP(c_Nat_OSuc,X18290))) )
& ( X18291 != X18290
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18291),hAPP(c_Nat_OSuc,X18290))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_9641,plain,
! [X18286,X18287] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18287),hAPP(c_Nat_OSuc,X18286)))
| X18287 = X18286
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18287),X18286)) )
& ( X18287 != X18286
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18287),hAPP(c_Nat_OSuc,X18286)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18287),X18286)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5890])])]) ).
fof(i_0_9642,plain,
! [X18284,X18285] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18285),X18284))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18285),hAPP(c_Nat_OSuc,X18284)))
| X18284 = X18285 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5891])]) ).
fof(i_0_9643,plain,
! [X18275,X18276] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18276),hAPP(c_Nat_OSuc,X18275)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18276),X18275))
| X18276 = X18275 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5892])]) ).
cnf(i_0_9644,plain,
hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_Divides_Odivmod__nat(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_5893]) ).
cnf(i_0_9645,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_5894]) ).
cnf(i_0_9646,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))),
inference(split_conjunct,[status(thm)],[i_0_5895]) ).
fof(i_0_9647,plain,
! [X27405,X27406,X27407] : hAPP(c_Relation_OImage(X27407,X27407,c_Relation_OId__on(X27407,X27406)),X27405) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27407,tc_HOL_Obool)),X27406),X27405),
inference(variable_rename,[status(thm)],[fact_Image__Id__on]) ).
fof(i_0_9648,plain,
! [X27210,X27211,X27212,X27213] :
( ~ class_Lattices_Osemilattice__inf(X27213)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27213),X27212),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27213),X27211),X27210)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27213),X27211),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27213),X27212),X27210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute])]) ).
fof(i_0_9649,plain,
! [X27202,X27203,X27204,X27205] :
( ~ class_Lattices_Osemilattice__inf(X27205)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27205),X27204),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27205),X27203),X27202)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27205),X27203),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27205),X27204),X27202)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])]) ).
fof(i_0_9650,plain,
! [X27206,X27207,X27208,X27209] :
( ~ class_Lattices_Olattice(X27209)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27209),X27208),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27209),X27207),X27206)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27209),X27207),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27209),X27208),X27206)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])]) ).
fof(i_0_9651,plain,
! [X23933,X23934,X23935,X23936] :
( ~ class_Lattices_Osemilattice__sup(X23936)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23936),X23935),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23936),X23934),X23933)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23936),X23934),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23936),X23935),X23933)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__commute])]) ).
fof(i_0_9652,plain,
! [X23925,X23926,X23927,X23928] :
( ~ class_Lattices_Osemilattice__sup(X23928)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23928),X23927),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23928),X23926),X23925)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23928),X23926),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23928),X23927),X23925)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__commute])]) ).
fof(i_0_9653,plain,
! [X23929,X23930,X23931,X23932] :
( ~ class_Lattices_Olattice(X23932)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23932),X23931),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23932),X23930),X23929)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23932),X23930),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23932),X23931),X23929)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J])]) ).
fof(i_0_9654,plain,
! [X22658,X22659,X22660,X22661] :
( ~ class_Orderings_Olinorder(X22661)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22661),X22660),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22661),X22659),X22658)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22661),X22659),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22661),X22660),X22658)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__commute])]) ).
fof(i_0_9655,plain,
! [X22654,X22655,X22656,X22657] :
( ~ class_Orderings_Olinorder(X22657)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22657),X22656),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22657),X22655),X22654)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22657),X22655),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22657),X22656),X22654)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__commute])]) ).
fof(i_0_9656,plain,
! [X22329,X22330,X22331,X22332] :
( ~ class_Orderings_Olinorder(X22332)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22332),X22331),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22332),X22330),X22329)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22332),X22330),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22332),X22331),X22329)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__commute])]) ).
fof(i_0_9657,plain,
! [X22325,X22326,X22327,X22328] :
( ~ class_Orderings_Olinorder(X22328)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22328),X22327),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22328),X22326),X22325)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22328),X22326),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22328),X22327),X22325)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__commute])]) ).
fof(i_0_9658,plain,
! [X18675,X18676,X18677,X18678] :
( ~ class_Rings_Ocomm__semiring__1(X18678)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18678),X18677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18678),X18676),X18675)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18678),X18676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18678),X18677),X18675)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).
fof(i_0_9659,plain,
! [X18149,X18150,X18151,X18152] :
( ~ class_Rings_Ocomm__semiring__1(X18152)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18152),X18151),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18152),X18150),X18149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18152),X18150),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18152),X18151),X18149)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_9660,plain,
! [X18772,X18773,X18774] :
( ~ class_Groups_Ogroup__add(X18774)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18774),X18773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18774),hAPP(c_Groups_Ouminus__class_Ouminus(X18774),X18773)),X18772)) = X18772 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).
fof(i_0_9661,plain,
! [X19725,X19726,X19727] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19727),X19726) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19727),X19725)
| X19726 = X19725
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19727)) )
& ( X19726 != X19725
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19727),X19726) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19727),X19725)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19727)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).
fof(i_0_9662,plain,
! [X19476,X19477] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19477),hAPP(c_Nat_OSuc,X19476)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19477),X19476)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19477),X19476))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19477),hAPP(c_Nat_OSuc,X19476))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_9663,plain,
! [X20911] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20911)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20911))),
inference(variable_rename,[status(thm)],[fact_one__div__nat__number__of]) ).
fof(i_0_9664,plain,
! [X18616,X18617,X18618,X18619,X18620] :
( ( X18616 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18618)
| hBOOL(hAPP(X18617,X18618))
| ~ hBOOL(hAPP(X18617,hAPP(c_Int_Onat,X18616))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18616),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(X18617,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X18617,hAPP(c_Int_Onat,X18616))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18619),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X18619 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk40_2(X18619,X18620))
| hBOOL(hAPP(X18620,hAPP(c_Int_Onat,X18619))) )
& ( ~ hBOOL(hAPP(X18620,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X18619 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk40_2(X18619,X18620))
| hBOOL(hAPP(X18620,hAPP(c_Int_Onat,X18619))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18619),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X18620,esk40_2(X18619,X18620)))
| hBOOL(hAPP(X18620,hAPP(c_Int_Onat,X18619))) )
& ( ~ hBOOL(hAPP(X18620,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X18620,esk40_2(X18619,X18620)))
| hBOOL(hAPP(X18620,hAPP(c_Int_Onat,X18619))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__nat])])])])])]) ).
fof(i_0_9665,plain,
! [X33357,X33358,X33359] :
( ~ hBOOL(hAPP(c_List_Odistinct(X33359),X33358))
| hBOOL(hAPP(c_List_Odistinct(X33359),hAPP(hAPP(c_List_Odrop(X33359),X33357),X33358))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__drop])]) ).
fof(i_0_9666,plain,
! [X33099,X33100,X33101] :
( ~ hBOOL(hAPP(c_List_Odistinct(X33101),X33100))
| hBOOL(hAPP(c_List_Odistinct(X33101),hAPP(hAPP(c_List_Otake(X33101),X33099),X33100))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__take])]) ).
fof(i_0_9667,plain,
! [X24515,X24516,X24517] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24517),X24516))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24517),hAPP(hAPP(c_Set_Oinsert(X24517),X24515),X24516))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).
fof(i_0_9668,plain,
! [X23757,X23758] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23758,X23757)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23758),hAPP(c_Nat_OSuc,X23757)),
inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastAtMost]) ).
fof(i_0_9669,plain,
! [X30955,X30956,X30957] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30957,tc_fun(X30956,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X30957,tc_HOL_Obool))),X30955) = c_Orderings_Otop__class_Otop(tc_fun(X30956,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_INT__empty]) ).
fof(i_0_9670,plain,
! [X20882,X20883] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20883)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20882)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20883),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20882))),
inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I6_J]) ).
fof(i_0_9671,plain,
! [X24339,X24340] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24340,tc_HOL_Obool)),X24339) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24340,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X24340,tc_HOL_Obool))),X24339),
inference(variable_rename,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).
fof(i_0_9672,plain,
! [X33801,X33802,X33803,X33804] : hAPP(hAPP(c_List_Omap(X33804,X33803),X33802),c_List_Obutlast(X33804,X33801)) = c_List_Obutlast(X33803,hAPP(hAPP(c_List_Omap(X33804,X33803),X33802),X33801)),
inference(variable_rename,[status(thm)],[fact_map__butlast]) ).
fof(i_0_9673,plain,
! [X25835,X25836] :
( ~ class_Orderings_Olinorder(X25836)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25836),X25835))
| X25835 = c_Orderings_Obot__class_Obot(tc_fun(X25836,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X25836),c_Big__Operators_Olinorder__class_OMin(X25836,X25835)),X25835)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__in])]) ).
fof(i_0_9674,plain,
! [X25837,X25838] :
( ~ class_Orderings_Olinorder(X25838)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25838),X25837))
| X25837 = c_Orderings_Obot__class_Obot(tc_fun(X25838,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X25838),c_Big__Operators_Olinorder__class_OMax(X25838,X25837)),X25837)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__in])]) ).
fof(i_0_9675,plain,
! [X19506,X19508,X19509,X19511] :
( ( ~ hBOOL(hAPP(X19506,esk50_1(X19506)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19508))
| hBOOL(hAPP(X19506,hAPP(c_Int_Onat,X19508))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk51_1(X19509)))
| hBOOL(hAPP(X19509,X19511)) )
& ( ~ hBOOL(hAPP(X19509,hAPP(c_Int_Onat,esk51_1(X19509))))
| hBOOL(hAPP(X19509,X19511)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__nat])])])])])]) ).
fof(i_0_9676,plain,
! [X25194,X25195,X25196] : hBOOL(hAPP(hAPP(c_member(X25196),X25195),hAPP(hAPP(c_Set_Oinsert(X25196),X25195),X25194))),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
fof(i_0_9677,plain,
! [X20011,X20012] :
( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20012,X20011)) != X20011
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20012),X20011) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20012,X20011)) = X20011
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20012),X20011) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20012,X20011)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__Suc])]) ).
cnf(i_0_9678,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5896]) ).
cnf(i_0_9679,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5897]) ).
fof(i_0_9680,plain,
! [X24428,X24429,X24430,X24431] : hAPP(hAPP(c_Set_Oinsert(X24431),X24430),hAPP(hAPP(c_Set_Oinsert(X24431),X24429),X24428)) = hAPP(hAPP(c_Set_Oinsert(X24431),X24429),hAPP(hAPP(c_Set_Oinsert(X24431),X24430),X24428)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
fof(i_0_9681,plain,
! [X25587,X25588,X25589,X25590] :
( ~ c_Finite__Set_Ofolding__one(X25590,X25589,X25588)
| hAPP(X25588,hAPP(hAPP(c_Set_Oinsert(X25590),X25587),c_Orderings_Obot__class_Obot(tc_fun(X25590,tc_HOL_Obool)))) = X25587 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton])]) ).
fof(i_0_9682,plain,
! [X20454,X20455] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20455),hAPP(c_Nat_OSuc,X20454)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20455),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20454),
inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).
fof(i_0_9683,plain,
! [X18456,X18457] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(X18456,X18457)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18457),X18456)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18457),esk34_2(X18456,X18457)) = X18456
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18457),X18456)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__add__positive])])])]) ).
fof(i_0_9684,plain,
! [X30653,X30654,X30655,X30656] : hAPP(hAPP(c_Finite__Set_Ofold(X30656,X30655,X30654),X30653),c_Orderings_Obot__class_Obot(tc_fun(X30656,tc_HOL_Obool))) = X30653,
inference(variable_rename,[status(thm)],[fact_fold__empty]) ).
fof(i_0_9685,plain,
! [X33331,X33332,X33333] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33333)),hAPP(hAPP(c_List_Odrop(X33333),X33332),X33331)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33333)),X33331)),X33332),
inference(variable_rename,[status(thm)],[fact_length__drop]) ).
fof(i_0_9686,plain,
! [X33146,X33147,X33148] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33148)),hAPP(hAPP(c_List_Otake(X33148),X33147),X33146)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33148)),X33146)),X33147),
inference(variable_rename,[status(thm)],[fact_length__take]) ).
cnf(i_0_9687,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_Opred(X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5898]) ).
fof(i_0_9688,plain,
! [X28219] :
( ~ class_Nat_Osemiring__char__0(X28219)
| c_Fun_Oinj__on(tc_Nat_Onat,X28219,c_Nat_Osemiring__1__class_Oof__nat(X28219),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__of__nat])]) ).
fof(i_0_9689,plain,
! [X17737,X17738,X17739,X17740] :
( hBOOL(hAPP(X17740,X17739))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17740,X17738),X17739,X17737,X17739) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5899])]) ).
fof(i_0_9690,plain,
! [X33519,X33520,X33521] : hAPP(hAPP(c_List_Otake(X33521),X33520),hAPP(c_List_Otl(X33521),X33519)) = hAPP(c_List_Otl(X33521),hAPP(hAPP(c_List_Otake(X33521),hAPP(c_Nat_OSuc,X33520)),X33519)),
inference(variable_rename,[status(thm)],[fact_take__tl]) ).
fof(i_0_9691,plain,
! [X18453,X18454] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18454),X18453))
| X18453 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18454),esk33_2(X18453,X18454))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__Suc__add])])]) ).
fof(i_0_9692,plain,
! [X18350,X18351,X18353,X18354,X18355] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18351),X18350))
| X18350 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18351),esk32_2(X18350,X18351))) )
& ( X18353 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18354),X18355))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18354),X18353)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add])])])])]) ).
fof(i_0_9693,plain,
! [X24789,X24790,X24791] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X24791,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X24791,X24790,X24789)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24791),X24790),X24789))
| ~ class_Orderings_Oorder(X24791) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24791),X24790),X24789))
| c_Orderings_Obot__class_Obot(tc_fun(X24791,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X24791,X24790,X24789)
| ~ class_Orderings_Oorder(X24791) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5900])])]) ).
fof(i_0_9694,plain,
! [X24740,X24741,X24742] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X24742,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(X24742,X24741,X24740)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24742),X24741),X24740))
| ~ class_Orderings_Oorder(X24742) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24742),X24741),X24740))
| c_Orderings_Obot__class_Obot(tc_fun(X24742,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X24742,X24741,X24740)
| ~ class_Orderings_Oorder(X24742) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5901])])]) ).
fof(i_0_9695,plain,
! [X24792,X24793,X24794] :
( ( c_SetInterval_Oord__class_OgreaterThanAtMost(X24794,X24793,X24792) != c_Orderings_Obot__class_Obot(tc_fun(X24794,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24794),X24793),X24792))
| ~ class_Orderings_Oorder(X24794) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24794),X24793),X24792))
| c_SetInterval_Oord__class_OgreaterThanAtMost(X24794,X24793,X24792) = c_Orderings_Obot__class_Obot(tc_fun(X24794,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X24794) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5902])])]) ).
fof(i_0_9696,plain,
! [X24743,X24744,X24745] :
( ( c_SetInterval_Oord__class_OatLeastAtMost(X24745,X24744,X24743) != c_Orderings_Obot__class_Obot(tc_fun(X24745,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24745),X24744),X24743))
| ~ class_Orderings_Oorder(X24745) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24745),X24744),X24743))
| c_SetInterval_Oord__class_OatLeastAtMost(X24745,X24744,X24743) = c_Orderings_Obot__class_Obot(tc_fun(X24745,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X24745) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5903])])]) ).
fof(i_0_9697,plain,
! [X23823] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X23823) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23823))),
inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J]) ).
fof(i_0_9698,plain,
! [X21573,X21574,X21575] :
( ~ class_Fields_Olinordered__field(X21575)
| X21574 = c_Groups_Ozero__class_Ozero(X21575)
| hAPP(c_Groups_Oabs__class_Oabs(X21575),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21574)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),hAPP(c_Groups_Oabs__class_Oabs(X21575),X21573)),hAPP(c_Groups_Oabs__class_Oabs(X21575),X21574)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide])]) ).
fof(i_0_9699,plain,
! [X30057,X30058] :
( ( hBOOL(hAPP(hAPP(c_member(X30058),esk356_2(X30057,X30058)),X30057))
| hAPP(c_Finite__Set_Ocard(X30058),X30057) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30058),X30057)) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(X30058),X30057) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30058),X30057)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oneutral])])])]) ).
fof(i_0_9700,plain,
! [X27382,X27383] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27383,tc_HOL_Obool)),X27382),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27383,tc_HOL_Obool)),X27382)) = c_Orderings_Obot__class_Obot(tc_fun(X27383,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__disjoint]) ).
fof(i_0_9701,plain,
! [X24335,X24336] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24336,tc_HOL_Obool)),X24335),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24336,tc_HOL_Obool)),X24335)) = c_Orderings_Otop__class_Otop(tc_fun(X24336,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__partition]) ).
fof(i_0_9702,plain,
! [X28228,X28229,X28230] : c_Fun_Oinj__on(X28230,tc_sum(X28230,X28229),c_Sum__Type_OInl(X28230,X28229),X28228),
inference(variable_rename,[status(thm)],[fact_inj__Inl]) ).
fof(i_0_9703,plain,
! [X28225,X28226,X28227] : c_Fun_Oinj__on(X28227,tc_sum(X28226,X28227),c_Sum__Type_OInr(X28227,X28226),X28225),
inference(variable_rename,[status(thm)],[fact_inj__Inr]) ).
fof(i_0_9704,plain,
! [X27879,X27880,X27881] : c_Fun_Oinj__on(X27881,X27880,X27879,c_Orderings_Obot__class_Obot(tc_fun(X27881,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_inj__on__empty]) ).
fof(i_0_9705,plain,
! [X23125,X23126] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23126),X23125))
| X23126 != X23125 )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23125),X23126))
| X23126 != X23125 )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23126),X23125))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23125),X23126))
| X23126 = X23125 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff])])]) ).
fof(i_0_9706,plain,
! [X23123,X23124] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23124),X23123))
| X23124 = X23123
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23124),X23123)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23123),X23124))
| X23124 = X23123
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23124),X23123)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23124),X23123))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23123),X23124))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23124),X23123)) )
& ( X23124 != X23123
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23124),X23123)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5904])])]) ).
fof(i_0_9707,plain,
! [X23121,X23122] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23122),X23121))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23122),X23121))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23121),X23122)) )
& ( X23122 != X23121
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23122),X23121))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23121),X23122)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23122),X23121))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23122),X23121))
| X23122 = X23121 )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23121),X23122))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23122),X23121))
| X23122 = X23121 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5905])])]) ).
fof(i_0_9708,plain,
! [X23119,X23120] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23120),X23119))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23120),X23119))
| X23120 = X23119 )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23119),X23120))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23120),X23119))
| X23120 = X23119 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5906])])]) ).
fof(i_0_9709,plain,
! [X23115,X23116] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23115),X23116))
| X23115 = X23116
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23116),X23115)) )
& ( X23115 != X23116
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23115),X23116))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23116),X23115)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv])])]) ).
fof(i_0_9710,plain,
! [X23113,X23114] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23114),X23113))
| X23114 = X23113
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23114),X23113)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23113),X23114))
| X23114 = X23113
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23114),X23113)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5907])])]) ).
fof(i_0_9711,plain,
! [X23111,X23112] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23112),X23111))
| X23112 = X23111
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23112),X23111)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23111),X23112))
| X23112 = X23111
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23112),X23111)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5908])])]) ).
fof(i_0_9712,plain,
! [X23103,X23104] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23104),X23103))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23103),X23104))
| X23104 = X23103 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__antisym])]) ).
fof(i_0_9713,plain,
! [X23101,X23102] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23102),X23101))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23101),X23102))
| X23102 = X23101 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym])]) ).
fof(i_0_9714,plain,
! [X19025,X19026] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19026),X19025))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19025),X19026))
| X19026 = X19025 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).
fof(i_0_9715,plain,
! [X19704,X19705] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19705),X19704))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19704),X19705))
| X19705 = X19704 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
cnf(i_0_9716,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| c_List_Oupt(X1,X2) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_5666]) ).
fof(i_0_9717,plain,
! [X21049] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21049))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X21049) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21049),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__minus1])]) ).
fof(i_0_9718,plain,
! [X27778,X27779,X27780] :
( ~ class_Lattices_Olattice(X27780)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27780),X27779))
| X27779 = c_Orderings_Obot__class_Obot(tc_fun(X27780,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X27780,hAPP(hAPP(c_Set_Oinsert(X27780),X27778),X27779)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27780),X27778),c_Big__Operators_Olattice__class_OInf__fin(X27780,X27779)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem])]) ).
fof(i_0_9719,plain,
! [X25851,X25852,X25853] :
( ~ class_Orderings_Olinorder(X25853)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25853),X25852))
| X25852 = c_Orderings_Obot__class_Obot(tc_fun(X25853,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25853,hAPP(hAPP(c_Set_Oinsert(X25853),X25851),X25852)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25853),X25851),c_Big__Operators_Olinorder__class_OMin(X25853,X25852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__insert])]) ).
fof(i_0_9720,plain,
! [X25854,X25855,X25856] :
( ~ class_Orderings_Olinorder(X25856)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25856),X25855))
| X25855 = c_Orderings_Obot__class_Obot(tc_fun(X25856,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25856,hAPP(hAPP(c_Set_Oinsert(X25856),X25854),X25855)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25856),X25854),c_Big__Operators_Olinorder__class_OMax(X25856,X25855)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__insert])]) ).
fof(i_0_9721,plain,
! [X25770,X25771,X25772] :
( ~ class_Lattices_Olattice(X25772)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25772),X25771))
| X25771 = c_Orderings_Obot__class_Obot(tc_fun(X25772,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25772,hAPP(hAPP(c_Set_Oinsert(X25772),X25770),X25771)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25772),X25770),c_Big__Operators_Olattice__class_OSup__fin(X25772,X25771)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem])]) ).
fof(i_0_9722,plain,
! [X24631,X24632,X24633] :
( ( X24632 = c_Orderings_Obot__class_Obot(tc_fun(X24633,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24633,tc_HOL_Obool)),X24632),X24631) != c_Orderings_Obot__class_Obot(tc_fun(X24633,tc_HOL_Obool)) )
& ( X24631 = c_Orderings_Obot__class_Obot(tc_fun(X24633,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24633,tc_HOL_Obool)),X24632),X24631) != c_Orderings_Obot__class_Obot(tc_fun(X24633,tc_HOL_Obool)) )
& ( X24632 != c_Orderings_Obot__class_Obot(tc_fun(X24633,tc_HOL_Obool))
| X24631 != c_Orderings_Obot__class_Obot(tc_fun(X24633,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24633,tc_HOL_Obool)),X24632),X24631) = c_Orderings_Obot__class_Obot(tc_fun(X24633,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__empty])])]) ).
fof(i_0_9723,plain,
! [X32924,X32925,X32926] :
( ~ class_Groups_Omonoid__add(X32926)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32926),hAPP(hAPP(c_List_Oappend(X32926),X32925),X32924)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32926),hAPP(c_List_Omonoid__add__class_Olistsum(X32926),X32925)),hAPP(c_List_Omonoid__add__class_Olistsum(X32926),X32924)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__append])]) ).
fof(i_0_9724,plain,
! [X21465,X21466,X21467] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21467)
| hAPP(c_Groups_Oabs__class_Oabs(X21467),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21466),X21465)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),hAPP(c_Groups_Oabs__class_Oabs(X21467),X21466)),hAPP(c_Groups_Oabs__class_Oabs(X21467),X21465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__divide])]) ).
fof(i_0_9725,plain,
! [X20628,X20629,X20630] :
( ~ class_Rings_Olinordered__idom(X20630)
| hAPP(c_Groups_Oabs__class_Oabs(X20630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20630),X20629),X20628)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20630),hAPP(c_Groups_Oabs__class_Oabs(X20630),X20629)),hAPP(c_Groups_Oabs__class_Oabs(X20630),X20628)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])]) ).
fof(i_0_9726,plain,
! [X27321,X27322,X27323] :
( ~ class_Lattices_Oboolean__algebra(X27323)
| hAPP(c_Groups_Ouminus__class_Ouminus(X27323),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27323),X27322),X27321)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27323),hAPP(c_Groups_Ouminus__class_Ouminus(X27323),X27322)),hAPP(c_Groups_Ouminus__class_Ouminus(X27323),X27321)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf])]) ).
fof(i_0_9727,plain,
! [X27318,X27319,X27320] :
( ~ class_Lattices_Oboolean__algebra(X27320)
| hAPP(c_Groups_Ouminus__class_Ouminus(X27320),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27320),X27319),X27318)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27320),hAPP(c_Groups_Ouminus__class_Ouminus(X27320),X27319)),hAPP(c_Groups_Ouminus__class_Ouminus(X27320),X27318)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup])]) ).
fof(i_0_9728,plain,
! [X22708,X22709,X22710] :
( ~ class_Groups_Olinordered__ab__group__add(X22710)
| hAPP(c_Groups_Ouminus__class_Ouminus(X22710),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22710),X22709),X22708)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22710),hAPP(c_Groups_Ouminus__class_Ouminus(X22710),X22709)),hAPP(c_Groups_Ouminus__class_Ouminus(X22710),X22708)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__max__eq__min])]) ).
fof(i_0_9729,plain,
! [X22705,X22706,X22707] :
( ~ class_Groups_Olinordered__ab__group__add(X22707)
| hAPP(c_Groups_Ouminus__class_Ouminus(X22707),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22707),X22706),X22705)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22707),hAPP(c_Groups_Ouminus__class_Ouminus(X22707),X22706)),hAPP(c_Groups_Ouminus__class_Ouminus(X22707),X22705)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__min__eq__max])]) ).
fof(i_0_9730,plain,
! [X18766,X18767,X18768] :
( ~ class_Groups_Oab__group__add(X18768)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18768),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18768),X18767),X18766)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18768),hAPP(c_Groups_Ouminus__class_Ouminus(X18768),X18767)),hAPP(c_Groups_Ouminus__class_Ouminus(X18768),X18766)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).
fof(i_0_9731,plain,
! [X18769,X18770,X18771] :
( ~ class_Groups_Ogroup__add(X18771)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18771),X18770),X18769)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18771),hAPP(c_Groups_Ouminus__class_Ouminus(X18771),X18769)),hAPP(c_Groups_Ouminus__class_Ouminus(X18771),X18770)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).
cnf(i_0_9732,plain,
( c_Divides_Odivmod__nat(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5489]) ).
cnf(i_0_9733,plain,
( c_Divides_Odivmod__nat(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5909]) ).
fof(i_0_9734,plain,
! [X26520,X26521,X26522] : hAPP(c_Set_Oimage(X26521,tc_fun(X26521,tc_HOL_Obool),X26522),X26520) != hAPP(c_Set_OPow(X26521),X26520),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cantors__paradox])]) ).
fof(i_0_9735,plain,
! [X22456,X22457,X22458] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22456,tc_HOL_Obool)),X22458),X22457))
| X22458 != X22457 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22456,tc_HOL_Obool)),X22457),X22458))
| X22458 != X22457 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5910])])]) ).
fof(i_0_9736,plain,
! [X22446,X22447,X22448] :
( X22448 != X22447
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22446,tc_HOL_Obool)),X22448),X22447)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_9737,plain,
! [X22449,X22450,X22451] :
( X22451 != X22450
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22449,tc_HOL_Obool)),X22450),X22451)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_9738,plain,
! [X19245] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19245)),X19245)),
inference(variable_rename,[status(thm)],[i_0_5911]) ).
fof(i_0_9739,plain,
! [X20193,X20194] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20194))
| c_SMT_Oz3div(X20193,X20194) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20193),X20194) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20194))
| c_SMT_Oz3div(X20193,X20194) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20193),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20194))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5912])]) ).
fof(i_0_9740,plain,
! [X33758,X33759] :
( X33759 = c_List_Olist_ONil(X33758)
| hBOOL(hAPP(hAPP(c_member(X33758),c_List_Olast(X33758,X33759)),hAPP(c_List_Oset(X33758),X33759))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__in__set])]) ).
fof(i_0_9741,plain,
! [X19222,X19223,X19224] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19224)),X19223) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19224)),X19222)
| X19223 = X19222 )
& ( X19223 != X19222
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19224)),X19223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19224)),X19222) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).
fof(i_0_9742,plain,
! [X22067,X22068,X22069,X22070,X22071,X22072] :
( ( X22070 = X22068
| hAPP(hAPP(c_Product__Type_OPair(X22072,X22071),X22070),X22069) != hAPP(hAPP(c_Product__Type_OPair(X22072,X22071),X22068),X22067) )
& ( X22069 = X22067
| hAPP(hAPP(c_Product__Type_OPair(X22072,X22071),X22070),X22069) != hAPP(hAPP(c_Product__Type_OPair(X22072,X22071),X22068),X22067) )
& ( X22070 != X22068
| X22069 != X22067
| hAPP(hAPP(c_Product__Type_OPair(X22072,X22071),X22070),X22069) = hAPP(hAPP(c_Product__Type_OPair(X22072,X22071),X22068),X22067) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])]) ).
fof(i_0_9743,plain,
! [X22061,X22062,X22063,X22064,X22065,X22066] :
( ( X22064 = X22062
| hAPP(hAPP(c_Product__Type_OPair(X22066,X22065),X22064),X22063) != hAPP(hAPP(c_Product__Type_OPair(X22066,X22065),X22062),X22061) )
& ( X22063 = X22061
| hAPP(hAPP(c_Product__Type_OPair(X22066,X22065),X22064),X22063) != hAPP(hAPP(c_Product__Type_OPair(X22066,X22065),X22062),X22061) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__inject])])]) ).
fof(i_0_9744,plain,
! [X20550,X20551] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20551,X20550) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20551),X20550) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20551,X20550) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20551),X20550) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20550),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20551,X20550)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__eq__if])]) ).
fof(i_0_9745,plain,
! [X20301,X20302] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20302),X20301))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20302,X20301) = X20302 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20302),X20301))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20302,X20301) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20302),X20301),X20301) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5913])]) ).
fof(i_0_9746,plain,
! [X20299,X20300] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20300),X20299))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20300,X20299) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20300),X20299),X20299) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5914])]) ).
fof(i_0_9747,plain,
! [X22441,X22442] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22442,tc_HOL_Obool)),X22441),X22441)),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_9748,plain,
! [X23755,X23756] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23756),X23755)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23756)),hAPP(c_Nat_OSuc,X23755)),
inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).
fof(i_0_9749,plain,
! [X34277,X34278,X34279] : hAPP(c_List_Orev(X34279),hAPP(hAPP(c_List_Oappend(X34279),X34278),X34277)) = hAPP(hAPP(c_List_Oappend(X34279),hAPP(c_List_Orev(X34279),X34277)),hAPP(c_List_Orev(X34279),X34278)),
inference(variable_rename,[status(thm)],[fact_rev__append]) ).
fof(i_0_9750,plain,
! [X33418,X33419,X33420,X33421] :
( hAPP(c_List_Orotate1(X33421),c_List_Olist_ONil(X33421)) = c_List_Olist_ONil(X33421)
& hAPP(c_List_Orotate1(X33420),hAPP(hAPP(c_List_Olist_OCons(X33420),X33419),X33418)) = hAPP(hAPP(c_List_Oappend(X33420),X33418),hAPP(hAPP(c_List_Olist_OCons(X33420),X33419),c_List_Olist_ONil(X33420))) ),
inference(variable_rename,[status(thm)],[fact_rotate__simps]) ).
fof(i_0_9751,plain,
! [X19252,X19253] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19253),X19252))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19253),hAPP(c_Nat_OSuc,X19252))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_9752,plain,
! [X19472,X19473] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19473),X19472))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19473),hAPP(c_Nat_OSuc,X19472))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_9753,plain,
! [X18282,X18283] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18283),X18282))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18283),hAPP(c_Nat_OSuc,X18282))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_9754,plain,
! [X32013,X32014] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X32014,X32013) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32014),c_Groups_Oone__class_Oone(tc_Int_Oint)),X32013)),
inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upto]) ).
fof(i_0_9755,plain,
! [X25768,X25769] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25769),X25768),X25768) != c_Groups_Ozero__class_Ozero(X25769)
| X25768 = c_Groups_Ozero__class_Ozero(X25769)
| ~ hBOOL(hAPP(hAPP(c_member(X25769),X25768),c_Int_Oring__1__class_OInts(X25769)))
| ~ class_Int_Oring__char__0(X25769) )
& ( X25768 != c_Groups_Ozero__class_Ozero(X25769)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25769),X25768),X25768) = c_Groups_Ozero__class_Ozero(X25769)
| ~ hBOOL(hAPP(hAPP(c_member(X25769),X25768),c_Int_Oring__1__class_OInts(X25769)))
| ~ class_Int_Oring__char__0(X25769) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).
fof(i_0_9756,plain,
! [X21089] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21089))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X21089) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__eq__minus1])]) ).
fof(i_0_9757,plain,
! [X27180,X27181,X27182] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27182,tc_HOL_Obool)),X27181),X27180) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27182,tc_HOL_Obool)),X27180),X27181),
inference(variable_rename,[status(thm)],[fact_Int__commute]) ).
fof(i_0_9758,plain,
! [X23903,X23904,X23905] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23905,tc_HOL_Obool)),X23904),X23903) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23905,tc_HOL_Obool)),X23903),X23904),
inference(variable_rename,[status(thm)],[fact_Un__commute]) ).
fof(i_0_9759,plain,
! [X25787,X25788,X25789,X25790,X25791] : c_Hoare__Mirabelle_Otriple_Otriple__size(X25791,X25790,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25791),X25789),X25788),X25787)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_triple_Osize_I1_J]) ).
fof(i_0_9760,plain,
! [X18606] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk39_1(X18606)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18606)) )
& ( X18606 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk39_1(X18606))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18606)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__imp__eq__int])])])]) ).
fof(i_0_9761,plain,
! [X21535,X21536,X21537,X21538,X21539] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21539),X21536),X21538) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21539),X21535),X21537)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21539),X21536),X21537) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21539),X21535),X21538)
| X21537 = c_Groups_Ozero__class_Ozero(X21539)
| X21538 = c_Groups_Ozero__class_Ozero(X21539)
| ~ class_Fields_Ofield(X21539) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21539),X21536),X21537) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21539),X21535),X21538)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21539),X21536),X21538) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21539),X21535),X21537)
| X21537 = c_Groups_Ozero__class_Ozero(X21539)
| X21538 = c_Groups_Ozero__class_Ozero(X21539)
| ~ class_Fields_Ofield(X21539) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__eq__eq])])]) ).
fof(i_0_9762,plain,
! [X20552,X20553] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20553),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20552),X20553)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20552),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20552,X20553)),
inference(variable_rename,[status(thm)],[fact_zmult__div__cancel]) ).
fof(i_0_9763,plain,
! [X20459,X20460] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20460),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20459),X20460)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20459),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20459,X20460)),
inference(variable_rename,[status(thm)],[fact_mult__div__cancel]) ).
fof(i_0_9764,plain,
! [X22760,X22761] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X22761),X22760) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22761)),hAPP(c_Code__Numeral_Onat__of,X22760))),
inference(variable_rename,[status(thm)],[fact_minus__code__numeral__def]) ).
fof(i_0_9765,plain,
! [X22764,X22765] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X22765),X22764) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22765)),hAPP(c_Code__Numeral_Onat__of,X22764))),
inference(variable_rename,[status(thm)],[fact_div__code__numeral__def]) ).
fof(i_0_9766,plain,
! [X22766,X22767] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X22767),X22766) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22767)),hAPP(c_Code__Numeral_Onat__of,X22766))),
inference(variable_rename,[status(thm)],[fact_times__code__numeral__def]) ).
fof(i_0_9767,plain,
! [X22762,X22763] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X22763),X22762) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22763)),hAPP(c_Code__Numeral_Onat__of,X22762))),
inference(variable_rename,[status(thm)],[fact_plus__code__numeral__def]) ).
fof(i_0_9768,plain,
! [X20324,X20325] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20325),X20324))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20324),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20324),X20325)) = X20325 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).
fof(i_0_9769,plain,
! [X23388,X23389] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23389),X23388))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23389),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23388),X23389)) = X23388 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mult__div__cancel])]) ).
fof(i_0_9770,plain,
! [X20439,X20440] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20440),X20439))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20440),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20439),X20440)) = X20439 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).
fof(i_0_9771,plain,
! [X21923,X21924,X21925,X21926] : c_Nat_Onat_Onat__case(X21926,X21925,X21924,hAPP(c_Nat_OSuc,X21923)) = hAPP(X21924,X21923),
inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).
fof(i_0_9772,plain,
! [X32492,X32493,X32494] :
( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X32492) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X32493),hAPP(c_List_Oset(tc_Nat_Onat),X32492)))
| X32493 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk447_1(X32494)),hAPP(c_List_Oset(tc_Nat_Onat),X32494)))
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X32494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( esk447_1(X32494) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X32494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__eq__0__nat__iff__nat])])])])])]) ).
fof(i_0_9773,plain,
! [X17479,X17480,X17481] :
( ~ hBOOL(hAPP(c_Com_OWT,X17481))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X17480,X17479,X17481))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OLocal])]) ).
fof(i_0_9774,plain,
! [X19140,X19141,X19142] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19142),X19141),X19140))
| X19141 = X19140
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19142),X19141),X19140))
| ~ class_Orderings_Olinorder(X19142) )
& ( X19141 != X19140
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19142),X19141),X19140))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19142),X19141),X19140))
| ~ class_Orderings_Olinorder(X19142) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5915])])]) ).
fof(i_0_9775,plain,
! [X19164,X19165,X19166] :
( ~ class_Orderings_Oorder(X19166)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19166),X19165),X19164))
| X19164 = X19165
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19166),X19165),X19164)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_9776,plain,
! [X19161,X19162,X19163] :
( ~ class_Orderings_Oorder(X19163)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19163),X19162),X19161))
| X19162 = X19161
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19163),X19162),X19161)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_9777,plain,
! [X19158,X19159,X19160] :
( ~ class_Orderings_Oorder(X19160)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19160),X19159),X19158))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19160),X19159),X19158))
| X19159 = X19158 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_9778,plain,
! [X19143,X19144,X19145] :
( ~ class_Orderings_Oorder(X19145)
| X19144 = X19143
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19145),X19144),X19143))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19145),X19144),X19143)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_9779,plain,
! [X19131,X19132,X19133] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19133),X19132),X19131))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19133),X19132),X19131))
| X19132 = X19131
| ~ class_Orderings_Oorder(X19133) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19133),X19132),X19131))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19133),X19132),X19131))
| ~ class_Orderings_Oorder(X19133) )
& ( X19132 != X19131
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19133),X19132),X19131))
| ~ class_Orderings_Oorder(X19133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_9780,plain,
! [X19125,X19126,X19127] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19127),X19126),X19125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19127),X19126),X19125))
| ~ class_Orderings_Oorder(X19127) )
& ( X19126 != X19125
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19127),X19126),X19125))
| ~ class_Orderings_Oorder(X19127) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19127),X19126),X19125))
| X19126 = X19125
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19127),X19126),X19125))
| ~ class_Orderings_Oorder(X19127) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_9781,plain,
! [X19146,X19147,X19148] :
( ~ class_Orderings_Oorder(X19148)
| X19147 = X19146
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19148),X19146),X19147))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19148),X19146),X19147)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_9782,plain,
! [X20764,X20765,X20766] :
( ~ class_Int_Onumber__ring(X20766)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20766),hAPP(c_Int_Onumber__class_Onumber__of(X20766),X20765)),hAPP(c_Int_Onumber__class_Onumber__of(X20766),X20764)) = hAPP(c_Int_Onumber__class_Onumber__of(X20766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20765),X20764)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])]) ).
fof(i_0_9783,plain,
! [X20753,X20754,X20755] :
( ~ class_Int_Onumber__ring(X20755)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20755),hAPP(c_Int_Onumber__class_Onumber__of(X20755),X20754)),hAPP(c_Int_Onumber__class_Onumber__of(X20755),X20753)) = hAPP(c_Int_Onumber__class_Onumber__of(X20755),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20754),X20753)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__eq])]) ).
fof(i_0_9784,plain,
! [X20773,X20774,X20775] :
( ~ class_Int_Onumber__ring(X20775)
| hAPP(c_Int_Onumber__class_Onumber__of(X20775),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20774),X20773)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20775),hAPP(c_Int_Onumber__class_Onumber__of(X20775),X20774)),hAPP(c_Int_Onumber__class_Onumber__of(X20775),X20773)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__diff])]) ).
fof(i_0_9785,plain,
! [X20761,X20762,X20763] :
( ~ class_Int_Onumber__ring(X20763)
| hAPP(c_Int_Onumber__class_Onumber__of(X20763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20762),X20761)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20763),hAPP(c_Int_Onumber__class_Onumber__of(X20763),X20762)),hAPP(c_Int_Onumber__class_Onumber__of(X20763),X20761)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])]) ).
fof(i_0_9786,plain,
! [X20756,X20757,X20758] :
( ~ class_Int_Onumber__ring(X20758)
| hAPP(c_Int_Onumber__class_Onumber__of(X20758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20757),X20756)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20758),hAPP(c_Int_Onumber__class_Onumber__of(X20758),X20757)),hAPP(c_Int_Onumber__class_Onumber__of(X20758),X20756)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).
fof(i_0_9787,plain,
! [X20223,X20224,X20225] :
( ~ class_Rings_Oring__1(X20225)
| hAPP(c_Int_Oring__1__class_Oof__int(X20225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20224),X20223)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20225),hAPP(c_Int_Oring__1__class_Oof__int(X20225),X20224)),hAPP(c_Int_Oring__1__class_Oof__int(X20225),X20223)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__diff])]) ).
fof(i_0_9788,plain,
! [X18661,X18662,X18663] :
( ~ class_Rings_Oring__1(X18663)
| hAPP(c_Int_Oring__1__class_Oof__int(X18663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18662),X18661)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18663),hAPP(c_Int_Oring__1__class_Oof__int(X18663),X18662)),hAPP(c_Int_Oring__1__class_Oof__int(X18663),X18661)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__mult])]) ).
fof(i_0_9789,plain,
! [X18950,X18951,X18952] :
( ~ class_Rings_Oring__1(X18952)
| hAPP(c_Int_Oring__1__class_Oof__int(X18952),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18951),X18950)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18952),hAPP(c_Int_Oring__1__class_Oof__int(X18952),X18951)),hAPP(c_Int_Oring__1__class_Oof__int(X18952),X18950)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__add])]) ).
fof(i_0_9790,plain,
! [X18739,X18740,X18741] :
( ~ class_Rings_Osemiring__1(X18741)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18740),X18739)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18741),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18741),X18740)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18741),X18739)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__mult])]) ).
fof(i_0_9791,plain,
! [X18501,X18502,X18503] :
( ~ class_Rings_Osemiring__1(X18503)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18503),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18502),X18501)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18503),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18503),X18502)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18503),X18501)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__add])]) ).
fof(i_0_9792,plain,
! [X21776,X21777] :
( ~ class_Fields_Ofield__inverse__zero(X21777)
| ~ class_Int_Onumber__ring(X21777)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21777),hAPP(c_Int_Onumber__class_Onumber__of(X21777),c_Int_OMin)),X21776) = hAPP(c_Groups_Ouminus__class_Ouminus(X21777),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21777),c_Groups_Oone__class_Oone(X21777)),X21776)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus1__divide])]) ).
fof(i_0_9793,plain,
! [X26053,X26054,X26055] :
( ~ class_Groups_Ocomm__monoid__mult(X26055)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26054,X26055),hAPP(c_COMBK(X26055,X26054),c_Groups_Oone__class_Oone(X26055))),X26053) = c_Groups_Oone__class_Oone(X26055) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__1])]) ).
fof(i_0_9794,plain,
! [X23248,X23249,X23250] :
( ~ class_Groups_Ocomm__monoid__add(X23250)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23249,X23250),hAPP(c_COMBK(X23250,X23249),c_Groups_Ozero__class_Ozero(X23250))),X23248) = c_Groups_Ozero__class_Ozero(X23250) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__0])]) ).
fof(i_0_9795,plain,
! [X23821,X23822] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23822),c_Groups_Oone__class_Oone(tc_Int_Oint))),X23821) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X23822,X23821),
inference(variable_rename,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int]) ).
fof(i_0_9796,plain,
! [X19152,X19153,X19154] :
( ~ class_Orderings_Opreorder(X19154)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19154),X19153),X19152))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19154),X19153),X19152)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_9797,plain,
! [X22034,X22035] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22035),X22034)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22035),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22034)),
inference(variable_rename,[status(thm)],[fact_negateSnd__eq]) ).
fof(i_0_9798,plain,
! [X21087,X21088] :
( ~ class_Int_Onumber__ring(X21088)
| ~ class_Rings_Olinordered__idom(X21088)
| hAPP(c_Groups_Oabs__class_Oabs(X21088),hAPP(hAPP(c_Power_Opower__class_Opower(X21088),hAPP(c_Int_Onumber__class_Onumber__of(X21088),c_Int_OMin)),X21087)) = c_Groups_Oone__class_Oone(X21088) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus__one])]) ).
fof(i_0_9799,plain,
! [X24767,X24768,X24769] :
( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24769,X24768),X24767) != c_Orderings_Obot__class_Obot(tc_fun(X24769,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24769),X24768),X24767))
| ~ class_Orderings_Oorder(X24769) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24769),X24768),X24767))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24769,X24768),X24767) = c_Orderings_Obot__class_Obot(tc_fun(X24769,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X24769) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5916])])]) ).
fof(i_0_9800,plain,
! [X24764,X24765,X24766] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X24766,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24766,X24765),X24764)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24766),X24765),X24764))
| ~ class_Orderings_Oorder(X24766) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24766),X24765),X24764))
| c_Orderings_Obot__class_Obot(tc_fun(X24766,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24766,X24765),X24764)
| ~ class_Orderings_Oorder(X24766) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5917])])]) ).
cnf(i_0_9801,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5918]) ).
fof(i_0_9802,plain,
! [X27159,X27160] :
( ~ c_Nat__Transfer_Onat__set(X27160)
| ~ c_Nat__Transfer_Onat__set(X27159)
| c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X27160),X27159)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J])]) ).
fof(i_0_9803,plain,
! [X23854,X23855] :
( ~ c_Nat__Transfer_Onat__set(X23855)
| ~ c_Nat__Transfer_Onat__set(X23854)
| c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23855),X23854)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J])]) ).
fof(i_0_9804,plain,
! [X19526,X19527,X19529,X19530,X19531] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19527),X19526))
| X19526 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19527),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk52_2(X19526,X19527))) )
& ( X19529 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19530),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19531))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19530),X19529)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__iff__zadd])])])])]) ).
fof(i_0_9805,plain,
! [X33899,X33900,X33901,X33902] : hAPP(c_List_Ofilter(X33902,X33901),c_List_Oremove1(X33902,X33900,X33899)) = c_List_Oremove1(X33902,X33900,hAPP(c_List_Ofilter(X33902,X33901),X33899)),
inference(variable_rename,[status(thm)],[fact_filter__remove1]) ).
fof(i_0_9806,plain,
! [X33841,X33842,X33843,X33844] :
( ( X33841 != c_List_Olist_ONil(X33844)
| hAPP(hAPP(c_List_Oappend(X33844),X33843),hAPP(hAPP(c_List_Olist_OCons(X33844),X33842),c_List_Olist_ONil(X33844))) != X33841 )
& ( c_List_Obutlast(X33844,X33841) = X33843
| hAPP(hAPP(c_List_Oappend(X33844),X33843),hAPP(hAPP(c_List_Olist_OCons(X33844),X33842),c_List_Olist_ONil(X33844))) != X33841 )
& ( c_List_Olast(X33844,X33841) = X33842
| hAPP(hAPP(c_List_Oappend(X33844),X33843),hAPP(hAPP(c_List_Olist_OCons(X33844),X33842),c_List_Olist_ONil(X33844))) != X33841 )
& ( X33841 = c_List_Olist_ONil(X33844)
| c_List_Obutlast(X33844,X33841) != X33843
| c_List_Olast(X33844,X33841) != X33842
| hAPP(hAPP(c_List_Oappend(X33844),X33843),hAPP(hAPP(c_List_Olist_OCons(X33844),X33842),c_List_Olist_ONil(X33844))) = X33841 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])]) ).
fof(i_0_9807,plain,
! [X18972] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18972),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X18972 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk41_1(X18972)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negD])])]) ).
fof(i_0_9808,plain,
! [X25745,X25746] :
( ~ class_Int_Onumber__ring(X25746)
| hBOOL(hAPP(hAPP(c_member(X25746),hAPP(c_Int_Onumber__class_Onumber__of(X25746),X25745)),c_Int_Oring__1__class_OInts(X25746))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__number__of])]) ).
fof(i_0_9809,plain,
! [X25763,X25764] :
( ~ class_Rings_Oring__1(X25764)
| hBOOL(hAPP(hAPP(c_member(X25764),hAPP(c_Int_Oring__1__class_Oof__int(X25764),X25763)),c_Int_Oring__1__class_OInts(X25764))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__int])]) ).
fof(i_0_9810,plain,
! [X25758,X25759] :
( ~ class_Rings_Oring__1(X25759)
| hBOOL(hAPP(hAPP(c_member(X25759),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25759),X25758)),c_Int_Oring__1__class_OInts(X25759))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__nat])]) ).
fof(i_0_9811,plain,
! [X25660,X25661] :
( ~ class_Rings_Osemiring__1(X25661)
| hBOOL(hAPP(hAPP(c_member(X25661),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25661),X25660)),c_Nat_Osemiring__1__class_ONats(X25661))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats])]) ).
fof(i_0_9812,plain,
! [X20559] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20559))
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20559),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X20559 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__1])]) ).
fof(i_0_9813,plain,
! [X20558] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20558))
| X20558 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20558),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred_H])]) ).
fof(i_0_9814,plain,
! [X25285] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X25285)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_nat__of]) ).
fof(i_0_9815,plain,
! [X20063,X20064,X20065] :
( ~ class_Divides_Osemiring__div(X20065)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20065),c_Divides_Odiv__class_Omod(X20065,X20064,X20063)),X20063) = c_Groups_Ozero__class_Ozero(X20065) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__trivial])]) ).
fof(i_0_9816,plain,
! [X21865] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X21865) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21865),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_negDivAlg__minus1]) ).
fof(i_0_9817,plain,
! [X23818,X23819] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23819))
| c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X23819,X23818)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures])]) ).
fof(i_0_9818,plain,
! [X25955,X25956] :
( ~ class_Orderings_Olinorder(X25956)
| c_Big__Operators_Olattice_OInf__fin(X25956,c_Orderings_Oord__class_Omin(X25956),hAPP(hAPP(c_Set_Oinsert(X25956),X25955),c_Orderings_Obot__class_Obot(tc_fun(X25956,tc_HOL_Obool)))) = X25955 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton])]) ).
fof(i_0_9819,plain,
! [X25957,X25958] :
( ~ class_Orderings_Olinorder(X25958)
| c_Big__Operators_Olattice_OSup__fin(X25958,c_Orderings_Oord__class_Omax(X25958),hAPP(hAPP(c_Set_Oinsert(X25958),X25957),c_Orderings_Obot__class_Obot(tc_fun(X25958,tc_HOL_Obool)))) = X25957 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton])]) ).
fof(i_0_9820,plain,
! [X19629] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19629))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19629)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19629))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19629)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).
fof(i_0_9821,plain,
! [X27144,X27145] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27145,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X27145,tc_HOL_Obool))),X27144) = c_Orderings_Obot__class_Obot(tc_fun(X27145,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Int__empty__left]) ).
fof(i_0_9822,plain,
! [X24313,X24314] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24314,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X24314,tc_HOL_Obool))),X24313) = c_Orderings_Otop__class_Otop(tc_fun(X24314,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Un__UNIV__left]) ).
fof(i_0_9823,plain,
! [X24650,X24651] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24651,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X24651,tc_HOL_Obool))),X24650) = c_Orderings_Obot__class_Obot(tc_fun(X24651,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_empty__Diff]) ).
fof(i_0_9824,plain,
! [X28650,X28651,X28652] : hAPP(hAPP(c_Product__Type_OSigma(X28652,X28651),c_Orderings_Obot__class_Obot(tc_fun(X28652,tc_HOL_Obool))),X28650) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28652,X28651),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Sigma__empty1]) ).
fof(i_0_9825,plain,
! [X19002] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19002),X19002))),
inference(variable_rename,[status(thm)],[fact_le__square]) ).
fof(i_0_9826,plain,
! [X19278,X19279] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19279),X19278))),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_9827,plain,
! [X19276,X19277] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19276),X19277))),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_9828,plain,
! [X21683,X21684,X21685,X21686] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684) = c_Groups_Ozero__class_Ozero(X21686)
| X21685 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21686),X21683),hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21686),X21685),hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684)) != X21683
| ~ class_Fields_Ofield__inverse__zero(X21686)
| ~ class_Int_Onumber(X21686) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684) != c_Groups_Ozero__class_Ozero(X21686)
| X21683 = c_Groups_Ozero__class_Ozero(X21686)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21686),X21685),hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684)) != X21683
| ~ class_Fields_Ofield__inverse__zero(X21686)
| ~ class_Int_Onumber(X21686) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684) = c_Groups_Ozero__class_Ozero(X21686)
| hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684) != c_Groups_Ozero__class_Ozero(X21686)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21686),X21685),hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684)) = X21683
| ~ class_Fields_Ofield__inverse__zero(X21686)
| ~ class_Int_Onumber(X21686) )
& ( X21683 != c_Groups_Ozero__class_Ozero(X21686)
| hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684) != c_Groups_Ozero__class_Ozero(X21686)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21686),X21685),hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684)) = X21683
| ~ class_Fields_Ofield__inverse__zero(X21686)
| ~ class_Int_Onumber(X21686) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684) = c_Groups_Ozero__class_Ozero(X21686)
| X21685 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21686),X21683),hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21686),X21685),hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684)) = X21683
| ~ class_Fields_Ofield__inverse__zero(X21686)
| ~ class_Int_Onumber(X21686) )
& ( X21683 != c_Groups_Ozero__class_Ozero(X21686)
| X21685 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21686),X21683),hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21686),X21685),hAPP(c_Int_Onumber__class_Onumber__of(X21686),X21684)) = X21683
| ~ class_Fields_Ofield__inverse__zero(X21686)
| ~ class_Int_Onumber(X21686) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1])])]) ).
fof(i_0_9829,plain,
! [X21695,X21696,X21697,X21698] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695) = c_Groups_Ozero__class_Ozero(X21698)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21698),X21697),hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695)) = X21696
| X21697 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21698),X21696),hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695))
| ~ class_Fields_Ofield__inverse__zero(X21698)
| ~ class_Int_Onumber(X21698) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695) != c_Groups_Ozero__class_Ozero(X21698)
| X21697 = c_Groups_Ozero__class_Ozero(X21698)
| X21697 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21698),X21696),hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695))
| ~ class_Fields_Ofield__inverse__zero(X21698)
| ~ class_Int_Onumber(X21698) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695) = c_Groups_Ozero__class_Ozero(X21698)
| hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695) != c_Groups_Ozero__class_Ozero(X21698)
| X21697 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21698),X21696),hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695))
| ~ class_Fields_Ofield__inverse__zero(X21698)
| ~ class_Int_Onumber(X21698) )
& ( X21697 != c_Groups_Ozero__class_Ozero(X21698)
| hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695) != c_Groups_Ozero__class_Ozero(X21698)
| X21697 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21698),X21696),hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695))
| ~ class_Fields_Ofield__inverse__zero(X21698)
| ~ class_Int_Onumber(X21698) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695) = c_Groups_Ozero__class_Ozero(X21698)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21698),X21697),hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695)) != X21696
| X21697 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21698),X21696),hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695))
| ~ class_Fields_Ofield__inverse__zero(X21698)
| ~ class_Int_Onumber(X21698) )
& ( X21697 != c_Groups_Ozero__class_Ozero(X21698)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21698),X21697),hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695)) != X21696
| X21697 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21698),X21696),hAPP(c_Int_Onumber__class_Onumber__of(X21698),X21695))
| ~ class_Fields_Ofield__inverse__zero(X21698)
| ~ class_Int_Onumber(X21698) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1])])]) ).
fof(i_0_9830,plain,
! [X18233,X18234,X18235] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18234),X18235))
| hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| X18235 = X18234
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18235),X18234)) )
& ( ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| X18235 = X18234
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18235),X18234)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18234),X18235))
| hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18235),X18234)) )
& ( ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18235),X18234)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18234),X18235))
| hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| X18235 = X18234
| ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235)) )
& ( ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| X18235 = X18234
| ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18234),X18235))
| hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235)) )
& ( ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235))
| ~ hBOOL(hAPP(hAPP(X18233,X18234),X18235)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_9831,plain,
! [X23815] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X23815) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23815)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).
fof(i_0_9832,plain,
! [X32965,X32966,X32967,X32968,X32969,X32970] :
( hAPP(hAPP(c_List_Oappend(X32970),X32969),X32968) != X32967
| X32966 != hAPP(hAPP(c_List_Oappend(X32970),X32968),X32965)
| hAPP(hAPP(c_List_Oappend(X32970),X32969),X32966) = hAPP(hAPP(c_List_Oappend(X32970),X32967),X32965) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__appendI])]) ).
fof(i_0_9833,plain,
! [X32914,X32915,X32916,X32917,X32918,X32919] :
( hAPP(hAPP(c_List_Olist_OCons(X32919),X32918),X32917) != X32916
| X32915 != hAPP(hAPP(c_List_Oappend(X32919),X32917),X32914)
| hAPP(hAPP(c_List_Olist_OCons(X32919),X32918),X32915) = hAPP(hAPP(c_List_Oappend(X32919),X32916),X32914) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__appendI])]) ).
fof(i_0_9834,plain,
! [X18543,X18544,X18545] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18545),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18544),X18543)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18544),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18545),X18543)),
inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).
fof(i_0_9835,plain,
! [X18041,X18042,X18043] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18042),X18041)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18042),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18043),X18041)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_9836,plain,
! [X32011,X32012] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X32012),X32011) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X32012,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X32011),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upto]) ).
fof(i_0_9837,plain,
! [X22711,X22712] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22712),X22711)),X22711) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22712),X22711),
inference(variable_rename,[status(thm)],[fact_nat__minus__add__max]) ).
fof(i_0_9838,plain,
! [X22758] :
( ~ class_Orderings_Olinorder(X22758)
| c_Orderings_Oord_Omax(X22758,hAPP(c_COMBC(X22758,X22758,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X22758))) = c_Orderings_Oord__class_Omin(X22758) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__max])]) ).
fof(i_0_9839,plain,
! [X22731] :
( ~ class_Orderings_Olinorder(X22731)
| c_Orderings_Oord_Omin(X22731,hAPP(c_COMBC(X22731,X22731,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X22731))) = c_Orderings_Oord__class_Omax(X22731) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__min])]) ).
fof(i_0_9840,plain,
! [X33601] :
( ~ class_Groups_Omonoid__add(X33601)
| c_List_Omonoid__add__class_Olistsum(X33601) = c_List_Ofoldl(X33601,X33601,c_Groups_Oplus__class_Oplus(X33601),c_Groups_Ozero__class_Ozero(X33601)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__foldl])]) ).
fof(i_0_9841,plain,
! [X25322,X25323,X25324] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25324),X25323),c_Option_Oset(X25324,X25322)))
| X25322 = hAPP(c_Option_Ooption_OSome(X25324),X25323) )
& ( X25322 != hAPP(c_Option_Ooption_OSome(X25324),X25323)
| hBOOL(hAPP(hAPP(c_member(X25324),X25323),c_Option_Oset(X25324,X25322))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__set])]) ).
fof(i_0_9842,plain,
! [X20051,X20052,X20053] :
( ~ class_Divides_Osemiring__div(X20053)
| X20052 = c_Groups_Ozero__class_Ozero(X20053)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20053),X20052),X20051)),X20052) = X20051 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id])]) ).
fof(i_0_9843,plain,
! [X20054,X20055,X20056] :
( ~ class_Divides_Osemiring__div(X20056)
| X20055 = c_Groups_Ozero__class_Ozero(X20056)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20056),X20054),X20055)),X20055) = X20054 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])]) ).
fof(i_0_9844,plain,
! [X20428,X20429,X20430] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20429),X20430) != X20428
| X20429 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20428),X20430)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20430),X20429)) )
& ( X20429 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20428),X20430)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20429),X20430) = X20428
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20430),X20429)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).
fof(i_0_9845,plain,
! [X19842,X19843] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X19843,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19842)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19843),X19842)),
inference(variable_rename,[status(thm)],[fact_zmod__zminus2]) ).
fof(i_0_9846,negated_conjecture,
( v_P(esk493_0,esk494_0)
& c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),esk494_0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),esk495_0)
& ~ v_Q(esk493_0,esk495_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5919])])]) ).
fof(i_0_9847,plain,
! [X18086,X18087,X18088,X18089] : c_Com_Ovname_Ovname__rec(X18089,X18088,X18087,c_Com_Ovname_OGlb(X18086)) = hAPP(X18088,X18086),
inference(variable_rename,[status(thm)],[fact_vname_Orecs_I1_J]) ).
fof(i_0_9848,plain,
! [X17895,X17896,X17897,X17898] : c_Com_Ovname_Ovname__rec(X17898,X17897,X17896,c_Com_Ovname_OLoc(X17895)) = hAPP(X17896,X17895),
inference(variable_rename,[status(thm)],[fact_vname_Orecs_I2_J]) ).
fof(i_0_9849,plain,
! [X18090,X18091,X18092,X18093] : c_Com_Ovname_Ovname__case(X18093,X18092,X18091,c_Com_Ovname_OGlb(X18090)) = hAPP(X18092,X18090),
inference(variable_rename,[status(thm)],[fact_vname_Osimps_I5_J]) ).
fof(i_0_9850,plain,
! [X17891,X17892,X17893,X17894] : c_Com_Ovname_Ovname__case(X17894,X17893,X17892,c_Com_Ovname_OLoc(X17891)) = hAPP(X17892,X17891),
inference(variable_rename,[status(thm)],[fact_vname_Osimps_I6_J]) ).
fof(i_0_9851,plain,
! [X28468,X28469,X28470,X28471,X28472] :
( hAPP(X28472,X28471) != hAPP(c_Option_Ooption_OSome(X28470),X28469)
| hAPP(hAPP(c_Set_Oinsert(X28468),X28471),c_Map_Odom(X28468,X28470,X28472)) = c_Map_Odom(X28468,X28470,X28472) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__dom])]) ).
fof(i_0_9852,plain,
! [X29897,X29898] :
( ( c_Wellfounded_Oacyclic(X29898,X29897)
| ~ c_Nitpick_Owf_H(X29898,X29897) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29898,X29898)),X29897))
| c_Nitpick_Ounknown(tc_HOL_Obool)
| ~ c_Nitpick_Owf_H(X29898,X29897) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29898,X29898)),X29897))
| ~ c_Wellfounded_Oacyclic(X29898,X29897)
| c_Nitpick_Owf_H(X29898,X29897) )
& ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
| ~ c_Wellfounded_Oacyclic(X29898,X29897)
| c_Nitpick_Owf_H(X29898,X29897) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def])])]) ).
fof(i_0_9853,plain,
! [X29890,X29891] :
( ( ~ c_Wellfounded_Owf(X29891,X29890)
| c_Wellfounded_Oacyclic(X29891,X29890)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29891,X29891)),X29890)) )
& ( ~ c_Wellfounded_Oacyclic(X29891,X29890)
| c_Wellfounded_Owf(X29891,X29890)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29891,X29891)),X29890)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__iff__acyclic__if__finite])])]) ).
fof(i_0_9854,plain,
! [X29888,X29889] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29889,X29889)),X29888))
| ~ c_Wellfounded_Oacyclic(X29889,X29888)
| c_Wellfounded_Owf(X29889,X29888) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf])]) ).
fof(i_0_9855,plain,
! [X34214,X34215] : c_Fun_Oinj__on(tc_List_Olist(X34215),tc_List_Olist(X34215),c_List_Orev(X34215),X34214),
inference(variable_rename,[status(thm)],[fact_inj__on__rev]) ).
fof(i_0_9856,plain,
! [X33892,X33893,X33894] :
( ~ hBOOL(hAPP(c_List_Odistinct(X33894),X33893))
| hBOOL(hAPP(c_List_Odistinct(X33894),hAPP(c_List_Ofilter(X33894,X33892),X33893))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__filter])]) ).
fof(i_0_9857,plain,
! [X25793,X25794,X25795,X25796] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X25796)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X25796),X25795),X25794),X25793)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_triple_Osize_I2_J]) ).
fof(i_0_9858,plain,
! [X27814,X27815,X27816,X27817,X27818,X27819,X27820,X27823] :
( ( ~ hBOOL(hAPP(hAPP(X27814,X27816),X27817))
| hAPP(X27814,X27816) = hAPP(X27814,X27817)
| ~ c_Equiv__Relations_Oequivp(X27815,X27814) )
& ( hAPP(X27814,X27818) != hAPP(X27814,X27819)
| hBOOL(hAPP(hAPP(X27814,X27818),X27819))
| ~ c_Equiv__Relations_Oequivp(X27815,X27814) )
& ( ~ hBOOL(hAPP(hAPP(X27820,esk259_1(X27820)),esk260_1(X27820)))
| hAPP(X27820,esk259_1(X27820)) != hAPP(X27820,esk260_1(X27820))
| c_Equiv__Relations_Oequivp(X27823,X27820) )
& ( hBOOL(hAPP(hAPP(X27820,esk259_1(X27820)),esk260_1(X27820)))
| hAPP(X27820,esk259_1(X27820)) = hAPP(X27820,esk260_1(X27820))
| c_Equiv__Relations_Oequivp(X27823,X27820) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__def])])])])])]) ).
fof(i_0_9859,plain,
! [X20256,X20257,X20258] :
( ~ class_Groups_Ogroup__add(X20258)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20258),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20258),X20257),X20256)),X20256) = X20257 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(i_0_9860,plain,
! [X20259,X20260,X20261] :
( ~ class_Groups_Ogroup__add(X20261)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20261),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20261),X20260),X20259)),X20259) = X20260 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
fof(i_0_9861,plain,
! [X29818,X29819,X29820] : hAPP(c_Set_Oimage(tc_prod(X29820,X29819),X29820,c_Product__Type_Ofst(X29820,X29819)),X29818) = hAPP(c_Relation_ODomain(X29820,X29819),X29818),
inference(variable_rename,[status(thm)],[fact_fst__eq__Domain]) ).
fof(i_0_9862,plain,
! [X29727,X29728,X29729] : hAPP(c_Set_Oimage(tc_prod(X29729,X29728),X29728,c_Product__Type_Osnd(X29729,X29728)),X29727) = hAPP(c_Relation_ORange(X29729,X29728),X29727),
inference(variable_rename,[status(thm)],[fact_snd__eq__Range]) ).
fof(i_0_9863,plain,
! [X18210,X18211] :
( ( hBOOL(hAPP(X18211,hAPP(c_Nat_OSuc,esk29_2(X18210,X18211))))
| hBOOL(hAPP(X18211,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X18211,X18210)) )
& ( ~ hBOOL(hAPP(X18211,esk29_2(X18210,X18211)))
| hBOOL(hAPP(X18211,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X18211,X18210)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__induct])])])]) ).
fof(i_0_9864,plain,
! [X30493,X30494,X30495] :
( ( ~ c_Relation_Ototal__on(X30495,X30494,hAPP(c_Relation_Oconverse(X30495,X30495),X30493))
| c_Relation_Ototal__on(X30495,X30494,X30493) )
& ( ~ c_Relation_Ototal__on(X30495,X30494,X30493)
| c_Relation_Ototal__on(X30495,X30494,hAPP(c_Relation_Oconverse(X30495,X30495),X30493)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__converse])]) ).
fof(i_0_9865,plain,
! [X30388,X30389,X30390] :
( ( ~ c_Relation_Orefl__on(X30390,X30389,hAPP(c_Relation_Oconverse(X30390,X30390),X30388))
| c_Relation_Orefl__on(X30390,X30389,X30388) )
& ( ~ c_Relation_Orefl__on(X30390,X30389,X30388)
| c_Relation_Orefl__on(X30390,X30389,hAPP(c_Relation_Oconverse(X30390,X30390),X30388)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__converse])]) ).
fof(i_0_9866,plain,
! [X18104,X18105,X18106] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X18106,X18105,X18104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X18104)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_com_Osize_I11_J]) ).
fof(i_0_9867,plain,
! [X23795] :
( ~ c_Nat__Transfer_Onat__set(X23795)
| hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X23795) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23795)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J])]) ).
fof(i_0_9868,plain,
! [X25335,X25336] :
( ~ c_Nat__Transfer_Onat__set(X25336)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25335),X25336))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J])]) ).
fof(i_0_9869,plain,
! [X23803,X23804,X23805] :
( ( ~ c_Nat__Transfer_Onat__set(X23803)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X23804),X23803))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23804)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk130_1(X23805)),X23805))
| c_Nat__Transfer_Onat__set(X23805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk130_1(X23805)))
| c_Nat__Transfer_Onat__set(X23805) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__set__def])])])])])]) ).
fof(i_0_9870,plain,
! [X28984] : c_Relation_Orefl__on(X28984,c_Orderings_Obot__class_Obot(tc_fun(X28984,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28984,X28984),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_refl__on__empty]) ).
fof(i_0_9871,plain,
! [X23765,X23766] : hAPP(c_Finite__Set_Ocard(X23766),X23765) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X23766,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X23766),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X23765),
inference(variable_rename,[status(thm)],[fact_card__eq__setsum]) ).
fof(i_0_9872,plain,
! [X21981,X21982,X21983,X21984] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21984,X21983),X21982))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21984,X21983),X21981))
| X21982 = X21981 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__unique])]) ).
fof(i_0_9873,plain,
! [X27882,X27883] :
( ~ class_Groups_Oordered__ab__group__add(X27883)
| c_Fun_Oinj__on(X27883,X27883,c_Groups_Ouminus__class_Ouminus(X27883),X27882) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__uminus])]) ).
fof(i_0_9874,plain,
! [X22768,X22769] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X22769,X22768) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X22769),hAPP(c_Code__Numeral_Onat__of,X22768))),
inference(variable_rename,[status(thm)],[fact_mod__code__numeral__def]) ).
fof(i_0_9875,plain,
! [X32625,X32626,X32627] : hAPP(hAPP(c_List_Onth(X32627),hAPP(hAPP(c_List_Olist_OCons(X32627),X32626),X32625)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X32626,
inference(variable_rename,[status(thm)],[fact_nth__Cons__0]) ).
fof(i_0_9876,plain,
! [X24656,X24657,X24658,X24659] :
( ( hAPP(c_Set_Oimage(X24659,X24658,X24657),X24656) != c_Orderings_Obot__class_Obot(tc_fun(X24658,tc_HOL_Obool))
| X24656 = c_Orderings_Obot__class_Obot(tc_fun(X24659,tc_HOL_Obool)) )
& ( X24656 != c_Orderings_Obot__class_Obot(tc_fun(X24659,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X24659,X24658,X24657),X24656) = c_Orderings_Obot__class_Obot(tc_fun(X24658,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__is__empty])]) ).
fof(i_0_9877,plain,
! [X24663,X24664,X24665,X24666] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X24666,tc_HOL_Obool)) != hAPP(c_Set_Oimage(X24665,X24666,X24664),X24663)
| X24663 = c_Orderings_Obot__class_Obot(tc_fun(X24665,tc_HOL_Obool)) )
& ( X24663 != c_Orderings_Obot__class_Obot(tc_fun(X24665,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X24666,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X24665,X24666,X24664),X24663) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__is__image])]) ).
fof(i_0_9878,plain,
! [X28223,X28224] : c_Fun_Oinj__on(X28224,tc_Option_Ooption(X28224),c_Option_Ooption_OSome(X28224),X28223),
inference(variable_rename,[status(thm)],[fact_inj__Some]) ).
fof(i_0_9879,plain,
! [X32510,X32511] : c_List_Olistrelp(X32511,X32510,c_List_Olist_ONil(X32511),c_List_Olist_ONil(X32511)),
inference(variable_rename,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).
fof(i_0_9880,plain,
! [X32508,X32509] : c_List_Olistrelp(X32509,X32508,c_List_Olist_ONil(X32509),c_List_Olist_ONil(X32509)),
inference(variable_rename,[status(thm)],[fact_listrelp_ONil]) ).
fof(i_0_9881,plain,
! [X33451,X33452,X33453,X33454] :
( X33454 = c_List_Olist_ONil(X33453)
| hAPP(c_List_Ohd(X33452),hAPP(hAPP(c_List_Omap(X33453,X33452),X33451),X33454)) = hAPP(X33451,hAPP(c_List_Ohd(X33453),X33454)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__map])]) ).
fof(i_0_9882,plain,
! [X18174,X18175,X18176] :
( ~ class_Rings_Osemiring__1(X18176)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X18176,X18175,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18174) = X18174 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J])]) ).
fof(i_0_9883,plain,
! [X24775,X24776,X24777,X24778] :
( ( X24777 = X24776
| c_SetInterval_Oord__class_OatLeastAtMost(X24778,X24777,X24776) != hAPP(hAPP(c_Set_Oinsert(X24778),X24775),c_Orderings_Obot__class_Obot(tc_fun(X24778,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X24778) )
& ( X24776 = X24775
| c_SetInterval_Oord__class_OatLeastAtMost(X24778,X24777,X24776) != hAPP(hAPP(c_Set_Oinsert(X24778),X24775),c_Orderings_Obot__class_Obot(tc_fun(X24778,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X24778) )
& ( X24777 != X24776
| X24776 != X24775
| c_SetInterval_Oord__class_OatLeastAtMost(X24778,X24777,X24776) = hAPP(hAPP(c_Set_Oinsert(X24778),X24775),c_Orderings_Obot__class_Obot(tc_fun(X24778,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X24778) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff])])]) ).
fof(i_0_9884,plain,
! [X29906,X29907,X29908,X29909,X29910] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X29910),X29909),X29908),X29907),X29906) = c_New__DSequence_Oneg__single(X29910,X29909),
inference(variable_rename,[status(thm)],[fact_neg__single__def]) ).
fof(i_0_9885,plain,
! [X29892,X29893,X29894,X29895,X29896] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X29896),X29895),X29894),X29893),X29892) = c_New__DSequence_Opos__single(X29896,X29895),
inference(variable_rename,[status(thm)],[fact_pos__single__def]) ).
fof(i_0_9886,plain,
! [X20912,X20913,X20914] :
( ~ class_Rings_Olinordered__idom(X20914)
| hAPP(c_Groups_Oabs__class_Oabs(X20914),hAPP(hAPP(c_Power_Opower__class_Opower(X20914),X20913),X20912)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20914),hAPP(c_Groups_Oabs__class_Oabs(X20914),X20913)),X20912) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).
fof(i_0_9887,plain,
! [X21458,X21459,X21460] :
( ~ class_Rings_Odivision__ring(X21460)
| hAPP(c_Groups_Ouminus__class_Ouminus(X21460),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21460),X21459),X21458)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21460),hAPP(c_Groups_Ouminus__class_Ouminus(X21460),X21459)),X21458) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__left])]) ).
fof(i_0_9888,plain,
! [X18641,X18642,X18643] :
( ~ class_Rings_Oring(X18643)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18643),X18642),X18641)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18643),hAPP(c_Groups_Ouminus__class_Ouminus(X18643),X18642)),X18641) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).
fof(i_0_9889,plain,
! [X21023,X21024,X21025,X21026] : hAPP(hAPP(c_Power_Opower_Opower(X21026,X21025,X21024),X21023),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21025,
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).
fof(i_0_9890,plain,
! [X33982,X33983,X33984] : c_List_Omap__filter(X33984,X33983,X33982,c_List_Olist_ONil(X33984)) = c_List_Olist_ONil(X33983),
inference(variable_rename,[status(thm)],[fact_map__filter__simps_I2_J]) ).
cnf(i_0_9891,plain,
( X1 = X2
| c_Code__Numeral_OSuc__code__numeral(X1) != c_Code__Numeral_OSuc__code__numeral(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5920]) ).
fof(i_0_9892,plain,
! [X24795,X24796,X24797] :
( ~ class_Orderings_Oorder(X24797)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24797),X24796),X24795))
| c_SetInterval_Oord__class_OgreaterThanLessThan(X24797,X24795,X24796) = c_Orderings_Obot__class_Obot(tc_fun(X24797,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty])]) ).
fof(i_0_9893,plain,
! [X24786,X24787,X24788] :
( ~ class_Orderings_Oorder(X24788)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24788),X24787),X24786))
| c_SetInterval_Oord__class_OgreaterThanAtMost(X24788,X24786,X24787) = c_Orderings_Obot__class_Obot(tc_fun(X24788,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty])]) ).
fof(i_0_9894,plain,
! [X24746,X24747,X24748] :
( ~ class_Orderings_Oorder(X24748)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24748),X24747),X24746))
| c_SetInterval_Oord__class_OatLeastAtMost(X24748,X24746,X24747) = c_Orderings_Obot__class_Obot(tc_fun(X24748,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty])]) ).
fof(i_0_9895,plain,
! [X23382] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23382),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X23382 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X23382 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23382),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1])]) ).
fof(i_0_9896,plain,
! [X33482,X33483,X33484] :
( X33484 = c_List_Olist_ONil(X33483)
| hAPP(c_List_Otl(X33483),hAPP(hAPP(c_List_Oappend(X33483),X33484),X33482)) = hAPP(hAPP(c_List_Oappend(X33483),hAPP(c_List_Otl(X33483),X33484)),X33482) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__append2])]) ).
fof(i_0_9897,plain,
! [X20031,X20032] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20032,X20031)),X20031) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial]) ).
fof(i_0_9898,plain,
! [X22377,X22378,X22379,X22380] :
( hAPP(c_Product__Type_Ofst(X22380,X22379),X22378) != hAPP(c_Product__Type_Ofst(X22380,X22379),X22377)
| hAPP(c_Product__Type_Osnd(X22380,X22379),X22378) != hAPP(c_Product__Type_Osnd(X22380,X22379),X22377)
| X22378 = X22377 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__eqI])]) ).
fof(i_0_9899,plain,
! [X22373,X22374,X22375,X22376] :
( ( hAPP(c_Product__Type_Ofst(X22374,X22373),X22376) = hAPP(c_Product__Type_Ofst(X22374,X22373),X22375)
| X22376 != X22375 )
& ( hAPP(c_Product__Type_Osnd(X22374,X22373),X22376) = hAPP(c_Product__Type_Osnd(X22374,X22373),X22375)
| X22376 != X22375 )
& ( hAPP(c_Product__Type_Ofst(X22374,X22373),X22376) != hAPP(c_Product__Type_Ofst(X22374,X22373),X22375)
| hAPP(c_Product__Type_Osnd(X22374,X22373),X22376) != hAPP(c_Product__Type_Osnd(X22374,X22373),X22375)
| X22376 = X22375 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq])])]) ).
fof(i_0_9900,plain,
! [X29420,X29421] : c_Fun_Oinj__on(X29421,X29421,c_Fun_Oid(X29421),X29420),
inference(variable_rename,[status(thm)],[fact_inj__on__id]) ).
fof(i_0_9901,plain,
! [X27943,X27944] : c_Fun_Oinj__on(X27944,X27944,c_COMBI(X27944),X27943),
inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).
fof(i_0_9902,plain,
! [X19334,X19335,X19336] :
( ~ class_Rings_Olinordered__idom(X19336)
| c_Groups_Osgn__class_Osgn(X19336,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19336),X19335),X19334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19336),c_Groups_Osgn__class_Osgn(X19336,X19335)),c_Groups_Osgn__class_Osgn(X19336,X19334)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])]) ).
fof(i_0_9903,plain,
! [X34096,X34097,X34098] :
( ~ class_Orderings_Olinorder(X34098)
| ~ c_List_Olinorder__class_Osorted(X34098,X34097)
| ~ hBOOL(hAPP(c_List_Odistinct(X34098),X34097))
| ~ c_List_Olinorder__class_Osorted(X34098,X34096)
| ~ hBOOL(hAPP(c_List_Odistinct(X34098),X34096))
| hAPP(c_List_Oset(X34098),X34097) != hAPP(c_List_Oset(X34098),X34096)
| X34097 = X34096 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__distinct__set__unique])]) ).
fof(i_0_9904,plain,
! [X33339,X33340,X33341,X33342] : hAPP(hAPP(c_List_Odrop(X33342),hAPP(c_Nat_OSuc,X33341)),hAPP(hAPP(c_List_Olist_OCons(X33342),X33340),X33339)) = hAPP(hAPP(c_List_Odrop(X33342),X33341),X33339),
inference(variable_rename,[status(thm)],[fact_drop__Suc__Cons]) ).
cnf(i_0_9905,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(split_conjunct,[status(thm)],[fact_less__than__def]) ).
fof(i_0_9906,plain,
! [X20633,X20634,X20635] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20635)
| hAPP(c_Groups_Oabs__class_Oabs(X20635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20635),X20634),X20633)) = hAPP(c_Groups_Oabs__class_Oabs(X20635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20635),X20633),X20634)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).
cnf(i_0_9907,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_5921]) ).
fof(i_0_9908,plain,
! [X21920,X21921,X21922] : c_Nat_Onat_Onat__case(X21922,X21921,X21920,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21921,
inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).
fof(i_0_9909,plain,
! [X21902,X21903,X21904] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X21904,X21903,X21902,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X21903,
inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I1_J]) ).
fof(i_0_9910,plain,
! [X21796,X21797,X21798] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X21798,X21797,X21796,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X21797,
inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I4_J]) ).
fof(i_0_9911,plain,
! [X19961,X19962] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19962)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19961)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19962),X19961)),
inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J]) ).
fof(i_0_9912,plain,
! [X20860,X20861] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20861)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20860)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20861),X20860)),
inference(variable_rename,[status(thm)],[fact_times__numeral__code_I5_J]) ).
fof(i_0_9913,plain,
! [X19524,X19525] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19525)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19524)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19525),X19524)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).
fof(i_0_9914,plain,
! [X19522,X19523] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19523)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19522)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19523),X19522)),
inference(variable_rename,[status(thm)],[fact_zmult__int]) ).
fof(i_0_9915,plain,
! [X20858,X20859] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20859)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20858)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20859),X20858)),
inference(variable_rename,[status(thm)],[fact_plus__numeral__code_I9_J]) ).
fof(i_0_9916,plain,
! [X18514,X18515] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18515)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18514)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18515),X18514)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).
fof(i_0_9917,plain,
! [X18483,X18484] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18484)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18483)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18484),X18483)),
inference(variable_rename,[status(thm)],[fact_zadd__int]) ).
cnf(i_0_9918,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X1)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[i_0_5922]) ).
fof(i_0_9919,plain,
! [X18829,X18830] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18830),X18829)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18830)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18829)),
inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(i_0_9920,plain,
! [X19959,X19960] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19960),X19959)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19960)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19959)),
inference(variable_rename,[status(thm)],[fact_zdiv__int]) ).
fof(i_0_9921,plain,
! [X19520,X19521] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19521),X19520)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19521)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19520)),
inference(variable_rename,[status(thm)],[fact_int__mult]) ).
fof(i_0_9922,plain,
! [X27070,X27071] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27071,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X27071,tc_HOL_Obool))),X27070) = X27070,
inference(variable_rename,[status(thm)],[fact_Int__UNIV__left]) ).
fof(i_0_9923,plain,
! [X24636,X24637] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24637,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X24637,tc_HOL_Obool))),X24636) = X24636,
inference(variable_rename,[status(thm)],[fact_Un__empty__left]) ).
fof(i_0_9924,plain,
! [X18746,X18747] :
( ( X18747 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18747),X18746) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18747)) )
& ( X18746 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18747),X18746) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18747)) )
& ( X18747 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X18746 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18747),X18746) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18747)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).
cnf(i_0_9925,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_succ__Pls]) ).
fof(i_0_9926,plain,
! [X29016,X29017,X29018] : hAPP(c_Finite__Set_Ofold1(X29018,X29017),hAPP(hAPP(c_Set_Oinsert(X29018),X29016),c_Orderings_Obot__class_Obot(tc_fun(X29018,tc_HOL_Obool)))) = X29016,
inference(variable_rename,[status(thm)],[fact_fold1__singleton]) ).
fof(i_0_9927,plain,
! [X32754,X32755,X32756,X32757] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32757)),hAPP(hAPP(c_List_Olist__update(X32757,X32756),X32755),X32754)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32757)),X32756),
inference(variable_rename,[status(thm)],[fact_length__list__update]) ).
fof(i_0_9928,plain,
! [X32170,X32171,X32172,X32173] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32173)),hAPP(hAPP(c_List_Omap(X32172,X32173),X32171),X32170)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32172)),X32170),
inference(variable_rename,[status(thm)],[fact_length__map]) ).
fof(i_0_9929,plain,
! [X17225,X17226] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X17226,X17225,X17226),
inference(variable_rename,[status(thm)],[fact_evaln_Oequations_I1_J]) ).
fof(i_0_9930,plain,
! [X17220,X17221] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X17221,X17220,X17221),
inference(variable_rename,[status(thm)],[fact_evaln_OSkip]) ).
fof(i_0_9931,plain,
! [X20602,X20603,X20604] :
( ~ class_Rings_Oring__1(X20604)
| hAPP(c_Int_Oring__1__class_Oof__int(X20604),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20603),X20602)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20604),hAPP(c_Int_Oring__1__class_Oof__int(X20604),X20603)),X20602) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__power])]) ).
fof(i_0_9932,plain,
! [X20904,X20905,X20906] :
( ~ class_Rings_Osemiring__1(X20906)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20906),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20905),X20904)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20906),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20906),X20905)),X20904) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__power])]) ).
fof(i_0_9933,plain,
! [X19311,X19312] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19312),X19311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19312),X19311)) )
& ( X19312 != X19311
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19312),X19311)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19312),X19311))
| X19312 = X19311
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19312),X19311)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).
fof(i_0_9934,plain,
! [X19268,X19269] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19269),X19268))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19269),X19268)) )
& ( X19269 != X19268
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19269),X19268)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19269),X19268))
| X19269 = X19268
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19269),X19268)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_9935,plain,
! [X19266,X19267] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19267),X19266))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19267),X19266))
| X19267 = X19266 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19267),X19266))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19267),X19266)) )
& ( X19267 != X19266
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19267),X19266)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_9936,plain,
! [X19262,X19263] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19263),X19262))
| X19263 = X19262
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19263),X19262)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_9937,plain,
! [X29019,X29020,X29021,X29022] :
( X29022 != c_Finite__Set_Ofold1(X29021,X29020)
| hAPP(X29022,hAPP(hAPP(c_Set_Oinsert(X29021),X29019),c_Orderings_Obot__class_Obot(tc_fun(X29021,tc_HOL_Obool)))) = X29019 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def])]) ).
fof(i_0_9938,plain,
! [X33543,X33544] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33544)),hAPP(c_List_Otl(X33544),X33543)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33544)),X33543)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_length__tl]) ).
fof(i_0_9939,plain,
! [X29127,X29128,X29129,X29130,X29131] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X29131,X29130,X29129)
| hAPP(hAPP(X29129,X29128),hAPP(hAPP(X29129,X29128),X29127)) = hAPP(hAPP(X29129,X29128),X29127) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem])]) ).
fof(i_0_9940,plain,
! [X23810] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23810)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J]) ).
fof(i_0_9941,plain,
! [X24390,X24391] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X24391,X24390))),
inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan__int]) ).
fof(i_0_9942,plain,
! [X24388,X24389] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X24389,X24388))),
inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost__int]) ).
fof(i_0_9943,plain,
! [X24378,X24379] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24379,X24378))),
inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost__int]) ).
fof(i_0_9944,plain,
! [X24392,X24393] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X24393,X24392))),
inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan]) ).
fof(i_0_9945,plain,
! [X24386,X24387] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X24387,X24386))),
inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost]) ).
fof(i_0_9946,plain,
! [X24380,X24381] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24381,X24380))),
inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost]) ).
fof(i_0_9947,plain,
! [X18337] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18337),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X18337 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18337 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18337),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc0])]) ).
fof(i_0_9948,plain,
! [X28222] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X28222),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(i_0_9949,plain,
! [X19264,X19265] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19265),X19264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19265),X19264)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_9950,plain,
! [X19260,X19261] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19261),X19260))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19261),X19260)) )
& ( X19261 != X19260
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19261),X19260)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_9951,plain,
! [X19258,X19259] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19259),X19258))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19259),X19258)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_9952,plain,
! [X24760,X24761,X24762] :
( ~ class_Orderings_Oorder(X24762)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24762),X24761),X24760))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24762,X24760),X24761) = c_Orderings_Obot__class_Obot(tc_fun(X24762,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty])]) ).
fof(i_0_9953,plain,
! [X25141,X25142,X25143] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25143),X25142),hAPP(c_fequal,X25141)))
| X25142 = X25141 )
& ( X25142 != X25141
| hBOOL(hAPP(hAPP(c_member(X25143),X25142),hAPP(c_fequal,X25141))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_9954,plain,
! [X33754,X33755,X33756,X33757] :
( X33757 = c_List_Olist_ONil(X33756)
| c_List_Olast(X33755,hAPP(hAPP(c_List_Omap(X33756,X33755),X33754),X33757)) = hAPP(X33754,c_List_Olast(X33756,X33757)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__map])]) ).
fof(i_0_9955,plain,
! [X32584,X32585,X32586] : hAPP(c_Map_Omap__of(X32586,X32585,c_List_Olist_ONil(tc_prod(X32586,X32585))),X32584) = c_Option_Ooption_ONone(X32585),
inference(variable_rename,[status(thm)],[fact_map__of__Cons__code_I1_J]) ).
fof(i_0_9956,plain,
! [X32581,X32582,X32583] : hAPP(c_Map_Omap__of(X32583,X32582,c_List_Olist_ONil(tc_prod(X32583,X32582))),X32581) = c_Option_Ooption_ONone(X32582),
inference(variable_rename,[status(thm)],[fact_map__of_Osimps_I1_J]) ).
cnf(i_0_9957,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_5923]) ).
fof(i_0_9958,plain,
! [X18775,X18776,X18777] :
( ~ class_Groups_Ogroup__add(X18777)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18777),hAPP(c_Groups_Ouminus__class_Ouminus(X18777),X18776)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18777),X18776),X18775)) = X18775 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).
fof(i_0_9959,plain,
! [X25028,X25029,X25030,X25031,X25032] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25029),X25030),X25028))
| X25028 != c_Orderings_Obot__class_Obot(tc_fun(X25029,tc_HOL_Obool)) )
& ( X25031 = c_Orderings_Obot__class_Obot(tc_fun(X25032,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X25032),esk166_2(X25031,X25032)),X25031)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__in__conv])])])])]) ).
fof(i_0_9960,plain,
! [X25022,X25023,X25025,X25026,X25027] :
( ( hBOOL(hAPP(hAPP(c_member(X25023),esk165_2(X25022,X25023)),X25022))
| X25022 = c_Orderings_Obot__class_Obot(tc_fun(X25023,tc_HOL_Obool)) )
& ( X25025 != c_Orderings_Obot__class_Obot(tc_fun(X25026,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25026),X25027),X25025)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5924])])])])]) ).
fof(i_0_9961,plain,
! [X32022,X32023,X32024] :
( hBOOL(hAPP(hAPP(c_member(X32024),X32023),hAPP(c_List_Oset(X32024),X32022)))
| c_List_Oremove1(X32024,X32023,X32022) = X32022 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5925])]) ).
cnf(i_0_9962,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_5926]) ).
fof(i_0_9963,plain,
! [X19663,X19664] :
( ~ class_Rings_Oring__1(X19664)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19663))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19664),hAPP(c_Int_Onat,X19663)) = hAPP(c_Int_Oring__1__class_Oof__int(X19664),X19663) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__nat])]) ).
fof(i_0_9964,plain,
! [X19844,X19845] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19845),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19844)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19845,X19844)),
inference(variable_rename,[status(thm)],[fact_zmod__zminus__zminus]) ).
fof(i_0_9965,plain,
! [X20041,X20042] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20042),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20041)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20042,X20041)),
inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J]) ).
fof(i_0_9966,plain,
! [X20039,X20040] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20040,X20039)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20040),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20039)),
inference(variable_rename,[status(thm)],[fact_zmod__int]) ).
fof(i_0_9967,plain,
! [X18974,X18975] :
( ( X18974 != c_Groups_Ozero__class_Ozero(X18975)
| c_Groups_Osgn__class_Osgn(X18975,X18974) = c_Groups_Ozero__class_Ozero(X18975)
| ~ class_Groups_Osgn__if(X18975) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18975),c_Groups_Ozero__class_Ozero(X18975)),X18974))
| c_Groups_Osgn__class_Osgn(X18975,X18974) = c_Groups_Oone__class_Oone(X18975)
| X18974 = c_Groups_Ozero__class_Ozero(X18975)
| ~ class_Groups_Osgn__if(X18975) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18975),c_Groups_Ozero__class_Ozero(X18975)),X18974))
| c_Groups_Osgn__class_Osgn(X18975,X18974) = hAPP(c_Groups_Ouminus__class_Ouminus(X18975),c_Groups_Oone__class_Oone(X18975))
| X18974 = c_Groups_Ozero__class_Ozero(X18975)
| ~ class_Groups_Osgn__if(X18975) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5927])])]) ).
fof(i_0_9968,plain,
! [X32452,X32453] :
( ~ class_Groups_Ocomm__monoid__add(X32453)
| ~ hBOOL(hAPP(c_List_Odistinct(X32453),X32452))
| hAPP(c_List_Omonoid__add__class_Olistsum(X32453),X32452) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32453,X32453),c_COMBI(X32453)),hAPP(c_List_Oset(X32453),X32452)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__listsum__conv__Setsum])]) ).
fof(i_0_9969,plain,
! [X20723,X20724,X20725] :
( ~ class_Rings_Ocomm__semiring__1(X20725)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20725),X20724),hAPP(hAPP(c_Power_Opower__class_Opower(X20725),X20724),X20723)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20725),X20724),hAPP(c_Nat_OSuc,X20723)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).
fof(i_0_9970,plain,
! [X20942,X20943,X20944] :
( ~ class_Power_Opower(X20944)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20944),X20943),hAPP(c_Nat_OSuc,X20942)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20944),X20943),hAPP(hAPP(c_Power_Opower__class_Opower(X20944),X20943),X20942)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).
fof(i_0_9971,plain,
! [X20726,X20727,X20728] :
( ~ class_Rings_Ocomm__semiring__1(X20728)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20728),X20727),hAPP(c_Nat_OSuc,X20726)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20728),X20727),hAPP(hAPP(c_Power_Opower__class_Opower(X20728),X20727),X20726)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).
fof(i_0_9972,plain,
! [X24181,X24182] :
( ~ class_Groups_Oordered__ab__group__add(X24182)
| hAPP(c_Set_Oimage(X24182,X24182,c_Groups_Ouminus__class_Ouminus(X24182)),hAPP(c_SetInterval_Oord__class_OatLeast(X24182),X24181)) = hAPP(c_SetInterval_Oord__class_OatMost(X24182),hAPP(c_Groups_Ouminus__class_Ouminus(X24182),X24181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast])]) ).
fof(i_0_9973,plain,
! [X24179,X24180] :
( ~ class_Groups_Oordered__ab__group__add(X24180)
| hAPP(c_Set_Oimage(X24180,X24180,c_Groups_Ouminus__class_Ouminus(X24180)),hAPP(c_SetInterval_Oord__class_OatMost(X24180),X24179)) = hAPP(c_SetInterval_Oord__class_OatLeast(X24180),hAPP(c_Groups_Ouminus__class_Ouminus(X24180),X24179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost])]) ).
fof(i_0_9974,plain,
! [X23748,X23749] :
( ~ class_Groups_Oordered__ab__group__add(X23749)
| hAPP(c_Set_Oimage(X23749,X23749,c_Groups_Ouminus__class_Ouminus(X23749)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X23749),X23748)) = hAPP(c_SetInterval_Oord__class_OlessThan(X23749),hAPP(c_Groups_Ouminus__class_Ouminus(X23749),X23748)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan])]) ).
fof(i_0_9975,plain,
! [X23784,X23785] :
( ~ class_Groups_Oordered__ab__group__add(X23785)
| hAPP(c_Set_Oimage(X23785,X23785,c_Groups_Ouminus__class_Ouminus(X23785)),hAPP(c_SetInterval_Oord__class_OlessThan(X23785),X23784)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X23785),hAPP(c_Groups_Ouminus__class_Ouminus(X23785),X23784)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan])]) ).
cnf(i_0_9976,plain,
( c_List_Oupt(X2,X1) = c_List_Olist_ONil(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5928]) ).
cnf(i_0_9977,plain,
( c_List_Oupt(X2,X1) = c_List_Olist_ONil(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5929]) ).
cnf(i_0_9978,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
| c_List_Oupt(X1,X2) != c_List_Olist_ONil(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_5928]) ).
fof(i_0_9979,plain,
! [X19920,X19921] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19921))
| c_SMT_Oz3mod(X19920,X19921) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X19920,X19921) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19921))
| c_SMT_Oz3mod(X19920,X19921) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X19920,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19921)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5930])]) ).
fof(i_0_9980,plain,
! [X20666,X20667] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20667)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20667),c_Groups_Ozero__class_Ozero(X20667)),X20666))
| hAPP(c_Groups_Oabs__class_Oabs(X20667),X20666) = X20666 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).
fof(i_0_9981,plain,
! [X20676,X20677] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20677)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20677),c_Groups_Ozero__class_Ozero(X20677)),X20676))
| hAPP(c_Groups_Oabs__class_Oabs(X20677),X20676) = X20676 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).
fof(i_0_9982,plain,
! [X20805,X20806] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20806),X20805),c_Groups_Ozero__class_Ozero(X20806)))
| hAPP(c_Groups_Oabs__class_Oabs(X20806),X20805) = hAPP(c_Groups_Ouminus__class_Ouminus(X20806),X20805)
| ~ class_Groups_Oabs__if(X20806) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20806),X20805),c_Groups_Ozero__class_Ozero(X20806)))
| hAPP(c_Groups_Oabs__class_Oabs(X20806),X20805) = X20805
| ~ class_Groups_Oabs__if(X20806) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5931])])]) ).
fof(i_0_9983,plain,
! [X20801,X20802] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20802)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20802),X20801),c_Groups_Ozero__class_Ozero(X20802)))
| hAPP(c_Groups_Oabs__class_Oabs(X20802),X20801) = hAPP(c_Groups_Ouminus__class_Ouminus(X20802),X20801) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).
fof(i_0_9984,plain,
! [X20807,X20808] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20808)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20808),X20807),c_Groups_Ozero__class_Ozero(X20808)))
| hAPP(c_Groups_Oabs__class_Oabs(X20808),X20807) = hAPP(c_Groups_Ouminus__class_Ouminus(X20808),X20807) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])]) ).
fof(i_0_9985,plain,
! [X18978,X18979] :
( ( c_Groups_Osgn__class_Osgn(X18979,X18978) != hAPP(c_Groups_Ouminus__class_Ouminus(X18979),c_Groups_Oone__class_Oone(X18979))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18979),X18978),c_Groups_Ozero__class_Ozero(X18979)))
| ~ class_Rings_Olinordered__idom(X18979) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18979),X18978),c_Groups_Ozero__class_Ozero(X18979)))
| c_Groups_Osgn__class_Osgn(X18979,X18978) = hAPP(c_Groups_Ouminus__class_Ouminus(X18979),c_Groups_Oone__class_Oone(X18979))
| ~ class_Rings_Olinordered__idom(X18979) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])]) ).
fof(i_0_9986,plain,
! [X18976,X18977] :
( ~ class_Rings_Olinordered__idom(X18977)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18977),X18976),c_Groups_Ozero__class_Ozero(X18977)))
| c_Groups_Osgn__class_Osgn(X18977,X18976) = hAPP(c_Groups_Ouminus__class_Ouminus(X18977),c_Groups_Oone__class_Oone(X18977)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])]) ).
fof(i_0_9987,plain,
! [X27827,X27828,X27829,X27830] :
( ~ c_Equiv__Relations_Oequivp(X27830,X27829)
| ~ hBOOL(hAPP(hAPP(X27829,X27828),X27827))
| hBOOL(hAPP(hAPP(X27829,X27827),X27828)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__symp])]) ).
fof(i_0_9988,plain,
! [X23311,X23312,X23313] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23313),X23312),X23311))
| c_Divides_Odiv__class_Omod(X23313,X23311,X23312) = c_Groups_Ozero__class_Ozero(X23313)
| ~ class_Divides_Osemiring__div(X23313) )
& ( c_Divides_Odiv__class_Omod(X23313,X23311,X23312) != c_Groups_Ozero__class_Ozero(X23313)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23313),X23312),X23311))
| ~ class_Divides_Osemiring__div(X23313) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0])])]) ).
fof(i_0_9989,plain,
! [X23308,X23309,X23310] :
( ~ class_Divides_Osemiring__div(X23310)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23310),X23309),X23308))
| c_Divides_Odiv__class_Omod(X23310,X23308,X23309) = c_Groups_Ozero__class_Ozero(X23310) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__mod__0])]) ).
fof(i_0_9990,plain,
! [X33833,X33834] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33834)),c_List_Obutlast(X33834,X33833)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33834)),X33833)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_length__butlast]) ).
fof(i_0_9991,plain,
! [X19430] :
( ~ class_Rings_Olinordered__semidom(X19430)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19430),c_Groups_Oone__class_Oone(X19430)),c_Groups_Ozero__class_Ozero(X19430))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5932])]) ).
fof(i_0_9992,plain,
! [X18918] :
( ~ class_Rings_Olinordered__semidom(X18918)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18918),c_Groups_Oone__class_Oone(X18918)),c_Groups_Ozero__class_Ozero(X18918))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5933])]) ).
fof(i_0_9993,plain,
! [X20409,X20410] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20410),X20409))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20409),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20410),X20409)) = X20410 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5934])]) ).
fof(i_0_9994,plain,
! [X33676,X33677] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33677)),c_List_Olist_ONil(X33677)),c_List_Olists(X33677,X33676))),
inference(variable_rename,[status(thm)],[fact_lists_ONil]) ).
fof(i_0_9995,plain,
! [X19665,X19666] :
( ~ class_Rings_Olinordered__idom(X19666)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19666),c_Groups_Ozero__class_Ozero(X19666)),X19665))
| c_Groups_Osgn__class_Osgn(X19666,X19665) = c_Groups_Oone__class_Oone(X19666) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])]) ).
fof(i_0_9996,plain,
! [X18990,X18991] :
( ( c_Groups_Osgn__class_Osgn(X18991,X18990) != c_Groups_Oone__class_Oone(X18991)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18991),c_Groups_Ozero__class_Ozero(X18991)),X18990))
| ~ class_Rings_Olinordered__idom(X18991) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18991),c_Groups_Ozero__class_Ozero(X18991)),X18990))
| c_Groups_Osgn__class_Osgn(X18991,X18990) = c_Groups_Oone__class_Oone(X18991)
| ~ class_Rings_Olinordered__idom(X18991) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])]) ).
fof(i_0_9997,plain,
! [X21563,X21564,X21565] :
( ~ class_Rings_Odivision__ring(X21565)
| X21564 = c_Groups_Ozero__class_Ozero(X21565)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21565),hAPP(c_Groups_Ouminus__class_Ouminus(X21565),X21563)),hAPP(c_Groups_Ouminus__class_Ouminus(X21565),X21564)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21565),X21563),X21564) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide])]) ).
fof(i_0_9998,plain,
! [X33706] : c_List_Olists(X33706,c_Orderings_Obot__class_Obot(tc_fun(X33706,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X33706)),c_List_Olist_ONil(X33706)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X33706),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_lists__empty]) ).
fof(i_0_9999,plain,
! [X32592] : c_List_Olistset(X32592,c_List_Olist_ONil(tc_fun(X32592,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32592)),c_List_Olist_ONil(X32592)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32592),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_listset_Osimps_I1_J]) ).
fof(i_0_10000,plain,
! [X29146,X29147,X29148] :
( ~ hBOOL(hAPP(X29148,X29147))
| hBOOL(hAPP(hAPP(c_member(X29146),X29147),hAPP(c_Set_OCollect(X29146),X29148))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectI])]) ).
fof(i_0_10001,plain,
! [X34272,X34273] :
( ( ~ hBOOL(hAPP(c_List_Odistinct(X34273),hAPP(c_List_Orev(X34273),X34272)))
| hBOOL(hAPP(c_List_Odistinct(X34273),X34272)) )
& ( ~ hBOOL(hAPP(c_List_Odistinct(X34273),X34272))
| hBOOL(hAPP(c_List_Odistinct(X34273),hAPP(c_List_Orev(X34273),X34272))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rev])]) ).
fof(i_0_10002,plain,
! [X33360,X33361] :
( ( ~ hBOOL(hAPP(c_List_Odistinct(X33361),hAPP(c_List_Orotate1(X33361),X33360)))
| hBOOL(hAPP(c_List_Odistinct(X33361),X33360)) )
& ( ~ hBOOL(hAPP(c_List_Odistinct(X33361),X33360))
| hBOOL(hAPP(c_List_Odistinct(X33361),hAPP(c_List_Orotate1(X33361),X33360))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])]) ).
fof(i_0_10003,plain,
! [X26878,X26879] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X26879),c_Orderings_Obot__class_Obot(tc_fun(X26879,tc_HOL_Obool))),X26878) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26879,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_quotient__empty]) ).
fof(i_0_10004,plain,
! [X29464,X29465] : hAPP(c_Product__Type_Oprod_Oprod__case(X29465,X29464,tc_prod(X29465,X29464)),c_Product__Type_OPair(X29465,X29464)) = c_Fun_Oid(tc_prod(X29465,X29464)),
inference(variable_rename,[status(thm)],[fact_split__Pair]) ).
fof(i_0_10005,plain,
! [X27019,X27020,X27021] :
( ~ class_Lattices_Osemilattice__inf(X27021)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27021),X27020),X27019))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27021),X27020),X27019) = X27020 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb1])]) ).
fof(i_0_10006,plain,
! [X27004,X27005,X27006] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27006),X27005),X27004))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27006),X27005),X27004) = X27005
| ~ class_Lattices_Osemilattice__inf(X27006) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27006),X27005),X27004) != X27005
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27006),X27005),X27004))
| ~ class_Lattices_Osemilattice__inf(X27006) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])]) ).
fof(i_0_10007,plain,
! [X27022,X27023,X27024] :
( ~ class_Lattices_Osemilattice__inf(X27024)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27024),X27023),X27022))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27024),X27022),X27023) = X27023 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb2])]) ).
fof(i_0_10008,plain,
! [X24047,X24048,X24049] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24049),X24048),X24047))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24049),X24048),X24047) = X24047
| ~ class_Lattices_Osemilattice__sup(X24049) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24049),X24048),X24047) != X24047
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24049),X24048),X24047))
| ~ class_Lattices_Osemilattice__sup(X24049) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__sup])])]) ).
fof(i_0_10009,plain,
! [X24032,X24033,X24034] :
( ~ class_Lattices_Osemilattice__sup(X24034)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24034),X24033),X24032))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24034),X24033),X24032) = X24032 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb2])]) ).
fof(i_0_10010,plain,
! [X24029,X24030,X24031] :
( ~ class_Lattices_Osemilattice__sup(X24031)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24031),X24030),X24029))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24031),X24029),X24030) = X24029 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb1])]) ).
fof(i_0_10011,plain,
! [X22625,X22626,X22627] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22627),X22626),X22625))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22627),X22626),X22625) = X22625
| ~ class_Orderings_Olinorder(X22627) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X22627),X22626),X22625) != X22625
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22627),X22626),X22625))
| ~ class_Orderings_Olinorder(X22627) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup])])]) ).
fof(i_0_10012,plain,
! [X22610,X22611,X22612] :
( ~ class_Orderings_Olinorder(X22612)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22612),X22611),X22610))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22612),X22611),X22610) = X22610 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb2])]) ).
fof(i_0_10013,plain,
! [X22607,X22608,X22609] :
( ~ class_Orderings_Olinorder(X22609)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22609),X22608),X22607))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22609),X22607),X22608) = X22607 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb1])]) ).
fof(i_0_10014,plain,
! [X22296,X22297,X22298] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22298),X22297),X22296))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22298),X22297),X22296) = X22297
| ~ class_Orderings_Olinorder(X22298) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X22298),X22297),X22296) != X22297
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22298),X22297),X22296))
| ~ class_Orderings_Olinorder(X22298) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf])])]) ).
fof(i_0_10015,plain,
! [X22281,X22282,X22283] :
( ~ class_Orderings_Olinorder(X22283)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22283),X22282),X22281))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22283),X22282),X22281) = X22282 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb1])]) ).
fof(i_0_10016,plain,
! [X22278,X22279,X22280] :
( ~ class_Orderings_Olinorder(X22280)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22280),X22279),X22278))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22280),X22278),X22279) = X22279 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb2])]) ).
fof(i_0_10017,plain,
! [X31385,X31386] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31386)
| c_Complete__Lattice_OSup__class_OSup(X31386,hAPP(hAPP(c_Set_Oinsert(X31386),X31385),c_Orderings_Obot__class_Obot(tc_fun(X31386,tc_HOL_Obool)))) = X31385 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__singleton])]) ).
fof(i_0_10018,plain,
! [X31396,X31397] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31397)
| c_Complete__Lattice_OInf__class_OInf(X31397,hAPP(hAPP(c_Set_Oinsert(X31397),X31396),c_Orderings_Obot__class_Obot(tc_fun(X31397,tc_HOL_Obool)))) = X31396 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__singleton])]) ).
fof(i_0_10019,plain,
! [X27770,X27771] :
( ~ class_Lattices_Olattice(X27771)
| c_Big__Operators_Olattice__class_OInf__fin(X27771,hAPP(hAPP(c_Set_Oinsert(X27771),X27770),c_Orderings_Obot__class_Obot(tc_fun(X27771,tc_HOL_Obool)))) = X27770 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton])]) ).
fof(i_0_10020,plain,
! [X25825,X25826] :
( ~ class_Orderings_Olinorder(X25826)
| c_Big__Operators_Olinorder__class_OMin(X25826,hAPP(hAPP(c_Set_Oinsert(X25826),X25825),c_Orderings_Obot__class_Obot(tc_fun(X25826,tc_HOL_Obool)))) = X25825 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osingleton])]) ).
fof(i_0_10021,plain,
! [X25827,X25828] :
( ~ class_Orderings_Olinorder(X25828)
| c_Big__Operators_Olinorder__class_OMax(X25828,hAPP(hAPP(c_Set_Oinsert(X25828),X25827),c_Orderings_Obot__class_Obot(tc_fun(X25828,tc_HOL_Obool)))) = X25827 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osingleton])]) ).
fof(i_0_10022,plain,
! [X25728,X25729] :
( ~ class_Lattices_Olattice(X25729)
| c_Big__Operators_Olattice__class_OSup__fin(X25729,hAPP(hAPP(c_Set_Oinsert(X25729),X25728),c_Orderings_Obot__class_Obot(tc_fun(X25729,tc_HOL_Obool)))) = X25728 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton])]) ).
fof(i_0_10023,plain,
! [X19462,X19463] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19463)),X19462) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19463),X19462)),
inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).
fof(i_0_10024,plain,
! [X25717,X25718,X25719,X25720] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X25720,X25719,X25718)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X25720,X25717,X25719)
| c_Hoare__Mirabelle_Ohoare__derivs(X25720,X25717,X25718) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut])]) ).
cnf(i_0_10025,plain,
( c_Int_OBit1(X1) = c_Int_OMin
| X1 != c_Int_OMin ),
inference(split_conjunct,[status(thm)],[i_0_5865]) ).
cnf(i_0_10026,plain,
( c_Int_OMin = c_Int_OBit1(X1)
| c_Int_OMin != X1 ),
inference(split_conjunct,[status(thm)],[i_0_5864]) ).
cnf(i_0_10027,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2)) = c_List_Olist_ONil(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_5716]) ).
fof(i_0_10028,plain,
! [X20305,X20306] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20306),X20305)),X20306) = X20305,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
fof(i_0_10029,plain,
! [X20303,X20304] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20304),X20303)),X20303) = X20304,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).
fof(i_0_10030,plain,
! [X31271,X31272,X31273] :
( ~ c_Equiv__Relations_Oequiv(X31273,X31272,X31271)
| c_Complete__Lattice_OSup__class_OSup(tc_fun(X31273,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X31273),X31272),X31271)) = X31272 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__quotient])]) ).
fof(i_0_10031,plain,
! [X21455,X21456,X21457] :
( ~ class_Fields_Ofield__inverse__zero(X21457)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21457),hAPP(c_Groups_Ouminus__class_Ouminus(X21457),X21456)),hAPP(c_Groups_Ouminus__class_Ouminus(X21457),X21455)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21457),X21456),X21455) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__divide])]) ).
fof(i_0_10032,plain,
! [X20631,X20632] :
( ~ class_Rings_Olinordered__idom(X20632)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20632),hAPP(c_Groups_Oabs__class_Oabs(X20632),X20631)),hAPP(c_Groups_Oabs__class_Oabs(X20632),X20631)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20632),X20631),X20631) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).
fof(i_0_10033,plain,
! [X18647,X18648,X18649] :
( ~ class_Rings_Oring(X18649)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18649),hAPP(c_Groups_Ouminus__class_Ouminus(X18649),X18648)),hAPP(c_Groups_Ouminus__class_Ouminus(X18649),X18647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18649),X18648),X18647) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).
fof(i_0_10034,plain,
! [X18644,X18645,X18646] :
( ~ class_Rings_Oring(X18646)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18646),hAPP(c_Groups_Ouminus__class_Ouminus(X18646),X18645)),X18644) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18646),X18645),hAPP(c_Groups_Ouminus__class_Ouminus(X18646),X18644)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).
fof(i_0_10035,plain,
! [X29788,X29789,X29790,X29791,X29792] :
( ( ~ c_Wellfounded_OwfP(X29789,X29788)
| hBOOL(hAPP(c_Wellfounded_Oaccp(X29789,X29788),X29790)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X29792,X29791),esk326_2(X29791,X29792)))
| c_Wellfounded_OwfP(X29792,X29791) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__accp__iff])])])])]) ).
fof(i_0_10036,plain,
! [X21566,X21567,X21568] :
( ~ class_Rings_Odivision__ring(X21568)
| X21567 = c_Groups_Ozero__class_Ozero(X21568)
| hAPP(c_Groups_Ouminus__class_Ouminus(X21568),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21568),X21566),X21567)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21568),X21566),hAPP(c_Groups_Ouminus__class_Ouminus(X21568),X21567)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right])]) ).
cnf(i_0_10037,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)),
inference(split_conjunct,[status(thm)],[i_0_5935]) ).
fof(i_0_10038,plain,
! [X26880,X26881,X26882] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26882,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X26882),X26881),X26880)
| X26881 = c_Orderings_Obot__class_Obot(tc_fun(X26882,tc_HOL_Obool)) )
& ( X26881 != c_Orderings_Obot__class_Obot(tc_fun(X26882,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26882,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X26882),X26881),X26880) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2])]) ).
fof(i_0_10039,plain,
! [X26883,X26884,X26885] :
( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X26885),X26884),X26883) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26885,tc_HOL_Obool),tc_HOL_Obool))
| X26884 = c_Orderings_Obot__class_Obot(tc_fun(X26885,tc_HOL_Obool)) )
& ( X26884 != c_Orderings_Obot__class_Obot(tc_fun(X26885,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X26885),X26884),X26883) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26885,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty])]) ).
fof(i_0_10040,plain,
! [X23750,X23751] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X23751,X23750)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23750),X23751)),
inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost__int]) ).
fof(i_0_10041,plain,
! [X18558,X18559,X18560] :
( ( X18559 = X18558
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18560),X18559),X18558))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18560),X18558),X18559))
| ~ class_Orderings_Olinorder(X18560) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18560),X18559),X18558))
| X18559 != X18558
| ~ class_Orderings_Olinorder(X18560) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18560),X18558),X18559))
| X18559 != X18558
| ~ class_Orderings_Olinorder(X18560) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_10042,plain,
! [X18570,X18571,X18572] :
( ~ class_Orderings_Olinorder(X18572)
| X18571 = X18570
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18572),X18571),X18570))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18572),X18570),X18571)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5936])]) ).
fof(i_0_10043,plain,
! [X18567,X18568,X18569] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18569),X18567),X18568))
| X18567 = X18568
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18569),X18568),X18567))
| ~ class_Orderings_Olinorder(X18569) )
& ( X18567 != X18568
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18569),X18567),X18568))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18569),X18568),X18567))
| ~ class_Orderings_Olinorder(X18569) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5937])])]) ).
fof(i_0_10044,plain,
! [X18564,X18565,X18566] :
( ~ class_Orderings_Olinorder(X18566)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18566),X18565),X18564))
| X18565 = X18564
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18566),X18564),X18565)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_10045,plain,
! [X18518,X18519,X18520] :
( ~ class_Orderings_Olinorder(X18520)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18520),X18519),X18518))
| X18519 = X18518
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18520),X18518),X18519)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5938])]) ).
fof(i_0_10046,plain,
! [X18401,X18402,X18403] :
( ~ class_Rings_Olinordered__idom(X18403)
| X18402 = X18401
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18403),X18402),X18401))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18403),X18401),X18402)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5939])]) ).
fof(i_0_10047,plain,
! [X19756,X19757,X19758] :
( ~ class_Divides_Osemiring__div(X19758)
| c_Divides_Odiv__class_Omod(X19758,c_Divides_Odiv__class_Omod(X19758,X19757,X19756),X19756) = c_Divides_Odiv__class_Omod(X19758,X19757,X19756) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])]) ).
fof(i_0_10048,plain,
! [X27142,X27143] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27143,tc_HOL_Obool)),X27142),c_Orderings_Obot__class_Obot(tc_fun(X27143,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X27143,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Int__empty__right]) ).
fof(i_0_10049,plain,
! [X24311,X24312] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24312,tc_HOL_Obool)),X24311),c_Orderings_Otop__class_Otop(tc_fun(X24312,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X24312,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Un__UNIV__right]) ).
fof(i_0_10050,plain,
! [X24770,X24771] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24771,tc_HOL_Obool)),X24770),c_Orderings_Otop__class_Otop(tc_fun(X24771,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X24771,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__UNIV]) ).
fof(i_0_10051,plain,
! [X29805,X29806] : hAPP(c_Relation_ODomain(X29806,X29805),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29806,X29805),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X29806,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Domain__empty]) ).
fof(i_0_10052,plain,
! [X29718,X29719] : hAPP(c_Relation_ORange(X29719,X29718),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29719,X29718),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X29718,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Range__empty]) ).
fof(i_0_10053,plain,
! [X26028,X26029,X26030,X26031] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26031,X26030),X26029),X26028),hAPP(X26029,X26028)) = X26029,
inference(variable_rename,[status(thm)],[fact_fun__upd__triv]) ).
fof(i_0_10054,plain,
! [X22364,X22365,X22366,X22367] : hAPP(c_Product__Type_Ofst(X22367,X22366),hAPP(hAPP(c_Product__Type_OPair(X22367,X22366),X22365),X22364)) = X22365,
inference(variable_rename,[status(thm)],[fact_fst__conv]) ).
fof(i_0_10055,plain,
! [X22153,X22154,X22155,X22156] : hAPP(c_Product__Type_Osnd(X22156,X22155),hAPP(hAPP(c_Product__Type_OPair(X22156,X22155),X22154),X22153)) = X22153,
inference(variable_rename,[status(thm)],[fact_snd__conv]) ).
cnf(i_0_10056,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_minus__Min]) ).
fof(i_0_10057,plain,
! [X19280,X19281,X19283,X19284,X19285] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19281),X19280))
| X19280 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19281),esk43_2(X19280,X19281)) )
& ( X19283 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19284),X19285)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19284),X19283)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__add])])])])]) ).
fof(i_0_10058,plain,
! [X25179,X25180,X25181] :
( ~ hBOOL(hAPP(hAPP(c_member(X25181),X25180),X25179))
| hAPP(hAPP(c_Set_Oinsert(X25181),X25180),X25179) = X25179 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(i_0_10059,plain,
! [X24905,X24906] : c_Set_Othe__elem(X24906,hAPP(hAPP(c_Set_Oinsert(X24906),X24905),c_Orderings_Obot__class_Obot(tc_fun(X24906,tc_HOL_Obool)))) = X24905,
inference(variable_rename,[status(thm)],[fact_the__elem__eq]) ).
fof(i_0_10060,plain,
! [X19087,X19088,X19089] :
( ~ class_Orderings_Olinorder(X19089)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19089),X19088),X19087))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19089),X19087),X19088)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_10061,plain,
! [X19035,X19036,X19037] :
( ~ class_Orderings_Olinorder(X19037)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19037),X19036),X19035))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19037),X19035),X19036)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5940])]) ).
fof(i_0_10062,plain,
! [X19134,X19135,X19136] :
( ~ class_Orderings_Olinorder(X19136)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19136),X19135),X19134))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19136),X19134),X19135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5941])]) ).
fof(i_0_10063,plain,
! [X19137,X19138,X19139] :
( ~ class_Orderings_Olinorder(X19139)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19139),X19138),X19137))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19139),X19137),X19138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5942])]) ).
fof(i_0_10064,plain,
! [X19122,X19123,X19124] :
( ~ class_Orderings_Olinorder(X19124)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19124),X19123),X19122))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19124),X19122),X19123)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_10065,plain,
! [X26096,X26097,X26098,X26099,X26100] :
( hAPP(X26100,X26099) != X26098
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26097,X26096),X26100),X26099),X26098) = X26100 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem])]) ).
cnf(i_0_10066,plain,
hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,X2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_5943]) ).
cnf(i_0_10067,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_5944]) ).
fof(i_0_10068,plain,
! [X32420,X32421,X32422] :
( ~ class_Groups_Omonoid__add(X32422)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32422),hAPP(hAPP(c_List_Olist_OCons(X32422),X32421),X32420)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32422),X32421),hAPP(c_List_Omonoid__add__class_Olistsum(X32422),X32420)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I2_J])]) ).
fof(i_0_10069,plain,
! [X21452,X21453,X21454] :
( ~ class_Fields_Ofield__inverse__zero(X21454)
| hAPP(c_Groups_Ouminus__class_Ouminus(X21454),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21454),X21453),X21452)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21454),X21453),hAPP(c_Groups_Ouminus__class_Ouminus(X21454),X21452)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])]) ).
fof(i_0_10070,plain,
! [X18638,X18639,X18640] :
( ~ class_Rings_Oring(X18640)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18640),X18639),X18638)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18640),X18639),hAPP(c_Groups_Ouminus__class_Ouminus(X18640),X18638)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).
fof(i_0_10071,plain,
! [X18005,X18006,X18007] : c_Option_Ooption_Ooption__size(X18007,X18006,hAPP(c_Option_Ooption_OSome(X18007),X18005)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X18006,X18005)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_option_Osize_I2_J]) ).
fof(i_0_10072,plain,
! [X33948,X33949] : c_List_Opartition(X33949,X33948,c_List_Olist_ONil(X33949)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33949),tc_List_Olist(X33949)),c_List_Olist_ONil(X33949)),c_List_Olist_ONil(X33949)),
inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J]) ).
cnf(i_0_10073,plain,
c_Int_Osucc(c_Int_Opred(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_5945]) ).
fof(i_0_10074,plain,
! [X33128,X33129,X33130] : hAPP(hAPP(c_List_Otake(X33130),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X33130),X33129),X33128)) = hAPP(hAPP(c_List_Olist_OCons(X33130),X33129),c_List_Olist_ONil(X33130)),
inference(variable_rename,[status(thm)],[fact_take__1__Cons]) ).
fof(i_0_10075,plain,
! [X29584,X29585,X29586,X29587] :
( ~ c_Wellfounded_Owf(X29587,X29586)
| c_Wellfounded_Owf(X29585,hAPP(hAPP(c_Relation_Oinv__image(X29587,X29585),X29586),X29584)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__inv__image])]) ).
fof(i_0_10076,plain,
! [X26385,X26386,X26387,X26388] :
( ~ c_FunDef_Oreduction__pair(X26388,X26387)
| c_FunDef_Oreduction__pair(X26386,hAPP(hAPP(c_FunDef_Orp__inv__image(X26388,X26386),X26387),X26385)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp])]) ).
fof(i_0_10077,plain,
! [X23059,X23060] :
( ~ class_Rings_Ocomm__semiring__1(X23060)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23060),c_Groups_Ozero__class_Ozero(X23060)),X23059))
| X23059 = c_Groups_Ozero__class_Ozero(X23060) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__left])]) ).
fof(i_0_10078,plain,
! [X19791,X19792,X19793] :
( ~ class_Divides_Osemiring__div(X19793)
| c_Divides_Odiv__class_Omod(X19793,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19793),X19792),X19791),X19792) = c_Divides_Odiv__class_Omod(X19793,X19791,X19792) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])]) ).
fof(i_0_10079,plain,
! [X19794,X19795,X19796] :
( ~ class_Divides_Osemiring__div(X19796)
| c_Divides_Odiv__class_Omod(X19796,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19796),X19795),X19794),X19794) = c_Divides_Odiv__class_Omod(X19796,X19795,X19794) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self2])]) ).
fof(i_0_10080,plain,
! [X33326,X33327,X33328,X33329,X33330] :
( hAPP(hAPP(c_List_Odrop(X33330),X33329),X33328) != hAPP(hAPP(c_List_Olist_OCons(X33330),X33327),X33326)
| hAPP(hAPP(c_List_Onth(X33330),X33328),X33329) = X33327 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__via__drop])]) ).
fof(i_0_10081,plain,
! [X22670,X22671] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22671)),hAPP(c_Nat_OSuc,X22670)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22671),X22670)),
inference(variable_rename,[status(thm)],[fact_max__Suc__Suc]) ).
fof(i_0_10082,plain,
! [X22255,X22256] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22256)),hAPP(c_Nat_OSuc,X22255)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22256),X22255)),
inference(variable_rename,[status(thm)],[fact_min__Suc__Suc]) ).
fof(i_0_10083,plain,
! [X21849,X21850] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21850)),hAPP(c_Code__Numeral_Oof__nat,X21849)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21850),X21849)),
inference(variable_rename,[status(thm)],[fact_times__code__numeral__code]) ).
fof(i_0_10084,plain,
! [X21877,X21878] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21878)),hAPP(c_Code__Numeral_Oof__nat,X21877)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21878),X21877)),
inference(variable_rename,[status(thm)],[fact_plus__code__numeral__code]) ).
fof(i_0_10085,plain,
! [X20878,X20879] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20879)),X20878) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20879),X20878)),
inference(variable_rename,[status(thm)],[fact_zpower__int]) ).
fof(i_0_10086,plain,
! [X20876,X20877] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20877)),X20876) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20877),X20876)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).
fof(i_0_10087,plain,
! [X18683,X18684] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18684)),X18683) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18684),X18683)),
inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).
fof(i_0_10088,plain,
! [X20880,X20881] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20881),X20880)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20881)),X20880),
inference(variable_rename,[status(thm)],[fact_int__power]) ).
cnf(i_0_10089,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_Osucc(X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5946]) ).
fof(i_0_10090,plain,
! [X20670,X20671] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20671)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20671),c_Groups_Ozero__class_Ozero(X20671)),hAPP(c_Groups_Oabs__class_Oabs(X20671),X20670))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).
fof(i_0_10091,plain,
! [X19443,X19444] :
( ~ class_Rings_Olinordered__semidom(X19444)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19444),c_Groups_Ozero__class_Ozero(X19444)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19444),X19443))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__le__iff])]) ).
fof(i_0_10092,plain,
! [X19441,X19442] :
( ~ class_Rings_Olinordered__semidom(X19442)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19442),c_Groups_Ozero__class_Ozero(X19442)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19442),X19441))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__imp__of__nat])]) ).
fof(i_0_10093,plain,
! [X27220,X27221,X27222] :
( ~ class_Lattices_Osemilattice__inf(X27222)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27222),X27221),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27222),X27221),X27220)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27222),X27221),X27220) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])]) ).
fof(i_0_10094,plain,
! [X27214,X27215,X27216] :
( ~ class_Lattices_Osemilattice__inf(X27216)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27216),X27215),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27216),X27215),X27214)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27216),X27215),X27214) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])]) ).
fof(i_0_10095,plain,
! [X27217,X27218,X27219] :
( ~ class_Lattices_Olattice(X27219)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27219),X27218),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27219),X27218),X27217)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27219),X27218),X27217) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])]) ).
fof(i_0_10096,plain,
! [X23943,X23944,X23945] :
( ~ class_Lattices_Osemilattice__sup(X23945)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23945),X23944),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23945),X23944),X23943)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23945),X23944),X23943) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__idem])]) ).
fof(i_0_10097,plain,
! [X23937,X23938,X23939] :
( ~ class_Lattices_Osemilattice__sup(X23939)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23939),X23938),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23939),X23938),X23937)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23939),X23938),X23937) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__idem])]) ).
fof(i_0_10098,plain,
! [X23940,X23941,X23942] :
( ~ class_Lattices_Olattice(X23942)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23942),X23941),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23942),X23941),X23940)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23942),X23941),X23940) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J])]) ).
fof(i_0_10099,plain,
! [X22651,X22652,X22653] :
( ~ class_Orderings_Olinorder(X22653)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22653),X22652),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22653),X22652),X22651)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22653),X22652),X22651) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__idem])]) ).
fof(i_0_10100,plain,
! [X22648,X22649,X22650] :
( ~ class_Orderings_Olinorder(X22650)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22650),X22649),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22650),X22649),X22648)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22650),X22649),X22648) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__idem])]) ).
fof(i_0_10101,plain,
! [X22322,X22323,X22324] :
( ~ class_Orderings_Olinorder(X22324)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22324),X22323),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22324),X22323),X22322)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22324),X22323),X22322) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__idem])]) ).
fof(i_0_10102,plain,
! [X22319,X22320,X22321] :
( ~ class_Orderings_Olinorder(X22321)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22321),X22320),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22321),X22320),X22319)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22321),X22320),X22319) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__idem])]) ).
fof(i_0_10103,plain,
! [X19898,X19899,X19900] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X19900)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19900),X19899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19900),X19899),X19898)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19900),X19899),X19898) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).
fof(i_0_10104,plain,
! [X33479,X33480,X33481] : hAPP(hAPP(c_List_Odrop(X33481),X33480),hAPP(c_List_Otl(X33481),X33479)) = hAPP(c_List_Otl(X33481),hAPP(hAPP(c_List_Odrop(X33481),X33480),X33479)),
inference(variable_rename,[status(thm)],[fact_drop__tl]) ).
fof(i_0_10105,plain,
! [X33476,X33477,X33478] : hAPP(c_List_Otl(X33478),hAPP(hAPP(c_List_Odrop(X33478),X33477),X33476)) = hAPP(hAPP(c_List_Odrop(X33478),X33477),hAPP(c_List_Otl(X33478),X33476)),
inference(variable_rename,[status(thm)],[fact_tl__drop]) ).
fof(i_0_10106,plain,
! [X32297,X32298,X32299] : hAPP(c_List_Oset(X32299),hAPP(hAPP(c_List_Olist_OCons(X32299),X32298),X32297)) = hAPP(hAPP(c_Set_Oinsert(X32299),X32298),hAPP(c_List_Oset(X32299),X32297)),
inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I2_J]) ).
fof(i_0_10107,plain,
! [X23813,X23814] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23814,X23813)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X23813)),X23814),
inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost]) ).
fof(i_0_10108,plain,
! [X25036,X25037,X25038] :
( X25038 != c_Orderings_Obot__class_Obot(tc_fun(X25037,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25037),X25036),X25038)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5947])]) ).
fof(i_0_10109,plain,
! [X29451] : hAPP(c_Set_Oimage(X29451,X29451,c_Fun_Oid(X29451)),c_Orderings_Otop__class_Otop(tc_fun(X29451,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X29451,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_surj__id]) ).
fof(i_0_10110,plain,
! [X30018,X30019,X30021,X30022,X30023] :
( ( ~ hBOOL(hAPP(X30019,c_Hilbert__Choice_OEps(X30018,X30019)))
| hBOOL(hAPP(X30019,esk350_2(X30018,X30019))) )
& ( ~ hBOOL(hAPP(X30022,X30023))
| hBOOL(hAPP(X30022,c_Hilbert__Choice_OEps(X30021,X30022))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_some__eq__ex])])])])]) ).
fof(i_0_10111,plain,
! [X33907,X33908,X33909] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X33909),tc_List_Olist(X33909)),c_List_Opartition(X33909,X33908,X33907)) = hAPP(c_List_Ofilter(X33909,X33908),X33907),
inference(variable_rename,[status(thm)],[fact_partition__filter1]) ).
fof(i_0_10112,plain,
! [X21019] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X21019))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21019)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21019))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X21019)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5948])]) ).
fof(i_0_10113,plain,
! [X23046] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X23046)),
inference(variable_rename,[status(thm)],[fact_dvd__1__left]) ).
fof(i_0_10114,plain,
! [X25819,X25820] : hBOOL(hAPP(hAPP(c_member(X25820),X25819),c_Orderings_Otop__class_Otop(tc_fun(X25820,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(i_0_10115,plain,
! [X24955,X24956] : hBOOL(hAPP(hAPP(c_member(X24956),X24955),c_Orderings_Otop__class_Otop(tc_fun(X24956,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(i_0_10116,plain,
! [X19653,X19654] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19654))
| X19654 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19653)
| hAPP(c_Int_Onat,X19654) != X19653 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19654))
| X19653 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Int_Onat,X19654) != X19653 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19654))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19654))
| hAPP(c_Int_Onat,X19654) = X19653 )
& ( X19653 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19654))
| hAPP(c_Int_Onat,X19654) = X19653 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19654))
| X19654 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19653)
| hAPP(c_Int_Onat,X19654) = X19653 )
& ( X19653 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19654 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19653)
| hAPP(c_Int_Onat,X19654) = X19653 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5949])])]) ).
fof(i_0_10117,plain,
! [X19655,X19656] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19655))
| X19655 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19656)
| X19656 != hAPP(c_Int_Onat,X19655) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19655))
| X19656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19656 != hAPP(c_Int_Onat,X19655) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19655))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19655))
| X19656 = hAPP(c_Int_Onat,X19655) )
& ( X19656 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19655))
| X19656 = hAPP(c_Int_Onat,X19655) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19655))
| X19655 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19656)
| X19656 = hAPP(c_Int_Onat,X19655) )
& ( X19656 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19655 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19656)
| X19656 = hAPP(c_Int_Onat,X19655) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5950])])]) ).
fof(i_0_10118,plain,
! [X22514,X22515,X22516] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22516,tc_HOL_Obool)),X22515) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22516,tc_HOL_Obool)),X22514)
| X22515 = X22514 )
& ( X22515 != X22514
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22516,tc_HOL_Obool)),X22515) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22516,tc_HOL_Obool)),X22514) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff])]) ).
fof(i_0_10119,plain,
! [X21836,X21837,X21838,X21839] :
( ~ class_Groups_Ouminus(X21839)
| hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21838,X21839)),X21837),X21836) = hAPP(c_Groups_Ouminus__class_Ouminus(X21839),hAPP(X21837,X21836)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__Compl__def])]) ).
fof(i_0_10120,plain,
! [X19903,X19904,X19905,X19906] :
( ~ class_Groups_Ouminus(X19906)
| hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19905,X19906)),X19904),X19903) = hAPP(c_Groups_Ouminus__class_Ouminus(X19906),hAPP(X19904,X19903)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).
fof(i_0_10121,plain,
! [X19633] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19633))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X19633)) = X19633 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19633))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X19633)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5951])]) ).
fof(i_0_10122,plain,
! [X19630] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19630))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X19630)) = X19630 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__le])]) ).
fof(i_0_10123,plain,
! [X20556,X20557] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20557),X20556))
| c_Nat__Transfer_Otsub(X20556,X20557) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20556),X20557) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20557),X20556))
| c_Nat__Transfer_Otsub(X20556,X20557) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5952])]) ).
fof(i_0_10124,plain,
! [X20463,X20464] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20464),X20463))
| c_Nat__Transfer_Otsub(X20463,X20464) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20463),X20464) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tsub__eq])]) ).
fof(i_0_10125,plain,
! [X21890,X21891] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X21891)),hAPP(c_Code__Numeral_Oof__nat,X21890)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21891),X21890)),
inference(variable_rename,[status(thm)],[fact_subtract__code__numeral__code]) ).
fof(i_0_10126,plain,
! [X31685,X31686] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X31686,X31685) = c_Smallcheck_Ofull__small_H(X31686,hAPP(c_Code__Numeral_Oint__of,X31685),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X31685))),
inference(variable_rename,[status(thm)],[fact_full__small__int__def]) ).
fof(i_0_10127,plain,
! [X19631,X19632] :
( ( X19632 = hAPP(c_Int_Onat,X19631)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19632) != X19631 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19631))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19632) != X19631 )
& ( X19632 != hAPP(c_Int_Onat,X19631)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19631))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19632) = X19631 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff])])]) ).
fof(i_0_10128,plain,
! [X29085,X29086,X29087,X29088] :
( ~ c_Big__Operators_Osemilattice__big(X29088,X29087,X29086)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29088),X29085))
| hAPP(X29086,X29085) = hAPP(c_Finite__Set_Ofold1(X29088,X29087),X29085) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq])]) ).
fof(i_0_10129,plain,
! [X29023,X29024,X29025,X29026] :
( ~ c_Finite__Set_Ofolding__one(X29026,X29025,X29024)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29026),X29023))
| hAPP(X29024,X29023) = hAPP(c_Finite__Set_Ofold1(X29026,X29025),X29023) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold])]) ).
fof(i_0_10130,plain,
! [X21040,X21041] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21040)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21041),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21040)) = c_Groups_Ozero__class_Ozero(X21041)
| ~ class_Int_Onumber__ring(X21041) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21040)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21041),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21040)) = hAPP(c_Int_Onumber__class_Onumber__of(X21041),X21040)
| ~ class_Int_Onumber__ring(X21041) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5953])])]) ).
fof(i_0_10131,plain,
! [X31307] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31307,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31307,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X31307,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Union__empty]) ).
fof(i_0_10132,plain,
! [X31359] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31359,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X31359,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X31359,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Union__UNIV]) ).
fof(i_0_10133,plain,
! [X31265] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31265,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31265,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X31265,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Inter__empty]) ).
fof(i_0_10134,plain,
! [X31377] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31377,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X31377,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X31377,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Inter__UNIV]) ).
cnf(i_0_10135,plain,
( X1 = X2
| c_List_Oupt(X1,X3) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_5666]) ).
fof(i_0_10136,plain,
! [X24425,X24426,X24427] : hAPP(hAPP(c_Set_Oinsert(X24427),X24426),hAPP(hAPP(c_Set_Oinsert(X24427),X24426),X24425)) = hAPP(hAPP(c_Set_Oinsert(X24427),X24426),X24425),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
cnf(i_0_10137,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(split_conjunct,[status(thm)],[fact_Bit1__Min]) ).
fof(i_0_10138,plain,
! [X30947,X30948,X30949,X30950] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X30950)
| X30949 = c_Orderings_Obot__class_Obot(tc_fun(X30948,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30948,X30950),X30949),hAPP(c_COMBK(X30950,X30948),X30947)) = X30947 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__const])]) ).
fof(i_0_10139,plain,
! [X24672,X24673,X24674,X24675] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X24675)
| X24674 = c_Orderings_Obot__class_Obot(tc_fun(X24673,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24673,X24675),X24674),hAPP(c_COMBK(X24675,X24673),X24672)) = X24672 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__const])]) ).
fof(i_0_10140,plain,
! [X27516,X27517,X27518] :
( ~ class_Lattices_Oboolean__algebra(X27518)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27518),X27517),X27516) != c_Orderings_Obot__class_Obot(X27518)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27518),X27517),X27516) != c_Orderings_Otop__class_Otop(X27518)
| hAPP(c_Groups_Ouminus__class_Ouminus(X27518),X27517) = X27516 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__unique])]) ).
fof(i_0_10141,plain,
! [X19464,X19465] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19465),hAPP(c_Nat_OSuc,X19464)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19465),X19464)),
inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).
cnf(i_0_10142,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_5954]) ).
fof(i_0_10143,plain,
! [X24468] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24468))),
inference(variable_rename,[status(thm)],[fact_finite__atLeastZeroLessThan__int]) ).
fof(i_0_10144,plain,
! [X33991,X33992] : c_List_Otranspose(X33992,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X33992)),c_List_Olist_ONil(X33992)),X33991)) = c_List_Otranspose(X33992,X33991),
inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I2_J]) ).
fof(i_0_10145,plain,
! [X33895,X33896,X33897,X33898] :
( hBOOL(hAPP(X33898,X33897))
| c_List_Oremove1(X33896,X33897,hAPP(c_List_Ofilter(X33896,X33898),X33895)) = hAPP(c_List_Ofilter(X33896,X33898),X33895) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5955])]) ).
fof(i_0_10146,plain,
! [X26428] : hAPP(c_Relation_OField(X26428),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X26428,X26428),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X26428,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Field__empty]) ).
fof(i_0_10147,plain,
! [X19980,X19981] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19981),X19980))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19981,X19980) = X19981 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less])]) ).
fof(i_0_10148,plain,
! [X23780,X23781] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23781),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23780) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X23781,X23780),
inference(variable_rename,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int]) ).
fof(i_0_10149,plain,
! [X31387,X31388,X31389] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31389)
| c_Complete__Lattice_OSup__class_OSup(X31389,hAPP(hAPP(c_Set_Oinsert(X31389),X31388),X31387)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X31389),X31388),c_Complete__Lattice_OSup__class_OSup(X31389,X31387)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__insert])]) ).
fof(i_0_10150,plain,
! [X31400,X31401,X31402] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31402)
| c_Complete__Lattice_OInf__class_OInf(X31402,hAPP(hAPP(c_Set_Oinsert(X31402),X31401),X31400)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31402),X31401),c_Complete__Lattice_OInf__class_OInf(X31402,X31400)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__insert])]) ).
fof(i_0_10151,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__int]) ).
fof(i_0_10152,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__nat]) ).
fof(i_0_10153,plain,
! [X31693,X31694] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X31694),X31693) = c_Smallcheck_Osmall_H(X31694,hAPP(c_Code__Numeral_Oint__of,X31693),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X31693))),
inference(variable_rename,[status(thm)],[fact_small__int__def]) ).
fof(i_0_10154,plain,
! [X33814,X33815,X33816] :
( ( X33816 != c_List_Olist_ONil(X33815)
| c_List_Obutlast(X33815,hAPP(hAPP(c_List_Oappend(X33815),X33814),X33816)) = c_List_Obutlast(X33815,X33814) )
& ( X33816 = c_List_Olist_ONil(X33815)
| c_List_Obutlast(X33815,hAPP(hAPP(c_List_Oappend(X33815),X33814),X33816)) = hAPP(hAPP(c_List_Oappend(X33815),X33814),c_List_Obutlast(X33815,X33816)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__append])]) ).
fof(i_0_10155,plain,
! [X33811,X33812,X33813] :
( ( X33813 != c_List_Olist_ONil(X33812)
| c_List_Obutlast(X33812,hAPP(hAPP(c_List_Olist_OCons(X33812),X33811),X33813)) = c_List_Olist_ONil(X33812) )
& ( X33813 = c_List_Olist_ONil(X33812)
| c_List_Obutlast(X33812,hAPP(hAPP(c_List_Olist_OCons(X33812),X33811),X33813)) = hAPP(hAPP(c_List_Olist_OCons(X33812),X33811),c_List_Obutlast(X33812,X33813)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J])]) ).
fof(i_0_10156,plain,
! [X28317,X28318,X28319] : hAPP(c_Set_Ovimage(X28319,X28318,X28317),c_Orderings_Obot__class_Obot(tc_fun(X28318,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X28319,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_vimage__empty]) ).
fof(i_0_10157,plain,
! [X28343,X28344,X28345] : hAPP(c_Set_Ovimage(X28345,X28344,X28343),c_Orderings_Otop__class_Otop(tc_fun(X28344,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X28345,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_vimage__UNIV]) ).
fof(i_0_10158,plain,
! [X26586,X26587,X26588] : hAPP(c_Relation_OImage(X26588,X26587,X26586),c_Orderings_Obot__class_Obot(tc_fun(X26588,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X26587,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Image__empty]) ).
fof(i_0_10159,plain,
! [X24660,X24661,X24662] : hAPP(c_Set_Oimage(X24662,X24661,X24660),c_Orderings_Obot__class_Obot(tc_fun(X24662,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X24661,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_image__empty]) ).
fof(i_0_10160,plain,
! [X33678,X33679,X33680] :
( ~ c_Relation_Orefl__on(X33680,X33679,X33678)
| c_Relation_Orefl__on(tc_List_Olist(X33680),c_List_Olists(X33680,X33679),c_List_Olistrel(X33680,X33678)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__refl__on])]) ).
fof(i_0_10161,plain,
! [X33681,X33682,X33683] :
( ~ c_Equiv__Relations_Oequiv(X33683,X33682,X33681)
| c_Equiv__Relations_Oequiv(tc_List_Olist(X33683),c_List_Olists(X33683,X33682),c_List_Olistrel(X33683,X33681)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__listrel])]) ).
fof(i_0_10162,plain,
! [X25126,X25127,X25128] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25128),X25127),X25126))
| hBOOL(hAPP(X25126,X25127)) )
& ( ~ hBOOL(hAPP(X25126,X25127))
| hBOOL(hAPP(hAPP(c_member(X25128),X25127),X25126)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_10163,plain,
! [X18107,X18108,X18109] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X18109,X18108,X18107)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X18107)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_com_Osize_I3_J]) ).
fof(i_0_10164,plain,
! [X23168,X23169,X23170,X23171] :
( ~ class_Rings_Odvd(X23171)
| X23170 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23171),X23169),X23168)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23171),X23169),X23170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvdI])]) ).
cnf(i_0_10165,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_5956]) ).
fof(i_0_10166,plain,
! [X20404,X20405] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20405),X20404) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20405),X20404)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20405),X20404))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20405),X20404) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])]) ).
fof(i_0_10167,plain,
! [X20402,X20403] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20403),X20402))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20403),X20402) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H])]) ).
fof(i_0_10168,plain,
! [X20005,X20006] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20006),X20005))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20006),X20005) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])]) ).
fof(i_0_10169,plain,
! [X27072,X27073] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27073,tc_HOL_Obool)),X27072),c_Orderings_Otop__class_Otop(tc_fun(X27073,tc_HOL_Obool))) = X27072,
inference(variable_rename,[status(thm)],[fact_Int__UNIV__right]) ).
fof(i_0_10170,plain,
! [X24634,X24635] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24635,tc_HOL_Obool)),X24634),c_Orderings_Obot__class_Obot(tc_fun(X24635,tc_HOL_Obool))) = X24634,
inference(variable_rename,[status(thm)],[fact_Un__empty__right]) ).
fof(i_0_10171,plain,
! [X24652,X24653] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24653,tc_HOL_Obool)),X24652),c_Orderings_Obot__class_Obot(tc_fun(X24653,tc_HOL_Obool))) = X24652,
inference(variable_rename,[status(thm)],[fact_Diff__empty]) ).
fof(i_0_10172,plain,
! [X22512,X22513] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22513,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22513,tc_HOL_Obool)),X22512)) = X22512,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
fof(i_0_10173,plain,
! [X30474,X30475] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30475,X30475),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X30474) = X30474,
inference(variable_rename,[status(thm)],[fact_rel__pow__1]) ).
fof(i_0_10174,plain,
! [X28477,X28478] : c_Map_Odom(X28478,X28477,hAPP(c_COMBK(tc_Option_Ooption(X28477),X28478),c_Option_Ooption_ONone(X28477))) = c_Orderings_Obot__class_Obot(tc_fun(X28478,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_dom__empty]) ).
fof(i_0_10175,plain,
! [X26296,X26297] : c_Map_Oran(X26297,X26296,hAPP(c_COMBK(tc_Option_Ooption(X26296),X26297),c_Option_Ooption_ONone(X26296))) = c_Orderings_Obot__class_Obot(tc_fun(X26296,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_ran__empty]) ).
fof(i_0_10176,plain,
! [X21039] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21039)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21039)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21039)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21039)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21039) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5957])]) ).
fof(i_0_10177,plain,
! [X32723,X32724,X32725] : hAPP(hAPP(c_List_Olist__update(X32725,X32724),X32723),hAPP(hAPP(c_List_Onth(X32725),X32724),X32723)) = X32724,
inference(variable_rename,[status(thm)],[fact_list__update__id]) ).
fof(i_0_10178,plain,
! [X18652,X18653,X18654] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18654),X18653),X18653) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18654),X18652),X18652)
| X18653 = X18652
| X18653 = hAPP(c_Groups_Ouminus__class_Ouminus(X18654),X18652)
| ~ class_Rings_Oidom(X18654) )
& ( X18653 != X18652
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18654),X18653),X18653) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18654),X18652),X18652)
| ~ class_Rings_Oidom(X18654) )
& ( X18653 != hAPP(c_Groups_Ouminus__class_Ouminus(X18654),X18652)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18654),X18653),X18653) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18654),X18652),X18652)
| ~ class_Rings_Oidom(X18654) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).
fof(i_0_10179,plain,
! [X18056,X18057] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18057)),X18056) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18057),X18056)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_10180,plain,
! [X33817,X33818,X33819] : hAPP(hAPP(c_List_Odrop(X33819),X33818),c_List_Obutlast(X33819,X33817)) = c_List_Obutlast(X33819,hAPP(hAPP(c_List_Odrop(X33819),X33818),X33817)),
inference(variable_rename,[status(thm)],[fact_drop__butlast]) ).
fof(i_0_10181,plain,
! [X33820,X33821,X33822] : c_List_Obutlast(X33822,hAPP(hAPP(c_List_Odrop(X33822),X33821),X33820)) = hAPP(hAPP(c_List_Odrop(X33822),X33821),c_List_Obutlast(X33822,X33820)),
inference(variable_rename,[status(thm)],[fact_butlast__drop]) ).
fof(i_0_10182,plain,
! [X21832] :
( ( X21832 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X21832)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X21832))
| X21832 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__not__eq__zero])]) ).
fof(i_0_10183,plain,
! [X29802,X29803,X29804] :
( ( hAPP(c_Relation_ODomain(X29804,X29803),X29802) != c_Orderings_Obot__class_Obot(tc_fun(X29804,tc_HOL_Obool))
| X29802 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29804,X29803),tc_HOL_Obool)) )
& ( X29802 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29804,X29803),tc_HOL_Obool))
| hAPP(c_Relation_ODomain(X29804,X29803),X29802) = c_Orderings_Obot__class_Obot(tc_fun(X29804,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff])]) ).
fof(i_0_10184,plain,
! [X29715,X29716,X29717] :
( ( hAPP(c_Relation_ORange(X29717,X29716),X29715) != c_Orderings_Obot__class_Obot(tc_fun(X29716,tc_HOL_Obool))
| X29715 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29717,X29716),tc_HOL_Obool)) )
& ( X29715 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29717,X29716),tc_HOL_Obool))
| hAPP(c_Relation_ORange(X29717,X29716),X29715) = c_Orderings_Obot__class_Obot(tc_fun(X29716,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__empty__iff])]) ).
fof(i_0_10185,plain,
! [X20814] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20814),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20814) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20814) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20814),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20814) = X20814 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5958])]) ).
fof(i_0_10186,plain,
! [X20771,X20772] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20772),X20771)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20772) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1])]) ).
fof(i_0_10187,plain,
! [X18551,X18552] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18552),X18551))
| X18552 = X18551
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18551),X18552)) ),
inference(variable_rename,[status(thm)],[fact_zless__linear]) ).
fof(i_0_10188,plain,
! [X18226,X18227] :
( X18227 = X18226
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18227),X18226))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18226),X18227)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5959])]) ).
fof(i_0_10189,plain,
! [X18224,X18225] :
( ( X18225 = X18224
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18225),X18224))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18224),X18225)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18225),X18224))
| X18225 != X18224 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18224),X18225))
| X18225 != X18224 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_10190,plain,
! [X23776,X23777] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X23777),X23776)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23776),X23777)),
inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan__int]) ).
cnf(i_0_10191,plain,
( c_Divides_Odivmod__nat(X1,X2) = X3
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_5960]) ).
fof(i_0_10192,plain,
! [X20617,X20618] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20618)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20618),X20617),hAPP(c_Groups_Oabs__class_Oabs(X20618),X20617))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).
fof(i_0_10193,plain,
! [X24092,X24093] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X24093,X24092)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24092),hAPP(c_Nat_OSuc,X24093)),
inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan]) ).
fof(i_0_10194,plain,
! [X19030,X19031] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19031),X19030))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19030),X19031)) ),
inference(variable_rename,[status(thm)],[fact_zle__linear]) ).
fof(i_0_10195,plain,
! [X19711,X19712] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19712),X19711))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19711),X19712)) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_10196,plain,
! [X19990,X19991] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19991)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19990)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19991),X19990),
inference(variable_rename,[status(thm)],[fact_zdiv__zminus__zminus]) ).
fof(i_0_10197,plain,
! [X19992,X19993] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19993),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19992)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19993)),X19992),
inference(variable_rename,[status(thm)],[fact_zdiv__zminus2]) ).
fof(i_0_10198,plain,
! [X33473,X33474,X33475] : hAPP(hAPP(c_List_Odrop(X33475),hAPP(c_Nat_OSuc,X33474)),X33473) = hAPP(hAPP(c_List_Odrop(X33475),X33474),hAPP(c_List_Otl(X33475),X33473)),
inference(variable_rename,[status(thm)],[fact_drop__Suc]) ).
fof(i_0_10199,plain,
! [X28479,X28480,X28481] :
( ( c_Map_Odom(X28481,X28480,X28479) != c_Orderings_Obot__class_Obot(tc_fun(X28481,tc_HOL_Obool))
| X28479 = hAPP(c_COMBK(tc_Option_Ooption(X28480),X28481),c_Option_Ooption_ONone(X28480)) )
& ( X28479 != hAPP(c_COMBK(tc_Option_Ooption(X28480),X28481),c_Option_Ooption_ONone(X28480))
| c_Map_Odom(X28481,X28480,X28479) = c_Orderings_Obot__class_Obot(tc_fun(X28481,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__eq__empty__conv])]) ).
fof(i_0_10200,plain,
! [X18459] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18459))
| X18459 = hAPP(c_Nat_OSuc,esk35_1(X18459)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__implies__Suc])])]) ).
fof(i_0_10201,plain,
! [X18333,X18335,X18336] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18333))
| X18333 = hAPP(c_Nat_OSuc,esk30_1(X18333)) )
& ( X18335 != hAPP(c_Nat_OSuc,X18336)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18335)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])]) ).
fof(i_0_10202,plain,
! [X29038,X29039] :
( ~ class_Orderings_Olinorder(X29039)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29039),X29038))
| c_Big__Operators_Olattice_OInf__fin(X29039,c_Orderings_Oord__class_Omin(X29039),X29038) = hAPP(c_Finite__Set_Ofold1(X29039,c_Orderings_Oord__class_Omin(X29039)),X29038) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq])]) ).
fof(i_0_10203,plain,
! [X29040,X29041] :
( ~ class_Orderings_Olinorder(X29041)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29041),X29040))
| c_Big__Operators_Olattice_OSup__fin(X29041,c_Orderings_Oord__class_Omax(X29041),X29040) = hAPP(c_Finite__Set_Ofold1(X29041,c_Orderings_Oord__class_Omax(X29041)),X29040) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq])]) ).
fof(i_0_10204,plain,
! [X32157] :
( ~ class_Orderings_Olinorder(X32157)
| c_Finite__Set_Ofun__left__comm(X32157,tc_List_Olist(X32157),c_List_Olinorder__class_Oinsort__key(X32157,X32157,c_COMBI(X32157))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__insort])]) ).
fof(i_0_10205,plain,
! [X18980] :
( ( X18980 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Osgn__class_Osgn(tc_Int_Oint,X18980) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18980))
| c_Groups_Osgn__class_Osgn(tc_Int_Oint,X18980) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X18980 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18980))
| c_Groups_Osgn__class_Osgn(tc_Int_Oint,X18980) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X18980 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5961])])]) ).
fof(i_0_10206,plain,
! [X33506,X33507] :
( ~ hBOOL(hAPP(c_List_Odistinct(X33507),X33506))
| hBOOL(hAPP(c_List_Odistinct(X33507),hAPP(c_List_Otl(X33507),X33506))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__tl])]) ).
fof(i_0_10207,plain,
! [X23637,X23638] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X23638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23637),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X23638,X23637),
inference(variable_rename,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int]) ).
fof(i_0_10208,plain,
! [X21020] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X21020))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21020),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21020),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X21020)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__def])]) ).
fof(i_0_10209,plain,
! [X32181,X32182] :
( hAPP(c_Finite__Set_Ocard(X32182),hAPP(c_List_Oset(X32182),X32181)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32182)),X32181)
| hBOOL(hAPP(c_List_Odistinct(X32182),X32181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__distinct])]) ).
fof(i_0_10210,plain,
! [X20465,X20466] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20466),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20465)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20466),X20465)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).
fof(i_0_10211,plain,
! [X34231,X34232,X34233] :
( ( hAPP(hAPP(c_List_Olist_OCons(X34233),X34232),c_List_Olist_ONil(X34233)) != hAPP(c_List_Orev(X34233),X34231)
| X34231 = hAPP(hAPP(c_List_Olist_OCons(X34233),X34232),c_List_Olist_ONil(X34233)) )
& ( X34231 != hAPP(hAPP(c_List_Olist_OCons(X34233),X34232),c_List_Olist_ONil(X34233))
| hAPP(hAPP(c_List_Olist_OCons(X34233),X34232),c_List_Olist_ONil(X34233)) = hAPP(c_List_Orev(X34233),X34231) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__rev__conv])]) ).
fof(i_0_10212,plain,
! [X34234,X34235,X34236] :
( ( hAPP(c_List_Orev(X34236),X34235) != hAPP(hAPP(c_List_Olist_OCons(X34236),X34234),c_List_Olist_ONil(X34236))
| X34235 = hAPP(hAPP(c_List_Olist_OCons(X34236),X34234),c_List_Olist_ONil(X34236)) )
& ( X34235 != hAPP(hAPP(c_List_Olist_OCons(X34236),X34234),c_List_Olist_ONil(X34236))
| hAPP(c_List_Orev(X34236),X34235) = hAPP(hAPP(c_List_Olist_OCons(X34236),X34234),c_List_Olist_ONil(X34236)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__singleton__conv])]) ).
fof(i_0_10213,plain,
! [X18094,X18095] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X18095,X18094)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X18094)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_com_Osize_I14_J]) ).
fof(i_0_10214,plain,
! [X33216,X33217] : c_List_Olistrel1(X33217,hAPP(c_Relation_Oconverse(X33217,X33217),X33216)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X33217),tc_List_Olist(X33217)),c_List_Olistrel1(X33217,X33216)),
inference(variable_rename,[status(thm)],[fact_listrel1__converse]) ).
fof(i_0_10215,plain,
! [X20262,X20263,X20264] :
( ~ class_Groups_Oab__group__add(X20264)
| hAPP(c_Groups_Ouminus__class_Ouminus(X20264),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20264),X20263),X20262)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20264),X20262),X20263) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).
cnf(i_0_10216,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| c_List_Oupt(X1,X2) = c_List_Olist_ONil(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_5758]) ).
fof(i_0_10217,plain,
! [X29602,X29603,X29604] :
( ~ c_Wellfounded_Owf(X29604,X29603)
| hBOOL(hAPP(hAPP(c_member(X29604),X29602),c_Wellfounded_Oacc(X29604,X29603))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__wfD])]) ).
fof(i_0_10218,plain,
! [X18656,X18657] :
( ~ class_Rings_Ocomm__ring__1(X18657)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18657),X18656) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18657),hAPP(c_Groups_Ouminus__class_Ouminus(X18657),c_Groups_Oone__class_Oone(X18657))),X18656) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).
fof(i_0_10219,plain,
! [X24384,X24385] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X24385),X24384))),
inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan__int]) ).
fof(i_0_10220,plain,
! [X24376,X24377] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24377),X24376))),
inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).
fof(i_0_10221,plain,
! [X18084] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18084)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X18084)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_nat_Osize_I4_J]) ).
cnf(i_0_10222,plain,
c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_5962]) ).
fof(i_0_10223,plain,
! [X18585,X18586,X18587] :
( ~ class_Orderings_Oorder(X18587)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18587),X18586),X18585))
| X18585 != X18586 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_10224,plain,
! [X18582,X18583,X18584] :
( ~ class_Orderings_Oorder(X18584)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18584),X18583),X18582))
| X18583 != X18582 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_10225,plain,
! [X18573,X18574,X18575] :
( ~ class_Orderings_Oorder(X18575)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18575),X18574),X18573))
| X18574 != X18573 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_10226,plain,
! [X23399] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23399),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23399) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23399) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23399),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd1__eq])]) ).
cnf(i_0_10227,plain,
c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_5963]) ).
fof(i_0_10228,plain,
! [X23197,X23198,X23199] :
( ~ class_Rings_Olinordered__idom(X23199)
| hAPP(c_Groups_Oabs__class_Oabs(X23199),X23198) != hAPP(c_Groups_Oabs__class_Oabs(X23199),X23197)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23199),X23198),X23197)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__if__abs__eq])]) ).
fof(i_0_10229,plain,
! [X20218,X20219,X20220,X20221,X20222] :
( ( X20221 != X20220
| X20219 = X20218
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20222),X20221),X20220) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20222),X20219),X20218)
| ~ class_Groups_Oab__group__add(X20222) )
& ( X20219 != X20218
| X20221 = X20220
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20222),X20221),X20220) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20222),X20219),X20218)
| ~ class_Groups_Oab__group__add(X20222) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).
fof(i_0_10230,plain,
! [X31895,X31896,X31897,X31898] : hAPP(hAPP(c_Option_Omap(X31898,X31897),X31896),hAPP(c_Option_Ooption_OSome(X31898),X31895)) = hAPP(c_Option_Ooption_OSome(X31897),hAPP(X31896,X31895)),
inference(variable_rename,[status(thm)],[fact_option__map__Some]) ).
fof(i_0_10231,plain,
! [X34310,X34311,X34312] : hAPP(c_List_Orev(X34312),hAPP(c_List_Ofilter(X34312,X34311),X34310)) = hAPP(c_List_Ofilter(X34312,X34311),hAPP(c_List_Orev(X34312),X34310)),
inference(variable_rename,[status(thm)],[fact_rev__filter]) ).
fof(i_0_10232,plain,
! [X19880,X19881] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19881),X19880) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19881,X19880) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__not__zero])]) ).
fof(i_0_10233,plain,
! [X19878,X19879] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X19879,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19878)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19879,X19878) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__not__zero])]) ).
fof(i_0_10234,plain,
! [X18556,X18557] :
( ~ class_Orderings_Opreorder(X18557)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18557),X18556),X18556)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5964])]) ).
fof(i_0_10235,plain,
! [X18266] :
( ( X18266 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18266)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18266))
| X18266 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_10236,plain,
! [X18028,X18029,X18030,X18031] :
( ~ class_Groups_Ocancel__semigroup__add(X18031)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18031),X18030),X18029) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18031),X18028),X18029)
| X18030 = X18028 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_10237,plain,
! [X18016,X18017,X18018,X18019] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18019),X18018),X18017) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18019),X18016),X18017)
| X18018 = X18016
| ~ class_Groups_Ocancel__semigroup__add(X18019) )
& ( X18018 != X18016
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18019),X18018),X18017) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18019),X18016),X18017)
| ~ class_Groups_Ocancel__semigroup__add(X18019) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_10238,plain,
! [X18024,X18025,X18026,X18027] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X18027)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18027),X18026),X18025) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18027),X18026),X18024)
| X18025 = X18024 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_10239,plain,
! [X18020,X18021,X18022,X18023] :
( ~ class_Groups_Ocancel__semigroup__add(X18023)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18023),X18022),X18021) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18023),X18022),X18020)
| X18021 = X18020 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_10240,plain,
! [X18012,X18013,X18014,X18015] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18015),X18014),X18013) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18015),X18014),X18012)
| X18013 = X18012
| ~ class_Groups_Ocancel__semigroup__add(X18015) )
& ( X18013 != X18012
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18015),X18014),X18013) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18015),X18014),X18012)
| ~ class_Groups_Ocancel__semigroup__add(X18015) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_10241,plain,
! [X17457,X17458,X17459,X17460,X17461,X17462] :
( ( X17462 = X17459
| c_Com_Ocom_OLocal(X17462,X17461,X17460) != c_Com_Ocom_OLocal(X17459,X17458,X17457) )
& ( X17461 = X17458
| c_Com_Ocom_OLocal(X17462,X17461,X17460) != c_Com_Ocom_OLocal(X17459,X17458,X17457) )
& ( X17460 = X17457
| c_Com_Ocom_OLocal(X17462,X17461,X17460) != c_Com_Ocom_OLocal(X17459,X17458,X17457) )
& ( X17462 != X17459
| X17461 != X17458
| X17460 != X17457
| c_Com_Ocom_OLocal(X17462,X17461,X17460) = c_Com_Ocom_OLocal(X17459,X17458,X17457) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I2_J])])]) ).
fof(i_0_10242,plain,
! [X17451,X17452,X17453,X17454,X17455,X17456] :
( ( X17456 = X17453
| c_Com_Ocom_OCond(X17456,X17455,X17454) != c_Com_Ocom_OCond(X17453,X17452,X17451) )
& ( X17455 = X17452
| c_Com_Ocom_OCond(X17456,X17455,X17454) != c_Com_Ocom_OCond(X17453,X17452,X17451) )
& ( X17454 = X17451
| c_Com_Ocom_OCond(X17456,X17455,X17454) != c_Com_Ocom_OCond(X17453,X17452,X17451) )
& ( X17456 != X17453
| X17455 != X17452
| X17454 != X17451
| c_Com_Ocom_OCond(X17456,X17455,X17454) = c_Com_Ocom_OCond(X17453,X17452,X17451) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I4_J])])]) ).
fof(i_0_10243,plain,
! [X17163,X17164,X17165,X17166,X17167,X17168] :
( ( X17168 = X17165
| c_Com_Ocom_OCall(X17168,X17167,X17166) != c_Com_Ocom_OCall(X17165,X17164,X17163) )
& ( X17167 = X17164
| c_Com_Ocom_OCall(X17168,X17167,X17166) != c_Com_Ocom_OCall(X17165,X17164,X17163) )
& ( X17166 = X17163
| c_Com_Ocom_OCall(X17168,X17167,X17166) != c_Com_Ocom_OCall(X17165,X17164,X17163) )
& ( X17168 != X17165
| X17167 != X17164
| X17166 != X17163
| c_Com_Ocom_OCall(X17168,X17167,X17166) = c_Com_Ocom_OCall(X17165,X17164,X17163) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I7_J])])]) ).
fof(i_0_10244,plain,
! [X19628] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19628),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,X19628) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__0])]) ).
fof(i_0_10245,plain,
! [X19627] :
( ( hAPP(c_Int_Onat,X19627) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19627),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19627),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,X19627) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__iff])]) ).
fof(i_0_10246,plain,
! [X21648] :
( ( ~ c_Nat__Transfer_Ois__nat(X21648)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21648)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21648))
| c_Nat__Transfer_Ois__nat(X21648) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__nat__def])]) ).
fof(i_0_10247,plain,
! [X18058,X18059] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18059),hAPP(c_Nat_OSuc,X18058)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18059),X18058)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_10248,plain,
! [X17441,X17442,X17443,X17444,X17445,X17446] : c_Com_Ocom_OLocal(X17446,X17445,X17444) != c_Com_Ocom_OCond(X17443,X17442,X17441),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I36_J]) ).
fof(i_0_10249,plain,
! [X17544,X17545,X17546,X17547,X17548,X17549] : c_Com_Ocom_OLocal(X17549,X17548,X17547) != c_Com_Ocom_OCall(X17546,X17545,X17544),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I42_J]) ).
fof(i_0_10250,plain,
! [X17435,X17436,X17437,X17438,X17439,X17440] : c_Com_Ocom_OCond(X17440,X17439,X17438) != c_Com_Ocom_OLocal(X17437,X17436,X17435),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I37_J]) ).
fof(i_0_10251,plain,
! [X17538,X17539,X17540,X17541,X17542,X17543] : c_Com_Ocom_OCall(X17543,X17542,X17541) != c_Com_Ocom_OLocal(X17540,X17539,X17538),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I43_J]) ).
fof(i_0_10252,plain,
! [X17576,X17577,X17578,X17579,X17580,X17581] : c_Com_Ocom_OCond(X17581,X17580,X17579) != c_Com_Ocom_OCall(X17578,X17577,X17576),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I56_J]) ).
fof(i_0_10253,plain,
! [X17570,X17571,X17572,X17573,X17574,X17575] : c_Com_Ocom_OCall(X17575,X17574,X17573) != c_Com_Ocom_OCond(X17572,X17571,X17570),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I57_J]) ).
fof(i_0_10254,plain,
! [X29698,X29699] : hAPP(c_List_Olexn(X29699,X29698),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X29699),tc_List_Olist(X29699)),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I1_J]) ).
fof(i_0_10255,plain,
! [X19485] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19485))),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).
fof(i_0_10256,plain,
! [X19484] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19484))),
inference(variable_rename,[status(thm)],[fact_zero__zle__int]) ).
fof(i_0_10257,plain,
! [X24654,X24655] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24655,tc_HOL_Obool)),X24654),X24654) = c_Orderings_Obot__class_Obot(tc_fun(X24655,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).
fof(i_0_10258,plain,
! [X29583] : c_Wellfounded_Owf(X29583,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29583,X29583),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_wf__empty]) ).
fof(i_0_10259,plain,
! [X24772,X24773,X24774] :
( ~ class_Orderings_Oorder(X24774)
| X24773 != X24772
| c_SetInterval_Oord__class_OatLeastAtMost(X24774,X24773,X24772) = hAPP(hAPP(c_Set_Oinsert(X24774),X24773),c_Orderings_Obot__class_Obot(tc_fun(X24774,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H])]) ).
fof(i_0_10260,plain,
! [X34177,X34178] :
( ( hAPP(c_List_Oset(X34178),c_List_Olinorder__class_Osorted__list__of__set(X34178,X34177)) = X34177
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34178),X34177))
| ~ class_Orderings_Olinorder(X34178) )
& ( c_List_Olinorder__class_Osorted(X34178,c_List_Olinorder__class_Osorted__list__of__set(X34178,X34177))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34178),X34177))
| ~ class_Orderings_Olinorder(X34178) )
& ( hBOOL(hAPP(c_List_Odistinct(X34178),c_List_Olinorder__class_Osorted__list__of__set(X34178,X34177)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34178),X34177))
| ~ class_Orderings_Olinorder(X34178) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set])])]) ).
fof(i_0_10261,plain,
! [X19851,X19852,X19853] :
( ~ class_Divides_Osemiring__div(X19853)
| c_Divides_Odiv__class_Omod(X19853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19853),X19852),X19851),X19852) = c_Groups_Ozero__class_Ozero(X19853) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])]) ).
fof(i_0_10262,plain,
! [X19848,X19849,X19850] :
( ~ class_Divides_Osemiring__div(X19850)
| c_Divides_Odiv__class_Omod(X19850,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19850),X19849),X19848),X19848) = c_Groups_Ozero__class_Ozero(X19850) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])]) ).
fof(i_0_10263,plain,
! [X33805,X33806] :
( X33806 = c_List_Olist_ONil(X33805)
| ~ hBOOL(hAPP(c_List_Odistinct(X33805),X33806))
| hBOOL(hAPP(c_List_Odistinct(X33805),c_List_Obutlast(X33805,X33806))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__butlast])]) ).
fof(i_0_10264,plain,
! [X23801,X23802] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X23802,X23801)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23801),X23802),
inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost]) ).
fof(i_0_10265,plain,
! [X32318,X32319,X32320,X32321,X32322] :
( ( X32321 = X32319
| hAPP(hAPP(c_List_Olist_OCons(X32322),X32321),X32320) != hAPP(hAPP(c_List_Olist_OCons(X32322),X32319),X32318) )
& ( X32320 = X32318
| hAPP(hAPP(c_List_Olist_OCons(X32322),X32321),X32320) != hAPP(hAPP(c_List_Olist_OCons(X32322),X32319),X32318) )
& ( X32321 != X32319
| X32320 != X32318
| hAPP(hAPP(c_List_Olist_OCons(X32322),X32321),X32320) = hAPP(hAPP(c_List_Olist_OCons(X32322),X32319),X32318) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])]) ).
fof(i_0_10266,plain,
! [X32961,X32962,X32963,X32964] :
( ( hAPP(hAPP(c_List_Oappend(X32964),X32963),X32962) != hAPP(hAPP(c_List_Oappend(X32964),X32961),X32962)
| X32963 = X32961 )
& ( X32963 != X32961
| hAPP(hAPP(c_List_Oappend(X32964),X32963),X32962) = hAPP(hAPP(c_List_Oappend(X32964),X32961),X32962) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])]) ).
fof(i_0_10267,plain,
! [X32957,X32958,X32959,X32960] :
( ( hAPP(hAPP(c_List_Oappend(X32960),X32959),X32958) != hAPP(hAPP(c_List_Oappend(X32960),X32959),X32957)
| X32958 = X32957 )
& ( X32958 != X32957
| hAPP(hAPP(c_List_Oappend(X32960),X32959),X32958) = hAPP(hAPP(c_List_Oappend(X32960),X32959),X32957) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])]) ).
fof(i_0_10268,plain,
! [X17231,X17232,X17233,X17234] : c_String_Ochar_Ochar__case(X17234,X17233,hAPP(hAPP(c_String_Ochar_OChar,X17232),X17231)) = hAPP(hAPP(X17233,X17232),X17231),
inference(variable_rename,[status(thm)],[fact_char_Osimps_I2_J]) ).
fof(i_0_10269,plain,
! [X17227,X17228,X17229,X17230] : c_String_Ochar_Ochar__rec(X17230,X17229,hAPP(hAPP(c_String_Ochar_OChar,X17228),X17227)) = hAPP(hAPP(X17229,X17228),X17227),
inference(variable_rename,[status(thm)],[fact_char_Orecs]) ).
fof(i_0_10270,plain,
! [X24779,X24780] :
( ~ class_Orderings_Oorder(X24780)
| c_SetInterval_Oord__class_OatLeastAtMost(X24780,X24779,X24779) = hAPP(hAPP(c_Set_Oinsert(X24780),X24779),c_Orderings_Obot__class_Obot(tc_fun(X24780,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton])]) ).
fof(i_0_10271,plain,
! [X17558,X17559] :
( ~ hBOOL(hAPP(c_Com_OWT,X17559))
| ~ hBOOL(hAPP(c_Com_OWT,X17558))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17559,X17558))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OSemi])]) ).
fof(i_0_10272,plain,
! [X17556,X17557] :
( ( hBOOL(hAPP(c_Com_OWT,X17557))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17557,X17556))) )
& ( hBOOL(hAPP(c_Com_OWT,X17556))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17557,X17556))) )
& ( ~ hBOOL(hAPP(c_Com_OWT,X17557))
| ~ hBOOL(hAPP(c_Com_OWT,X17556))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17557,X17556))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I4_J])])]) ).
fof(i_0_10273,plain,
! [X32524,X32525] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32525),X32524))
| c_List_Oupto(X32524,X32525) = c_List_Olist_ONil(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto__empty])]) ).
fof(i_0_10274,plain,
! [X24452] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24452)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24452)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24452)),
inference(variable_rename,[status(thm)],[fact_atMost__Suc]) ).
fof(i_0_10275,plain,
! [X22973,X22974] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X22974),X22973))
| c_Quickcheck_Obeyond(X22974,X22973) = X22973 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X22974),X22973))
| c_Quickcheck_Obeyond(X22974,X22973) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5965])]) ).
fof(i_0_10276,plain,
! [X21125] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21125) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21125),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21125),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21125) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__0])]) ).
fof(i_0_10277,plain,
! [X21032] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21032)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21032) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__number__of__eq__0])]) ).
fof(i_0_10278,plain,
! [X21124] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21124)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21124),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21124),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21124) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])]) ).
cnf(i_0_10279,plain,
c_List_Orotate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X1)),
inference(split_conjunct,[status(thm)],[i_0_5966]) ).
fof(i_0_10280,plain,
! [X27129,X27130,X27131] :
( ~ class_Lattices_Olattice(X27131)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27131),X27130),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27131),X27130),X27129)) = X27130 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb])]) ).
fof(i_0_10281,plain,
! [X27126,X27127,X27128] :
( ~ class_Lattices_Olattice(X27128)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27128),X27127),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27128),X27127),X27126)) = X27127 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__absorb])]) ).
fof(i_0_10282,plain,
! [X22544,X22545,X22546] :
( ~ class_Orderings_Olinorder(X22546)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22546),X22545),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22546),X22545),X22544)) = X22545 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__absorb])]) ).
fof(i_0_10283,plain,
! [X22547,X22548,X22549] :
( ~ class_Orderings_Olinorder(X22549)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22549),X22548),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22549),X22548),X22547)) = X22548 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb])]) ).
fof(i_0_10284,plain,
! [X23239] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23239),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X23239 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X23239 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23239),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__dvd__1__iff__1])]) ).
fof(i_0_10285,plain,
! [X19225] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19225),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X19225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19225 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19225),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])]) ).
fof(i_0_10286,plain,
! [X33336,X33337,X33338] : hAPP(hAPP(c_List_Odrop(X33338),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X33338),X33337),X33336)) = X33336,
inference(variable_rename,[status(thm)],[fact_drop__1__Cons]) ).
fof(i_0_10287,plain,
! [X20288,X20289] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20289)),hAPP(c_Nat_OSuc,X20288)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20289),X20288),
inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc]) ).
fof(i_0_10288,plain,
! [X18054,X18055] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18055)),X18054) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18055),hAPP(c_Nat_OSuc,X18054)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_10289,plain,
! [X29027,X29028,X29029] : hAPP(c_Finite__Set_Ofold1(X29029,X29028),X29027) = c_HOL_OThe(X29029,c_Finite__Set_Ofold1Set(X29029,X29028,X29027)),
inference(variable_rename,[status(thm)],[fact_fold1__def]) ).
fof(i_0_10290,plain,
! [X19872,X19873,X19875,X19876,X19877] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X19873,X19872) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X19873 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19872),esk54_2(X19872,X19873)) )
& ( X19876 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19875),X19877)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19876,X19875) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__eq__0__iff])])])])]) ).
fof(i_0_10291,plain,
! [X20024,X20025,X20027,X20028,X20029] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20025,X20024) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20025 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20024),esk60_2(X20024,X20025)) )
& ( X20028 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20027),X20029)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20028,X20027) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq__0__iff])])])])]) ).
fof(i_0_10292,plain,
! [X25286,X25287] :
( ~ c_Nat__Transfer_Onat__set(X25287)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25286),X25287))
| c_Nat__Transfer_Ois__nat(X25286) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J])]) ).
fof(i_0_10293,plain,
! [X30344,X30345] :
( ( ~ c_Wellfounded_Oacyclic(X30345,hAPP(c_Relation_Oconverse(X30345,X30345),X30344))
| c_Wellfounded_Oacyclic(X30345,X30344) )
& ( ~ c_Wellfounded_Oacyclic(X30345,X30344)
| c_Wellfounded_Oacyclic(X30345,hAPP(c_Relation_Oconverse(X30345,X30345),X30344)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__converse])]) ).
fof(i_0_10294,plain,
! [X18267] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18267),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_5967]) ).
fof(i_0_10295,plain,
! [X18265] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18265),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_5968]) ).
fof(i_0_10296,plain,
! [X18213] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18213),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_5969]) ).
fof(i_0_10297,plain,
! [X32179,X32180] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32180),X32179))
| hAPP(c_Finite__Set_Ocard(X32180),hAPP(c_List_Oset(X32180),X32179)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32180)),X32179) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__card])]) ).
fof(i_0_10298,plain,
! [X30402,X30403,X30404] : hAPP(c_Relation_ODomain(X30404,X30403),hAPP(c_Relation_Oconverse(X30403,X30404),X30402)) = hAPP(c_Relation_ORange(X30403,X30404),X30402),
inference(variable_rename,[status(thm)],[fact_Domain__converse]) ).
fof(i_0_10299,plain,
! [X30399,X30400,X30401] : hAPP(c_Relation_ORange(X30401,X30400),hAPP(c_Relation_Oconverse(X30400,X30401),X30399)) = hAPP(c_Relation_ODomain(X30400,X30401),X30399),
inference(variable_rename,[status(thm)],[fact_Range__converse]) ).
fof(i_0_10300,plain,
! [X30341,X30342] : c_Transitive__Closure_Ortrancl(X30342,hAPP(c_Relation_Oconverse(X30342,X30342),X30341)) = hAPP(c_Relation_Oconverse(X30342,X30342),c_Transitive__Closure_Ortrancl(X30342,X30341)),
inference(variable_rename,[status(thm)],[fact_rtrancl__converse]) ).
fof(i_0_10301,plain,
! [X30405,X30406,X30407] : hAPP(c_Relation_ORange(X30407,X30406),X30405) = hAPP(c_Relation_ODomain(X30406,X30407),hAPP(c_Relation_Oconverse(X30407,X30406),X30405)),
inference(variable_rename,[status(thm)],[fact_Range__def]) ).
fof(i_0_10302,plain,
! [X32731,X32732,X32733,X32734] :
( ( hAPP(hAPP(c_List_Olist__update(X32734,X32733),X32732),X32731) != c_List_Olist_ONil(X32734)
| X32733 = c_List_Olist_ONil(X32734) )
& ( X32733 != c_List_Olist_ONil(X32734)
| hAPP(hAPP(c_List_Olist__update(X32734,X32733),X32732),X32731) = c_List_Olist_ONil(X32734) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__nonempty])]) ).
fof(i_0_10303,plain,
! [X32504,X32505,X32506,X32507] :
( ( hAPP(hAPP(c_List_Omap(X32507,X32506),X32505),X32504) != c_List_Olist_ONil(X32506)
| X32504 = c_List_Olist_ONil(X32507) )
& ( X32504 != c_List_Olist_ONil(X32507)
| hAPP(hAPP(c_List_Omap(X32507,X32506),X32505),X32504) = c_List_Olist_ONil(X32506) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__is__Nil__conv])]) ).
fof(i_0_10304,plain,
! [X31899,X31900,X31901,X31902] :
( ( hAPP(hAPP(c_Option_Omap(X31902,X31901),X31900),X31899) != c_Option_Ooption_ONone(X31901)
| X31899 = c_Option_Ooption_ONone(X31902) )
& ( X31899 != c_Option_Ooption_ONone(X31902)
| hAPP(hAPP(c_Option_Omap(X31902,X31901),X31900),X31899) = c_Option_Ooption_ONone(X31901) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option__map__is__None])]) ).
fof(i_0_10305,plain,
! [X32497,X32498,X32499,X32500] :
( ( c_List_Olist_ONil(X32500) != hAPP(hAPP(c_List_Omap(X32499,X32500),X32498),X32497)
| X32497 = c_List_Olist_ONil(X32499) )
& ( X32497 != c_List_Olist_ONil(X32499)
| c_List_Olist_ONil(X32500) = hAPP(hAPP(c_List_Omap(X32499,X32500),X32498),X32497) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__map__conv])]) ).
fof(i_0_10306,plain,
! [X24907,X24908] : c_Option_Oset(X24908,hAPP(c_Option_Ooption_OSome(X24908),X24907)) = hAPP(hAPP(c_Set_Oinsert(X24908),X24907),c_Orderings_Obot__class_Obot(tc_fun(X24908,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_Option_Oset_Osimps_I2_J]) ).
fof(i_0_10307,plain,
! [X20283,X20284] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20284),X20283) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20283),X20284) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20284 = X20283 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).
fof(i_0_10308,plain,
! [X26121,X26122,X26123] :
( ~ class_Groups_Ocomm__monoid__mult(X26123)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26122,X26123),X26121),c_Orderings_Obot__class_Obot(tc_fun(X26122,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X26123) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__empty])]) ).
fof(i_0_10309,plain,
! [X26118,X26119,X26120] :
( ~ class_Groups_Ocomm__monoid__mult(X26120)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26119,X26120),X26118),c_Orderings_Obot__class_Obot(tc_fun(X26119,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X26120) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oempty])]) ).
fof(i_0_10310,plain,
! [X24731,X24732,X24733] :
( ~ class_Groups_Ocomm__monoid__add(X24733)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24732,X24733),X24731),c_Orderings_Obot__class_Obot(tc_fun(X24732,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X24733) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__empty])]) ).
fof(i_0_10311,plain,
! [X24728,X24729,X24730] :
( ~ class_Groups_Ocomm__monoid__add(X24730)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24729,X24730),X24728),c_Orderings_Obot__class_Obot(tc_fun(X24729,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X24730) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oempty])]) ).
fof(i_0_10312,plain,
! [X18268,X18269] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18269),X18268))
| X18268 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr__implies__not0])]) ).
fof(i_0_10313,plain,
! [X24536] :
( ~ class_Finite__Set_Ofinite(X24536)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24536),c_Orderings_Otop__class_Otop(tc_fun(X24536,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).
fof(i_0_10314,plain,
! [X21523,X21524,X21525,X21526] :
( ( X21524 = c_Groups_Ozero__class_Ozero(X21526)
| X21525 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21526),X21523),X21524)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21526),X21525),X21524) != X21523
| ~ class_Fields_Ofield__inverse__zero(X21526) )
& ( X21524 != c_Groups_Ozero__class_Ozero(X21526)
| X21523 = c_Groups_Ozero__class_Ozero(X21526)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21526),X21525),X21524) != X21523
| ~ class_Fields_Ofield__inverse__zero(X21526) )
& ( X21524 = c_Groups_Ozero__class_Ozero(X21526)
| X21524 != c_Groups_Ozero__class_Ozero(X21526)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21526),X21525),X21524) = X21523
| ~ class_Fields_Ofield__inverse__zero(X21526) )
& ( X21523 != c_Groups_Ozero__class_Ozero(X21526)
| X21524 != c_Groups_Ozero__class_Ozero(X21526)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21526),X21525),X21524) = X21523
| ~ class_Fields_Ofield__inverse__zero(X21526) )
& ( X21524 = c_Groups_Ozero__class_Ozero(X21526)
| X21525 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21526),X21523),X21524)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21526),X21525),X21524) = X21523
| ~ class_Fields_Ofield__inverse__zero(X21526) )
& ( X21523 != c_Groups_Ozero__class_Ozero(X21526)
| X21525 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21526),X21523),X21524)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21526),X21525),X21524) = X21523
| ~ class_Fields_Ofield__inverse__zero(X21526) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq])])]) ).
fof(i_0_10315,plain,
! [X21519,X21520,X21521,X21522] :
( ( X21519 = c_Groups_Ozero__class_Ozero(X21522)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21521),X21519) = X21520
| X21521 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21520),X21519)
| ~ class_Fields_Ofield__inverse__zero(X21522) )
& ( X21519 != c_Groups_Ozero__class_Ozero(X21522)
| X21521 = c_Groups_Ozero__class_Ozero(X21522)
| X21521 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21520),X21519)
| ~ class_Fields_Ofield__inverse__zero(X21522) )
& ( X21519 = c_Groups_Ozero__class_Ozero(X21522)
| X21519 != c_Groups_Ozero__class_Ozero(X21522)
| X21521 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21520),X21519)
| ~ class_Fields_Ofield__inverse__zero(X21522) )
& ( X21521 != c_Groups_Ozero__class_Ozero(X21522)
| X21519 != c_Groups_Ozero__class_Ozero(X21522)
| X21521 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21520),X21519)
| ~ class_Fields_Ofield__inverse__zero(X21522) )
& ( X21519 = c_Groups_Ozero__class_Ozero(X21522)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21521),X21519) != X21520
| X21521 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21520),X21519)
| ~ class_Fields_Ofield__inverse__zero(X21522) )
& ( X21521 != c_Groups_Ozero__class_Ozero(X21522)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21521),X21519) != X21520
| X21521 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21520),X21519)
| ~ class_Fields_Ofield__inverse__zero(X21522) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])]) ).
fof(i_0_10316,plain,
! [X18968,X18969] :
( ~ class_Rings_Osemiring__1(X18969)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18969),hAPP(c_Nat_OSuc,X18968)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18969),c_Groups_Oone__class_Oone(X18969)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18969),X18968)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__Suc])]) ).
fof(i_0_10317,plain,
! [X18207] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X18207))),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_10318,plain,
! [X18392,X18393,X18394] : hAPP(c_Nat_Osize__class_Osize(tc_sum(X18394,X18393)),hAPP(c_Sum__Type_OInl(X18394,X18393),X18392)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_sum_Osize_I3_J]) ).
fof(i_0_10319,plain,
! [X18395,X18396,X18397] : hAPP(c_Nat_Osize__class_Osize(tc_sum(X18397,X18396)),hAPP(c_Sum__Type_OInr(X18396,X18397),X18395)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_sum_Osize_I4_J]) ).
fof(i_0_10320,plain,
! [X18231,X18232] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18232),X18231))
| X18232 != X18231 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_10321,plain,
! [X18229,X18230] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18230),X18229))
| X18229 != X18230 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_10322,plain,
! [X17313,X17314] :
( ( hBOOL(hAPP(c_Com_OWT,X17314))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17314,X17313))) )
& ( hBOOL(hAPP(c_Com_OWT,X17313))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17314,X17313))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5970])])]) ).
fof(i_0_10323,plain,
! [X17789,X17790] :
( ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X17790,X17789)))
| hBOOL(hAPP(c_Com_OWT,X17789)) )
& ( ~ hBOOL(hAPP(c_Com_OWT,X17789))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X17790,X17789))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I6_J])]) ).
fof(i_0_10324,plain,
! [X17721,X17722] :
( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X17722,X17721)))
| hBOOL(hAPP(c_Com_OWT,X17721)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I6_J])]) ).
cnf(i_0_10325,plain,
c_Divides_Odivmod__nat(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(split_conjunct,[status(thm)],[i_0_5971]) ).
fof(i_0_10326,plain,
! [X24850] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24850),hAPP(c_Nat_OSuc,X24850)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24850),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_atLeastLessThan__singleton]) ).
cnf(i_0_10327,plain,
( c_Divides_Odivmod__nat(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_5489]) ).
fof(i_0_10328,plain,
! [X34104,X34105,X34106] :
( ~ class_Orderings_Olinorder(X34106)
| ~ c_List_Olinorder__class_Osorted(X34106,X34105)
| c_List_Olinorder__class_Osorted(X34106,c_List_Oremove1(X34106,X34104,X34105)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__remove1])]) ).
fof(i_0_10329,plain,
! [X19212,X19213,X19214] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19214),X19213) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19212),X19213)
| X19214 = X19212
| X19213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19214 != X19212
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19214),X19213) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19212),X19213) )
& ( X19213 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19214),X19213) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19212),X19213) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).
fof(i_0_10330,plain,
! [X19718,X19719,X19720] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19720),X19719) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19720),X19718)
| X19720 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19719 = X19718 )
& ( X19720 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19720),X19719) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19720),X19718) )
& ( X19719 != X19718
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19720),X19719) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19720),X19718) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_10331,plain,
! [X19215,X19216,X19217] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19217),X19216) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19217),X19215)
| X19216 = X19215
| X19217 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19216 != X19215
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19217),X19216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19217),X19215) )
& ( X19217 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19217),X19216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19217),X19215) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).
fof(i_0_10332,plain,
! [X33458,X33459,X33460] :
( ( X33460 != c_List_Olist_ONil(X33459)
| hAPP(c_List_Ohd(X33459),hAPP(hAPP(c_List_Oappend(X33459),X33460),X33458)) = hAPP(c_List_Ohd(X33459),X33458) )
& ( X33460 = c_List_Olist_ONil(X33459)
| hAPP(c_List_Ohd(X33459),hAPP(hAPP(c_List_Oappend(X33459),X33460),X33458)) = hAPP(c_List_Ohd(X33459),X33460) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append])]) ).
fof(i_0_10333,plain,
! [X17971] :
( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17971)))
| hAPP(c_Com_Obody,X17971) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk22_1(X17971)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I7_J])])]) ).
fof(i_0_10334,plain,
! [X17904,X17906,X17907] :
( ( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17904)))
| hAPP(c_Com_Obody,X17904) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk16_1(X17904)) )
& ( hAPP(c_Com_Obody,X17906) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X17907)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17906))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I7_J])])])])]) ).
fof(i_0_10335,plain,
! [X17388,X17389] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X17389),X17388))
| X17388 = X17389 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I1_J])]) ).
fof(i_0_10336,plain,
! [X20785,X20786] :
( ~ class_Rings_Olinordered__idom(X20786)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20786),c_Groups_Osgn__class_Osgn(X20786,X20785)),hAPP(c_Groups_Oabs__class_Oabs(X20786),X20785)) = X20785 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs])]) ).
fof(i_0_10337,plain,
! [X25747] :
( ~ class_Rings_Oring__1(X25747)
| hBOOL(hAPP(hAPP(c_member(X25747),c_Groups_Oone__class_Oone(X25747)),c_Int_Oring__1__class_OInts(X25747))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).
fof(i_0_10338,plain,
! [X25659] :
( ~ class_Rings_Osemiring__1(X25659)
| hBOOL(hAPP(hAPP(c_member(X25659),c_Groups_Oone__class_Oone(X25659)),c_Nat_Osemiring__1__class_ONats(X25659))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__1])]) ).
fof(i_0_10339,plain,
! [X25735] :
( ~ class_Rings_Oring__1(X25735)
| hBOOL(hAPP(hAPP(c_member(X25735),c_Groups_Ozero__class_Ozero(X25735)),c_Int_Oring__1__class_OInts(X25735))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).
fof(i_0_10340,plain,
! [X25652] :
( ~ class_Rings_Osemiring__1(X25652)
| hBOOL(hAPP(hAPP(c_member(X25652),c_Groups_Ozero__class_Ozero(X25652)),c_Nat_Osemiring__1__class_ONats(X25652))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__0])]) ).
fof(i_0_10341,plain,
! [X19429] :
( ~ class_Rings_Olinordered__semidom(X19429)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19429),c_Groups_Ozero__class_Ozero(X19429)),c_Groups_Oone__class_Oone(X19429))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_10342,plain,
! [X18919] :
( ~ class_Rings_Olinordered__semidom(X18919)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18919),c_Groups_Ozero__class_Ozero(X18919)),c_Groups_Oone__class_Oone(X18919))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_10343,plain,
! [X21544,X21545,X21546,X21547] :
( ~ class_Rings_Odivision__ring(X21547)
| X21546 = c_Groups_Ozero__class_Ozero(X21547)
| X21545 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21547),X21544),X21546)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21547),X21545),X21546) = X21544 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__imp])]) ).
fof(i_0_10344,plain,
! [X21548,X21549,X21550,X21551] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21551),X21549),X21550) != X21548
| X21549 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21551),X21548),X21550)
| X21550 = c_Groups_Ozero__class_Ozero(X21551)
| ~ class_Rings_Odivision__ring(X21551) )
& ( X21549 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21551),X21548),X21550)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21551),X21549),X21550) = X21548
| X21550 = c_Groups_Ozero__class_Ozero(X21551)
| ~ class_Rings_Odivision__ring(X21551) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq])])]) ).
fof(i_0_10345,plain,
! [X21552,X21553,X21554,X21555] :
( ( X21553 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21555),X21552),X21554)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21555),X21553),X21554) = X21552
| X21554 = c_Groups_Ozero__class_Ozero(X21555)
| ~ class_Rings_Odivision__ring(X21555) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21555),X21553),X21554) != X21552
| X21553 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21555),X21552),X21554)
| X21554 = c_Groups_Ozero__class_Ozero(X21555)
| ~ class_Rings_Odivision__ring(X21555) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq])])]) ).
fof(i_0_10346,plain,
! [X21540,X21541,X21542,X21543] :
( ~ class_Rings_Odivision__ring(X21543)
| X21542 = c_Groups_Ozero__class_Ozero(X21543)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21543),X21541),X21542) != X21540
| X21541 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21543),X21540),X21542) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__imp])]) ).
fof(i_0_10347,plain,
! [X20386,X20387,X20388] :
( ~ class_Groups_Ogroup__add(X20388)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20388),X20387),hAPP(c_Groups_Ouminus__class_Ouminus(X20388),X20386)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20388),X20387),X20386) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).
fof(i_0_10348,plain,
! [X27315,X27316,X27317] :
( ~ class_Lattices_Oboolean__algebra(X27317)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27317),X27316),X27315) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27317),X27316),hAPP(c_Groups_Ouminus__class_Ouminus(X27317),X27315)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq])]) ).
fof(i_0_10349,plain,
! [X20383,X20384,X20385] :
( ~ class_Groups_Oab__group__add(X20385)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20385),X20384),X20383) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20385),X20384),hAPP(c_Groups_Ouminus__class_Ouminus(X20385),X20383)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).
fof(i_0_10350,plain,
! [X20380,X20381,X20382] :
( ~ class_Groups_Ogroup__add(X20382)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20382),X20381),X20380) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20382),X20381),hAPP(c_Groups_Ouminus__class_Ouminus(X20382),X20380)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).
fof(i_0_10351,plain,
! [X20389,X20390,X20391] :
( ~ class_Rings_Ocomm__ring__1(X20391)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20391),X20390),X20389) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20391),X20390),hAPP(c_Groups_Ouminus__class_Ouminus(X20391),X20389)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).
fof(i_0_10352,plain,
! [X21072,X21073] :
( ~ class_Int_Onumber__ring(X21073)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21073),hAPP(c_Int_Onumber__class_Onumber__of(X21073),c_Int_OMin)),X21072) = hAPP(c_Groups_Ouminus__class_Ouminus(X21073),X21072) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1])]) ).
fof(i_0_10353,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(fof_simplification,[status(thm)],[fact_bin__less__0__simps_I1_J]) ).
fof(i_0_10354,plain,
! [X18228] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18228),X18228)),
inference(variable_rename,[status(thm)],[i_0_5972]) ).
fof(i_0_10355,plain,
! [X18223] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18223),X18223)),
inference(variable_rename,[status(thm)],[i_0_5973]) ).
fof(i_0_10356,plain,
! [X33461,X33462,X33463] :
( X33463 = c_List_Olist_ONil(X33462)
| hAPP(c_List_Ohd(X33462),hAPP(hAPP(c_List_Oappend(X33462),X33463),X33461)) = hAPP(c_List_Ohd(X33462),X33463) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append2])]) ).
cnf(i_0_10357,plain,
( X1 = X2
| c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5974]) ).
fof(i_0_10358,plain,
! [X18032,X18033,X18034] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18034),X18033) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18032),X18033)
| X18034 = X18032 )
& ( X18034 != X18032
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18034),X18033) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18032),X18033) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_10359,plain,
! [X18035,X18036,X18037] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18037),X18036) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18037),X18035)
| X18036 = X18035 )
& ( X18036 != X18035
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18037),X18036) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18037),X18035) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_10360,plain,
! [X29162,X29163] : hAPP(c_Set_OCollect(X29163),hAPP(c_fequal,X29162)) = hAPP(hAPP(c_Set_Oinsert(X29163),X29162),c_Orderings_Obot__class_Obot(tc_fun(X29163,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).
fof(i_0_10361,plain,
! [X34080,X34081,X34082] :
( ~ class_Orderings_Olinorder(X34082)
| ~ c_List_Olinorder__class_Osorted(X34082,X34081)
| c_List_Olinorder__class_Osorted(X34082,hAPP(hAPP(c_List_Odrop(X34082),X34080),X34081)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__drop])]) ).
fof(i_0_10362,plain,
! [X34115,X34116,X34117] :
( ~ class_Orderings_Olinorder(X34117)
| ~ c_List_Olinorder__class_Osorted(X34117,X34116)
| c_List_Olinorder__class_Osorted(X34117,hAPP(hAPP(c_List_Otake(X34117),X34115),X34116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__take])]) ).
fof(i_0_10363,plain,
! [X24616] : hBOOL(hAPP(c_Finite__Set_Ofinite(X24616),c_Orderings_Obot__class_Obot(tc_fun(X24616,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_finite_Oequations_I1_J]) ).
fof(i_0_10364,plain,
! [X24613] : hBOOL(hAPP(c_Finite__Set_Ofinite(X24613),c_Orderings_Obot__class_Obot(tc_fun(X24613,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_finite_OemptyI]) ).
fof(i_0_10365,plain,
! [X26499,X26500] : hAPP(c_Set_OPow(X26500),X26499) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26500,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Pow__not__empty]) ).
fof(i_0_10366,plain,
! [X26128,X26129,X26130,X26131] :
( ~ class_Groups_Ocomm__monoid__mult(X26131)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X26130),X26129))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26130,X26131),X26128),X26129) = c_Groups_Oone__class_Oone(X26131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5975])]) ).
fof(i_0_10367,plain,
! [X26124,X26125,X26126,X26127] :
( ~ class_Groups_Ocomm__monoid__mult(X26127)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X26126),X26125))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26126,X26127),X26124),X26125) = c_Groups_Oone__class_Oone(X26127) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5976])]) ).
fof(i_0_10368,plain,
! [X24447,X24448,X24449,X24450] :
( ~ class_Groups_Ocomm__monoid__add(X24450)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24449),X24448))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24449,X24450),X24447),X24448) = c_Groups_Ozero__class_Ozero(X24450) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5977])]) ).
fof(i_0_10369,plain,
! [X24443,X24444,X24445,X24446] :
( ~ class_Groups_Ocomm__monoid__add(X24446)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24445),X24444))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24445,X24446),X24443),X24444) = c_Groups_Ozero__class_Ozero(X24446) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5978])]) ).
fof(i_0_10370,plain,
! [X24783] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24783,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X24783,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X24783,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
fof(i_0_10371,plain,
! [X24784] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24784,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X24784,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X24784,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
fof(i_0_10372,plain,
! [X26512] : hAPP(c_Set_OPow(X26512),c_Orderings_Otop__class_Otop(tc_fun(X26512,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X26512,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Pow__UNIV]) ).
fof(i_0_10373,plain,
! [X26427] : c_Relation_OId__on(X26427,c_Orderings_Obot__class_Obot(tc_fun(X26427,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X26427,X26427),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Id__on__empty]) ).
fof(i_0_10374,plain,
! [X27183,X27184] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27184,tc_HOL_Obool)),X27183),X27183) = X27183,
inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).
fof(i_0_10375,plain,
! [X23906,X23907] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23907,tc_HOL_Obool)),X23906),X23906) = X23906,
inference(variable_rename,[status(thm)],[fact_Un__absorb]) ).
fof(i_0_10376,plain,
! [X29846,X29847] :
( ~ c_Wellfounded_Owf(X29847,X29846)
| c_Wellfounded_OwfP(X29847,c_FunDef_Oin__rel(X29847,X29847,X29846)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__in__rel])]) ).
fof(i_0_10377,plain,
! [X29647,X29648,X29649] :
( ~ c_Wellfounded_Owf(X29649,X29648)
| c_Wellfounded_Owf(X29649,c_Wellfounded_Omlex__prod(X29649,X29647,X29648)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__mlex])]) ).
fof(i_0_10378,plain,
! [X21018] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21018))),
inference(variable_rename,[status(thm)],[i_0_5979]) ).
fof(i_0_10379,plain,
! [X29032,X29033] :
( ~ class_Lattices_Olattice(X29033)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29033),X29032))
| c_Big__Operators_Olattice__class_OInf__fin(X29033,X29032) = hAPP(c_Finite__Set_Ofold1(X29033,c_Lattices_Osemilattice__inf__class_Oinf(X29033)),X29032) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq])]) ).
fof(i_0_10380,plain,
! [X29034,X29035] :
( ~ class_Orderings_Olinorder(X29035)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29035),X29034))
| c_Big__Operators_Olinorder__class_OMin(X29035,X29034) = hAPP(c_Finite__Set_Ofold1(X29035,c_Orderings_Oord__class_Omin(X29035)),X29034) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_OF__eq])]) ).
fof(i_0_10381,plain,
! [X29036,X29037] :
( ~ class_Orderings_Olinorder(X29037)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29037),X29036))
| c_Big__Operators_Olinorder__class_OMax(X29037,X29036) = hAPP(c_Finite__Set_Ofold1(X29037,c_Orderings_Oord__class_Omax(X29037)),X29036) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_OF__eq])]) ).
fof(i_0_10382,plain,
! [X29030,X29031] :
( ~ class_Lattices_Olattice(X29031)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29031),X29030))
| c_Big__Operators_Olattice__class_OSup__fin(X29031,X29030) = hAPP(c_Finite__Set_Ofold1(X29031,c_Lattices_Osemilattice__sup__class_Osup(X29031)),X29030) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq])]) ).
fof(i_0_10383,plain,
! [X18216] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18216),hAPP(c_Nat_OSuc,X18216))),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_10384,plain,
! [X27311,X27312] :
( ~ class_Lattices_Oboolean__algebra(X27312)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27312),hAPP(c_Groups_Ouminus__class_Ouminus(X27312),X27311)),X27311) = c_Orderings_Obot__class_Obot(X27312) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf__bot])]) ).
fof(i_0_10385,plain,
! [X24343,X24344] :
( ~ class_Lattices_Oboolean__algebra(X24344)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24344),hAPP(c_Groups_Ouminus__class_Ouminus(X24344),X24343)),X24343) = c_Orderings_Otop__class_Otop(X24344) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup__top])]) ).
fof(i_0_10386,plain,
! [X18850,X18851] :
( ~ class_Groups_Oab__group__add(X18851)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18851),hAPP(c_Groups_Ouminus__class_Ouminus(X18851),X18850)),X18850) = c_Groups_Ozero__class_Ozero(X18851) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).
fof(i_0_10387,plain,
! [X18852,X18853] :
( ~ class_Groups_Ogroup__add(X18853)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18853),hAPP(c_Groups_Ouminus__class_Ouminus(X18853),X18852)),X18852) = c_Groups_Ozero__class_Ozero(X18853) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).
fof(i_0_10388,plain,
! [X33742,X33743,X33744] :
( ( X33744 != c_List_Olist_ONil(X33743)
| c_List_Olast(X33743,hAPP(hAPP(c_List_Oappend(X33743),X33742),X33744)) = c_List_Olast(X33743,X33742) )
& ( X33744 = c_List_Olist_ONil(X33743)
| c_List_Olast(X33743,hAPP(hAPP(c_List_Oappend(X33743),X33742),X33744)) = c_List_Olast(X33743,X33744) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__append])]) ).
fof(i_0_10389,plain,
! [X33736,X33737,X33738] :
( X33738 != c_List_Olist_ONil(X33737)
| c_List_Olast(X33737,hAPP(hAPP(c_List_Oappend(X33737),X33736),X33738)) = c_List_Olast(X33737,X33736) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendL])]) ).
fof(i_0_10390,plain,
! [X20400,X20401] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20401),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20401),X20400)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
fof(i_0_10391,plain,
! [X33081,X33082,X33083] : c_List_Osublist(X33083,X33082,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X33081)) = hAPP(hAPP(c_List_Otake(X33083),X33081),X33082),
inference(variable_rename,[status(thm)],[fact_sublist__upt__eq__take]) ).
fof(i_0_10392,plain,
! [X23065,X23066] :
( ~ class_Rings_Ocomm__semiring__1(X23066)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23066),c_Groups_Oone__class_Oone(X23066)),X23065)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__dvd])]) ).
fof(i_0_10393,plain,
! [X24670,X24671] :
( ~ class_Orderings_Obot(X24671)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24671),c_Orderings_Obot__class_Obot(X24671)),X24670)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__least])]) ).
fof(i_0_10394,plain,
! [X22192,X22193] :
( X22193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22192,X22193),c_Divides_Odivmod__int(X22192,X22193))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__correct])]) ).
fof(i_0_10395,plain,
! [X22122,X22123] :
( ( X22123 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Opdivmod(X22122,X22123) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22122)) )
& ( X22123 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Opdivmod(X22122,X22123) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22122),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22123)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__posDivAlg])]) ).
fof(i_0_10396,plain,
! [X34020,X34021] :
( ~ class_Orderings_Olinorder(X34021)
| c_List_Olinorder__class_Osorted(X34021,hAPP(hAPP(c_List_Olist_OCons(X34021),X34020),c_List_Olist_ONil(X34021))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__single])]) ).
fof(i_0_10397,plain,
! [X33739,X33740,X33741] :
( X33741 = c_List_Olist_ONil(X33740)
| c_List_Olast(X33740,hAPP(hAPP(c_List_Oappend(X33740),X33739),X33741)) = c_List_Olast(X33740,X33741) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendR])]) ).
fof(i_0_10398,plain,
! [X33751,X33752,X33753] :
( ( X33753 != c_List_Olist_ONil(X33752)
| c_List_Olast(X33752,hAPP(hAPP(c_List_Olist_OCons(X33752),X33751),X33753)) = X33751 )
& ( X33753 = c_List_Olist_ONil(X33752)
| c_List_Olast(X33752,hAPP(hAPP(c_List_Olist_OCons(X33752),X33751),X33753)) = c_List_Olast(X33752,X33753) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last_Osimps])]) ).
fof(i_0_10399,plain,
! [X33748,X33749,X33750] :
( X33750 = c_List_Olist_ONil(X33749)
| c_List_Olast(X33749,hAPP(hAPP(c_List_Olist_OCons(X33749),X33748),X33750)) = c_List_Olast(X33749,X33750) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsR])]) ).
fof(i_0_10400,plain,
! [X20600,X20601] :
( ( X20601 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nitpick_Onat__gcd(X20600,X20601) = X20600 )
& ( X20601 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nitpick_Onat__gcd(X20600,X20601) = c_Nitpick_Onat__gcd(X20601,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20600,X20601)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Osimps])]) ).
fof(i_0_10401,plain,
! [X24095,X24096] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24096)),X24095) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X24096,X24095),
inference(variable_rename,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan]) ).
fof(i_0_10402,plain,
! [X23799,X23800] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23800),X23799)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23799),X23800),
inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan]) ).
fof(i_0_10403,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(fof_simplification,[status(thm)],[fact_rel__simps_I20_J]) ).
fof(i_0_10404,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(fof_simplification,[status(thm)],[fact_rel__simps_I2_J]) ).
fof(i_0_10405,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(fof_simplification,[status(thm)],[fact_rel__simps_I3_J]) ).
fof(i_0_10406,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(fof_simplification,[status(thm)],[fact_rel__simps_I7_J]) ).
fof(i_0_10407,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(fof_simplification,[status(thm)],[fact_not__neg__number__of__Pls]) ).
fof(i_0_10408,plain,
! [X32529,X32530,X32531] : hAPP(hAPP(c_List_Ozip(X32531,X32530),c_List_Olist_ONil(X32531)),X32529) = c_List_Olist_ONil(tc_prod(X32531,X32530)),
inference(variable_rename,[status(thm)],[fact_zip__Nil]) ).
fof(i_0_10409,plain,
! [X24309,X24310] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X24310,tc_HOL_Obool)),X24309)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(i_0_10410,plain,
! [X29435,X29436] : hAPP(c_Set_Ovimage(X29436,X29436,c_Fun_Oid(X29436)),X29435) = X29435,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
fof(i_0_10411,plain,
! [X28320,X28321] : hAPP(c_Set_Ovimage(X28321,X28321,c_COMBI(X28321)),X28320) = X28320,
inference(variable_rename,[status(thm)],[fact_vimage__ident]) ).
fof(i_0_10412,plain,
! [X29449,X29450] : hAPP(c_Set_Oimage(X29450,X29450,c_Fun_Oid(X29450)),X29449) = X29449,
inference(variable_rename,[status(thm)],[fact_image__id]) ).
fof(i_0_10413,plain,
! [X24307,X24308] : hAPP(c_Set_Oimage(X24308,X24308,c_COMBI(X24308)),X24307) = X24307,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_10414,plain,
! [X18426,X18427,X18428] : c_Sum__Type_OProjr(X18428,X18427,hAPP(c_Sum__Type_OInr(X18427,X18428),X18426)) = X18426,
inference(variable_rename,[status(thm)],[fact_Projr_Osimps]) ).
fof(i_0_10415,plain,
! [X18423,X18424,X18425] : c_Sum__Type_OProjl(X18425,X18424,hAPP(c_Sum__Type_OInl(X18425,X18424),X18423)) = X18423,
inference(variable_rename,[status(thm)],[fact_Projl_Osimps]) ).
fof(i_0_10416,plain,
! [X30256,X30257] : c_Relation_Orefl__on(X30257,c_Orderings_Otop__class_Otop(tc_fun(X30257,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30257,X30256)),
inference(variable_rename,[status(thm)],[fact_refl__rtrancl]) ).
cnf(i_0_10417,plain,
c_Code__Numeral_OSuc__code__numeral(X1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[i_0_5980]) ).
cnf(i_0_10418,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X1),
inference(split_conjunct,[status(thm)],[i_0_5981]) ).
fof(i_0_10419,plain,
! [X34467,X34468] :
( ~ hBOOL(hAPP(hAPP(c_fimplies,X34468),X34467))
| ~ hBOOL(X34468)
| hBOOL(X34467) ),
inference(variable_rename,[status(thm)],[i_0_5982]) ).
fof(i_0_10420,plain,
! [X24166,X24167] :
( ~ class_Orderings_Olinorder(X24167)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24167,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X24167),X24166)) = hAPP(c_SetInterval_Oord__class_OlessThan(X24167),X24166) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atLeast])]) ).
fof(i_0_10421,plain,
! [X24119,X24120] :
( ~ class_Orderings_Olinorder(X24120)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24120,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24120),X24119)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X24120),X24119) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atMost])]) ).
fof(i_0_10422,plain,
! [X24117,X24118] :
( ~ class_Orderings_Olinorder(X24118)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24118,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X24118),X24117)) = hAPP(c_SetInterval_Oord__class_OatMost(X24118),X24117) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan])]) ).
fof(i_0_10423,plain,
! [X24164,X24165] :
( ~ class_Orderings_Olinorder(X24165)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24165,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24165),X24164)) = hAPP(c_SetInterval_Oord__class_OatLeast(X24165),X24164) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__lessThan])]) ).
fof(i_0_10424,plain,
! [X24842,X24843] :
( ( hAPP(c_Finite__Set_Ocard(X24843),X24842) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X24842 = c_Orderings_Obot__class_Obot(tc_fun(X24843,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24843),X24842)) )
& ( X24842 != c_Orderings_Obot__class_Obot(tc_fun(X24843,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(X24843),X24842) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24843),X24842))
| hAPP(c_Finite__Set_Ocard(X24843),X24842) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5983])])]) ).
fof(i_0_10425,plain,
! [X25698,X25699] : c_Hoare__Mirabelle_Ohoare__derivs(X25699,X25698,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25699),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_empty]) ).
fof(i_0_10426,plain,
! [X25696,X25697] : c_Hoare__Mirabelle_Ohoare__derivs(X25697,X25696,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X25697),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I1_J]) ).
fof(i_0_10427,plain,
! [X31429,X31430] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31430)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31430),X31429))
| X31429 = c_Orderings_Obot__class_Obot(tc_fun(X31430,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X31430,X31429) = c_Complete__Lattice_OSup__class_OSup(X31430,X31429) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup])]) ).
fof(i_0_10428,plain,
! [X31434,X31435] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31435)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31435),X31434))
| X31434 = c_Orderings_Obot__class_Obot(tc_fun(X31435,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X31435,X31434) = c_Complete__Lattice_OInf__class_OInf(X31435,X31434) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf])]) ).
fof(i_0_10429,plain,
! [X21113,X21114] :
( ~ class_Int_Onumber__ring(X21114)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21114),hAPP(c_Int_Onumber__class_Onumber__of(X21114),c_Int_OPls)),X21113) = X21113 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).
fof(i_0_10430,plain,
! [X18072,X18073] :
( ( X18073 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18073 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18073),X18072) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X18072 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18073 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18073),X18072) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X18073 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18073),X18072) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X18072 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18073),X18072) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X18073 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18072 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18073),X18072) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X18073 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18072 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18073),X18072) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__1])])]) ).
fof(i_0_10431,plain,
! [X18070,X18071] :
( ( X18071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18071 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18071),X18070) )
& ( X18070 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18071 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18071),X18070) )
& ( X18071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18071),X18070) )
& ( X18070 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18071),X18070) )
& ( X18071 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18070 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18071),X18070) )
& ( X18071 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18070 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18071),X18070) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_10432,plain,
! [X30024,X30025,X30026] :
( ~ hBOOL(hAPP(X30025,X30026))
| hBOOL(hAPP(X30025,c_Hilbert__Choice_OEps(X30024,X30025))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI__ex])])]) ).
fof(i_0_10433,plain,
! [X30011,X30012,X30013] :
( ~ hBOOL(hAPP(X30013,X30012))
| hBOOL(hAPP(X30013,c_Hilbert__Choice_OEps(X30011,X30013))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI])]) ).
fof(i_0_10434,plain,
! [X30008,X30009,X30010] :
( ~ hBOOL(hAPP(X30009,X30010))
| hBOOL(hAPP(X30009,c_Hilbert__Choice_OEps(X30008,X30009))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__some])])]) ).
fof(i_0_10435,plain,
! [X34461,X34462] :
( ~ hBOOL(hAPP(hAPP(c_fdisj,X34462),X34461))
| hBOOL(X34462)
| hBOOL(X34461) ),
inference(variable_rename,[status(thm)],[i_0_5984]) ).
fof(i_0_10436,plain,
! [X23725,X23726] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23726),X23725) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X23726,X23725),
inference(variable_rename,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost]) ).
fof(i_0_10437,plain,
! [X18650,X18651] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18651),X18650),X18650) != c_Groups_Oone__class_Oone(X18651)
| X18650 = c_Groups_Oone__class_Oone(X18651)
| X18650 = hAPP(c_Groups_Ouminus__class_Ouminus(X18651),c_Groups_Oone__class_Oone(X18651))
| ~ class_Rings_Oring__1__no__zero__divisors(X18651) )
& ( X18650 != c_Groups_Oone__class_Oone(X18651)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18651),X18650),X18650) = c_Groups_Oone__class_Oone(X18651)
| ~ class_Rings_Oring__1__no__zero__divisors(X18651) )
& ( X18650 != hAPP(c_Groups_Ouminus__class_Ouminus(X18651),c_Groups_Oone__class_Oone(X18651))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18651),X18650),X18650) = c_Groups_Oone__class_Oone(X18651)
| ~ class_Rings_Oring__1__no__zero__divisors(X18651) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).
fof(i_0_10438,plain,
! [X18416,X18417,X18418,X18419] :
( hAPP(c_Sum__Type_OInl(X18419,X18418),X18417) != hAPP(c_Sum__Type_OInl(X18419,X18418),X18416)
| X18417 = X18416 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inl__inject])]) ).
fof(i_0_10439,plain,
! [X18412,X18413,X18414,X18415] :
( ( hAPP(c_Sum__Type_OInl(X18415,X18414),X18413) != hAPP(c_Sum__Type_OInl(X18415,X18414),X18412)
| X18413 = X18412 )
& ( X18413 != X18412
| hAPP(c_Sum__Type_OInl(X18415,X18414),X18413) = hAPP(c_Sum__Type_OInl(X18415,X18414),X18412) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum_Osimps_I1_J])]) ).
fof(i_0_10440,plain,
! [X18408,X18409,X18410,X18411] :
( hAPP(c_Sum__Type_OInr(X18411,X18410),X18409) != hAPP(c_Sum__Type_OInr(X18411,X18410),X18408)
| X18409 = X18408 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inr__inject])]) ).
fof(i_0_10441,plain,
! [X18404,X18405,X18406,X18407] :
( ( hAPP(c_Sum__Type_OInr(X18407,X18406),X18405) != hAPP(c_Sum__Type_OInr(X18407,X18406),X18404)
| X18405 = X18404 )
& ( X18405 != X18404
| hAPP(c_Sum__Type_OInr(X18407,X18406),X18405) = hAPP(c_Sum__Type_OInr(X18407,X18406),X18404) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum_Osimps_I2_J])]) ).
fof(i_0_10442,plain,
! [X17092,X17093] :
( hAPP(X17093,esk1_2(X17092,X17093)) != hAPP(X17092,esk1_2(X17092,X17093))
| X17093 = X17092 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_10443,plain,
! [X32526,X32527,X32528] : hAPP(hAPP(c_List_Ozip(X32528,X32527),X32526),c_List_Olist_ONil(X32527)) = c_List_Olist_ONil(tc_prod(X32528,X32527)),
inference(variable_rename,[status(thm)],[fact_zip_Osimps_I1_J]) ).
fof(i_0_10444,plain,
! [X17131,X17132,X17133,X17134] :
( ~ c_Groups_Ocomm__monoid(X17134,X17133,X17132)
| hAPP(hAPP(X17133,X17131),X17132) = X17131 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__monoid_Ocomm__neutral])]) ).
fof(i_0_10445,plain,
! [X26513,X26514,X26515,X26516] :
( ~ c_Finite__Set_Ofolding__one__idem(X26516,X26515,X26514)
| hAPP(hAPP(X26515,X26513),X26513) = X26513 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem])]) ).
fof(i_0_10446,plain,
! [X17109,X17110,X17111] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X17111,X17110,X17109)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I16_J]) ).
fof(i_0_10447,plain,
! [X23044,X23045] :
( ~ class_Rings_Ocomm__semiring__1(X23045)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23045),X23044),c_Groups_Ozero__class_Ozero(X23045))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__right])]) ).
fof(i_0_10448,plain,
! [X24325,X24326] :
( ~ class_Orderings_Otop(X24326)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24326),X24325),c_Orderings_Otop__class_Otop(X24326))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).
fof(i_0_10449,plain,
! [X18388,X18389,X18390,X18391] : hAPP(c_Sum__Type_OInl(X18391,X18390),X18389) != hAPP(c_Sum__Type_OInr(X18390,X18391),X18388),
inference(variable_rename,[status(thm)],[fact_Inl__not__Inr]) ).
fof(i_0_10450,plain,
! [X18384,X18385,X18386,X18387] : hAPP(c_Sum__Type_OInl(X18387,X18386),X18385) != hAPP(c_Sum__Type_OInr(X18386,X18387),X18384),
inference(variable_rename,[status(thm)],[fact_sum_Osimps_I3_J]) ).
fof(i_0_10451,plain,
! [X18380,X18381,X18382,X18383] : hAPP(c_Sum__Type_OInr(X18383,X18382),X18381) != hAPP(c_Sum__Type_OInl(X18382,X18383),X18380),
inference(variable_rename,[status(thm)],[fact_Inr__not__Inl]) ).
fof(i_0_10452,plain,
! [X18376,X18377,X18378,X18379] : hAPP(c_Sum__Type_OInr(X18379,X18378),X18377) != hAPP(c_Sum__Type_OInl(X18378,X18379),X18376),
inference(variable_rename,[status(thm)],[fact_sum_Osimps_I4_J]) ).
fof(i_0_10453,plain,
! [X33745,X33746,X33747] :
( X33747 != c_List_Olist_ONil(X33746)
| c_List_Olast(X33746,hAPP(hAPP(c_List_Olist_OCons(X33746),X33745),X33747)) = X33745 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsL])]) ).
fof(i_0_10454,plain,
! [X21988,X21989,X21990] : hAPP(c_Nat_Onat_Onat__rec(X21990,X21989,X21988),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21989,
inference(variable_rename,[status(thm)],[fact_nat__rec__0]) ).
fof(i_0_10455,plain,
! [X24620,X24621,X24622] : hAPP(hAPP(c_Set_Oinsert(X24622),X24621),X24620) != c_Orderings_Obot__class_Obot(tc_fun(X24622,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_insert__not__empty]) ).
fof(i_0_10456,plain,
! [X24617,X24618,X24619] : c_Orderings_Obot__class_Obot(tc_fun(X24619,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X24619),X24618),X24617),
inference(variable_rename,[status(thm)],[fact_empty__not__insert]) ).
fof(i_0_10457,plain,
! [X34453,X34454] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X34454),X34453))
| hBOOL(X34454) ),
inference(variable_rename,[status(thm)],[i_0_5985]) ).
fof(i_0_10458,plain,
! [X34455,X34456] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X34456),X34455))
| hBOOL(X34455) ),
inference(variable_rename,[status(thm)],[i_0_5986]) ).
fof(i_0_10459,plain,
! [X18625] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X18625)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18625)),
inference(variable_rename,[status(thm)],[fact_int__Suc]) ).
fof(i_0_10460,plain,
! [X20450,X20451] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20451),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20450)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20451),X20450),
inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(i_0_10461,plain,
! [X20452,X20453] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20453),X20452) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20453),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20452)),
inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).
fof(i_0_10462,plain,
! [X33491,X33492,X33493] : hAPP(c_List_Otl(X33493),hAPP(hAPP(c_List_Olist_OCons(X33493),X33492),X33491)) = X33491,
inference(variable_rename,[status(thm)],[fact_tl_Osimps_I2_J]) ).
fof(i_0_10463,plain,
! [X33455,X33456,X33457] : hAPP(c_List_Ohd(X33457),hAPP(hAPP(c_List_Olist_OCons(X33457),X33456),X33455)) = X33456,
inference(variable_rename,[status(thm)],[fact_hd_Osimps]) ).
fof(i_0_10464,plain,
! [X20927,X20928,X20929] :
( ( X20928 = c_Groups_Ozero__class_Ozero(X20929)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20929),X20928),X20927) != c_Groups_Ozero__class_Ozero(X20929)
| ~ class_Power_Opower(X20929)
| ~ class_Rings_Omult__zero(X20929)
| ~ class_Rings_Ono__zero__divisors(X20929)
| ~ class_Rings_Ozero__neq__one(X20929) )
& ( X20927 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20929),X20928),X20927) != c_Groups_Ozero__class_Ozero(X20929)
| ~ class_Power_Opower(X20929)
| ~ class_Rings_Omult__zero(X20929)
| ~ class_Rings_Ono__zero__divisors(X20929)
| ~ class_Rings_Ozero__neq__one(X20929) )
& ( X20928 != c_Groups_Ozero__class_Ozero(X20929)
| X20927 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20929),X20928),X20927) = c_Groups_Ozero__class_Ozero(X20929)
| ~ class_Power_Opower(X20929)
| ~ class_Rings_Omult__zero(X20929)
| ~ class_Rings_Ono__zero__divisors(X20929)
| ~ class_Rings_Ozero__neq__one(X20929) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).
fof(i_0_10465,plain,
! [X21473,X21474] :
( ~ c_Nat__Transfer_Ois__nat(X21474)
| ~ c_Nat__Transfer_Ois__nat(X21473)
| c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X21474,X21473)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J])]) ).
fof(i_0_10466,plain,
! [X17787,X17788] :
( ~ hBOOL(hAPP(c_Com_OWT,X17788))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X17787,X17788))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_While])]) ).
fof(i_0_10467,plain,
! [X29182,X29183,X29184,X29185,X29187] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X29183,tc_HOL_Obool)) != hAPP(c_Set_OCollect(X29183),X29182)
| ~ hBOOL(hAPP(X29182,X29184)) )
& ( hBOOL(hAPP(X29185,esk310_1(X29185)))
| c_Orderings_Obot__class_Obot(tc_fun(X29187,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X29187),X29185) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5987])])])])]) ).
fof(i_0_10468,plain,
! [X29188,X29189,X29190,X29191,X29193] :
( ( hAPP(c_Set_OCollect(X29189),X29188) != c_Orderings_Obot__class_Obot(tc_fun(X29189,tc_HOL_Obool))
| ~ hBOOL(hAPP(X29188,X29190)) )
& ( hBOOL(hAPP(X29191,esk311_1(X29191)))
| hAPP(c_Set_OCollect(X29193),X29191) = c_Orderings_Obot__class_Obot(tc_fun(X29193,tc_HOL_Obool)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5988])])])])]) ).
fof(i_0_10469,plain,
! [X34445,X34446] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X34446),X34445))
| X34446 = X34445 ),
inference(variable_rename,[status(thm)],[i_0_5989]) ).
fof(i_0_10470,plain,
! [X21714,X21715] :
( ~ class_Fields_Ofield__inverse__zero(X21715)
| ~ class_Int_Onumber__ring(X21715)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21715),X21714),hAPP(c_Int_Onumber__class_Onumber__of(X21715),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X21715),X21714) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__minus1])]) ).
fof(i_0_10471,plain,
! [X29695,X29696,X29697] :
( ~ c_Wellfounded_Owf(X29697,X29696)
| c_Wellfounded_Owf(tc_List_Olist(X29697),hAPP(c_List_Olexn(X29697,X29696),X29695)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lexn])]) ).
fof(i_0_10472,plain,
! [X32738,X32739,X32740] : hAPP(hAPP(c_List_Olist__update(X32740,c_List_Olist_ONil(X32740)),X32739),X32738) = c_List_Olist_ONil(X32740),
inference(variable_rename,[status(thm)],[fact_list__update__code_I1_J]) ).
fof(i_0_10473,plain,
! [X32735,X32736,X32737] : hAPP(hAPP(c_List_Olist__update(X32737,c_List_Olist_ONil(X32737)),X32736),X32735) = c_List_Olist_ONil(X32737),
inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I1_J]) ).
fof(i_0_10474,plain,
! [X20865] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20865) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).
fof(i_0_10475,plain,
! [X31833,X31834] : hBOOL(hAPP(c_Finite__Set_Ofinite(X31834),hAPP(c_List_Oset(X31834),X31833))),
inference(variable_rename,[status(thm)],[fact_finite__set]) ).
fof(i_0_10476,plain,
! [X30362,X30363,X30364] : hAPP(c_Relation_Oconverse(X30364,X30363),hAPP(c_Relation_Oconverse(X30363,X30364),X30362)) = X30362,
inference(variable_rename,[status(thm)],[fact_converse__converse]) ).
fof(i_0_10477,plain,
! [X17159,X17160,X17161,X17162] :
( ( X17162 = X17160
| hAPP(hAPP(c_String_Ochar_OChar,X17162),X17161) != hAPP(hAPP(c_String_Ochar_OChar,X17160),X17159) )
& ( X17161 = X17159
| hAPP(hAPP(c_String_Ochar_OChar,X17162),X17161) != hAPP(hAPP(c_String_Ochar_OChar,X17160),X17159) )
& ( X17162 != X17160
| X17161 != X17159
| hAPP(hAPP(c_String_Ochar_OChar,X17162),X17161) = hAPP(hAPP(c_String_Ochar_OChar,X17160),X17159) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_char_Oinject])])]) ).
fof(i_0_10478,plain,
! [X24451] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24451)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24451),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24451)),
inference(variable_rename,[status(thm)],[fact_lessThan__Suc]) ).
fof(i_0_10479,plain,
! [X30367,X30368] : hAPP(c_Relation_OField(X30368),hAPP(c_Relation_Oconverse(X30368,X30368),X30367)) = hAPP(c_Relation_OField(X30368),X30367),
inference(variable_rename,[status(thm)],[fact_Field__converse]) ).
fof(i_0_10480,plain,
! [X20781,X20782] :
( ~ class_Int_Onumber__ring(X20782)
| hAPP(c_Int_Onumber__class_Onumber__of(X20782),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20781)) = hAPP(c_Groups_Ouminus__class_Ouminus(X20782),hAPP(c_Int_Onumber__class_Onumber__of(X20782),X20781)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__minus])]) ).
fof(i_0_10481,plain,
! [X18659,X18660] :
( ~ class_Rings_Oring__1(X18660)
| hAPP(c_Int_Oring__1__class_Oof__int(X18660),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18659)) = hAPP(c_Groups_Ouminus__class_Ouminus(X18660),hAPP(c_Int_Oring__1__class_Oof__int(X18660),X18659)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__minus])]) ).
fof(i_0_10482,plain,
! [X20779,X20780] :
( ~ class_Int_Onumber__ring(X20780)
| hAPP(c_Groups_Ouminus__class_Ouminus(X20780),hAPP(c_Int_Onumber__class_Onumber__of(X20780),X20779)) = hAPP(c_Int_Onumber__class_Onumber__of(X20780),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20779)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])]) ).
fof(i_0_10483,plain,
! [X20863,X20864] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20864),X20863) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X20863 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20864 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X20863 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20864),X20863) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X20864 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20864),X20863) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff])])]) ).
fof(i_0_10484,plain,
! [X19081,X19082,X19083] :
( ~ class_Orderings_Opreorder(X19083)
| X19082 != X19081
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19083),X19082),X19081)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_10485,plain,
! [X18096,X18097] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X18097,X18096)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X18096)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_com_Osize_I6_J]) ).
fof(i_0_10486,plain,
! [X18847,X18848,X18849] :
( ~ class_Groups_Ogroup__add(X18849)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18849),X18848),X18847) != c_Groups_Ozero__class_Ozero(X18849)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18849),X18848) = X18847 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).
fof(i_0_10487,plain,
! [X18854,X18855,X18856] :
( ( X18855 != hAPP(c_Groups_Ouminus__class_Ouminus(X18856),X18854)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18856),X18855),X18854) = c_Groups_Ozero__class_Ozero(X18856)
| ~ class_Groups_Ogroup__add(X18856) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18856),X18855),X18854) != c_Groups_Ozero__class_Ozero(X18856)
| X18855 = hAPP(c_Groups_Ouminus__class_Ouminus(X18856),X18854)
| ~ class_Groups_Ogroup__add(X18856) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).
fof(i_0_10488,plain,
! [X29181] : c_Orderings_Obot__class_Obot(tc_fun(X29181,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X29181),hAPP(c_COMBK(tc_HOL_Obool,X29181),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(i_0_10489,plain,
! [X29210] : c_Orderings_Otop__class_Otop(tc_fun(X29210,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X29210),hAPP(c_COMBK(tc_HOL_Obool,X29210),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(i_0_10490,plain,
! [X23811,X23812] :
( ~ c_Nat__Transfer_Ois__nat(X23812)
| c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X23812,X23811)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures])]) ).
fof(i_0_10491,plain,
! [X21074,X21075] :
( ~ class_Int_Onumber__ring(X21075)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21075),X21074),hAPP(c_Int_Onumber__class_Onumber__of(X21075),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X21075),X21074) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1__right])]) ).
fof(i_0_10492,plain,
! [X19439,X19440] :
( ( X19440 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19440),X19439) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X19439 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19440),X19439) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X19440 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X19439 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19440),X19439) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff])])]) ).
fof(i_0_10493,plain,
! [X18085] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X18085)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X18085)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_nat_Osize_I2_J]) ).
fof(i_0_10494,plain,
! [X23134,X23135] :
( ~ class_Rings_Ocomm__semiring__1(X23135)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23135),X23134),X23134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__refl])]) ).
fof(i_0_10495,plain,
! [X18992,X18993] :
( ~ class_Orderings_Opreorder(X18993)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18993),X18992),X18992)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_10496,plain,
! [X23775] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23775)) = hAPP(c_Int_Onat,X23775),
inference(variable_rename,[status(thm)],[fact_card__atLeastZeroLessThan__int]) ).
fof(i_0_10497,plain,
! [X17106,X17107,X17108] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X17108,X17107,X17106)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I8_J]) ).
fof(i_0_10498,plain,
! [X18931] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18931)),X18931) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(i_0_10499,plain,
! [X23569,X23570] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23570),hAPP(c_Nat_OSuc,X23569)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23570,X23569),
inference(variable_rename,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost]) ).
fof(i_0_10500,plain,
! [X22171,X22172] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X22172,X22171) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X22172,X22171)),
inference(variable_rename,[status(thm)],[fact_mod__int__def]) ).
fof(i_0_10501,plain,
! [X27229,X27230,X27231] :
( ~ class_Lattices_Osemilattice__inf(X27231)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27231),X27230),X27229) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27231),X27229),X27230) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Ocommute])]) ).
fof(i_0_10502,plain,
! [X27223,X27224,X27225] :
( ~ class_Lattices_Osemilattice__inf(X27225)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27225),X27224),X27223) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27225),X27223),X27224) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])]) ).
fof(i_0_10503,plain,
! [X27226,X27227,X27228] :
( ~ class_Lattices_Olattice(X27228)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27228),X27227),X27226) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27228),X27226),X27227) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])]) ).
fof(i_0_10504,plain,
! [X23952,X23953,X23954] :
( ~ class_Lattices_Osemilattice__sup(X23954)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23954),X23953),X23952) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23954),X23952),X23953) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Ocommute])]) ).
fof(i_0_10505,plain,
! [X23946,X23947,X23948] :
( ~ class_Lattices_Osemilattice__sup(X23948)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23948),X23947),X23946) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23948),X23946),X23947) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__commute])]) ).
fof(i_0_10506,plain,
! [X23949,X23950,X23951] :
( ~ class_Lattices_Olattice(X23951)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23951),X23950),X23949) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23951),X23949),X23950) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J])]) ).
fof(i_0_10507,plain,
! [X22645,X22646,X22647] :
( ~ class_Orderings_Olinorder(X22647)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22647),X22646),X22645) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22647),X22645),X22646) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__commute])]) ).
fof(i_0_10508,plain,
! [X22642,X22643,X22644] :
( ~ class_Orderings_Olinorder(X22644)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22644),X22643),X22642) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22644),X22642),X22643) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Ocommute])]) ).
fof(i_0_10509,plain,
! [X22316,X22317,X22318] :
( ~ class_Orderings_Olinorder(X22318)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22318),X22317),X22316) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22318),X22316),X22317) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__commute])]) ).
fof(i_0_10510,plain,
! [X22313,X22314,X22315] :
( ~ class_Orderings_Olinorder(X22315)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22315),X22314),X22313) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22315),X22313),X22314) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute])]) ).
fof(i_0_10511,plain,
! [X18670,X18671,X18672] :
( ~ class_Rings_Ocomm__semiring__1(X18672)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18672),X18671),X18670) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18672),X18670),X18671) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(i_0_10512,plain,
! [X18146,X18147,X18148] :
( ~ class_Rings_Ocomm__semiring__1(X18148)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18148),X18147),X18146) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18148),X18146),X18147) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_10513,plain,
! [X18745] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18745))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat__zminus__int]) ).
fof(i_0_10514,plain,
! [X18270] :
( X18270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_10515,plain,
! [X21475,X21476] :
( ~ c_Nat__Transfer_Ois__nat(X21476)
| ~ c_Nat__Transfer_Ois__nat(X21475)
| c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21476),X21475)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J])]) ).
fof(i_0_10516,plain,
! [X21471,X21472] :
( ~ c_Nat__Transfer_Ois__nat(X21472)
| ~ c_Nat__Transfer_Ois__nat(X21471)
| c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21472),X21471)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J])]) ).
fof(i_0_10517,plain,
! [X21468,X21469] :
( ~ c_Nat__Transfer_Ois__nat(X21469)
| ~ c_Nat__Transfer_Ois__nat(X21468)
| c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21469),X21468)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J])]) ).
fof(i_0_10518,plain,
! [X18932,X18933] :
( ( X18933 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18933)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18932) )
& ( X18932 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18933)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18932) )
& ( X18933 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18932 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18933)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18932) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__eq__positive])])]) ).
fof(i_0_10519,plain,
! [X17825,X17826,X17827,X17828,X17829] : c_Com_Ocom_OLocal(X17829,X17828,X17827) != c_Com_Ocom_OWhile(X17826,X17825),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I38_J]) ).
fof(i_0_10520,plain,
! [X17430,X17431,X17432,X17433,X17434] : c_Com_Ocom_OLocal(X17434,X17433,X17432) != c_Com_Ocom_OSemi(X17431,X17430),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I34_J]) ).
fof(i_0_10521,plain,
! [X17533,X17534,X17535,X17536,X17537] : c_Com_Ocom_OLocal(X17537,X17536,X17535) != c_Com_Ocom_OAss(X17534,X17533),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I23_J]) ).
fof(i_0_10522,plain,
! [X17797,X17798,X17799,X17800,X17801] : c_Com_Ocom_OCond(X17801,X17800,X17799) != c_Com_Ocom_OWhile(X17798,X17797),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I52_J]) ).
fof(i_0_10523,plain,
! [X17425,X17426,X17427,X17428,X17429] : c_Com_Ocom_OCond(X17429,X17428,X17427) != c_Com_Ocom_OSemi(X17426,X17425),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I45_J]) ).
fof(i_0_10524,plain,
! [X17565,X17566,X17567,X17568,X17569] : c_Com_Ocom_OCond(X17569,X17568,X17567) != c_Com_Ocom_OAss(X17566,X17565),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I27_J]) ).
fof(i_0_10525,plain,
! [X17815,X17816,X17817,X17818,X17819] : c_Com_Ocom_OCall(X17819,X17818,X17817) != c_Com_Ocom_OWhile(X17816,X17815),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I61_J]) ).
fof(i_0_10526,plain,
! [X17607,X17608,X17609,X17610,X17611] : c_Com_Ocom_OCall(X17611,X17610,X17609) != c_Com_Ocom_OSemi(X17608,X17607),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I51_J]) ).
fof(i_0_10527,plain,
! [X17150,X17151,X17152,X17153,X17154] : c_Com_Ocom_OCall(X17154,X17153,X17152) != c_Com_Ocom_OAss(X17151,X17150),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I33_J]) ).
fof(i_0_10528,plain,
! [X17830,X17831,X17832,X17833,X17834] : c_Com_Ocom_OWhile(X17834,X17833) != c_Com_Ocom_OLocal(X17832,X17831,X17830),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I39_J]) ).
fof(i_0_10529,plain,
! [X17802,X17803,X17804,X17805,X17806] : c_Com_Ocom_OWhile(X17806,X17805) != c_Com_Ocom_OCond(X17804,X17803,X17802),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I53_J]) ).
fof(i_0_10530,plain,
! [X17820,X17821,X17822,X17823,X17824] : c_Com_Ocom_OWhile(X17824,X17823) != c_Com_Ocom_OCall(X17822,X17821,X17820),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I60_J]) ).
fof(i_0_10531,plain,
! [X17420,X17421,X17422,X17423,X17424] : c_Com_Ocom_OSemi(X17424,X17423) != c_Com_Ocom_OLocal(X17422,X17421,X17420),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I35_J]) ).
fof(i_0_10532,plain,
! [X17415,X17416,X17417,X17418,X17419] : c_Com_Ocom_OSemi(X17419,X17418) != c_Com_Ocom_OCond(X17417,X17416,X17415),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I44_J]) ).
fof(i_0_10533,plain,
! [X17602,X17603,X17604,X17605,X17606] : c_Com_Ocom_OSemi(X17606,X17605) != c_Com_Ocom_OCall(X17604,X17603,X17602),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I50_J]) ).
fof(i_0_10534,plain,
! [X17528,X17529,X17530,X17531,X17532] : c_Com_Ocom_OAss(X17532,X17531) != c_Com_Ocom_OLocal(X17530,X17529,X17528),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I22_J]) ).
fof(i_0_10535,plain,
! [X17560,X17561,X17562,X17563,X17564] : c_Com_Ocom_OAss(X17564,X17563) != c_Com_Ocom_OCond(X17562,X17561,X17560),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I26_J]) ).
fof(i_0_10536,plain,
! [X17142,X17143,X17144,X17145,X17146] : c_Com_Ocom_OAss(X17146,X17145) != c_Com_Ocom_OCall(X17144,X17143,X17142),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I32_J]) ).
cnf(i_0_10537,plain,
hAPP(c_Code__Numeral_Onat__of,X1) = c_Code__Numeral_Onat__of__aux(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_5990]) ).
fof(i_0_10538,plain,
! [X19226] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19226)),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_10539,plain,
! [X18994] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18994)),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_10540,plain,
! [X30491,X30492] : c_Relation_Ototal__on(X30492,c_Orderings_Obot__class_Obot(tc_fun(X30492,tc_HOL_Obool)),X30491),
inference(variable_rename,[status(thm)],[fact_total__on__empty]) ).
fof(i_0_10541,plain,
! [X18792,X18793,X18794] :
( ~ class_Rings_Ono__zero__divisors(X18794)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18794),X18793),X18792) != c_Groups_Ozero__class_Ozero(X18794)
| X18793 = c_Groups_Ozero__class_Ozero(X18794)
| X18792 = c_Groups_Ozero__class_Ozero(X18794) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).
fof(i_0_10542,plain,
! [X18789,X18790,X18791] :
( ~ class_Rings_Ono__zero__divisors(X18791)
| X18790 = c_Groups_Ozero__class_Ozero(X18791)
| X18789 = c_Groups_Ozero__class_Ozero(X18791)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18791),X18790),X18789) != c_Groups_Ozero__class_Ozero(X18791) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
fof(i_0_10543,plain,
! [X18786,X18787,X18788] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18788),X18787),X18786) != c_Groups_Ozero__class_Ozero(X18788)
| X18787 = c_Groups_Ozero__class_Ozero(X18788)
| X18786 = c_Groups_Ozero__class_Ozero(X18788)
| ~ class_Rings_Oring__no__zero__divisors(X18788) )
& ( X18787 != c_Groups_Ozero__class_Ozero(X18788)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18788),X18787),X18786) = c_Groups_Ozero__class_Ozero(X18788)
| ~ class_Rings_Oring__no__zero__divisors(X18788) )
& ( X18786 != c_Groups_Ozero__class_Ozero(X18788)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18788),X18787),X18786) = c_Groups_Ozero__class_Ozero(X18788)
| ~ class_Rings_Oring__no__zero__divisors(X18788) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).
fof(i_0_10544,plain,
! [X21927] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21927) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_posDivAlg__0]) ).
fof(i_0_10545,plain,
! [X22403,X22404] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22404),X22403) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X22404,X22403)),
inference(variable_rename,[status(thm)],[fact_div__int__def]) ).
fof(i_0_10546,plain,
! [X20933,X20934] :
( ~ class_Power_Opower(X20934)
| ~ class_Rings_Osemiring__0(X20934)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20934),c_Groups_Ozero__class_Ozero(X20934)),hAPP(c_Nat_OSuc,X20933)) = c_Groups_Ozero__class_Ozero(X20934) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).
fof(i_0_10547,plain,
! [X21705,X21706] :
( ~ class_Fields_Ofield__inverse__zero(X21706)
| ~ class_Int_Onumber__ring(X21706)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21706),X21705),hAPP(c_Int_Onumber__class_Onumber__of(X21706),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X21706) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral0])]) ).
fof(i_0_10548,plain,
! [X20783,X20784] :
( ~ class_Rings_Olinordered__idom(X20784)
| hAPP(c_Groups_Oabs__class_Oabs(X20784),X20783) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20784),X20783),c_Groups_Osgn__class_Osgn(X20784,X20783)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__sgn])]) ).
fof(i_0_10549,plain,
! [X17498,X17499,X17500,X17501] : c_Com_Ocom_OLocal(X17501,X17500,X17499) != hAPP(c_Com_Ocom_OBODY,X17498),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I40_J]) ).
fof(i_0_10550,plain,
! [X17512,X17513,X17514,X17515] : c_Com_Ocom_OCond(X17515,X17514,X17513) != hAPP(c_Com_Ocom_OBODY,X17512),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I54_J]) ).
fof(i_0_10551,plain,
! [X17214,X17215,X17216,X17217] : c_Com_Ocom_OCall(X17217,X17216,X17215) != hAPP(c_Com_Ocom_OBODY,X17214),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I63_J]) ).
fof(i_0_10552,plain,
! [X17494,X17495,X17496,X17497] : hAPP(c_Com_Ocom_OBODY,X17497) != c_Com_Ocom_OLocal(X17496,X17495,X17494),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I41_J]) ).
fof(i_0_10553,plain,
! [X17508,X17509,X17510,X17511] : hAPP(c_Com_Ocom_OBODY,X17511) != c_Com_Ocom_OCond(X17510,X17509,X17508),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I55_J]) ).
fof(i_0_10554,plain,
! [X17210,X17211,X17212,X17213] : hAPP(c_Com_Ocom_OBODY,X17213) != c_Com_Ocom_OCall(X17212,X17211,X17210),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I62_J]) ).
fof(i_0_10555,plain,
! [X33691] : c_List_Olists(X33691,c_Orderings_Otop__class_Otop(tc_fun(X33691,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X33691),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_lists__UNIV]) ).
fof(i_0_10556,plain,
! [X31753,X31754] : hAPP(hAPP(c_List_Omap(X31754,X31754),c_COMBI(X31754)),X31753) = X31753,
inference(variable_rename,[status(thm)],[fact_map__ident]) ).
fof(i_0_10557,plain,
! [X29794,X29795,X29796] :
( ~ c_Wellfounded_OwfP(X29796,X29795)
| hBOOL(hAPP(c_Wellfounded_Oaccp(X29796,X29795),X29794)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__wfPD])]) ).
fof(i_0_10558,plain,
! [X29358,X29359,X29360] :
( ~ c_Predicate_Oreflp(X29360,X29359)
| hBOOL(hAPP(hAPP(X29359,X29358),X29358)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflpE])]) ).
fof(i_0_10559,plain,
! [X27824,X27825,X27826] :
( ~ c_Equiv__Relations_Oequivp(X27826,X27825)
| hBOOL(hAPP(hAPP(X27825,X27824),X27824)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp])]) ).
fof(i_0_10560,plain,
! [X32551,X32552] : c_List_Osublist(X32552,X32551,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X32552),
inference(variable_rename,[status(thm)],[fact_sublist__empty]) ).
fof(i_0_10561,plain,
! [X21556,X21557,X21558] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21558),X21556),X21557) != c_Groups_Oone__class_Oone(X21558)
| X21556 = X21557
| X21557 = c_Groups_Ozero__class_Ozero(X21558)
| ~ class_Rings_Odivision__ring(X21558) )
& ( X21556 != X21557
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21558),X21556),X21557) = c_Groups_Oone__class_Oone(X21558)
| X21557 = c_Groups_Ozero__class_Ozero(X21558)
| ~ class_Rings_Odivision__ring(X21558) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])]) ).
fof(i_0_10562,plain,
! [X34280,X34281] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34281)),hAPP(c_List_Orev(X34281),X34280)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34281)),X34280),
inference(variable_rename,[status(thm)],[fact_length__rev]) ).
fof(i_0_10563,plain,
! [X33334,X33335] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33335)),hAPP(c_List_Orotate1(X33335),X33334)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33335)),X33334),
inference(variable_rename,[status(thm)],[fact_length__rotate1]) ).
fof(i_0_10564,plain,
! [X30004,X30005,X30006,X30007] :
( ~ hBOOL(hAPP(X30006,X30007))
| X30005 != c_Hilbert__Choice_OEps(X30004,X30006)
| hBOOL(hAPP(X30006,X30005)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exE__some])])]) ).
fof(i_0_10565,plain,
! [X30522,X30523] : hAPP(hAPP(c_Nat_Ocompow(X30523,X30523),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30522) = c_Fun_Oid(X30523),
inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I1_J]) ).
fof(i_0_10566,plain,
! [X31903,X31904,X31905] : hAPP(hAPP(c_Option_Omap(X31905,X31904),X31903),c_Option_Ooption_ONone(X31905)) = c_Option_Ooption_ONone(X31904),
inference(variable_rename,[status(thm)],[fact_option__map__None]) ).
fof(i_0_10567,plain,
! [X32501,X32502,X32503] : hAPP(hAPP(c_List_Omap(X32503,X32502),X32501),c_List_Olist_ONil(X32503)) = c_List_Olist_ONil(X32502),
inference(variable_rename,[status(thm)],[fact_map_Osimps_I1_J]) ).
fof(i_0_10568,plain,
! [X27313,X27314] :
( ~ class_Lattices_Oboolean__algebra(X27314)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27314),X27313),hAPP(c_Groups_Ouminus__class_Ouminus(X27314),X27313)) = c_Orderings_Obot__class_Obot(X27314) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__compl__bot])]) ).
fof(i_0_10569,plain,
! [X24341,X24342] :
( ~ class_Lattices_Oboolean__algebra(X24342)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24342),X24341),hAPP(c_Groups_Ouminus__class_Ouminus(X24342),X24341)) = c_Orderings_Otop__class_Otop(X24342) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__compl__top])]) ).
fof(i_0_10570,plain,
! [X18857,X18858] :
( ~ class_Groups_Ogroup__add(X18858)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18858),X18857),hAPP(c_Groups_Ouminus__class_Ouminus(X18858),X18857)) = c_Groups_Ozero__class_Ozero(X18858) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).
fof(i_0_10571,plain,
! [X21477,X21478] :
( ~ c_Nat__Transfer_Ois__nat(X21478)
| c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21478),X21477)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J])]) ).
fof(i_0_10572,plain,
! [X21082,X21083] :
( ( X21083 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X21083 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21083),X21082) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X21082 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X21083 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21083),X21082) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X21083 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X21082 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21083),X21082) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X21082 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X21082 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21083),X21082) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X21083 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X21082 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21083),X21082) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X21083 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X21082 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21083),X21082) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff])])]) ).
fof(i_0_10573,plain,
! [X24707,X24708,X24709] :
( ( X24708 = c_Orderings_Obot__class_Obot(X24709)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24709),X24708),X24707) != c_Orderings_Obot__class_Obot(X24709)
| ~ class_Lattices_Obounded__lattice__bot(X24709) )
& ( X24707 = c_Orderings_Obot__class_Obot(X24709)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24709),X24708),X24707) != c_Orderings_Obot__class_Obot(X24709)
| ~ class_Lattices_Obounded__lattice__bot(X24709) )
& ( X24708 != c_Orderings_Obot__class_Obot(X24709)
| X24707 != c_Orderings_Obot__class_Obot(X24709)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24709),X24708),X24707) = c_Orderings_Obot__class_Obot(X24709)
| ~ class_Lattices_Obounded__lattice__bot(X24709) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff])])]) ).
fof(i_0_10574,plain,
! [X27067,X27068,X27069] :
( ( X27068 = c_Orderings_Otop__class_Otop(X27069)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27069),X27068),X27067) != c_Orderings_Otop__class_Otop(X27069)
| ~ class_Lattices_Obounded__lattice__top(X27069) )
& ( X27067 = c_Orderings_Otop__class_Otop(X27069)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27069),X27068),X27067) != c_Orderings_Otop__class_Otop(X27069)
| ~ class_Lattices_Obounded__lattice__top(X27069) )
& ( X27068 != c_Orderings_Otop__class_Otop(X27069)
| X27067 != c_Orderings_Otop__class_Otop(X27069)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27069),X27068),X27067) = c_Orderings_Otop__class_Otop(X27069)
| ~ class_Lattices_Obounded__lattice__top(X27069) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff])])]) ).
fof(i_0_10575,plain,
! [X20892,X20893,X20894] :
( ~ class_Rings_Oring__1__no__zero__divisors(X20894)
| X20893 = c_Groups_Ozero__class_Ozero(X20894)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20894),X20893),X20892) != c_Groups_Ozero__class_Ozero(X20894) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).
fof(i_0_10576,plain,
! [X18121,X18122] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18122),X18121),X18121) != c_Groups_Ozero__class_Ozero(X18122)
| X18121 = c_Groups_Ozero__class_Ozero(X18122)
| ~ class_Groups_Olinordered__ab__group__add(X18122) )
& ( X18121 != c_Groups_Ozero__class_Ozero(X18122)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18122),X18121),X18121) = c_Groups_Ozero__class_Ozero(X18122)
| ~ class_Groups_Olinordered__ab__group__add(X18122) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_10577,plain,
! [X18064,X18065] :
( ( c_Groups_Ozero__class_Ozero(X18065) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18065),X18064),X18064)
| X18064 = c_Groups_Ozero__class_Ozero(X18065)
| ~ class_Groups_Olinordered__ab__group__add(X18065) )
& ( X18064 != c_Groups_Ozero__class_Ozero(X18065)
| c_Groups_Ozero__class_Ozero(X18065) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18065),X18064),X18064)
| ~ class_Groups_Olinordered__ab__group__add(X18065) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_10578,plain,
! [X24383] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24383))),
inference(variable_rename,[status(thm)],[fact_finite__atMost]) ).
fof(i_0_10579,plain,
! [X24382] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24382))),
inference(variable_rename,[status(thm)],[fact_finite__lessThan]) ).
cnf(i_0_10580,plain,
( c_Code__Numeral_Onat__of__aux(X1,X2) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(split_conjunct,[status(thm)],[i_0_5773]) ).
fof(i_0_10581,plain,
! [X20862] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20862)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20862)),
inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I5_J]) ).
fof(i_0_10582,plain,
! [X20244,X20245,X20246] :
( ( X20245 != X20244
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20246),X20245),X20244) = c_Groups_Ozero__class_Ozero(X20246)
| ~ class_Groups_Oab__group__add(X20246) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20246),X20245),X20244) != c_Groups_Ozero__class_Ozero(X20246)
| X20245 = X20244
| ~ class_Groups_Oab__group__add(X20246) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).
fof(i_0_10583,plain,
! [X20241,X20242,X20243] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20243),X20242),X20241) != c_Groups_Ozero__class_Ozero(X20243)
| X20242 = X20241
| ~ class_Groups_Ogroup__add(X20243) )
& ( X20242 != X20241
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20243),X20242),X20241) = c_Groups_Ozero__class_Ozero(X20243)
| ~ class_Groups_Ogroup__add(X20243) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).
fof(i_0_10584,plain,
! [X23117,X23118] :
( X23118 != X23117
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23118),X23117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl])]) ).
fof(i_0_10585,plain,
! [X19709,X19710] :
( X19710 != X19709
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19710),X19709)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_10586,plain,
! [X33076,X33077,X33078] :
( ( hAPP(hAPP(c_List_Otake(X33078),X33077),X33076) != c_List_Olist_ONil(X33078)
| X33077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X33076 = c_List_Olist_ONil(X33078) )
& ( X33077 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X33078),X33077),X33076) = c_List_Olist_ONil(X33078) )
& ( X33076 != c_List_Olist_ONil(X33078)
| hAPP(hAPP(c_List_Otake(X33078),X33077),X33076) = c_List_Olist_ONil(X33078) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__eq__Nil])])]) ).
fof(i_0_10587,plain,
! [X21080,X21081] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21081),X21080) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X21081 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X21081 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff__lemma])]) ).
fof(i_0_10588,plain,
! [X18118,X18119,X18120] :
( ( X18119 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18120),X18119),X18118)
| X18118 = c_Groups_Ozero__class_Ozero(X18120)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18120) )
& ( X18118 != c_Groups_Ozero__class_Ozero(X18120)
| X18119 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18120),X18119),X18118)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18120) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_10589,plain,
! [X20456] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20456)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20456,
inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).
fof(i_0_10590,plain,
! [X32005,X32006] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X32006,X32005)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X32006,X32005),
inference(variable_rename,[status(thm)],[fact_set__upto]) ).
fof(i_0_10591,plain,
! [X32007,X32008] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X32008,X32007) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X32008,X32007)),
inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upto]) ).
fof(i_0_10592,plain,
! [X21111,X21112] :
( ~ class_Int_Onumber__ring(X21112)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21112),X21111),hAPP(c_Int_Onumber__class_Onumber__of(X21112),c_Int_OPls)) = X21111 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).
fof(i_0_10593,plain,
! [X23043] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23043),X23043)),
inference(variable_rename,[status(thm)],[fact_dvd_Oorder__refl]) ).
fof(i_0_10594,plain,
! [X19032] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19032),X19032)),
inference(variable_rename,[status(thm)],[fact_zle__refl]) ).
fof(i_0_10595,plain,
! [X19713] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19713),X19713)),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_10596,plain,
! [X17475] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X17475),X17475)),
inference(variable_rename,[status(thm)],[fact_evalc_Oequations_I1_J]) ).
fof(i_0_10597,plain,
! [X17390] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X17390),X17390)),
inference(variable_rename,[status(thm)],[fact_evalc_OSkip]) ).
fof(i_0_10598,plain,
! [X32995,X32996,X32997] :
( ( X32996 = c_List_Olist_ONil(X32997)
| hAPP(hAPP(c_List_Oappend(X32997),X32996),X32995) != c_List_Olist_ONil(X32997) )
& ( X32995 = c_List_Olist_ONil(X32997)
| hAPP(hAPP(c_List_Oappend(X32997),X32996),X32995) != c_List_Olist_ONil(X32997) )
& ( X32996 != c_List_Olist_ONil(X32997)
| X32995 != c_List_Olist_ONil(X32997)
| hAPP(hAPP(c_List_Oappend(X32997),X32996),X32995) = c_List_Olist_ONil(X32997) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv])])]) ).
fof(i_0_10599,plain,
! [X33006,X33007,X33008] :
( ( X33007 = c_List_Olist_ONil(X33008)
| c_List_Olist_ONil(X33008) != hAPP(hAPP(c_List_Oappend(X33008),X33007),X33006) )
& ( X33006 = c_List_Olist_ONil(X33008)
| c_List_Olist_ONil(X33008) != hAPP(hAPP(c_List_Oappend(X33008),X33007),X33006) )
& ( X33007 != c_List_Olist_ONil(X33008)
| X33006 != c_List_Olist_ONil(X33008)
| c_List_Olist_ONil(X33008) = hAPP(hAPP(c_List_Oappend(X33008),X33007),X33006) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv])])]) ).
cnf(i_0_10600,plain,
c_Int_Osucc(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_5991]) ).
cnf(i_0_10601,plain,
c_Int_Opred(X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_5992]) ).
cnf(i_0_10602,plain,
c_List_Oupt(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_5993]) ).
fof(i_0_10603,plain,
! [X30197,X30198] : hAPP(c_Relation_ODomain(X30198,X30198),c_Transitive__Closure_Ortrancl(X30198,X30197)) = c_Orderings_Otop__class_Otop(tc_fun(X30198,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Domain__rtrancl]) ).
fof(i_0_10604,plain,
! [X30199,X30200] : hAPP(c_Relation_ORange(X30200,X30200),c_Transitive__Closure_Ortrancl(X30200,X30199)) = c_Orderings_Otop__class_Otop(tc_fun(X30200,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Range__rtrancl]) ).
fof(i_0_10605,plain,
! [X34423,X34424,X34425,X34426] : hAPP(hAPP(c_COMBK(X34426,X34425),X34424),X34423) = X34424,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(i_0_10606,plain,
( c_List_Oupt(X2,X1) = c_List_Olist_ONil(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_5928]) ).
fof(i_0_10607,plain,
! [X21085] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21085),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21085),
inference(variable_rename,[status(thm)],[fact_zdiv__minus1__right]) ).
fof(i_0_10608,plain,
! [X18673,X18674] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18674),X18673) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18673),X18674),
inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).
fof(i_0_10609,plain,
! [X19008,X19009] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19009),X19008) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19008),X19009),
inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).
fof(i_0_10610,plain,
! [X18541,X18542] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18542),X18541) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18541),X18542),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(i_0_10611,plain,
! [X18044,X18045] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18045),X18044) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18044),X18045),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_10612,plain,
! [X22773,X22774,X22775] : hAPP(hAPP(c_Nitpick_Ofrac(X22775),X22774),X22773) = c_Nitpick_OAbs__Frac(X22775,c_Nitpick_Onorm__frac(X22774,X22773)),
inference(variable_rename,[status(thm)],[fact_Nitpick_Ofrac__def]) ).
fof(i_0_10613,plain,
! [X20378,X20379] :
( ~ class_Groups_Ogroup__add(X20379)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20379),c_Groups_Ozero__class_Ozero(X20379)),X20378) = hAPP(c_Groups_Ouminus__class_Ouminus(X20379),X20378) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).
fof(i_0_10614,plain,
! [X17202,X17203] : hAPP(c_Nat_Osize__class_Osize(tc_String_Ochar),hAPP(hAPP(c_String_Ochar_OChar,X17203),X17202)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_char_Osize_I2_J]) ).
fof(i_0_10615,plain,
! [X34451,X34452] :
( ~ hBOOL(X34452)
| ~ hBOOL(X34451)
| hBOOL(hAPP(hAPP(c_fconj,X34452),X34451)) ),
inference(variable_rename,[status(thm)],[i_0_5994]) ).
fof(i_0_10616,plain,
! [X32989,X32990,X32991] :
( ( hAPP(hAPP(c_List_Oappend(X32991),X32990),X32989) != X32989
| X32990 = c_List_Olist_ONil(X32991) )
& ( X32990 != c_List_Olist_ONil(X32991)
| hAPP(hAPP(c_List_Oappend(X32991),X32990),X32989) = X32989 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv2])]) ).
fof(i_0_10617,plain,
! [X32992,X32993,X32994] :
( ( hAPP(hAPP(c_List_Oappend(X32994),X32993),X32992) != X32993
| X32992 = c_List_Olist_ONil(X32994) )
& ( X32992 != c_List_Olist_ONil(X32994)
| hAPP(hAPP(c_List_Oappend(X32994),X32993),X32992) = X32993 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv])]) ).
fof(i_0_10618,plain,
! [X33001,X33002,X33003] :
( ( X33003 != hAPP(hAPP(c_List_Oappend(X33002),X33003),X33001)
| X33001 = c_List_Olist_ONil(X33002) )
& ( X33001 != c_List_Olist_ONil(X33002)
| X33003 = hAPP(hAPP(c_List_Oappend(X33002),X33003),X33001) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv])]) ).
fof(i_0_10619,plain,
! [X32998,X32999,X33000] :
( ( X33000 != hAPP(hAPP(c_List_Oappend(X32999),X32998),X33000)
| X32998 = c_List_Olist_ONil(X32999) )
& ( X32998 != c_List_Olist_ONil(X32999)
| X33000 = hAPP(hAPP(c_List_Oappend(X32999),X32998),X33000) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])]) ).
fof(i_0_10620,plain,
! [X20972,X20973] :
( ( X20972 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20973),c_Groups_Ozero__class_Ozero(X20973)),X20972) = c_Groups_Oone__class_Oone(X20973)
| ~ class_Power_Opower(X20973)
| ~ class_Rings_Osemiring__0(X20973) )
& ( X20972 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20973),c_Groups_Ozero__class_Ozero(X20973)),X20972) = c_Groups_Ozero__class_Ozero(X20973)
| ~ class_Power_Opower(X20973)
| ~ class_Rings_Osemiring__0(X20973) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).
fof(i_0_10621,plain,
! [X32541,X32542,X32543] : hAPP(hAPP(c_List_Olist_OCons(X32543),X32542),X32541) != c_List_Olist_ONil(X32543),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J]) ).
fof(i_0_10622,plain,
! [X32544,X32545,X32546] : c_List_Olist_ONil(X32546) != hAPP(hAPP(c_List_Olist_OCons(X32546),X32545),X32544),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).
fof(i_0_10623,plain,
! [X17903] :
( hAPP(c_Com_Obody,X17903) = c_Option_Ooption_ONone(tc_Com_Ocom)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17903))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OBody])]) ).
fof(i_0_10624,plain,
! [X32009,X32010] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X32010,X32009))),
inference(variable_rename,[status(thm)],[fact_distinct__upto]) ).
cnf(i_0_10625,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1) = c_Int_Opred(X1),
inference(split_conjunct,[status(thm)],[i_0_5995]) ).
fof(i_0_10626,plain,
! [X17553,X17554,X17555] : c_Com_Ocom_OLocal(X17555,X17554,X17553) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I11_J]) ).
fof(i_0_10627,plain,
! [X17585,X17586,X17587] : c_Com_Ocom_OCond(X17587,X17586,X17585) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I15_J]) ).
fof(i_0_10628,plain,
! [X17147,X17148,X17149] : c_Com_Ocom_OCall(X17149,X17148,X17147) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I21_J]) ).
fof(i_0_10629,plain,
! [X17550,X17551,X17552] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X17552,X17551,X17550),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I10_J]) ).
fof(i_0_10630,plain,
! [X17582,X17583,X17584] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X17584,X17583,X17582),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I14_J]) ).
fof(i_0_10631,plain,
! [X17137,X17138,X17139] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X17139,X17138,X17137),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I20_J]) ).
fof(i_0_10632,plain,
! [X33218,X33219] : c_List_Olistrel(X33219,c_Transitive__Closure_Ortrancl(X33219,X33218)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X33219),c_List_Olistrel1(X33219,X33218)),
inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).
fof(i_0_10633,plain,
! [X29650,X29651] :
( ~ c_Wellfounded_Owf(X29651,X29650)
| c_Wellfounded_Owf(tc_fun(X29651,tc_HOL_Obool),c_Wellfounded_Omax__ext(X29651,X29650)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__wf])]) ).
fof(i_0_10634,plain,
! [X29628,X29629] :
( ~ c_Wellfounded_Owf(X29629,X29628)
| c_Wellfounded_Owf(tc_fun(X29629,tc_HOL_Obool),c_Wellfounded_Omin__ext(X29629,X29628)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__wf])]) ).
fof(i_0_10635,plain,
! [X34282,X34283] :
( ~ class_Groups_Ocomm__monoid__add(X34283)
| hAPP(c_List_Omonoid__add__class_Olistsum(X34283),hAPP(c_List_Orev(X34283),X34282)) = hAPP(c_List_Omonoid__add__class_Olistsum(X34283),X34282) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__rev])]) ).
fof(i_0_10636,plain,
! [X20613,X20614] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20614)
| hAPP(c_Groups_Oabs__class_Oabs(X20614),hAPP(c_Groups_Oabs__class_Oabs(X20614),X20613)) = hAPP(c_Groups_Oabs__class_Oabs(X20614),X20613) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).
fof(i_0_10637,plain,
! [X20637,X20638] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20638)
| hAPP(c_Groups_Oabs__class_Oabs(X20638),hAPP(c_Groups_Ouminus__class_Ouminus(X20638),X20637)) = hAPP(c_Groups_Oabs__class_Oabs(X20638),X20637) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])]) ).
fof(i_0_10638,plain,
! [X20643,X20644] :
( ~ class_Rings_Olinordered__idom(X20644)
| hAPP(c_Groups_Oabs__class_Oabs(X20644),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20644),X20643)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20644),X20643) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nat])]) ).
fof(i_0_10639,plain,
! [X21066] :
( ~ class_Int_Onumber__ring(X21066)
| ~ c_Int_Oiszero(X21066,hAPP(c_Int_Onumber__class_Onumber__of(X21066),c_Int_OMin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5996])]) ).
fof(i_0_10640,plain,
! [X24669] : c_Orderings_Otop__class_Otop(tc_fun(X24669,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X24669,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__not__empty]) ).
fof(i_0_10641,plain,
! [X21079] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X21079,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__minus1__right]) ).
fof(i_0_10642,plain,
! [X20010] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20010,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mod__1]) ).
fof(i_0_10643,plain,
! [X19218,X19219] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19219),X19218) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19219 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19218 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19219 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19219),X19218) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19218 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19219),X19218) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__is__0])])]) ).
fof(i_0_10644,plain,
! [X32323,X32324,X32325] : hAPP(hAPP(c_List_Olist_OCons(X32325),X32324),X32323) != X32323,
inference(variable_rename,[status(thm)],[fact_not__Cons__self2]) ).
fof(i_0_10645,plain,
! [X32326,X32327,X32328] : X32328 != hAPP(hAPP(c_List_Olist_OCons(X32327),X32326),X32328),
inference(variable_rename,[status(thm)],[fact_not__Cons__self]) ).
fof(i_0_10646,plain,
! [X29132] : c_Finite__Set_Ofun__left__comm__idem(X29132,tc_fun(X29132,tc_HOL_Obool),c_Set_Oinsert(X29132)),
inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__insert]) ).
fof(i_0_10647,plain,
! [X34457,X34458] :
( ~ hBOOL(X34458)
| hBOOL(hAPP(hAPP(c_fdisj,X34458),X34457)) ),
inference(variable_rename,[status(thm)],[i_0_5997]) ).
fof(i_0_10648,plain,
! [X34459,X34460] :
( ~ hBOOL(X34460)
| hBOOL(hAPP(hAPP(c_fdisj,X34459),X34460)) ),
inference(variable_rename,[status(thm)],[i_0_5998]) ).
fof(i_0_10649,plain,
! [X34465,X34466] :
( ~ hBOOL(X34466)
| hBOOL(hAPP(hAPP(c_fimplies,X34465),X34466)) ),
inference(variable_rename,[status(thm)],[i_0_5999]) ).
fof(i_0_10650,plain,
! [X24643,X24644,X24645] :
( ~ class_Orderings_Obot(X24645)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X24644,X24645)),X24643) = c_Orderings_Obot__class_Obot(X24645) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).
fof(i_0_10651,plain,
! [X24640,X24641,X24642] :
( ~ class_Orderings_Obot(X24642)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X24641,X24642)),X24640) = c_Orderings_Obot__class_Obot(X24642) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])]) ).
fof(i_0_10652,plain,
! [X24317,X24318,X24319] :
( ~ class_Orderings_Otop(X24319)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X24318,X24319)),X24317) = c_Orderings_Otop__class_Otop(X24319) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).
fof(i_0_10653,plain,
! [X21812,X21813] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X21813),X21812) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X21813),X21812),
inference(variable_rename,[status(thm)],[fact_minus__code__numeral__code]) ).
fof(i_0_10654,plain,
! [X18141,X18142] : ~ c_Option_Ois__none(X18142,hAPP(c_Option_Ooption_OSome(X18142),X18141)),
inference(variable_rename,[status(thm)],[i_0_6000]) ).
fof(i_0_10655,plain,
! [X34118,X34119] :
( ~ class_Orderings_Olinorder(X34119)
| ~ c_List_Olinorder__class_Osorted(X34119,X34118)
| c_List_Olinorder__class_Osorted(X34119,hAPP(c_List_Otl(X34119),X34118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__tl])]) ).
fof(i_0_10656,plain,
! [X18997,X18998] :
( X18998 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18998),X18997)
| X18997 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X18998 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10])]) ).
fof(i_0_10657,plain,
! [X33466,X33467] :
( X33467 = c_List_Olist_ONil(X33466)
| hAPP(c_List_Ohd(X33466),X33467) = hAPP(hAPP(c_List_Onth(X33466),X33467),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__conv__nth])]) ).
fof(i_0_10658,plain,
! [X34463,X34464] :
( hBOOL(X34464)
| hBOOL(hAPP(hAPP(c_fimplies,X34464),X34463)) ),
inference(variable_rename,[status(thm)],[help_c__fimplies__1]) ).
fof(i_0_10659,plain,
! [X30583,X30584] : c_Relation_Osingle__valued(X30584,X30584,c_Relation_OId__on(X30584,X30583)),
inference(variable_rename,[status(thm)],[fact_single__valued__Id__on]) ).
fof(i_0_10660,plain,
! [X28982,X28983] : c_Relation_Orefl__on(X28983,X28982,c_Relation_OId__on(X28983,X28982)),
inference(variable_rename,[status(thm)],[fact_refl__on__Id__on]) ).
fof(i_0_10661,plain,
! [X19010,X19011] :
( ( X19011 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19011),X19010) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X19010 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19011),X19010) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X19011 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X19010 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19011),X19010) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff])])]) ).
fof(i_0_10662,plain,
! [X18050,X18051] :
( ( X18051 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18051),X18050) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18050 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18051),X18050) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18051 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18050 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18051),X18050) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__0])])]) ).
fof(i_0_10663,plain,
! [X19005,X19006] :
( ( X19006 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19006),X19005) )
& ( X19005 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19006),X19005) )
& ( X19006 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X19005 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19006),X19005) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).
fof(i_0_10664,plain,
! [X20610,X20611,X20612] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X20612),X20611) != hAPP(c_Int_Onumber__class_Onumber__of(X20612),X20610)
| X20611 = X20610
| ~ class_Int_Onumber__ring(X20612)
| ~ class_Int_Oring__char__0(X20612) )
& ( X20611 != X20610
| hAPP(c_Int_Onumber__class_Onumber__of(X20612),X20611) = hAPP(c_Int_Onumber__class_Onumber__of(X20612),X20610)
| ~ class_Int_Onumber__ring(X20612)
| ~ class_Int_Oring__char__0(X20612) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])]) ).
fof(i_0_10665,plain,
! [X30365,X30366] : hAPP(c_Relation_Oconverse(X30366,X30366),c_Relation_OId__on(X30366,X30365)) = c_Relation_OId__on(X30366,X30365),
inference(variable_rename,[status(thm)],[fact_converse__Id__on]) ).
fof(i_0_10666,plain,
! [X34447,X34448] :
( X34448 != X34447
| hBOOL(hAPP(hAPP(c_fequal,X34448),X34447)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_10667,plain,
! [X20605,X20606] :
( ~ class_Int_Onumber__ring(X20606)
| hAPP(c_Int_Oring__1__class_Oof__int(X20606),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20605)) = hAPP(c_Int_Onumber__class_Onumber__of(X20606),X20605) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__number__of__eq])]) ).
fof(i_0_10668,plain,
! [X18953,X18954] :
( ~ class_Rings_Oring__1(X18954)
| hAPP(c_Int_Oring__1__class_Oof__int(X18954),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18953)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18954),X18953) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__of__nat__eq])]) ).
fof(i_0_10669,plain,
! [X32537,X32538] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X32538,tc_HOL_Obool)) != hAPP(c_List_Oset(X32538),X32537)
| X32537 = c_List_Olist_ONil(X32538) )
& ( X32537 != c_List_Olist_ONil(X32538)
| c_Orderings_Obot__class_Obot(tc_fun(X32538,tc_HOL_Obool)) = hAPP(c_List_Oset(X32538),X32537) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty2])]) ).
fof(i_0_10670,plain,
! [X32539,X32540] :
( ( hAPP(c_List_Oset(X32540),X32539) != c_Orderings_Obot__class_Obot(tc_fun(X32540,tc_HOL_Obool))
| X32539 = c_List_Olist_ONil(X32540) )
& ( X32539 != c_List_Olist_ONil(X32540)
| hAPP(c_List_Oset(X32540),X32539) = c_Orderings_Obot__class_Obot(tc_fun(X32540,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty])]) ).
fof(i_0_10671,plain,
! [X17276,X17277] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X17277,X17276))),
inference(variable_rename,[status(thm)],[fact_WT_OAssign]) ).
fof(i_0_10672,plain,
! [X17274,X17275] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X17275,X17274))),
inference(variable_rename,[status(thm)],[fact_WT_Oequations_I2_J]) ).
fof(i_0_10673,plain,
! [X34304,X34305] : hAPP(c_List_Oset(X34305),hAPP(c_List_Orev(X34305),X34304)) = hAPP(c_List_Oset(X34305),X34304),
inference(variable_rename,[status(thm)],[fact_set__rev]) ).
fof(i_0_10674,plain,
! [X33352,X33353] : hAPP(c_List_Oset(X33353),hAPP(c_List_Orotate1(X33353),X33352)) = hAPP(c_List_Oset(X33353),X33352),
inference(variable_rename,[status(thm)],[fact_set__rotate1]) ).
fof(i_0_10675,plain,
! [X21011] :
( ~ class_Power_Opower(X21011)
| c_Power_Opower__class_Opower(X21011) = c_Power_Opower_Opower(X21011,c_Groups_Oone__class_Oone(X21011),c_Groups_Otimes__class_Otimes(X21011)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).
fof(i_0_10676,plain,
! [X18052,X18053] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18053),X18052) != X18053
| X18052 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])]) ).
fof(i_0_10677,plain,
! [X34313,X34314] :
( X34314 = c_List_Olist_ONil(X34313)
| hAPP(c_List_Ohd(X34313),hAPP(c_List_Orev(X34313),X34314)) = c_List_Olast(X34313,X34314) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rev])]) ).
fof(i_0_10678,plain,
! [X34315,X34316] :
( X34316 = c_List_Olist_ONil(X34315)
| c_List_Olast(X34315,hAPP(c_List_Orev(X34315),X34316)) = hAPP(c_List_Ohd(X34315),X34316) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__rev])]) ).
fof(i_0_10679,plain,
! [X32535] :
( ~ class_Orderings_Olinorder(X32535)
| c_List_Olinorder__class_Osorted__list__of__set(X32535,c_Orderings_Obot__class_Obot(tc_fun(X32535,tc_HOL_Obool))) = c_List_Olist_ONil(X32535) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty])]) ).
fof(i_0_10680,plain,
! [X31384] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31384)
| c_Complete__Lattice_OSup__class_OSup(X31384,c_Orderings_Obot__class_Obot(tc_fun(X31384,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X31384) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__empty])]) ).
fof(i_0_10681,plain,
! [X31395] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31395)
| c_Complete__Lattice_OSup__class_OSup(X31395,c_Orderings_Otop__class_Otop(tc_fun(X31395,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X31395) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__UNIV])]) ).
fof(i_0_10682,plain,
! [X31398] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31398)
| c_Complete__Lattice_OInf__class_OInf(X31398,c_Orderings_Obot__class_Obot(tc_fun(X31398,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X31398) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__empty])]) ).
fof(i_0_10683,plain,
! [X31399] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31399)
| c_Complete__Lattice_OInf__class_OInf(X31399,c_Orderings_Otop__class_Otop(tc_fun(X31399,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X31399) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__UNIV])]) ).
fof(i_0_10684,plain,
! [X20004] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20004),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X20004,
inference(variable_rename,[status(thm)],[fact_div__1]) ).
fof(i_0_10685,plain,
! [X31284,X31285] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31285,tc_HOL_Obool),hAPP(c_Set_OPow(X31285),X31284)) = X31284,
inference(variable_rename,[status(thm)],[fact_Union__Pow__eq]) ).
fof(i_0_10686,plain,
! [X27148,X27149] :
( ~ class_Lattices_Obounded__lattice__bot(X27149)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27149),c_Orderings_Obot__class_Obot(X27149)),X27148) = c_Orderings_Obot__class_Obot(X27149) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__left])]) ).
fof(i_0_10687,plain,
! [X24327,X24328] :
( ~ class_Lattices_Obounded__lattice__top(X24328)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24328),c_Orderings_Otop__class_Otop(X24328)),X24327) = c_Orderings_Otop__class_Otop(X24328) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__left])]) ).
fof(i_0_10688,plain,
! [X21431,X21432] :
( ~ class_Rings_Odivision__ring(X21432)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21432),c_Groups_Ozero__class_Ozero(X21432)),X21431) = c_Groups_Ozero__class_Ozero(X21432) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).
fof(i_0_10689,plain,
! [X20902,X20903] :
( ~ class_Groups_Omonoid__mult(X20903)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20903),c_Groups_Oone__class_Oone(X20903)),X20902) = c_Groups_Oone__class_Oone(X20903) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(i_0_10690,plain,
! [X19994,X19995] :
( ~ class_Divides_Osemiring__div(X19995)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19995),c_Groups_Ozero__class_Ozero(X19995)),X19994) = c_Groups_Ozero__class_Ozero(X19995) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])]) ).
fof(i_0_10691,plain,
! [X18782,X18783] :
( ~ class_Rings_Omult__zero(X18783)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18783),c_Groups_Ozero__class_Ozero(X18783)),X18782) = c_Groups_Ozero__class_Ozero(X18783) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(i_0_10692,plain,
! [X18778,X18779] :
( ~ class_Rings_Ocomm__semiring__1(X18779)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18779),c_Groups_Ozero__class_Ozero(X18779)),X18778) = c_Groups_Ozero__class_Ozero(X18779) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(i_0_10693,plain,
! [X34037,X34038] :
( ~ class_Orderings_Olinorder(X34038)
| X34037 = c_List_Olist_ONil(X34038)
| ~ c_List_Olinorder__class_Osorted(X34038,X34037)
| c_List_Olinorder__class_Osorted(X34038,c_List_Obutlast(X34038,X34037)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__butlast])]) ).
fof(i_0_10694,plain,
! [X17962,X17963] :
( ~ c_Com_OWT__bodies
| hAPP(c_Com_Obody,X17963) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X17962)
| hBOOL(hAPP(c_Com_OWT,X17962)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT__bodiesD])]) ).
fof(i_0_10695,plain,
! [X21084] :
( ~ class_Int_Onumber__ring(X21084)
| hAPP(c_Int_Oring__1__class_Oof__int(X21084),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X21084),c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__m1])]) ).
fof(i_0_10696,plain,
! [X24763] : hAPP(c_Finite__Set_Ocard(X24763),c_Orderings_Obot__class_Obot(tc_fun(X24763,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_card_Oempty]) ).
cnf(i_0_10697,plain,
( c_Int_OPls = X1
| c_Int_OPls != c_Int_OBit0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6001]) ).
cnf(i_0_10698,plain,
( X1 = c_Int_OPls
| c_Int_OBit0(X1) != c_Int_OPls ),
inference(split_conjunct,[status(thm)],[i_0_6002]) ).
fof(i_0_10699,plain,
! [X21078] :
( ~ class_Int_Onumber__ring(X21078)
| ~ class_Rings_Olinordered__idom(X21078)
| hAPP(c_Groups_Oabs__class_Oabs(X21078),hAPP(c_Int_Onumber__class_Onumber__of(X21078),c_Int_OMin)) = c_Groups_Oone__class_Oone(X21078) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__one])]) ).
fof(i_0_10700,plain,
! [X17994,X17995] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X17995)),hAPP(c_Option_Ooption_OSome(X17995),X17994)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_option_Osize_I4_J]) ).
fof(i_0_10701,plain,
! [X24091] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24091) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24091),
inference(variable_rename,[status(thm)],[fact_atLeast0AtMost]) ).
cnf(i_0_10702,plain,
c_Int_OBit0(X1) != c_Int_OMin,
inference(split_conjunct,[status(thm)],[i_0_6003]) ).
cnf(i_0_10703,plain,
c_Int_OMin != c_Int_OBit0(X1),
inference(split_conjunct,[status(thm)],[i_0_6004]) ).
fof(i_0_10704,plain,
! [X24145,X24146,X24147] :
( ( hAPP(c_SetInterval_Oord__class_OatLeast(X24147),X24146) != hAPP(c_SetInterval_Oord__class_OatLeast(X24147),X24145)
| X24146 = X24145
| ~ class_Orderings_Olinorder(X24147) )
& ( X24146 != X24145
| hAPP(c_SetInterval_Oord__class_OatLeast(X24147),X24146) = hAPP(c_SetInterval_Oord__class_OatLeast(X24147),X24145)
| ~ class_Orderings_Olinorder(X24147) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff])])]) ).
fof(i_0_10705,plain,
! [X23977,X23978,X23979] :
( ( hAPP(c_SetInterval_Oord__class_OatMost(X23979),X23978) != hAPP(c_SetInterval_Oord__class_OatMost(X23979),X23977)
| X23978 = X23977
| ~ class_Orderings_Olinorder(X23979) )
& ( X23978 != X23977
| hAPP(c_SetInterval_Oord__class_OatMost(X23979),X23978) = hAPP(c_SetInterval_Oord__class_OatMost(X23979),X23977)
| ~ class_Orderings_Olinorder(X23979) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff])])]) ).
fof(i_0_10706,plain,
! [X23752,X23753,X23754] :
( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X23754),X23753) != hAPP(c_SetInterval_Oord__class_OgreaterThan(X23754),X23752)
| X23753 = X23752
| ~ class_Orderings_Olinorder(X23754) )
& ( X23753 != X23752
| hAPP(c_SetInterval_Oord__class_OgreaterThan(X23754),X23753) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X23754),X23752)
| ~ class_Orderings_Olinorder(X23754) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff])])]) ).
fof(i_0_10707,plain,
! [X23127,X23128,X23129] :
( ( hAPP(c_SetInterval_Oord__class_OlessThan(X23129),X23128) != hAPP(c_SetInterval_Oord__class_OlessThan(X23129),X23127)
| X23128 = X23127
| ~ class_Orderings_Olinorder(X23129) )
& ( X23128 != X23127
| hAPP(c_SetInterval_Oord__class_OlessThan(X23129),X23128) = hAPP(c_SetInterval_Oord__class_OlessThan(X23129),X23127)
| ~ class_Orderings_Olinorder(X23129) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff])])]) ).
fof(i_0_10708,plain,
! [X19907,X19908,X19909] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X19909),X19908) != hAPP(c_Groups_Ouminus__class_Ouminus(X19909),X19907)
| X19908 = X19907
| ~ class_Lattices_Oboolean__algebra(X19909) )
& ( X19908 != X19907
| hAPP(c_Groups_Ouminus__class_Ouminus(X19909),X19908) = hAPP(c_Groups_Ouminus__class_Ouminus(X19909),X19907)
| ~ class_Lattices_Oboolean__algebra(X19909) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).
fof(i_0_10709,plain,
! [X18732,X18733,X18734] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18734),X18733) != hAPP(c_Groups_Ouminus__class_Ouminus(X18734),X18732)
| X18733 = X18732
| ~ class_Groups_Ogroup__add(X18734) )
& ( X18733 != X18732
| hAPP(c_Groups_Ouminus__class_Ouminus(X18734),X18733) = hAPP(c_Groups_Ouminus__class_Ouminus(X18734),X18732)
| ~ class_Groups_Ogroup__add(X18734) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).
fof(i_0_10710,plain,
! [X18685,X18686,X18687] :
( ( hAPP(c_Int_Oring__1__class_Oof__int(X18687),X18686) != hAPP(c_Int_Oring__1__class_Oof__int(X18687),X18685)
| X18686 = X18685
| ~ class_Int_Oring__char__0(X18687) )
& ( X18686 != X18685
| hAPP(c_Int_Oring__1__class_Oof__int(X18687),X18686) = hAPP(c_Int_Oring__1__class_Oof__int(X18687),X18685)
| ~ class_Int_Oring__char__0(X18687) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff])])]) ).
fof(i_0_10711,plain,
! [X18461,X18462,X18463] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18463),X18462) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18463),X18461)
| X18462 = X18461
| ~ class_Nat_Osemiring__char__0(X18463) )
& ( X18462 != X18461
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18463),X18462) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18463),X18461)
| ~ class_Nat_Osemiring__char__0(X18463) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff])])]) ).
fof(i_0_10712,plain,
! [X27063,X27064] :
( ~ class_Lattices_Obounded__lattice__top(X27064)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27064),c_Orderings_Otop__class_Otop(X27064)),X27063) = X27063 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__left])]) ).
fof(i_0_10713,plain,
! [X24703,X24704] :
( ~ class_Lattices_Obounded__lattice__bot(X24704)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24704),c_Orderings_Obot__class_Obot(X24704)),X24703) = X24703 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__left])]) ).
fof(i_0_10714,plain,
! [X18718,X18719] :
( ~ class_Groups_Ocomm__monoid__mult(X18719)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18719),c_Groups_Oone__class_Oone(X18719)),X18718) = X18718 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).
fof(i_0_10715,plain,
! [X18716,X18717] :
( ~ class_Groups_Omonoid__mult(X18717)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18717),c_Groups_Oone__class_Oone(X18717)),X18716) = X18716 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).
fof(i_0_10716,plain,
! [X18664,X18665] :
( ~ class_Rings_Ocomm__semiring__1(X18665)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18665),c_Groups_Oone__class_Oone(X18665)),X18664) = X18664 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).
fof(i_0_10717,plain,
! [X18114,X18115] :
( ~ class_Rings_Ocomm__semiring__1(X18115)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18115),c_Groups_Ozero__class_Ozero(X18115)),X18114) = X18114 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_10718,plain,
! [X18062,X18063] :
( ~ class_Groups_Ocomm__monoid__add(X18063)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18063),c_Groups_Ozero__class_Ozero(X18063)),X18062) = X18062 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_10719,plain,
! [X18060,X18061] :
( ~ class_Groups_Omonoid__add(X18061)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18061),c_Groups_Ozero__class_Ozero(X18061)),X18060) = X18060 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_10720,plain,
! [X21561,X21562] :
( ( X21561 != c_Groups_Ozero__class_Ozero(X21562)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21562),X21561),X21561) = c_Groups_Ozero__class_Ozero(X21562)
| ~ class_Rings_Odivision__ring__inverse__zero(X21562) )
& ( X21561 = c_Groups_Ozero__class_Ozero(X21562)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21562),X21561),X21561) = c_Groups_Oone__class_Oone(X21562)
| ~ class_Rings_Odivision__ring__inverse__zero(X21562) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self__if])])]) ).
fof(i_0_10721,plain,
! [X19759,X19760] :
( ~ class_Divides_Osemiring__div(X19760)
| c_Divides_Odiv__class_Omod(X19760,c_Groups_Ozero__class_Ozero(X19760),X19759) = c_Groups_Ozero__class_Ozero(X19760) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__0])]) ).
fof(i_0_10722,plain,
! [X19862,X19863] :
( ~ class_Divides_Osemiring__div(X19863)
| c_Divides_Odiv__class_Omod(X19863,X19862,c_Groups_Oone__class_Oone(X19863)) = c_Groups_Ozero__class_Ozero(X19863) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])]) ).
fof(i_0_10723,plain,
! [X24911,X24912] :
( ( c_Option_Oset(X24912,X24911) != c_Orderings_Obot__class_Obot(tc_fun(X24912,tc_HOL_Obool))
| X24911 = c_Option_Ooption_ONone(X24912) )
& ( X24911 != c_Option_Ooption_ONone(X24912)
| c_Option_Oset(X24912,X24911) = c_Orderings_Obot__class_Obot(tc_fun(X24912,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty__eq])]) ).
fof(i_0_10724,plain,
! [X27146,X27147] :
( ~ class_Lattices_Obounded__lattice__bot(X27147)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27147),X27146),c_Orderings_Obot__class_Obot(X27147)) = c_Orderings_Obot__class_Obot(X27147) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__right])]) ).
fof(i_0_10725,plain,
! [X24329,X24330] :
( ~ class_Lattices_Obounded__lattice__top(X24330)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24330),X24329),c_Orderings_Otop__class_Otop(X24330)) = c_Orderings_Otop__class_Otop(X24330) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__right])]) ).
fof(i_0_10726,plain,
! [X21429,X21430] :
( ~ class_Rings_Odivision__ring__inverse__zero(X21430)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21430),X21429),c_Groups_Ozero__class_Ozero(X21430)) = c_Groups_Ozero__class_Ozero(X21430) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])]) ).
fof(i_0_10727,plain,
! [X19996,X19997] :
( ~ class_Divides_Osemiring__div(X19997)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19997),X19996),c_Groups_Ozero__class_Ozero(X19997)) = c_Groups_Ozero__class_Ozero(X19997) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])]) ).
fof(i_0_10728,plain,
! [X18784,X18785] :
( ~ class_Rings_Omult__zero(X18785)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18785),X18784),c_Groups_Ozero__class_Ozero(X18785)) = c_Groups_Ozero__class_Ozero(X18785) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).
fof(i_0_10729,plain,
! [X18780,X18781] :
( ~ class_Rings_Ocomm__semiring__1(X18781)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18781),X18780),c_Groups_Ozero__class_Ozero(X18781)) = c_Groups_Ozero__class_Ozero(X18781) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).
fof(i_0_10730,plain,
! [X29691,X29692] :
( ~ c_Wellfounded_Owf(X29692,X29691)
| c_Wellfounded_Owf(tc_List_Olist(X29692),c_List_Olex(X29692,X29691)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex])]) ).
fof(i_0_10731,plain,
! [X29684,X29685] :
( ~ c_Wellfounded_Owf(X29685,X29684)
| c_Wellfounded_Owf(tc_List_Olist(X29685),c_List_Olenlex(X29685,X29684)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lenlex])]) ).
fof(i_0_10732,plain,
! [X32986,X32987,X32988] :
( X32988 != X32987
| X32988 = hAPP(hAPP(c_List_Oappend(X32986),c_List_Olist_ONil(X32986)),X32987) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Nil__appendI])]) ).
fof(i_0_10733,plain,
! [X21559,X21560] :
( ~ class_Rings_Odivision__ring(X21560)
| X21559 = c_Groups_Ozero__class_Ozero(X21560)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21560),X21559),X21559) = c_Groups_Oone__class_Oone(X21560) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).
fof(i_0_10734,plain,
! [X20061,X20062] :
( ~ class_Divides_Osemiring__div(X20062)
| X20061 = c_Groups_Ozero__class_Ozero(X20062)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20062),X20061),X20061) = c_Groups_Oone__class_Oone(X20062) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])]) ).
fof(i_0_10735,plain,
! [X19761,X19762] :
( ~ class_Divides_Osemiring__div(X19762)
| c_Divides_Odiv__class_Omod(X19762,X19761,c_Groups_Ozero__class_Ozero(X19762)) = X19761 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])]) ).
fof(i_0_10736,plain,
! [X21022] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X21022))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X21022)) = X21022 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6005])]) ).
fof(i_0_10737,plain,
! [X30803] :
( ~ class_Groups_Oab__semigroup__mult(X30803)
| c_Finite__Set_Ofun__left__comm(X30803,X30803,c_Groups_Otimes__class_Otimes(X30803)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm])]) ).
fof(i_0_10738,plain,
! [X29133] :
( ~ class_Lattices_Osemilattice__inf(X29133)
| c_Finite__Set_Ofun__left__comm__idem(X29133,X29133,c_Lattices_Osemilattice__inf__class_Oinf(X29133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf])]) ).
fof(i_0_10739,plain,
! [X29121] :
( ~ class_Lattices_Osemilattice__sup(X29121)
| c_Finite__Set_Ofun__left__comm__idem(X29121,X29121,c_Lattices_Osemilattice__sup__class_Osup(X29121)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup])]) ).
fof(i_0_10740,plain,
! [X29134] :
( ~ class_Orderings_Olinorder(X29134)
| c_Finite__Set_Ofun__left__comm__idem(X29134,X29134,c_Orderings_Oord__class_Omax(X29134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup])]) ).
fof(i_0_10741,plain,
! [X29119] :
( ~ class_Orderings_Olinorder(X29119)
| c_Finite__Set_Ofun__left__comm__idem(X29119,X29119,c_Orderings_Oord__class_Omin(X29119)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf])]) ).
fof(i_0_10742,plain,
! [X29120] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X29120)
| c_Finite__Set_Ofun__left__comm__idem(X29120,X29120,c_Groups_Otimes__class_Otimes(X29120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem])]) ).
fof(i_0_10743,plain,
! [X29797,X29798] : hAPP(c_Relation_ODomain(X29798,X29798),c_Relation_OId__on(X29798,X29797)) = X29797,
inference(variable_rename,[status(thm)],[fact_Domain__Id__on]) ).
fof(i_0_10744,plain,
! [X29713,X29714] : hAPP(c_Relation_ORange(X29714,X29714),c_Relation_OId__on(X29714,X29713)) = X29713,
inference(variable_rename,[status(thm)],[fact_Range__Id__on]) ).
fof(i_0_10745,plain,
! [X20945,X20946] :
( ~ class_Power_Opower(X20946)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20946),X20945),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X20946) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(i_0_10746,plain,
! [X20740,X20741] :
( ~ class_Rings_Ocomm__semiring__1(X20741)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20741),X20740),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X20741) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).
fof(i_0_10747,plain,
! [X27065,X27066] :
( ~ class_Lattices_Obounded__lattice__top(X27066)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27066),X27065),c_Orderings_Otop__class_Otop(X27066)) = X27065 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__right])]) ).
fof(i_0_10748,plain,
! [X24705,X24706] :
( ~ class_Lattices_Obounded__lattice__bot(X24706)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24706),X24705),c_Orderings_Obot__class_Obot(X24706)) = X24705 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__right])]) ).
fof(i_0_10749,plain,
! [X21450,X21451] :
( ~ class_Rings_Odivision__ring(X21451)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21451),X21450),c_Groups_Oone__class_Oone(X21451)) = X21450 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).
fof(i_0_10750,plain,
! [X20249,X20250] :
( ~ class_Groups_Ogroup__add(X20250)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20250),X20249),c_Groups_Ozero__class_Ozero(X20250)) = X20249 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).
fof(i_0_10751,plain,
! [X19998,X19999] :
( ~ class_Divides_Osemiring__div(X19999)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19999),X19998),c_Groups_Oone__class_Oone(X19999)) = X19998 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])]) ).
fof(i_0_10752,plain,
! [X18724,X18725] :
( ~ class_Groups_Ocomm__monoid__mult(X18725)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18725),X18724),c_Groups_Oone__class_Oone(X18725)) = X18724 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).
fof(i_0_10753,plain,
! [X18722,X18723] :
( ~ class_Groups_Omonoid__mult(X18723)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18723),X18722),c_Groups_Oone__class_Oone(X18723)) = X18722 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).
fof(i_0_10754,plain,
! [X18667,X18668] :
( ~ class_Rings_Ocomm__semiring__1(X18668)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18668),X18667),c_Groups_Oone__class_Oone(X18668)) = X18667 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).
fof(i_0_10755,plain,
! [X18116,X18117] :
( ~ class_Rings_Ocomm__semiring__1(X18117)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18117),X18116),c_Groups_Ozero__class_Ozero(X18117)) = X18116 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_10756,plain,
! [X18068,X18069] :
( ~ class_Groups_Ocomm__monoid__add(X18069)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18069),X18068),c_Groups_Ozero__class_Ozero(X18069)) = X18068 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_10757,plain,
! [X18066,X18067] :
( ~ class_Groups_Omonoid__add(X18067)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18067),X18066),c_Groups_Ozero__class_Ozero(X18067)) = X18066 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_10758,plain,
! [X19901,X19902] :
( ~ class_Lattices_Oboolean__algebra(X19902)
| hAPP(c_Groups_Ouminus__class_Ouminus(X19902),hAPP(c_Groups_Ouminus__class_Ouminus(X19902),X19901)) = X19901 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).
fof(i_0_10759,plain,
! [X18714,X18715] :
( ~ class_Groups_Ogroup__add(X18715)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18715),hAPP(c_Groups_Ouminus__class_Ouminus(X18715),X18714)) = X18714 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
fof(i_0_10760,plain,
! [X20645] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20645)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20645),
inference(variable_rename,[status(thm)],[fact_abs__int__eq]) ).
fof(i_0_10761,plain,
! [X18837] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18837)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18837),
inference(variable_rename,[status(thm)],[fact_of__int__int__eq]) ).
fof(i_0_10762,plain,
! [X19763,X19764] :
( ~ class_Divides_Osemiring__div(X19764)
| c_Divides_Odiv__class_Omod(X19764,X19763,X19763) = c_Groups_Ozero__class_Ozero(X19764) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__self])]) ).
fof(i_0_10763,plain,
! [X34289,X34290,X34291] :
( ( hAPP(c_List_Orev(X34291),X34290) != hAPP(c_List_Orev(X34291),X34289)
| X34290 = X34289 )
& ( X34290 != X34289
| hAPP(c_List_Orev(X34291),X34290) = hAPP(c_List_Orev(X34291),X34289) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv])]) ).
fof(i_0_10764,plain,
! [X17989,X17990,X17991] :
( ( hAPP(c_Option_Ooption_OSome(X17991),X17990) != hAPP(c_Option_Ooption_OSome(X17991),X17989)
| X17990 = X17989 )
& ( X17990 != X17989
| hAPP(c_Option_Ooption_OSome(X17991),X17990) = hAPP(c_Option_Ooption_OSome(X17991),X17989) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option_Oinject])]) ).
fof(i_0_10765,plain,
! [X24568,X24569] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X24569),X24568))
| hAPP(c_Finite__Set_Ocard(X24569),X24568) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6006])]) ).
fof(i_0_10766,plain,
! [X21808,X21809] :
( ( X21809 != X21808
| c_Random_Oinc__shift(X21809,X21808) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
& ( X21809 = X21808
| c_Random_Oinc__shift(X21809,X21808) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X21808),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inc__shift__def])]) ).
fof(i_0_10767,plain,
! [X33009,X33010] : hAPP(hAPP(c_List_Oappend(X33010),c_List_Olist_ONil(X33010)),X33009) = X33009,
inference(variable_rename,[status(thm)],[fact_append__Nil]) ).
fof(i_0_10768,plain,
! [X19481] : hAPP(c_Nat_OSuc,X19481) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X19481),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_10769,plain,
! [X32553,X32554] : c_List_Osublist(X32554,c_List_Olist_ONil(X32554),X32553) = c_List_Olist_ONil(X32554),
inference(variable_rename,[status(thm)],[fact_sublist__nil]) ).
fof(i_0_10770,plain,
! [X32518,X32519] : c_List_Oremove1(X32519,X32518,c_List_Olist_ONil(X32519)) = c_List_Olist_ONil(X32519),
inference(variable_rename,[status(thm)],[fact_remove1_Osimps_I1_J]) ).
fof(i_0_10771,plain,
! [X24785] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24785),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_atLeastLessThan0]) ).
fof(i_0_10772,plain,
! [X20915,X20916] :
( ~ class_Groups_Omonoid__mult(X20916)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20916),X20915),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20915 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).
fof(i_0_10773,plain,
! [X20653,X20654] :
( ~ class_Rings_Ocomm__semiring__1(X20654)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20654),X20653),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20653 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).
fof(i_0_10774,plain,
! [X20247,X20248] :
( ~ class_Groups_Ogroup__add(X20248)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20248),X20247),X20247) = c_Groups_Ozero__class_Ozero(X20248) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).
fof(i_0_10775,plain,
! [X33613,X33614] : c_List_Olist_Olist__size(X33614,X33613,c_List_Olist_ONil(X33614)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_list_Osize_I1_J]) ).
fof(i_0_10776,plain,
! [X17969,X17970] : c_Option_Ooption_Ooption__size(X17970,X17969,c_Option_Ooption_ONone(X17970)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_option_Osize_I1_J]) ).
fof(i_0_10777,plain,
! [X33079,X33080] : hAPP(hAPP(c_List_Otake(X33080),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33079) = c_List_Olist_ONil(X33080),
inference(variable_rename,[status(thm)],[fact_take__0]) ).
fof(i_0_10778,plain,
! [X33375,X33376] : hAPP(hAPP(c_List_Odrop(X33376),X33375),c_List_Olist_ONil(X33376)) = c_List_Olist_ONil(X33376),
inference(variable_rename,[status(thm)],[fact_drop__Nil]) ).
fof(i_0_10779,plain,
! [X33074,X33075] : hAPP(hAPP(c_List_Otake(X33075),X33074),c_List_Olist_ONil(X33075)) = c_List_Olist_ONil(X33075),
inference(variable_rename,[status(thm)],[fact_take__Nil]) ).
fof(i_0_10780,plain,
! [X18729,X18730,X18731] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18731),X18730) != X18729
| hAPP(c_Groups_Ouminus__class_Ouminus(X18731),X18729) = X18730
| ~ class_Groups_Ogroup__add(X18731) )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(X18731),X18729) != X18730
| hAPP(c_Groups_Ouminus__class_Ouminus(X18731),X18730) = X18729
| ~ class_Groups_Ogroup__add(X18731) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).
fof(i_0_10781,plain,
! [X18726,X18727,X18728] :
( ( X18727 != hAPP(c_Groups_Ouminus__class_Ouminus(X18728),X18726)
| X18726 = hAPP(c_Groups_Ouminus__class_Ouminus(X18728),X18727)
| ~ class_Groups_Ogroup__add(X18728) )
& ( X18726 != hAPP(c_Groups_Ouminus__class_Ouminus(X18728),X18727)
| X18727 = hAPP(c_Groups_Ouminus__class_Ouminus(X18728),X18726)
| ~ class_Groups_Ogroup__add(X18728) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).
fof(i_0_10782,plain,
! [X32015] :
( ( ~ c_List_Onat__list(X32015)
| c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X32015)) )
& ( ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X32015))
| c_List_Onat__list(X32015) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__list__def])]) ).
fof(i_0_10783,plain,
! [X24062] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24062)) = hAPP(c_Nat_OSuc,X24062),
inference(variable_rename,[status(thm)],[fact_card__atMost]) ).
fof(i_0_10784,plain,
! [X22748] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X22748)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22748),
inference(variable_rename,[status(thm)],[fact_nat__of__number]) ).
fof(i_0_10785,plain,
! [X20875] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20875)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20875),
inference(variable_rename,[status(thm)],[fact_nat__number__of]) ).
fof(i_0_10786,plain,
! [X20874] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20874) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20874)),
inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).
fof(i_0_10787,plain,
! [X19480] : hAPP(c_Nat_OSuc,X19480) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19480),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_10788,plain,
! [X19033,X19034] :
( ~ class_Rings_Olinordered__idom(X19034)
| c_Groups_Osgn__class_Osgn(X19034,c_Groups_Osgn__class_Osgn(X19034,X19033)) = c_Groups_Osgn__class_Osgn(X19034,X19033) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])]) ).
fof(i_0_10789,plain,
! [X27234,X27235] :
( ~ class_Lattices_Osemilattice__inf(X27235)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27235),X27234),X27234) = X27234 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oidem])]) ).
fof(i_0_10790,plain,
! [X27232,X27233] :
( ~ class_Lattices_Osemilattice__inf(X27233)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27233),X27232),X27232) = X27232 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__idem])]) ).
fof(i_0_10791,plain,
! [X27242,X27243] :
( ~ class_Lattices_Olattice(X27243)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27243),X27242),X27242) = X27242 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oidem])]) ).
fof(i_0_10792,plain,
! [X23957,X23958] :
( ~ class_Lattices_Osemilattice__sup(X23958)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23958),X23957),X23957) = X23957 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oidem])]) ).
fof(i_0_10793,plain,
! [X23955,X23956] :
( ~ class_Lattices_Osemilattice__sup(X23956)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23956),X23955),X23955) = X23955 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__idem])]) ).
fof(i_0_10794,plain,
! [X23974,X23975] :
( ~ class_Lattices_Olattice(X23975)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23975),X23974),X23974) = X23974 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem])]) ).
fof(i_0_10795,plain,
! [X22756,X22757] :
( ~ class_Orderings_Olinorder(X22757)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22757),X22756),X22756) = X22756 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oidem])]) ).
fof(i_0_10796,plain,
! [X22640,X22641] :
( ~ class_Orderings_Olinorder(X22641)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22641),X22640),X22640) = X22640 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oidem])]) ).
fof(i_0_10797,plain,
! [X22754,X22755] :
( ~ class_Orderings_Olinorder(X22755)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22755),X22754),X22754) = X22754 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oidem])]) ).
fof(i_0_10798,plain,
! [X22311,X22312] :
( ~ class_Orderings_Olinorder(X22312)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22312),X22311),X22311) = X22311 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oidem])]) ).
fof(i_0_10799,plain,
! [X19896,X19897] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X19897)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19897),X19896),X19896) = X19896 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).
fof(i_0_10800,plain,
! [X19894,X19895] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X19895)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19895),X19894),X19894) = X19894 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])]) ).
fof(i_0_10801,plain,
! [X32532,X32533] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32533)),X32532) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X32532 = c_List_Olist_ONil(X32533) )
& ( X32532 != c_List_Olist_ONil(X32533)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32533)),X32532) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__0__conv])]) ).
fof(i_0_10802,plain,
! [X21071] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X21071) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21071),
inference(variable_rename,[status(thm)],[fact_mult__Min]) ).
fof(i_0_10803,plain,
! [X23571] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23571) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X23571),
inference(variable_rename,[status(thm)],[fact_atLeast0LessThan]) ).
fof(i_0_10804,plain,
! [X33366,X33367] : hAPP(hAPP(c_List_Odrop(X33367),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33366) = X33366,
inference(variable_rename,[status(thm)],[fact_drop__0]) ).
fof(i_0_10805,plain,
! [X33004,X33005] : hAPP(hAPP(c_List_Oappend(X33005),X33004),c_List_Olist_ONil(X33005)) = X33004,
inference(variable_rename,[status(thm)],[fact_append__Nil2]) ).
fof(i_0_10806,plain,
! [X34284,X34285] : hAPP(c_List_Orev(X34285),hAPP(c_List_Orev(X34285),X34284)) = X34284,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
fof(i_0_10807,plain,
! [X17973,X17974] : hAPP(c_Option_Othe(X17974),hAPP(c_Option_Ooption_OSome(X17974),X17973)) = X17973,
inference(variable_rename,[status(thm)],[fact_the_Osimps]) ).
fof(i_0_10808,plain,
! [X19834] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19834) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__zero]) ).
fof(i_0_10809,plain,
! [X21021] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X21021))
| hAPP(c_Int_Onat,X21021) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__nat])]) ).
fof(i_0_10810,plain,
! [X24160] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24160)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X24160),
inference(variable_rename,[status(thm)],[fact_atLeast__Suc__greaterThan]) ).
fof(i_0_10811,plain,
! [X24094] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24094)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24094),
inference(variable_rename,[status(thm)],[fact_lessThan__Suc__atMost]) ).
fof(i_0_10812,plain,
! [X21847] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21847) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21847)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(i_0_10813,plain,
! [X20030] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20030),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& c_Divides_Odiv__class_Omod(tc_Int_Oint,X20030,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X20030 ),
inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO]) ).
fof(i_0_10814,plain,
! [X21117] :
( ~ class_Int_Onumber__ring(X21117)
| c_Int_Oiszero(X21117,hAPP(c_Int_Onumber__class_Onumber__of(X21117),c_Int_OPls)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0])]) ).
fof(i_0_10815,plain,
! [X31882] : hAPP(c_Option_Omap(X31882,X31882),c_Fun_Oid(X31882)) = c_Fun_Oid(tc_Option_Ooption(X31882)),
inference(variable_rename,[status(thm)],[fact_Option_Omap_Oid]) ).
fof(i_0_10816,plain,
! [X31881] : hAPP(c_Option_Omap(X31881,X31881),c_COMBI(X31881)) = c_Fun_Oid(tc_Option_Ooption(X31881)),
inference(variable_rename,[status(thm)],[fact_Option_Omap_Oidentity]) ).
fof(i_0_10817,plain,
! [X31752] : hAPP(c_List_Omap(X31752,X31752),c_Fun_Oid(X31752)) = c_Fun_Oid(tc_List_Olist(X31752)),
inference(variable_rename,[status(thm)],[fact_List_Omap_Oid]) ).
fof(i_0_10818,plain,
! [X31751] : hAPP(c_List_Omap(X31751,X31751),c_COMBI(X31751)) = c_Fun_Oid(tc_List_Olist(X31751)),
inference(variable_rename,[status(thm)],[fact_List_Omap_Oidentity]) ).
fof(i_0_10819,plain,
! [X18539,X18540] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18540) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18539)
| X18540 = X18539 )
& ( X18540 != X18539
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18540) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18539) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I1_J])]) ).
fof(i_0_10820,plain,
! [X18537,X18538] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18538) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18537)
| X18538 = X18537 )
& ( X18538 != X18537
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18538) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18537) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__int__eq])]) ).
fof(i_0_10821,plain,
! [X19835] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X19835,X19835) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__self]) ).
fof(i_0_10822,plain,
! [X34286,X34287,X34288] :
( ( hAPP(c_List_Orev(X34288),X34287) != X34286
| X34287 = hAPP(c_List_Orev(X34288),X34286) )
& ( X34287 != hAPP(c_List_Orev(X34288),X34286)
| hAPP(c_List_Orev(X34288),X34287) = X34286 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__swap])]) ).
fof(i_0_10823,plain,
! [X22306] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22306) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_min__0L]) ).
fof(i_0_10824,plain,
! [X20287] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20287) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).
fof(i_0_10825,plain,
! [X19974] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19974) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zdiv__zero]) ).
fof(i_0_10826,plain,
! [X19221] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19221) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0]) ).
fof(i_0_10827,plain,
! [X32517] : hBOOL(hAPP(c_List_Odistinct(X32517),c_List_Olist_ONil(X32517))),
inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).
fof(i_0_10828,plain,
! [X29916,X29917,X29918] : hAPP(c_New__DSequence_Oneg__single(X29918,X29917),X29916) = c_Lazy__Sequence_Ohb__single(X29918,X29917),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__single__def]) ).
fof(i_0_10829,plain,
! [X29899,X29900,X29901] : hAPP(c_New__DSequence_Opos__single(X29901,X29900),X29899) = c_Lazy__Sequence_Osingle(X29901,X29900),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__single__def]) ).
fof(i_0_10830,plain,
! [X30237,X30238] : c_Transitive__Closure_Ortrancl(X30238,c_Transitive__Closure_Ortrancl(X30238,X30237)) = c_Transitive__Closure_Ortrancl(X30238,X30237),
inference(variable_rename,[status(thm)],[fact_rtrancl__idemp]) ).
fof(i_0_10831,plain,
! [X32536] : hAPP(c_List_Oset(X32536),c_List_Olist_ONil(X32536)) = c_Orderings_Obot__class_Obot(tc_fun(X32536,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I1_J]) ).
fof(i_0_10832,plain,
! [X22635] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22635) = X22635,
inference(variable_rename,[status(thm)],[fact_max__0L]) ).
fof(i_0_10833,plain,
! [X18666] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18666) = X18666,
inference(variable_rename,[status(thm)],[fact_zmult__1]) ).
fof(i_0_10834,plain,
! [X19004] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X19004) = X19004,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(i_0_10835,plain,
! [X18550] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18550) = X18550,
inference(variable_rename,[status(thm)],[fact_zadd__0]) ).
fof(i_0_10836,plain,
! [X18048] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18048) = X18048,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_10837,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(fof_simplification,[status(thm)],[fact_not__neg__1]) ).
fof(i_0_10838,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(fof_simplification,[status(thm)],[fact_not__neg__0]) ).
fof(i_0_10839,plain,
! [X20023] :
( X20023 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20023),X20023) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])]) ).
fof(i_0_10840,plain,
! [X18204,X18205] :
( X18205 = c_Option_Ooption_ONone(X18204)
| X18205 = hAPP(c_Option_Ooption_OSome(X18204),esk27_2(X18204,X18205)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option_Oexhaust])])]) ).
fof(i_0_10841,plain,
! [X17981,X17982,X17984,X17985,X17986] :
( ( X17982 = hAPP(c_Option_Ooption_OSome(X17981),esk24_2(X17981,X17982))
| X17982 = c_Option_Ooption_ONone(X17981) )
& ( X17985 != c_Option_Ooption_ONone(X17984)
| X17985 != hAPP(c_Option_Ooption_OSome(X17984),X17986) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_not__Some__eq])])])])]) ).
fof(i_0_10842,plain,
! [X17975,X17976,X17978,X17979,X17980] :
( ( X17976 = c_Option_Ooption_ONone(X17975)
| X17976 = hAPP(c_Option_Ooption_OSome(X17975),esk23_2(X17975,X17976)) )
& ( X17979 != hAPP(c_Option_Ooption_OSome(X17978),X17980)
| X17979 != c_Option_Ooption_ONone(X17978) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_not__None__eq])])])])]) ).
fof(i_0_10843,plain,
! [X21077] :
( ~ class_Int_Onumber__ring(X21077)
| hAPP(c_Groups_Ouminus__class_Ouminus(X21077),c_Groups_Oone__class_Oone(X21077)) = hAPP(c_Int_Onumber__class_Onumber__of(X21077),c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I31_J])]) ).
fof(i_0_10844,plain,
! [X21076] :
( ~ class_Int_Onumber__ring(X21076)
| hAPP(c_Int_Onumber__class_Onumber__of(X21076),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X21076),c_Groups_Oone__class_Oone(X21076)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Min])]) ).
fof(i_0_10845,plain,
! [X22305] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22305),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_min__0R]) ).
fof(i_0_10846,plain,
! [X19220] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19220),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0__right]) ).
fof(i_0_10847,plain,
! [X18749,X18750] :
( ( c_Groups_Ozero__class_Ozero(X18750) != hAPP(c_Groups_Ouminus__class_Ouminus(X18750),X18749)
| c_Groups_Ozero__class_Ozero(X18750) = X18749
| ~ class_Groups_Ogroup__add(X18750) )
& ( c_Groups_Ozero__class_Ozero(X18750) != X18749
| c_Groups_Ozero__class_Ozero(X18750) = hAPP(c_Groups_Ouminus__class_Ouminus(X18750),X18749)
| ~ class_Groups_Ogroup__add(X18750) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).
fof(i_0_10848,plain,
! [X20623,X20624] :
( ( hAPP(c_Groups_Oabs__class_Oabs(X20624),X20623) != c_Groups_Ozero__class_Ozero(X20624)
| X20623 = c_Groups_Ozero__class_Ozero(X20624)
| ~ class_Groups_Oordered__ab__group__add__abs(X20624) )
& ( X20623 != c_Groups_Ozero__class_Ozero(X20624)
| hAPP(c_Groups_Oabs__class_Oabs(X20624),X20623) = c_Groups_Ozero__class_Ozero(X20624)
| ~ class_Groups_Oordered__ab__group__add__abs(X20624) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).
fof(i_0_10849,plain,
! [X18753,X18754] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18754),X18753) != c_Groups_Ozero__class_Ozero(X18754)
| X18753 = c_Groups_Ozero__class_Ozero(X18754)
| ~ class_Groups_Ogroup__add(X18754) )
& ( X18753 != c_Groups_Ozero__class_Ozero(X18754)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18754),X18753) = c_Groups_Ozero__class_Ozero(X18754)
| ~ class_Groups_Ogroup__add(X18754) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).
fof(i_0_10850,plain,
! [X34449] :
( ~ hBOOL(hAPP(c_fNot,X34449))
| ~ hBOOL(X34449) ),
inference(variable_rename,[status(thm)],[i_0_6007]) ).
fof(i_0_10851,plain,
! [X22634] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22634),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22634,
inference(variable_rename,[status(thm)],[fact_max__0R]) ).
fof(i_0_10852,plain,
! [X20286] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20286),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X20286,
inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(i_0_10853,plain,
! [X18669] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18669),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X18669,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(i_0_10854,plain,
! [X19007] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19007),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X19007,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
fof(i_0_10855,plain,
! [X18549] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18549),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X18549,
inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).
fof(i_0_10856,plain,
! [X18049] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18049),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18049,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_10857,plain,
! [X23796] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X23796)) = X23796,
inference(variable_rename,[status(thm)],[fact_card__lessThan]) ).
fof(i_0_10858,plain,
! [X18658] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18658)) = X18658,
inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).
fof(i_0_10859,plain,
! [X33918,X33919] : hAPP(c_List_Ofilter(X33919,X33918),c_List_Olist_ONil(X33919)) = c_List_Olist_ONil(X33919),
inference(variable_rename,[status(thm)],[fact_filter_Osimps_I1_J]) ).
fof(i_0_10860,plain,
! [X24525,X24526] :
( ~ class_Finite__Set_Ofinite(X24526)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24526),X24525)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).
fof(i_0_10861,plain,
! [X24523,X24524] :
( ~ class_Finite__Set_Ofinite(X24524)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24524),X24523)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).
fof(i_0_10862,plain,
! [X18945,X18946] :
( ( hAPP(c_Int_Oring__1__class_Oof__int(X18946),X18945) != c_Groups_Ozero__class_Ozero(X18946)
| X18945 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Int_Oring__char__0(X18946) )
& ( X18945 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(X18946),X18945) = c_Groups_Ozero__class_Ozero(X18946)
| ~ class_Int_Oring__char__0(X18946) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff])])]) ).
fof(i_0_10863,plain,
! [X18943,X18944] :
( ( c_Groups_Ozero__class_Ozero(X18944) != hAPP(c_Int_Oring__1__class_Oof__int(X18944),X18943)
| X18943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Int_Oring__char__0(X18944) )
& ( X18943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(X18944) = hAPP(c_Int_Oring__1__class_Oof__int(X18944),X18943)
| ~ class_Int_Oring__char__0(X18944) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff])])]) ).
cnf(i_0_10864,plain,
( c_Int_OBit0(X1) = c_Int_OPls
| X1 != c_Int_OPls ),
inference(split_conjunct,[status(thm)],[i_0_6002]) ).
cnf(i_0_10865,plain,
( c_Int_OPls = c_Int_OBit0(X1)
| c_Int_OPls != X1 ),
inference(split_conjunct,[status(thm)],[i_0_6001]) ).
fof(i_0_10866,plain,
! [X20285] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20285),X20285) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).
fof(i_0_10867,plain,
! [X20660,X20661] :
( ~ class_Int_Onumber__ring(X20661)
| hAPP(c_Int_Onumber__class_Onumber__of(X20661),X20660) = hAPP(c_Int_Oring__1__class_Oof__int(X20661),X20660) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__eq])]) ).
fof(i_0_10868,plain,
! [X24913] : c_Option_Oset(X24913,c_Option_Ooption_ONone(X24913)) = c_Orderings_Obot__class_Obot(tc_fun(X24913,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Option_Oset_Osimps_I1_J]) ).
fof(i_0_10869,plain,
! [X17741,X17742,X17743,X17744] :
( ( X17744 = X17742
| c_Com_Ocom_OWhile(X17744,X17743) != c_Com_Ocom_OWhile(X17742,X17741) )
& ( X17743 = X17741
| c_Com_Ocom_OWhile(X17744,X17743) != c_Com_Ocom_OWhile(X17742,X17741) )
& ( X17744 != X17742
| X17743 != X17741
| c_Com_Ocom_OWhile(X17744,X17743) = c_Com_Ocom_OWhile(X17742,X17741) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I5_J])])]) ).
fof(i_0_10870,plain,
! [X17447,X17448,X17449,X17450] :
( ( X17450 = X17448
| c_Com_Ocom_OSemi(X17450,X17449) != c_Com_Ocom_OSemi(X17448,X17447) )
& ( X17449 = X17447
| c_Com_Ocom_OSemi(X17450,X17449) != c_Com_Ocom_OSemi(X17448,X17447) )
& ( X17450 != X17448
| X17449 != X17447
| c_Com_Ocom_OSemi(X17450,X17449) = c_Com_Ocom_OSemi(X17448,X17447) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I3_J])])]) ).
fof(i_0_10871,plain,
! [X17155,X17156,X17157,X17158] :
( ( X17158 = X17156
| c_Com_Ocom_OAss(X17158,X17157) != c_Com_Ocom_OAss(X17156,X17155) )
& ( X17157 = X17155
| c_Com_Ocom_OAss(X17158,X17157) != c_Com_Ocom_OAss(X17156,X17155) )
& ( X17158 != X17156
| X17157 != X17155
| c_Com_Ocom_OAss(X17158,X17157) = c_Com_Ocom_OAss(X17156,X17155) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I1_J])])]) ).
fof(i_0_10872,plain,
! [X18755,X18756] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18756),X18755) != X18755
| X18755 = c_Groups_Ozero__class_Ozero(X18756)
| ~ class_Groups_Olinordered__ab__group__add(X18756) )
& ( X18755 != c_Groups_Ozero__class_Ozero(X18756)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18756),X18755) = X18755
| ~ class_Groups_Olinordered__ab__group__add(X18756) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).
fof(i_0_10873,plain,
! [X18751,X18752] :
( ( X18751 != hAPP(c_Groups_Ouminus__class_Ouminus(X18752),X18751)
| X18751 = c_Groups_Ozero__class_Ozero(X18752)
| ~ class_Groups_Olinordered__ab__group__add(X18752) )
& ( X18751 != c_Groups_Ozero__class_Ozero(X18752)
| X18751 = hAPP(c_Groups_Ouminus__class_Ouminus(X18752),X18751)
| ~ class_Groups_Olinordered__ab__group__add(X18752) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).
fof(i_0_10874,plain,
! [X17114,X17115] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X17115,X17114)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I10_J]) ).
fof(i_0_10875,plain,
! [X21107] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21107),c_Int_OPls) = X21107,
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J]) ).
fof(i_0_10876,plain,
! [X21104] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21104),c_Int_OPls) = X21104,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(i_0_10877,plain,
! [X18797] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18797)) = X18797,
inference(variable_rename,[status(thm)],[fact_nat__int]) ).
fof(i_0_10878,plain,
! [X34419,X34420] :
( ~ class_Smallcheck_Osmall(X34420)
| ~ class_Smallcheck_Osmall(X34419)
| class_Smallcheck_Osmall(tc_prod(X34420,X34419)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Smallcheck_Osmall])]) ).
fof(i_0_10879,plain,
! [X34417,X34418] :
( ~ class_Finite__Set_Ofinite(X34418)
| ~ class_Finite__Set_Ofinite(X34417)
| class_Finite__Set_Ofinite(tc_prod(X34418,X34417)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).
fof(i_0_10880,plain,
! [X34398,X34399] :
( ~ class_Finite__Set_Ofinite(X34399)
| ~ class_Finite__Set_Ofinite(X34398)
| class_Finite__Set_Ofinite(tc_fun(X34399,X34398)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).
fof(i_0_10881,plain,
! [X34414,X34415] :
( ~ class_Finite__Set_Ofinite(X34415)
| ~ class_Finite__Set_Ofinite(X34414)
| class_Finite__Set_Ofinite(tc_sum(X34415,X34414)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).
fof(i_0_10882,plain,
! [X21579,X21580] :
( ~ c_Nat__Transfer_Ois__nat(X21580)
| ~ c_Nat__Transfer_Ois__nat(X21579)
| c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X21580,X21579)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J])]) ).
fof(i_0_10883,plain,
! [X17835,X17836,X17837,X17838] : c_Com_Ocom_OWhile(X17838,X17837) != c_Com_Ocom_OSemi(X17836,X17835),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I47_J]) ).
fof(i_0_10884,plain,
! [X17807,X17808,X17809,X17810] : c_Com_Ocom_OWhile(X17810,X17809) != c_Com_Ocom_OAss(X17808,X17807),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I29_J]) ).
fof(i_0_10885,plain,
! [X17839,X17840,X17841,X17842] : c_Com_Ocom_OSemi(X17842,X17841) != c_Com_Ocom_OWhile(X17840,X17839),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I46_J]) ).
fof(i_0_10886,plain,
! [X17811,X17812,X17813,X17814] : c_Com_Ocom_OAss(X17814,X17813) != c_Com_Ocom_OWhile(X17812,X17811),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I28_J]) ).
fof(i_0_10887,plain,
! [X17598,X17599,X17600,X17601] : c_Com_Ocom_OSemi(X17601,X17600) != c_Com_Ocom_OAss(X17599,X17598),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I25_J]) ).
fof(i_0_10888,plain,
! [X17594,X17595,X17596,X17597] : c_Com_Ocom_OAss(X17597,X17596) != c_Com_Ocom_OSemi(X17595,X17594),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I24_J]) ).
fof(i_0_10889,plain,
! [X21105] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X21105) = X21105,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
fof(i_0_10890,plain,
! [X34249,X34250] :
( ( hAPP(c_List_Orev(X34250),X34249) != c_List_Olist_ONil(X34250)
| X34249 = c_List_Olist_ONil(X34250) )
& ( X34249 != c_List_Olist_ONil(X34250)
| hAPP(c_List_Orev(X34250),X34249) = c_List_Olist_ONil(X34250) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__Nil__conv])]) ).
fof(i_0_10891,plain,
! [X33373,X33374] :
( ( hAPP(c_List_Orotate1(X33374),X33373) != c_List_Olist_ONil(X33374)
| X33373 = c_List_Olist_ONil(X33374) )
& ( X33373 != c_List_Olist_ONil(X33374)
| hAPP(c_List_Orotate1(X33374),X33373) = c_List_Olist_ONil(X33374) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])]) ).
fof(i_0_10892,plain,
! [X34251,X34252] :
( ( c_List_Olist_ONil(X34252) != hAPP(c_List_Orev(X34252),X34251)
| X34251 = c_List_Olist_ONil(X34252) )
& ( X34251 != c_List_Olist_ONil(X34252)
| c_List_Olist_ONil(X34252) = hAPP(c_List_Orev(X34252),X34251) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__rev__conv])]) ).
fof(i_0_10893,plain,
! [X21106] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X21106) = c_Int_OPls,
inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).
fof(i_0_10894,plain,
! [X29630] : c_Wellfounded_Owf(tc_fun(X29630,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X29630)),
inference(variable_rename,[status(thm)],[fact_wf__finite__psubset]) ).
fof(i_0_10895,plain,
! [X17100] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X17100)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I15_J]) ).
fof(i_0_10896,plain,
! [X33981] : c_List_Otranspose(X33981,c_List_Olist_ONil(tc_List_Olist(X33981))) = c_List_Olist_ONil(tc_List_Olist(X33981)),
inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I1_J]) ).
fof(i_0_10897,plain,
! [X17794,X17795,X17796] : hAPP(c_Com_Ocom_OBODY,X17796) != c_Com_Ocom_OWhile(X17795,X17794),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I59_J]) ).
fof(i_0_10898,plain,
! [X17588,X17589,X17590] : hAPP(c_Com_Ocom_OBODY,X17590) != c_Com_Ocom_OSemi(X17589,X17588),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I49_J]) ).
fof(i_0_10899,plain,
! [X17204,X17205,X17206] : hAPP(c_Com_Ocom_OBODY,X17206) != c_Com_Ocom_OAss(X17205,X17204),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I31_J]) ).
fof(i_0_10900,plain,
! [X17791,X17792,X17793] : c_Com_Ocom_OWhile(X17793,X17792) != hAPP(c_Com_Ocom_OBODY,X17791),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I58_J]) ).
fof(i_0_10901,plain,
! [X17591,X17592,X17593] : c_Com_Ocom_OSemi(X17593,X17592) != hAPP(c_Com_Ocom_OBODY,X17591),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I48_J]) ).
fof(i_0_10902,plain,
! [X17207,X17208,X17209] : c_Com_Ocom_OAss(X17209,X17208) != hAPP(c_Com_Ocom_OBODY,X17207),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I30_J]) ).
cnf(i_0_10903,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_succ__Min]) ).
cnf(i_0_10904,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_Bit0__Pls]) ).
cnf(i_0_10905,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(split_conjunct,[status(thm)],[fact_pred__Pls]) ).
fof(i_0_10906,plain,
! [X25124,X25125] :
( ( hAPP(c_Int_ORep__Integ,X25125) != hAPP(c_Int_ORep__Integ,X25124)
| X25125 = X25124 )
& ( X25125 != X25124
| hAPP(c_Int_ORep__Integ,X25125) = hAPP(c_Int_ORep__Integ,X25124) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject])]) ).
fof(i_0_10907,plain,
! [X22741,X22742] :
( ( hAPP(c_Code__Numeral_Onat__of,X22742) != hAPP(c_Code__Numeral_Onat__of,X22741)
| X22742 = X22741 )
& ( X22742 != X22741
| hAPP(c_Code__Numeral_Onat__of,X22742) = hAPP(c_Code__Numeral_Onat__of,X22741) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Onat__of__inject])]) ).
fof(i_0_10908,plain,
! [X22739,X22740] :
( ( hAPP(c_Code__Numeral_Onat__of,X22740) != hAPP(c_Code__Numeral_Onat__of,X22739)
| X22740 = X22739 )
& ( X22740 != X22739
| hAPP(c_Code__Numeral_Onat__of,X22740) = hAPP(c_Code__Numeral_Onat__of,X22739) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Onat__of__inject])]) ).
fof(i_0_10909,plain,
! [X21834,X21835] :
( ( hAPP(c_Code__Numeral_Oof__nat,X21835) != hAPP(c_Code__Numeral_Oof__nat,X21834)
| X21835 = X21834 )
& ( X21835 != X21834
| hAPP(c_Code__Numeral_Oof__nat,X21835) = hAPP(c_Code__Numeral_Oof__nat,X21834) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject])]) ).
fof(i_0_10910,plain,
! [X18080,X18081] :
( ( hAPP(c_Nat_OSuc,X18081) != hAPP(c_Nat_OSuc,X18080)
| X18081 = X18080 )
& ( X18081 != X18080
| hAPP(c_Nat_OSuc,X18081) = hAPP(c_Nat_OSuc,X18080) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_10911,plain,
! [X18078,X18079] :
( hAPP(c_Nat_OSuc,X18079) != hAPP(c_Nat_OSuc,X18078)
| X18079 = X18078 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_10912,plain,
! [X17095,X17096] :
( ( hAPP(c_Com_Ocom_OBODY,X17096) != hAPP(c_Com_Ocom_OBODY,X17095)
| X17096 = X17095 )
& ( X17096 != X17095
| hAPP(c_Com_Ocom_OBODY,X17096) = hAPP(c_Com_Ocom_OBODY,X17095) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I6_J])]) ).
fof(i_0_10913,plain,
! [X19331,X19332] :
( ( c_Groups_Osgn__class_Osgn(X19332,X19331) != c_Groups_Ozero__class_Ozero(X19332)
| X19331 = c_Groups_Ozero__class_Ozero(X19332)
| ~ class_Rings_Olinordered__idom(X19332) )
& ( X19331 != c_Groups_Ozero__class_Ozero(X19332)
| c_Groups_Osgn__class_Osgn(X19332,X19331) = c_Groups_Ozero__class_Ozero(X19332)
| ~ class_Rings_Olinordered__idom(X19332) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])]) ).
fof(i_0_10914,plain,
! [X32534] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32534)),c_List_Olist_ONil(X32534)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_list_Osize_I3_J]) ).
fof(i_0_10915,plain,
! [X17996] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X17996)),c_Option_Ooption_ONone(X17996)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_option_Osize_I3_J]) ).
fof(i_0_10916,plain,
! [X21070] :
( ~ class_Rings_Osemiring__1(X21070)
| ~ c_Int_Oiszero(X21070,c_Groups_Oone__class_Oone(X21070)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6008])]) ).
fof(i_0_10917,plain,
! [X34109,X34110] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X34110,X34109)),
inference(variable_rename,[status(thm)],[fact_sorted__upto]) ).
fof(i_0_10918,plain,
! [X17987,X17988] : hAPP(c_Option_Ooption_OSome(X17988),X17987) != c_Option_Ooption_ONone(X17988),
inference(variable_rename,[status(thm)],[fact_option_Osimps_I3_J]) ).
fof(i_0_10919,plain,
! [X17992,X17993] : c_Option_Ooption_ONone(X17993) != hAPP(c_Option_Ooption_OSome(X17993),X17992),
inference(variable_rename,[status(thm)],[fact_option_Osimps_I2_J]) ).
fof(i_0_10920,plain,
! [X30014,X30015] : c_Hilbert__Choice_OEps(X30015,hAPP(c_fequal,X30014)) = X30014,
inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial]) ).
fof(i_0_10921,plain,
! [X22992,X22993] : c_HOL_OThe(X22993,hAPP(c_fequal,X22992)) = X22992,
inference(variable_rename,[status(thm)],[fact_the__sym__eq__trivial]) ).
fof(i_0_10922,plain,
! [X32496] :
( ~ class_Groups_Omonoid__add(X32496)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32496),c_List_Olist_ONil(X32496)) = c_Groups_Ozero__class_Ozero(X32496) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I1_J])]) ).
fof(i_0_10923,plain,
! [X20636] :
( ~ class_Rings_Olinordered__idom(X20636)
| hAPP(c_Groups_Oabs__class_Oabs(X20636),c_Groups_Oone__class_Oone(X20636)) = c_Groups_Oone__class_Oone(X20636) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).
fof(i_0_10924,plain,
! [X20622] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20622)
| hAPP(c_Groups_Oabs__class_Oabs(X20622),c_Groups_Ozero__class_Ozero(X20622)) = c_Groups_Ozero__class_Ozero(X20622) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).
fof(i_0_10925,plain,
! [X24841] :
( ~ class_Lattices_Oboolean__algebra(X24841)
| hAPP(c_Groups_Ouminus__class_Ouminus(X24841),c_Orderings_Obot__class_Obot(X24841)) = c_Orderings_Otop__class_Otop(X24841) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])]) ).
fof(i_0_10926,plain,
! [X24840] :
( ~ class_Lattices_Oboolean__algebra(X24840)
| hAPP(c_Groups_Ouminus__class_Ouminus(X24840),c_Orderings_Otop__class_Otop(X24840)) = c_Orderings_Obot__class_Obot(X24840) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__top__eq])]) ).
fof(i_0_10927,plain,
! [X18748] :
( ~ class_Groups_Ogroup__add(X18748)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18748),c_Groups_Ozero__class_Ozero(X18748)) = c_Groups_Ozero__class_Ozero(X18748) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).
fof(i_0_10928,plain,
! [X34380,X34381] :
( ~ class_Lattices_Obounded__lattice(X34381)
| class_Lattices_Obounded__lattice(tc_fun(X34380,X34381)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice])]) ).
fof(i_0_10929,plain,
! [X34392,X34393] :
( ~ class_Lattices_Odistrib__lattice(X34393)
| class_Lattices_Odistrib__lattice(tc_fun(X34392,X34393)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Odistrib__lattice])]) ).
fof(i_0_10930,plain,
! [X34390,X34391] :
( ~ class_Lattices_Olattice(X34391)
| class_Lattices_Osemilattice__inf(tc_fun(X34390,X34391)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])]) ).
fof(i_0_10931,plain,
! [X34386,X34387] :
( ~ class_Lattices_Obounded__lattice(X34387)
| class_Lattices_Obounded__lattice__bot(tc_fun(X34386,X34387)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot])]) ).
fof(i_0_10932,plain,
! [X34408,X34409] :
( ~ class_Orderings_Obot(X34409)
| class_Orderings_Obot(tc_fun(X34408,X34409)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])]) ).
fof(i_0_10933,plain,
! [X34384,X34385] :
( ~ class_Lattices_Obounded__lattice(X34385)
| class_Lattices_Obounded__lattice__top(tc_fun(X34384,X34385)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__top])]) ).
fof(i_0_10934,plain,
! [X34404,X34405] :
( ~ class_Orderings_Otop(X34405)
| class_Orderings_Otop(tc_fun(X34404,X34405)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).
fof(i_0_10935,plain,
! [X34382,X34383] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X34383)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X34382,X34383)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Complete__Lattice_Ocomplete__lattice])]) ).
fof(i_0_10936,plain,
! [X34388,X34389] :
( ~ class_Lattices_Olattice(X34389)
| class_Lattices_Osemilattice__sup(tc_fun(X34388,X34389)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__sup])]) ).
fof(i_0_10937,plain,
! [X34400,X34401] :
( ~ class_Lattices_Olattice(X34401)
| class_Lattices_Olattice(tc_fun(X34400,X34401)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice])]) ).
fof(i_0_10938,plain,
! [X34412,X34413] :
( ~ class_Groups_Ominus(X34413)
| class_Groups_Ominus(tc_fun(X34412,X34413)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).
fof(i_0_10939,plain,
! [X34410,X34411] :
( ~ class_Groups_Ouminus(X34411)
| class_Groups_Ouminus(tc_fun(X34410,X34411)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).
fof(i_0_10940,plain,
! [X34394,X34395] :
( ~ class_Lattices_Oboolean__algebra(X34395)
| class_Lattices_Oboolean__algebra(tc_fun(X34394,X34395)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).
fof(i_0_10941,plain,
! [X34406,X34407] :
( ~ class_Orderings_Oord(X34407)
| class_Orderings_Oord(tc_fun(X34406,X34407)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_10942,plain,
! [X34396,X34397] :
( ~ class_Orderings_Opreorder(X34397)
| class_Orderings_Opreorder(tc_fun(X34396,X34397)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_10943,plain,
! [X34402,X34403] :
( ~ class_Orderings_Oorder(X34403)
| class_Orderings_Oorder(tc_fun(X34402,X34403)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_10944,plain,
! [X29883,X29884] :
( ~ c_Wellfounded_Owf(X29884,X29883)
| c_Wellfounded_Oacyclic(X29884,X29883) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acyclic])]) ).
fof(i_0_10945,plain,
! [X21470] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21470)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J]) ).
fof(i_0_10946,plain,
! [X26744] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X26744)) = X26744,
inference(variable_rename,[status(thm)],[fact_Rep__Integ__inverse]) ).
fof(i_0_10947,plain,
! [X22745] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X22745)) = X22745,
inference(variable_rename,[status(thm)],[fact_nat__of__of__nat]) ).
fof(i_0_10948,plain,
! [X22744] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X22744)) = X22744,
inference(variable_rename,[status(thm)],[fact_of__nat__nat__of]) ).
fof(i_0_10949,plain,
! [X22743] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X22743)) = X22743,
inference(variable_rename,[status(thm)],[fact_nat__of__inverse]) ).
fof(i_0_10950,plain,
! [X21067,X21068] :
( ( ~ c_Int_Oiszero(X21068,X21067)
| X21067 = c_Groups_Ozero__class_Ozero(X21068)
| ~ class_Rings_Osemiring__1(X21068) )
& ( X21067 != c_Groups_Ozero__class_Ozero(X21068)
| c_Int_Oiszero(X21068,X21067)
| ~ class_Rings_Osemiring__1(X21068) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__def])])]) ).
fof(i_0_10951,plain,
! [X18474] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18474) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X18474 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18474 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18474) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv])]) ).
fof(i_0_10952,plain,
! [X18655] :
( ~ class_Rings_Oring__1(X18655)
| hAPP(c_Int_Oring__1__class_Oof__int(X18655),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X18655) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__1])]) ).
fof(i_0_10953,plain,
! [X18942] :
( ~ class_Rings_Oring__1(X18942)
| hAPP(c_Int_Oring__1__class_Oof__int(X18942),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X18942) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0])]) ).
fof(i_0_10954,plain,
! [X18742] :
( ~ class_Rings_Osemiring__1(X18742)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18742),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X18742) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__1])]) ).
fof(i_0_10955,plain,
! [X18491] :
( ~ class_Rings_Osemiring__1(X18491)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18491),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X18491) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0])]) ).
fof(i_0_10956,plain,
! [X20871] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20871) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X20871),
inference(variable_rename,[status(thm)],[fact_int__number__of__def]) ).
fof(i_0_10957,plain,
! [X17112,X17113] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X17113,X17112)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I2_J]) ).
fof(i_0_10958,plain,
! [X34450] :
( hBOOL(X34450)
| hBOOL(hAPP(c_fNot,X34450)) ),
inference(variable_rename,[status(thm)],[i_0_6009]) ).
fof(i_0_10959,plain,
! [X19333] :
( ~ class_Groups_Osgn__if(X19333)
| c_Groups_Osgn__class_Osgn(X19333,c_Groups_Ozero__class_Ozero(X19333)) = c_Groups_Ozero__class_Ozero(X19333) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])]) ).
fof(i_0_10960,plain,
! [X22732] :
( ~ class_Orderings_Oord(X22732)
| c_Orderings_Oord__class_Omax(X22732) = c_Orderings_Oord_Omax(X22732,c_Orderings_Oord__class_Oless__eq(X22732)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ord__max])]) ).
fof(i_0_10961,plain,
! [X22505] :
( ~ class_Orderings_Oord(X22505)
| c_Orderings_Oord__class_Omin(X22505) = c_Orderings_Oord_Omin(X22505,c_Orderings_Oord__class_Oless__eq(X22505)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ord__min])]) ).
fof(i_0_10962,plain,
! [X34254] : hAPP(c_List_Orev(X34254),c_List_Olist_ONil(X34254)) = c_List_Olist_ONil(X34254),
inference(variable_rename,[status(thm)],[fact_rev_Osimps_I1_J]) ).
fof(i_0_10963,plain,
! [X33518] : hAPP(c_List_Otl(X33518),c_List_Olist_ONil(X33518)) = c_List_Olist_ONil(X33518),
inference(variable_rename,[status(thm)],[fact_tl_Osimps_I1_J]) ).
fof(i_0_10964,plain,
! [X21110] :
( ~ class_Int_Onumber__ring(X21110)
| hAPP(c_Int_Onumber__class_Onumber__of(X21110),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X21110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])]) ).
fof(i_0_10965,plain,
! [X21109] :
( ~ class_Int_Onumber__ring(X21109)
| c_Groups_Ozero__class_Ozero(X21109) = hAPP(c_Int_Onumber__class_Onumber__of(X21109),c_Int_OPls) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).
fof(i_0_10966,plain,
! [X17099] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X17099)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I7_J]) ).
fof(i_0_10967,plain,
! [X18143,X18144] :
( ( ~ c_Option_Ois__none(X18144,X18143)
| X18143 = c_Option_Ooption_ONone(X18144) )
& ( X18143 != c_Option_Ooption_ONone(X18144)
| c_Option_Ois__none(X18144,X18143) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__none__def])]) ).
fof(i_0_10968,plain,
! [X34114] :
( ~ class_Orderings_Olinorder(X34114)
| c_List_Olinorder__class_Osorted(X34114,c_List_Olist_ONil(X34114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I1_J])]) ).
fof(i_0_10969,plain,
! [X34019] :
( ~ class_Orderings_Olinorder(X34019)
| c_List_Olinorder__class_Osorted(X34019,c_List_Olist_ONil(X34019)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_ONil])]) ).
fof(i_0_10970,plain,
! [X21069] :
( ~ class_Rings_Osemiring__1(X21069)
| c_Int_Oiszero(X21069,c_Groups_Ozero__class_Ozero(X21069)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__0])]) ).
fof(i_0_10971,plain,
! [X18004] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X18004)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_vname_Osize_I3_J]) ).
fof(i_0_10972,plain,
! [X17886] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X17886)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_vname_Osize_I4_J]) ).
fof(i_0_10973,plain,
! [X22912,X22913] : hAPP(c_New__DSequence_Opos__empty(X22913),X22912) = c_Lazy__Sequence_Oempty(X22913),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__empty__def]) ).
fof(i_0_10974,plain,
! [X33807] : c_List_Obutlast(X33807,c_List_Olist_ONil(X33807)) = c_List_Olist_ONil(X33807),
inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J]) ).
fof(i_0_10975,plain,
! [X18000] : hAPP(c_Nat_OSuc,X18000) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_10976,plain,
! [X17999] : hAPP(c_Nat_OSuc,X17999) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_10977,plain,
! [X17997] : hAPP(c_Nat_OSuc,X17997) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_10978,plain,
! [X18002] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X18002),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_10979,plain,
! [X18001] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X18001),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_10980,plain,
! [X17998] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X17998),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_10981,plain,
! [X18208] :
( X18208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18208 = hAPP(c_Nat_OSuc,esk28_1(X18208)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oexhaust])])]) ).
fof(i_0_10982,plain,
! [X17843,X17844] : c_Com_Ocom_OWhile(X17844,X17843) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I17_J]) ).
fof(i_0_10983,plain,
! [X17614,X17615] : c_Com_Ocom_OSemi(X17615,X17614) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I13_J]) ).
fof(i_0_10984,plain,
! [X17140,X17141] : c_Com_Ocom_OAss(X17141,X17140) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I9_J]) ).
fof(i_0_10985,plain,
! [X17845,X17846] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X17846,X17845),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I16_J]) ).
fof(i_0_10986,plain,
! [X17612,X17613] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X17613,X17612),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I12_J]) ).
fof(i_0_10987,plain,
! [X17135,X17136] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X17136,X17135),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I8_J]) ).
fof(i_0_10988,plain,
! [X27241] :
( ~ class_Lattices_Osemilattice__inf(X27241)
| ~ class_Orderings_Olinorder(X27241)
| c_Lattices_Osemilattice__inf__class_Oinf(X27241) = c_Orderings_Oord__class_Omin(X27241) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__min])]) ).
fof(i_0_10989,plain,
! [X23976] :
( ~ class_Lattices_Osemilattice__sup(X23976)
| ~ class_Orderings_Olinorder(X23976)
| c_Lattices_Osemilattice__sup__class_Osup(X23976) = c_Orderings_Oord__class_Omax(X23976) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__max])]) ).
fof(i_0_10990,plain,
! [X18082] : hAPP(c_Nat_OSuc,X18082) != X18082,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_10991,plain,
! [X18083] : X18083 != hAPP(c_Nat_OSuc,X18083),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_10992,plain,
! [X29439,X29440] : hAPP(c_Fun_Oid(X29440),X29439) = X29439,
inference(variable_rename,[status(thm)],[fact_id__apply]) ).
fof(i_0_10993,plain,
! [X29437,X29438] : hAPP(c_Fun_Oid(X29438),X29437) = X29437,
inference(variable_rename,[status(thm)],[fact_id__def]) ).
fof(i_0_10994,plain,
! [X29176,X29177] : hAPP(c_Set_OCollect(X29177),X29176) = X29176,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(i_0_10995,plain,
! [X34421,X34422] : hAPP(c_COMBI(X34422),X34421) = X34421,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_10996,plain,
! [X18145] : c_Option_Ois__none(X18145,c_Option_Ooption_ONone(X18145)),
inference(variable_rename,[status(thm)],[fact_is__none__code_I1_J]) ).
fof(i_0_10997,plain,
! [X18796] :
( ~ class_Rings_Ozero__neq__one(X18796)
| c_Groups_Ozero__class_Ozero(X18796) != c_Groups_Oone__class_Oone(X18796) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_10998,plain,
! [X18795] :
( ~ class_Rings_Ozero__neq__one(X18795)
| c_Groups_Oone__class_Oone(X18795) != c_Groups_Ozero__class_Ozero(X18795) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_10999,plain,
! [X17219] : hAPP(c_Com_Ocom_OBODY,X17219) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I19_J]) ).
fof(i_0_11000,plain,
! [X17218] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X17218),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I18_J]) ).
fof(i_0_11001,plain,
! [X17103] : hAPP(c_Nat_Osize__class_Osize(tc_String_Ochar),X17103) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_size__char]) ).
fof(i_0_11002,plain,
! [X17101] : hAPP(c_Nat_Osize__class_Osize(tc_String_Oliteral),X17101) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_size__literal__def]) ).
fof(i_0_11003,plain,
! [X22975] : c_Quickcheck_Obeyond(X22975,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(variable_rename,[status(thm)],[fact_beyond__zero]) ).
fof(i_0_11004,plain,
! [X29658] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X29658)),
inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than2]) ).
fof(i_0_11005,plain,
! [X29601] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X29601)),
inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than]) ).
fof(i_0_11006,plain,
! [X20853] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20853) = X20853,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
fof(i_0_11007,plain,
! [X17201] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X17201) = X17201,
inference(variable_rename,[status(thm)],[fact_nat__size]) ).
fof(i_0_11008,plain,
! [X34416] :
( ~ class_Finite__Set_Ofinite(X34416)
| class_Finite__Set_Ofinite(tc_Option_Ooption(X34416)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).
fof(i_0_11009,plain,
! [X18046,X18047] :
( ( c_Com_Ovname_OGlb(X18047) != c_Com_Ovname_OGlb(X18046)
| X18047 = X18046 )
& ( X18047 != X18046
| c_Com_Ovname_OGlb(X18047) = c_Com_Ovname_OGlb(X18046) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vname_Osimps_I1_J])]) ).
fof(i_0_11010,plain,
! [X17745,X17746] :
( ( c_Com_Ovname_OLoc(X17746) != c_Com_Ovname_OLoc(X17745)
| X17746 = X17745 )
& ( X17746 != X17745
| c_Com_Ovname_OLoc(X17746) = c_Com_Ovname_OLoc(X17745) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vname_Osimps_I2_J])]) ).
fof(i_0_11011,plain,
! [X18074,X18075] : c_Com_Ovname_OGlb(X18075) != c_Com_Ovname_OLoc(X18074),
inference(variable_rename,[status(thm)],[fact_vname_Osimps_I3_J]) ).
fof(i_0_11012,plain,
! [X18076,X18077] : c_Com_Ovname_OLoc(X18077) != c_Com_Ovname_OGlb(X18076),
inference(variable_rename,[status(thm)],[fact_vname_Osimps_I4_J]) ).
fof(i_0_11013,plain,
! [X18003] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X18003)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_vname_Osize_I1_J]) ).
fof(i_0_11014,plain,
! [X17872] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X17872)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_vname_Osize_I2_J]) ).
fof(i_0_11015,plain,
! [X27813] : c_Equiv__Relations_Oequivp(X27813,c_fequal),
inference(variable_rename,[status(thm)],[fact_identity__equivp]) ).
fof(i_0_11016,plain,
~ hBOOL(c_fFalse),
inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).
cnf(i_0_11017,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X11),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X1,tc_HOL_Obool)),X4)),X2))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(X2,esk247_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11)),esk248_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X8,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X8),X7),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X11,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X11),X10),X9)))
| ~ c_Equiv__Relations_Ocongruent2(X11,X8,tc_fun(X1,tc_HOL_Obool),X9,X6,X2)
| ~ c_Equiv__Relations_Oequiv(X8,X7,X6)
| ~ c_Equiv__Relations_Oequiv(X11,X10,X9) ),
inference(split_conjunct,[status(thm)],[i_0_6010]),
[final] ).
cnf(i_0_11018,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk248_11(X2,X3,X4,X5,X6,X7,X8,X1,X9,X10,X11)),X8))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,tc_fun(X6,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X6,tc_HOL_Obool)),tc_fun(X6,tc_HOL_Obool),X11),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool)),X3)),X5))),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X8),X7)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X11,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X11),X10),X9)))
| ~ c_Equiv__Relations_Ocongruent2(X11,X1,tc_fun(X6,tc_HOL_Obool),X9,X7,X5)
| ~ c_Equiv__Relations_Oequiv(X1,X8,X7)
| ~ c_Equiv__Relations_Oequiv(X11,X10,X9) ),
inference(split_conjunct,[status(thm)],[i_0_6010]),
[final] ).
cnf(i_0_11019,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk247_11(X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X1)),X11))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X9,tc_fun(X6,tc_HOL_Obool)),tc_fun(X6,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,tc_fun(X6,tc_HOL_Obool)),X3)),X5))),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X9,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X9),X8),X7)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X11),X10)))
| ~ c_Equiv__Relations_Ocongruent2(X1,X9,tc_fun(X6,tc_HOL_Obool),X10,X7,X5)
| ~ c_Equiv__Relations_Oequiv(X9,X8,X7)
| ~ c_Equiv__Relations_Oequiv(X1,X11,X10) ),
inference(split_conjunct,[status(thm)],[i_0_6010]),
[final] ).
cnf(i_0_11020,plain,
c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OCond(X10,X11,X12)) = hAPP(hAPP(hAPP(hAPP(hAPP(X6,X10),X11),X12),c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X11)),c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X12)),
inference(split_conjunct,[status(thm)],[i_0_6011]),
[final] ).
cnf(i_0_11021,plain,
c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OSemi(X10,X11)) = hAPP(hAPP(hAPP(hAPP(X5,X10),X11),c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10)),c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X11)),
inference(split_conjunct,[status(thm)],[i_0_6012]),
[final] ).
cnf(i_0_11022,plain,
c_Divides_Oadjust(X1) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6013,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11023,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X5),X7)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),tc_fun(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBS(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X3)),c_fequal))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)))))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X6)))),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X7)))))))
| ~ class_Rings_Osemiring__0(X1)
| ~ c_Fun_Oinj__on(tc_prod(X2,X3),X1,hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X7))) ),
inference(split_conjunct,[status(thm)],[i_0_6017]),
[final] ).
cnf(i_0_11024,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X5) = hAPP(c_Set_OCollect(tc_prod(X1,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(X2,tc_HOL_Obool)),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,tc_fun(X2,tc_HOL_Obool)),tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_fun(X2,tc_HOL_Obool)),tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X3)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4))))),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X3)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X2,X3)))),hAPP(c_COMBC(X2,X3,tc_prod(X2,X3)),c_Product__Type_OPair(X2,X3))))),X5))))),
inference(split_conjunct,[status(thm)],[i_0_6018]),
[final] ).
cnf(i_0_11025,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)) = c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Orderings_Oord__class_Omax(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6019]),
[final] ).
cnf(i_0_11026,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)) = c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Orderings_Oord__class_Omin(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6020]),
[final] ).
cnf(i_0_11027,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3)) = c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))
| ~ class_Lattices_Odistrib__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6021]),
[final] ).
cnf(i_0_11028,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3)) = c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))
| ~ class_Lattices_Odistrib__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6022]),
[final] ).
cnf(i_0_11029,plain,
c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OLocal(X10,X11,X12)) = hAPP(hAPP(hAPP(hAPP(X4,X10),X11),X12),c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X12)),
inference(split_conjunct,[status(thm)],[i_0_6023]),
[final] ).
cnf(i_0_11030,plain,
c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OWhile(X10,X11)) = hAPP(hAPP(hAPP(X7,X10),X11),c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X11)),
inference(split_conjunct,[status(thm)],[i_0_6024]),
[final] ).
cnf(i_0_11031,plain,
c_List_Oset__Cons(X1,X2,X3) = hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_List_Olist(X1)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBS(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_HOL_Obool,tc_List_Olist(X1))),c_fequal))),c_List_Olist_OCons(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X1))),X3)))))),
inference(split_conjunct,[status(thm)],[i_0_6025]),
[final] ).
cnf(i_0_11032,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk291_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk292_8(X3,X4,X5,X2,X1,X6,X7,X8))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X7)),X6),hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X8,X7),c_Product__Type_Omap__pair(X1,X8,X2,X7,X5,X4)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6026]),
[final] ).
cnf(i_0_11033,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,X6)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X3)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),X8)))),c_Com_Ocom_OCall(X7,X4,X8)),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X5)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,X6)))),X7)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_6027]),
[final] ).
cnf(i_0_11034,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X2,X1) = hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1)))) ),
inference(rw,[status(thm)],[i_0_6028,c_0_6029]),
[final] ).
cnf(i_0_11035,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X2,X1) = hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1)))) ),
inference(rw,[status(thm)],[i_0_6030,c_0_6029]),
[final] ).
cnf(i_0_11036,plain,
( hAPP(c_Set_Oimage(X1,X8,X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X8,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X5),c_Set_Oimage(X1,X8,X7)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk403_8(X3,X2,X4,X5,X6,X7,X8,X1))),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X4))
| ~ c_Fun_Oinj__on(X1,X8,X7,X6) ),
inference(split_conjunct,[status(thm)],[i_0_6031]),
[final] ).
cnf(i_0_11037,plain,
c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OCall(X10,X11,X12)) = hAPP(hAPP(hAPP(X9,X10),X11),X12),
inference(split_conjunct,[status(thm)],[i_0_6032]),
[final] ).
cnf(i_0_11038,plain,
c_Com_Ocom_Ocom__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OLocal(X10,X11,X12)) = hAPP(hAPP(hAPP(X4,X10),X11),X12),
inference(split_conjunct,[status(thm)],[i_0_6033]),
[final] ).
cnf(i_0_11039,plain,
c_Com_Ocom_Ocom__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OCond(X10,X11,X12)) = hAPP(hAPP(hAPP(X6,X10),X11),X12),
inference(split_conjunct,[status(thm)],[i_0_6034]),
[final] ).
cnf(i_0_11040,plain,
c_Com_Ocom_Ocom__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OCall(X10,X11,X12)) = hAPP(hAPP(hAPP(X9,X10),X11),X12),
inference(split_conjunct,[status(thm)],[i_0_6035]),
[final] ).
cnf(i_0_11041,plain,
c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OAss(X10,X11)) = hAPP(hAPP(X3,X10),X11),
inference(split_conjunct,[status(thm)],[i_0_6036]),
[final] ).
cnf(i_0_11042,plain,
c_Com_Ocom_Ocom__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OWhile(X10,X11)) = hAPP(hAPP(X7,X10),X11),
inference(split_conjunct,[status(thm)],[i_0_6037]),
[final] ).
cnf(i_0_11043,plain,
c_Com_Ocom_Ocom__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OSemi(X10,X11)) = hAPP(hAPP(X5,X10),X11),
inference(split_conjunct,[status(thm)],[i_0_6038]),
[final] ).
cnf(i_0_11044,plain,
c_Com_Ocom_Ocom__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OAss(X10,X11)) = hAPP(hAPP(X3,X10),X11),
inference(split_conjunct,[status(thm)],[i_0_6039]),
[final] ).
cnf(i_0_11045,plain,
c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,hAPP(c_Com_Ocom_OBODY,X10)) = hAPP(X8,X10),
inference(split_conjunct,[status(thm)],[i_0_6040]),
[final] ).
cnf(i_0_11046,plain,
c_Com_Ocom_Ocom__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,hAPP(c_Com_Ocom_OBODY,X10)) = hAPP(X8,X10),
inference(split_conjunct,[status(thm)],[i_0_6041]),
[final] ).
cnf(i_0_11047,plain,
c_Com_Ocom_Ocom__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OSKIP) = X2,
inference(split_conjunct,[status(thm)],[i_0_6042]),
[final] ).
cnf(i_0_11048,plain,
c_Com_Ocom_Ocom__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,c_Com_Ocom_OSKIP) = X2,
inference(split_conjunct,[status(thm)],[i_0_6043]),
[final] ).
cnf(i_0_11049,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6044]),
[final] ).
cnf(i_0_11050,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6045]),
[final] ).
cnf(i_0_11051,plain,
c_List_Olenlex(X1,X2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))))),c_List_Olex(X1,X2)))))),
inference(split_conjunct,[status(thm)],[i_0_6046]),
[final] ).
cnf(i_0_11052,plain,
c_Nitpick_Oplus__frac(X1,X2,X3) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),c_Nitpick_Oint__lcm(hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X1),tc_Int_Oint),c_Nitpick_Ofrac(X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3)))))),c_COMBI(tc_Int_Oint))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6047,c_0_6048]),c_0_6048]),c_0_6048]),c_0_6048]),c_0_6049]),c_0_6049]),
[final] ).
cnf(i_0_11053,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X5),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3))))),X4)),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6050]),
[final] ).
cnf(i_0_11054,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X5),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3))))),X4)),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6051]),
[final] ).
cnf(i_0_11055,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),c_fequal),X3),X4)) ),
inference(rw,[status(thm)],[i_0_6052,c_0_6053]),
[final] ).
cnf(i_0_11056,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6044]),
[final] ).
cnf(i_0_11057,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6045]),
[final] ).
cnf(i_0_11058,plain,
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk245_7(X2,X3,X4,X5,X6,X7,X1)),esk246_7(X2,X3,X4,X5,X6,X7,X1))),X6))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),X4)
| ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)
| ~ c_Equiv__Relations_Oequiv(X1,X7,X6) ),
inference(split_conjunct,[status(thm)],[i_0_6054]),
[final] ).
cnf(i_0_11059,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,esk291_8(X5,X6,X4,X7,X8,X1,X3,X2))),hAPP(X6,esk292_8(X5,X6,X4,X7,X8,X1,X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),hAPP(c_Set_Oimage(tc_prod(X8,X7),tc_prod(X2,X3),c_Product__Type_Omap__pair(X8,X2,X7,X3,X4,X6)),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6026]),
[final] ).
cnf(i_0_11060,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6055]),
[final] ).
cnf(i_0_11061,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))),X6)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6050]),
[final] ).
cnf(i_0_11062,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))),X6)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6051]),
[final] ).
cnf(i_0_11063,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4)),c_fequal),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))) ),
inference(rw,[status(thm)],[i_0_6056,c_0_6053]),
[final] ).
cnf(i_0_11064,plain,
hAPP(c_Divides_Oadjust(X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6057,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11065,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,X3),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X1,X3),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBB(X3,tc_HOL_Obool,X1)),c_fequal)),X4)))),X2)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6058]),
[final] ).
cnf(i_0_11066,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X8),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X1),X4)
| hAPP(X1,esk364_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,hAPP(X5,esk364_8(X2,X1,X3,X4,X5,X6,X7,X8)))
| X3 != hAPP(c_Set_Oimage(X7,X6,X5),X4)
| ~ c_Fun_Oinj__on(X7,X6,X5,X4)
| ~ class_Groups_Ocomm__monoid__add(X8) ),
inference(split_conjunct,[status(thm)],[i_0_6059]),
[final] ).
cnf(i_0_11067,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,X7)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X3)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(X6))),X8)))),c_Com_Ocom_OLocal(X6,X8,X4)),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X5)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(X6))),hAPP(hAPP(c_Natural_Ogetlocs,X7),X6))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_6060]),
[final] ).
cnf(i_0_11068,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(hAPP(c_COMBC(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),X2))),c_Transitive__Closure_Ortrancl(X1,X4))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(c_Product__Type_OPair(X1,X1),X3))),c_Transitive__Closure_Ortrancl(X1,X4)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6061,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_11069,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X2),X2),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),tc_Int_Oint),c_COMBB(tc_fun(X2,X2),X2,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,X2),X2),tc_Int_Oint),c_HOL_OLet(X2,X2)),c_Int_Oring__1__class_Oof__int(X2)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,X2)),tc_Int_Oint),c_COMBS(X2,X2,X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),tc_Int_Oint),c_COMBB(X2,tc_fun(X2,X2),X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),tc_Int_Oint),c_If(X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2))))),hAPP(hAPP(c_COMBC(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Oplus__class_Oplus(X2)),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2)))),c_Groups_Oone__class_Oone(X2))))),c_Divides_Odivmod__int(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Oring__1(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6063,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11070,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk403_8(X2,X3,X4,X1,X5,X6,X7,X8)),X4))
| hAPP(c_Set_Oimage(X8,X7,X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X8,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X7,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X1),c_Set_Oimage(X8,X7,X6)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ c_Fun_Oinj__on(X8,X7,X6,X5) ),
inference(split_conjunct,[status(thm)],[i_0_6031]),
[final] ).
cnf(i_0_11071,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk272_8(X2,X3,X4,X5,X6,X7,X1,X8)),X5))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X8),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X8),X3),X5)
| X4 != hAPP(c_Set_Oimage(X1,X7,X6),X5)
| ~ c_Fun_Oinj__on(X1,X7,X6,X5)
| ~ class_Groups_Ocomm__monoid__mult(X8) ),
inference(split_conjunct,[status(thm)],[i_0_6064]),
[final] ).
cnf(i_0_11072,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk364_8(X2,X3,X4,X5,X6,X7,X1,X8)),X5))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X3),X5)
| X4 != hAPP(c_Set_Oimage(X1,X7,X6),X5)
| ~ c_Fun_Oinj__on(X1,X7,X6,X5)
| ~ class_Groups_Ocomm__monoid__add(X8) ),
inference(split_conjunct,[status(thm)],[i_0_6059]),
[final] ).
cnf(i_0_11073,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk129_8(X2,X3,X4,X5,X6,X7,X1,X8)),X4))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X7),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X6),X4))
| X5 != X4
| X7 != X6
| ~ class_Groups_Ocomm__monoid__add(X8)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6065]),
[final] ).
cnf(i_0_11074,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
inference(split_conjunct,[status(thm)],[i_0_6066]),
[final] ).
cnf(i_0_11075,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,X3),X2),X4)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(X2,esk92_7(X3,X2,X1,X4,X5,X6,X7)),esk93_7(X3,X2,X1,X4,X5,X6,X7))))
| ~ hBOOL(hAPP(hAPP(X7,hAPP(c_Product__Type_Osnd(X6,X5),X4)),hAPP(c_Product__Type_Ofst(X6,X5),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6067]),
[final] ).
cnf(i_0_11076,plain,
c_FunDef_Orp__inv__image(X1,X2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_COMBS(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(X2,X1)),c_Product__Type_OPair(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),c_Relation_Oinv__image(X1,X2))))),c_Relation_Oinv__image(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_6068]),
[final] ).
cnf(i_0_11077,plain,
c_Map_Omap__add(X1,X2,X3,c_Map_Omap__of(X1,X2,X4)) = hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)))))),c_Option_Ooption_OSome(X2)))),X3),hAPP(c_List_Orev(tc_prod(X1,X2)),X4)),
inference(rw,[status(thm)],[i_0_6069,c_0_6070]),
[final] ).
cnf(i_0_11078,plain,
hAPP(hAPP(c_Relation_Oinv__image(X1,X2),X3),X4) = hAPP(c_Set_OCollect(tc_prod(X2,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X2),c_COMBC(X2,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X1)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X1)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,X1),tc_fun(X2,tc_prod(X1,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(tc_fun(X2,X1),tc_fun(X2,tc_prod(X1,X1))),X2),c_COMBB(X1,tc_prod(X1,X1),X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_prod(X1,X1)),X2),c_Product__Type_OPair(X1,X1)),X4))),X4)))),X3))),
inference(split_conjunct,[status(thm)],[i_0_6071]),
[final] ).
cnf(i_0_11079,plain,
hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)) = hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X2)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X1,X2)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X2,tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),tc_Nat_Onat),c_Product__Type_OPair(X1,X2)),hAPP(c_List_Onth(X1),X3))),hAPP(c_List_Onth(X2),X4)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)))))),
inference(split_conjunct,[status(thm)],[i_0_6072]),
[final] ).
cnf(i_0_11080,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X6,X8),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X8),X1),X4)
| hAPP(X1,esk272_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(hAPP(c_Fun_Ocomp(X6,X8,X7,X2),X5),esk272_8(X2,X1,X3,X4,X5,X6,X7,X8))
| X3 != hAPP(c_Set_Oimage(X7,X6,X5),X4)
| ~ c_Fun_Oinj__on(X7,X6,X5,X4)
| ~ class_Groups_Ocomm__monoid__mult(X8) ),
inference(split_conjunct,[status(thm)],[i_0_6064]),
[final] ).
cnf(i_0_11081,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X6),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X5),X3))
| hAPP(X1,esk129_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,esk129_8(X2,X1,X3,X4,X5,X6,X7,X8))
| X4 != X3
| X6 != X5
| ~ class_Groups_Ocomm__monoid__add(X8)
| ~ class_Orderings_Oord(X7) ),
inference(split_conjunct,[status(thm)],[i_0_6065]),
[final] ).
cnf(i_0_11082,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6073]),
[final] ).
cnf(i_0_11083,plain,
hAPP(c_Set_OPow(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = hAPP(c_Set_OCollect(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2)),c_Set_OPow(X1))))),
inference(split_conjunct,[status(thm)],[i_0_6074]),
[final] ).
cnf(i_0_11084,plain,
c_Map_Omap__upds(X1,X2,X3,X4,X5) = hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(X1,tc_Option_Ooption(X2))),c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)),X2))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2))))),c_Option_Ooption_OSome(X2))),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_6075]),
[final] ).
cnf(i_0_11085,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X1,tc_HOL_Obool)),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk249_7(X3,X4,X2,X1,X5,X6,X7))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5)))
| ~ c_Equiv__Relations_Ocongruent(X7,tc_fun(X1,tc_HOL_Obool),X5,X2)
| ~ c_Equiv__Relations_Oequiv(X7,X6,X5) ),
inference(split_conjunct,[status(thm)],[i_0_6076]),
[final] ).
cnf(i_0_11086,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X6,tc_fun(X5,tc_HOL_Obool))),X4),X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(X1,esk397_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6077]),
[final] ).
cnf(i_0_11087,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)) = c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6078]),
[final] ).
cnf(i_0_11088,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)) = c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6079]),
[final] ).
cnf(i_0_11089,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)) = c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
| ~ class_Lattices_Odistrib__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6080]),
[final] ).
cnf(i_0_11090,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)) = c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
| ~ class_Lattices_Odistrib__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6081]),
[final] ).
cnf(i_0_11091,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2)) = c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
| ~ class_Groups_Olinordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6082]),
[final] ).
cnf(i_0_11092,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2)) = c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))
| ~ class_Groups_Olinordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6083]),
[final] ).
cnf(i_0_11093,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Lazy__Sequence_Oanamorph(X2,X3,X4,X1),X5) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X3),X2),tc_prod(X3,X2),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),X2),c_List_Olist_ONil(X3)),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X2,tc_prod(tc_List_Olist(X3),X2)),hAPP(hAPP(c_COMBC(X3,tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2)),tc_fun(tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),X3),c_COMBB(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),tc_fun(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2)),X3),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X3),X2,tc_prod(tc_List_Olist(X3),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3),tc_List_Olist(X3)),tc_fun(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),X3),hAPP(c_COMBB(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_List_Olist(X3)),c_Product__Type_OPair(tc_List_Olist(X3),X2))),c_List_Olist_OCons(X3))))),c_Lazy__Sequence_Oanamorph(X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X4,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6084]),
[final] ).
cnf(i_0_11094,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),esk442_4(X2,X3,X4,X1)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6085]),
[final] ).
cnf(i_0_11095,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),X3)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6086]),
[final] ).
cnf(i_0_11096,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3)))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6087]),
[final] ).
cnf(i_0_11097,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6088]),
[final] ).
cnf(i_0_11098,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk129_8(X3,X4,X5,X6,X2,X7,X1,X8)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X7),X6)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X5))
| X6 != X5
| X7 != X2
| ~ class_Groups_Ocomm__monoid__add(X8)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6065]),
[final] ).
cnf(i_0_11099,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6073]),
[final] ).
cnf(i_0_11100,plain,
( c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),esk198_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk199_7(X6,X7,X5,X4,X3,X2,X1))
| hAPP(hAPP(X3,X7),X6) = X4
| ~ c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X7),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6089]),
[final] ).
cnf(i_0_11101,plain,
( c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),esk198_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk199_7(X6,X7,X5,X4,X3,X2,X1))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X7),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6089]),
[final] ).
cnf(i_0_11102,plain,
( hBOOL(hAPP(hAPP(hAPP(X1,esk174_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X6,tc_fun(X5,tc_HOL_Obool))),X4),X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6090]),
[final] ).
cnf(i_0_11103,plain,
c_List_Opartition(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_fun(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),hAPP(c_If(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(X2,X3)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_List_Olist_OCons(X1),X3))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(c_List_Olist_OCons(X1),X3)))),c_List_Opartition(X1,X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_6091]),
[final] ).
cnf(i_0_11104,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X3)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X4)),X5))),c_Com_Ocom_OAss(X4,X5)),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_6092]),
[final] ).
cnf(i_0_11105,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X3)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X4)),X5))),c_Com_Ocom_OAss(X4,X5)),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_6093]),
[final] ).
cnf(i_0_11106,plain,
hAPP(c_List_Olexn(X1,X2),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X1,tc_List_Olist(X1)),tc_prod(X1,tc_List_Olist(X1))),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),c_Product__Type_Omap__pair(tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),c_Wellfounded_Olex__prod(X1,tc_List_Olist(X1),X2,hAPP(c_List_Olexn(X1,X2),X3)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3)))))),
inference(split_conjunct,[status(thm)],[i_0_6094]),
[final] ).
cnf(i_0_11107,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),c_Groups_Ozero__class_Ozero(X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6095,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11108,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),c_Groups_Ozero__class_Ozero(X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6096,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11109,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6097,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11110,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel(X1,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6085]),
[final] ).
cnf(i_0_11111,plain,
( hBOOL(hAPP(c_Predicate_ODomainP(X1,X3,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBC(X3,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X3),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X1,X3)))),c_Product__Type_OPair(X1,X3)))),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6086]),
[final] ).
cnf(i_0_11112,plain,
( hBOOL(hAPP(c_Predicate_ORangeP(X3,X1,hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6087]),
[final] ).
cnf(i_0_11113,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6088]),
[final] ).
cnf(i_0_11114,plain,
hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X3))))),
inference(split_conjunct,[status(thm)],[i_0_6098]),
[final] ).
cnf(i_0_11115,plain,
( hBOOL(hAPP(hAPP(X1,esk93_7(X2,X3,X4,X5,X6,X7,X1)),esk92_7(X2,X3,X4,X5,X6,X7,X1)))
| hBOOL(hAPP(X4,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X6,X2),X3),X5)))
| ~ hBOOL(hAPP(hAPP(X1,hAPP(c_Product__Type_Osnd(X7,X6),X5)),hAPP(c_Product__Type_Ofst(X7,X6),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6067]),
[final] ).
cnf(i_0_11116,plain,
( c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X4)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X3),hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X4)))))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X1)),c_List_Otranspose__rel(X1)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6099,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_11117,plain,
c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X4)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X3),hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X4))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6101,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_11118,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X6),X7)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X5)))
| ~ c_Predicate_Opred__comp(X1,X2,X3,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3)))),X5),X6,X7) ),
inference(split_conjunct,[status(thm)],[i_0_6102]),
[final] ).
cnf(i_0_11119,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X6)))),X4)))),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X5),X6)
| hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),X4),esk314_6(X5,X4,X6,X3,X2,X1))))) != hAPP(X5,esk314_6(X5,X4,X6,X3,X2,X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6103]),
[final] ).
cnf(i_0_11120,plain,
hAPP(c_List_Oset(X1),X2) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))),
inference(split_conjunct,[status(thm)],[i_0_6104]),
[final] ).
cnf(i_0_11121,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X2),c_Set_Oinsert(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_6105]),
[final] ).
cnf(i_0_11122,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3)))),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6106,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11123,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X6)))),X4)))),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),hAPP(c_Finite__Set_Ocard(X3),X6))
| hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),X4),esk312_6(X5,X4,X6,X3,X2,X1))))) != X5
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6107]),
[final] ).
cnf(i_0_11124,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,tc_fun(X4,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X4,X1),tc_fun(tc_fun(X4,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1)),X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2),c_Set_OCollect(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5)))),X7)))),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),hAPP(hAPP(c_COMBS(X4,tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_fun(tc_fun(X2,tc_HOL_Obool),X1),X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1)),hAPP(c_COMBC(X2,X4,X1),X6))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),hAPP(c_COMBC(X2,X4,tc_HOL_Obool),X7))))),X5)
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6108]),
[final] ).
cnf(i_0_11125,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X3))),hAPP(X2,X4))),c_Transitive__Closure_Ortrancl(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(c_Nat_OSuc,esk366_5(X3,X4,X5,X2,X1)))),hAPP(X2,esk366_5(X3,X4,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6109]),
[final] ).
cnf(i_0_11126,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk429_6(X3,X4,X1,X5,X2,X6)),esk430_6(X3,X4,X1,X5,X2,X6))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X2)),X5),hAPP(hAPP(c_Relation_Orel__comp(X6,X1,X2),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6110]),
[final] ).
cnf(i_0_11127,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk428_6(X3,X4,X2,X5,X6,X1)),esk429_6(X3,X4,X2,X5,X6,X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X6)),X5),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X6),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6110]),
[final] ).
cnf(i_0_11128,plain,
c_Divides_Odivmod__int__rel(X1,X2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X1))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
inference(split_conjunct,[status(thm)],[i_0_6111]),
[final] ).
cnf(i_0_11129,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X6),X7)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X5,X1),tc_fun(tc_fun(X5,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,X1),tc_fun(X5,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X5,X1),tc_fun(X5,X1)),X2),c_COMBB(X1,X1,X5)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3))),X6))),X7)),X4)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6112]),
[final] ).
cnf(i_0_11130,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBS(X5,tc_fun(X1,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBC(X5,X6,tc_fun(tc_fun(X1,tc_HOL_Obool),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,X6),tc_fun(X6,tc_fun(tc_fun(X1,tc_HOL_Obool),X6)),X5),c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6))),X3)),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,tc_prod(X5,X1),c_Groups_Otimes__class_Otimes(X6)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X1,X6),X3)),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X4),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk284_6(X3,X2,X1,X4,X5,X6))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
| ~ class_Groups_Ocomm__monoid__mult(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6113]),
[final] ).
cnf(i_0_11131,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6114,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11132,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6115]),
[final] ).
cnf(i_0_11133,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6116]),
[final] ).
cnf(i_0_11134,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),c_Groups_Ozero__class_Ozero(X2)))
| X3 != c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6117,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11135,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk309_7(X2,X3,X4,X5,X6,X7,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
| hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(X7,hAPP(X4,X3)),hAPP(X4,X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ c_Finite__Set_Ofolding__image__simple(X8,X1,X7,X6,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6118]),
[final] ).
cnf(i_0_11136,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk198_7(X2,X3,X4,X5,X6,X7,X1)),X4))
| hAPP(hAPP(X6,X3),X2) = X5
| ~ c_Nitpick_Ofold__graph_H(X1,X7,X6,X5,X4,hAPP(hAPP(X6,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6089]),
[final] ).
cnf(i_0_11137,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk198_7(X2,X3,X4,X5,X6,X7,X1)),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X1,X7,X6,X5,X4,hAPP(hAPP(X6,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6089]),
[final] ).
cnf(i_0_11138,plain,
hAPP(c_Int_Onat,X1) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
inference(split_conjunct,[status(thm)],[i_0_6119]),
[final] ).
cnf(i_0_11139,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk174_7(X2,X3,X4,X5,X6,X7,X1)),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X6,tc_HOL_Obool))),X5),X4),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6090]),
[final] ).
cnf(i_0_11140,plain,
( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X1),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,X1),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk17_6(X1,X4,X2,X5,X6,X3)),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,esk17_6(X1,X4,X2,X5,X6,X3)),c_Com_ORes))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X3,X6,X5),X2,X4,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X1),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,X1),c_Com_ORes))) ),
inference(split_conjunct,[status(thm)],[i_0_6120]),
[final] ).
cnf(i_0_11141,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk397_7(X2,X3,X4,X5,X6,X7,X1)),X5))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X7,tc_fun(X6,tc_HOL_Obool))),X5),X4),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6077]),
[final] ).
cnf(i_0_11142,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk249_7(X2,X3,X4,X5,X6,X7,X1)),X7))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
| ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)
| ~ c_Equiv__Relations_Oequiv(X1,X7,X6) ),
inference(split_conjunct,[status(thm)],[i_0_6076]),
[final] ).
cnf(i_0_11143,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk246_7(X2,X3,X4,X5,X6,X7,X1)),X7))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),X4)
| ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)
| ~ c_Equiv__Relations_Oequiv(X1,X7,X6) ),
inference(split_conjunct,[status(thm)],[i_0_6054]),
[final] ).
cnf(i_0_11144,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk245_7(X2,X3,X4,X5,X6,X7,X1)),X7))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),X4)
| ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)
| ~ c_Equiv__Relations_Oequiv(X1,X7,X6) ),
inference(split_conjunct,[status(thm)],[i_0_6054]),
[final] ).
cnf(i_0_11145,plain,
( X1 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk20_6(X1,X2,X3,X4,X5,X6)),hAPP(c_Natural_Ogetlocs,X3))),X6),hAPP(hAPP(c_Natural_Ogetlocs,esk20_6(X1,X2,X3,X4,X5,X6)),c_Com_ORes))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X6,X5,X4),X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_6121]),
[final] ).
cnf(i_0_11146,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_4(X1,X2,X3,X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk76_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk76_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6122]),
[final] ).
cnf(i_0_11147,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk77_4(X2,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk76_4(X2,X3,X4,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3,esk76_4(X2,X3,X4,X1))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6122]),
[final] ).
cnf(i_0_11148,plain,
( hAPP(X1,esk77_4(X2,X1,X3,X4)) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk76_4(X2,X1,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk76_4(X2,X1,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6122]),
[final] ).
cnf(i_0_11149,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk284_6(X2,X3,X4,X5,X1,X6)),X5))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBS(X1,tc_fun(X4,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBC(X1,X6,tc_fun(tc_fun(X4,tc_HOL_Obool),X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,X6),tc_fun(X6,tc_fun(tc_fun(X4,tc_HOL_Obool),X6)),X1),c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6))),X2)),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,tc_prod(X1,X4),c_Groups_Otimes__class_Otimes(X6)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,X6),X2)),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ class_Groups_Ocomm__monoid__mult(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6113]),
[final] ).
cnf(i_0_11150,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X1),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X6,X1),X5),X2)),hAPP(hAPP(c_Product__Type_OSigma(X6,X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk352_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk352_6(X3,X2,X1,X4,X5,X6))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6123]),
[final] ).
cnf(i_0_11151,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X6,X1),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X6,X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(X2,esk360_6(X3,X2,X4,X5,X6,X1))),hAPP(X3,esk360_6(X3,X2,X4,X5,X6,X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X4),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6124]),
[final] ).
cnf(i_0_11152,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X4,tc_fun(X1,tc_HOL_Obool)),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk346_6(X3,X2,X1,X4,X5,X6)),esk347_6(X3,X2,X1,X4,X5,X6)))) ),
inference(split_conjunct,[status(thm)],[i_0_6125]),
[final] ).
cnf(i_0_11153,plain,
( c_Predicate_Opred__comp(X1,X5,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X1),c_COMBC(X5,tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X1,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X5),tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X1,X5)))),c_Product__Type_OPair(X1,X5)))),X6),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X5),c_COMBC(X2,tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X5,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X2),tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X5,X2)))),c_Product__Type_OPair(X5,X2)))),X7),X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X2),X6),X7))) ),
inference(split_conjunct,[status(thm)],[i_0_6102]),
[final] ).
cnf(i_0_11154,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6126,c_0_6014]),c_0_6014]),c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11155,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6127,c_0_6014]),c_0_6014]),c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11156,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6128]),
[final] ).
cnf(i_0_11157,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6129]),
[final] ).
cnf(i_0_11158,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6129]),
[final] ).
cnf(i_0_11159,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6128]),
[final] ).
cnf(i_0_11160,plain,
hAPP(c_Relation_Oconverse(X1,X2),X3) = hAPP(c_Set_OCollect(tc_prod(X2,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X2)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X2)))),hAPP(c_COMBC(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2))))),X3))),
inference(split_conjunct,[status(thm)],[i_0_6130]),
[final] ).
cnf(i_0_11161,plain,
( c_Nitpick_Osetsum_H(X1,X3,X4,X2) = hAPP(c_List_Omonoid__add__class_Olistsum(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X2))),c_List_Odistinct(X1)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_6131]),
[final] ).
cnf(i_0_11162,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk314_6(X2,X3,X4,X1,X5,X6)),X4))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X6),c_Finite__Set_Ocard(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),X3)))),X5) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6103]),
[final] ).
cnf(i_0_11163,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk312_6(X2,X3,X4,X1,X5,X6)),X4))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X6),c_Finite__Set_Ocard(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),X3)))),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6107]),
[final] ).
cnf(i_0_11164,plain,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6132,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11165,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X3),hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X3)),X4))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X3),hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X3)),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_List_Olist(X3),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X3)))),X4))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6133,c_0_6070]),c_0_6070]),
[final] ).
cnf(i_0_11166,plain,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk198_7(X3,X2,X4,X5,X1,X6,X7)),esk199_7(X3,X2,X4,X5,X1,X6,X7))
| hAPP(hAPP(X1,X2),X3) = X5
| ~ c_Nitpick_Ofold__graph_H(X7,X6,X1,X5,X4,hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6089]),
[final] ).
cnf(i_0_11167,plain,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk198_7(X3,X2,X4,X5,X1,X6,X7)),esk199_7(X3,X2,X4,X5,X1,X6,X7))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X7,X6,X1,X5,X4,hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6089]),
[final] ).
cnf(i_0_11168,plain,
hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))))) = hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X1,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X4))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6134,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_11169,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6136]),
[final] ).
cnf(i_0_11170,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),X1,X5),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X5),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X5),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),hAPP(c_COMBC(X2,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,tc_HOL_Obool),X2),c_fequal),X6)))))),hAPP(c_Set_Oimage(X2,X5,X6),X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6137]),
[final] ).
cnf(i_0_11171,plain,
( c_Relation_Orefl__on(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk332_3(X2,X3,X1)),esk332_3(X2,X3,X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),esk331_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6138]),
[final] ).
cnf(i_0_11172,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
| c_Random__Sequence_ORandom(X2,X3,X1,X4) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X3,X4)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X4))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2))))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X2)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X2)),c_Product__Type_Ofst(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ),
inference(split_conjunct,[status(thm)],[i_0_6139]),
[final] ).
cnf(i_0_11173,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk332_3(X2,X3,X1)),X3))
| c_Relation_Orefl__on(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),esk331_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6138]),
[final] ).
cnf(i_0_11174,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6140,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11175,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6141,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11176,plain,
hAPP(c_New__DSequence_Opos__not__seq(X1),X2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6142,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11177,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X1,X2)),X1,c_List_Olist_ONil(tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2)))),X1),c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),X1),c_List_Olist_OCons(tc_prod(X1,X2))),hAPP(hAPP(c_COMBC(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),X4)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),c_List_Ozip(X1,X2)),X5))),X3),
inference(split_conjunct,[status(thm)],[i_0_6143]),
[final] ).
cnf(i_0_11178,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X4)),c_Wellfounded_Omax__ext(X1,X2)))
| ~ c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6144]),
[final] ).
cnf(i_0_11179,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel(X1,X2)))
| ~ c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6145]),
[final] ).
cnf(i_0_11180,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X1,X2),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X6))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_fun(X4,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,tc_fun(X4,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X1),c_Product__Type_OSigma(X3,X4)),X7))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),X2),c_COMBK(tc_fun(X4,tc_HOL_Obool),X3)),X8)))) = hAPP(hAPP(c_Product__Type_OSigma(X3,X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X5),X7)),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X4,tc_HOL_Obool)),X6),X8))),
inference(split_conjunct,[status(thm)],[i_0_6146]),
[final] ).
cnf(i_0_11181,plain,
( c_Equiv__Relations_Oequiv(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)
| ~ c_Equiv__Relations_Oequivp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6147]),
[final] ).
cnf(i_0_11182,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_OwfP(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6148]),
[final] ).
cnf(i_0_11183,plain,
( X3 = X4
| hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3) != hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4) ),
inference(split_conjunct,[status(thm)],[i_0_6149]),
[final] ).
cnf(i_0_11184,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk348_6(X4,X3,X5,X6,X2,X1)),esk349_6(X4,X3,X5,X6,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6150]),
[final] ).
cnf(i_0_11185,plain,
hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X3),X4),hAPP(hAPP(c_List_Ozip(X1,X2),X5),hAPP(hAPP(c_List_Omap(X6,X2),X7),X8))) = hAPP(hAPP(c_List_Omap(tc_prod(X1,X6),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X6,X3),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X1,X2)),tc_fun(X6,X3),X1),hAPP(c_COMBB(tc_prod(X1,X2),X3,X6),X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(X6,X2),tc_fun(X6,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X6,X2),tc_fun(X6,tc_prod(X1,X2))),X1),c_COMBB(X2,tc_prod(X1,X2),X6)),c_Product__Type_OPair(X1,X2))),X7)))),hAPP(hAPP(c_List_Ozip(X1,X6),X5),X8)),
inference(split_conjunct,[status(thm)],[i_0_6151]),
[final] ).
cnf(i_0_11186,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),esk389_7(X6,X7,X5,X4,X3,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X7))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6152]),
[final] ).
cnf(i_0_11187,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk413_7(X6,X5,X7,X4,X3,X2,X1)))
| hBOOL(hAPP(hAPP(c_member(X1),X7),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Set_Oinsert(X1),X7),X5)),X6))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6153]),
[final] ).
cnf(i_0_11188,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6129]),
[final] ).
cnf(i_0_11189,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6128]),
[final] ).
cnf(i_0_11190,plain,
c_Map_Omap__of(X1,X2,hAPP(hAPP(c_List_Omap(tc_prod(X1,X3),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),X1),c_COMBB(X2,tc_prod(X1,X2),X3)),c_Product__Type_OPair(X1,X2))),X4))),X5)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),c_Map_Omap__of(X1,X3,X5)),
inference(split_conjunct,[status(thm)],[i_0_6154]),
[final] ).
cnf(i_0_11191,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),X5) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X1,X2)),X2,c_List_Olist_ONil(tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),X2),c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(X2))),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),X2),c_List_Olist_OCons(tc_prod(X1,X2))),hAPP(c_Product__Type_OPair(X1,X2),X3)))),hAPP(c_List_Ozip(X1,X2),X4))),X5),
inference(split_conjunct,[status(thm)],[i_0_6155]),
[final] ).
cnf(i_0_11192,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Code__Numeral_Oint__of,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6156,c_0_6014]),c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11193,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6157,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11194,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6158,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11195,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6159,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11196,plain,
( hAPP(X1,esk245_7(X2,X3,X1,X4,X5,X6,X7)) = hAPP(X1,esk246_7(X2,X3,X1,X4,X5,X6,X7))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X1) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X2),X1)
| ~ c_Equiv__Relations_Ocongruent(X7,tc_fun(X4,tc_HOL_Obool),X5,X1)
| ~ c_Equiv__Relations_Oequiv(X7,X6,X5) ),
inference(split_conjunct,[status(thm)],[i_0_6054]),
[final] ).
cnf(i_0_11197,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X1),c_fequal),X4)),hAPP(X4,esk330_4(X4,X3,X2,X1)))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6160]),
[final] ).
cnf(i_0_11198,plain,
( c_Wellfounded_Owf(X3,hAPP(c_Set_OCollect(tc_prod(X3,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X3),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),X4))),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,X3),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,X3),tc_fun(X3,tc_HOL_Obool)),X3),c_COMBB(X3,tc_HOL_Obool,X3)),c_fequal)),X2)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,hAPP(X2,esk321_4(X3,X2,X1,X4)))),hAPP(X1,esk321_4(X3,X2,X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_6161]),
[final] ).
cnf(i_0_11199,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X3)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6162]),
[final] ).
cnf(i_0_11200,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X3)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6163]),
[final] ).
cnf(i_0_11201,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OCond(X4,X5,X7)),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4))),X7),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_6164]),
[final] ).
cnf(i_0_11202,plain,
( X2 = X3
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)
| hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) != hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk492_3(X2,X3,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6165,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_11203,plain,
( X2 = X3
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)
| hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) != hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk491_3(X3,X2,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6166,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_11204,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X5)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X5))),X4)),c_Groups_Ozero__class_Ozero(X1))),X3)
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6167]),
[final] ).
cnf(i_0_11205,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4))),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3))
| ~ c_Relation_Orefl__on(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6138]),
[final] ).
cnf(i_0_11206,plain,
hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)),X5)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X2,X3)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))))),
inference(rw,[status(thm)],[i_0_6168,c_0_6169]),
[final] ).
cnf(i_0_11207,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6170,c_0_6014]),c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11208,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)),hAPP(hAPP(c_List_Omap(X6,X2),X7),X8)) = hAPP(hAPP(c_List_Omap(tc_prod(X3,X6),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X6,tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X3,tc_fun(X6,X2),tc_fun(X6,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X6,X2),tc_fun(X6,tc_prod(X1,X2))),X3),c_COMBB(X2,tc_prod(X1,X2),X6)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),X3),c_Product__Type_OPair(X1,X2)),X4))),X7))),hAPP(hAPP(c_List_Ozip(X3,X6),X5),X8)),
inference(split_conjunct,[status(thm)],[i_0_6171]),
[final] ).
cnf(i_0_11209,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6172,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11210,plain,
( hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(X6,hAPP(X4,X3)),hAPP(X4,X2))
| hAPP(X1,esk309_7(X2,X3,X4,X1,X5,X6,X7)) != X5
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))
| ~ c_Finite__Set_Ofolding__image__simple(X8,X7,X6,X5,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6118]),
[final] ).
cnf(i_0_11211,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6173,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11212,plain,
( hBOOL(hAPP(X1,esk321_4(X2,X3,X4,X1)))
| c_Wellfounded_Owf(X2,hAPP(c_Set_OCollect(tc_prod(X2,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X2),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X1))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,X2),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,X2),tc_fun(X2,tc_HOL_Obool)),X2),c_COMBB(X2,tc_HOL_Obool,X2)),c_fequal)),X3))))) ),
inference(split_conjunct,[status(thm)],[i_0_6161]),
[final] ).
cnf(i_0_11213,plain,
c_Wellfounded_Ofinite__psubset(X1) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X1)))),
inference(split_conjunct,[status(thm)],[i_0_6174]),
[final] ).
cnf(i_0_11214,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Nat_OSuc,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2))))) ),
inference(rw,[status(thm)],[i_0_6175,c_0_6169]),
[final] ).
cnf(i_0_11215,plain,
( hAPP(c_Nat_OSuc,X2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2))))) ),
inference(rw,[status(thm)],[i_0_6176,c_0_6169]),
[final] ).
cnf(i_0_11216,plain,
( c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6144]),
[final] ).
cnf(i_0_11217,plain,
( c_Nitpick_Ocard_H(X1,X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X2))),c_List_Odistinct(X1))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6177]),
[final] ).
cnf(i_0_11218,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))) ),
inference(split_conjunct,[status(thm)],[i_0_6178]),
[final] ).
cnf(i_0_11219,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X7)),hAPP(hAPP(c_Product__Type_OPair(X6,X7),hAPP(X8,X3)),hAPP(X9,X4))),hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X6,X7),c_Product__Type_Omap__pair(X1,X6,X2,X7,X8,X9)),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6179]),
[final] ).
cnf(i_0_11220,plain,
( c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6145]),
[final] ).
cnf(i_0_11221,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6180,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11222,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6181,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11223,plain,
c_New__Random__Sequence_Oneg__decr__bind(X1,X2,X3,X4,X5,X6,X7) = c_New__DSequence_Oneg__decr__bind(X1,X2,hAPP(hAPP(hAPP(X3,X5),X6),X7),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X4),X5)),X6)),X7)),
inference(split_conjunct,[status(thm)],[i_0_6182]),
[final] ).
cnf(i_0_11224,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1)),c_member(X2))),X4)))),
inference(split_conjunct,[status(thm)],[i_0_6183]),
[final] ).
cnf(i_0_11225,plain,
( c_Equiv__Relations_Oequivp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))
| ~ c_Equiv__Relations_Oequiv(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_6147]),
[final] ).
cnf(i_0_11226,plain,
( c_Wellfounded_OwfP(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6148]),
[final] ).
cnf(i_0_11227,plain,
( c_Equiv__Relations_Ocongruent(X1,X2,X4,X3)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3))),X3)),esk334_4(X3,X4,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6184]),
[final] ).
cnf(i_0_11228,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4),X5))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4)))))
| ~ hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(c_Set_OCollect(X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6185]),
[final] ).
cnf(i_0_11229,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X6),hAPP(hAPP(c_COMBS(X5,tc_fun(X1,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X1,X6),tc_fun(tc_fun(X1,tc_HOL_Obool),X6),X5),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X6)),X3)),X2)),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X5,X1),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X1,X6),X3)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X4),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk286_6(X3,X2,X1,X4,X5,X6))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
| ~ class_Groups_Ocomm__monoid__mult(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6186]),
[final] ).
cnf(i_0_11230,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(hAPP(c_COMBS(X5,tc_fun(X1,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X1,X6),tc_fun(tc_fun(X1,tc_HOL_Obool),X6),X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6)),X3)),X2)),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X5,X1),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X1,X6),X3)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X4),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk287_6(X3,X2,X1,X4,X5,X6))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
| ~ class_Groups_Ocomm__monoid__add(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6187]),
[final] ).
cnf(i_0_11231,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X5))),X4)),c_Groups_Ozero__class_Ozero(X1))),X3)
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6188]),
[final] ).
cnf(i_0_11232,plain,
( hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6189]),
[final] ).
cnf(i_0_11233,plain,
( hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X5)
| hBOOL(hAPP(hAPP(c_member(X1),X6),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6189]),
[final] ).
cnf(i_0_11234,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3) = X5
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6189]),
[final] ).
cnf(i_0_11235,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6189]),
[final] ).
cnf(i_0_11236,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk149_4(X2,X3,X4,X1))),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk149_4(X2,X3,X4,X1)),X3))),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6190]),
[final] ).
cnf(i_0_11237,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6191,c_0_6014]),c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11238,plain,
c_New__Random__Sequence_Opos__decr__bind(X1,X2,X3,X4,X5,X6,X7) = c_New__DSequence_Opos__decr__bind(X1,X2,hAPP(hAPP(hAPP(X3,X5),X6),X7),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X4),X5)),X6)),X7)),
inference(split_conjunct,[status(thm)],[i_0_6192]),
[final] ).
cnf(i_0_11239,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6193,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11240,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6194,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11241,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6195,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11242,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6196,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11243,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6197,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11244,plain,
hAPP(c_Set_Oimage(X1,tc_prod(X2,X3),hAPP(hAPP(c_COMBS(X1,X3,tc_prod(X2,X3)),hAPP(hAPP(c_COMBB(X2,tc_fun(X3,tc_prod(X2,X3)),X1),c_Product__Type_OPair(X2,X3)),X4)),X5)),X6) = hAPP(hAPP(c_Product__Type_OSigma(X2,X3),hAPP(c_Set_Oimage(X1,X2,X4),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),c_Set_Oimage(X1,X3,X5)),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Set_Ovimage(X1,X2,X4)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_Oinsert(X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))),X6))),
inference(split_conjunct,[status(thm)],[i_0_6198]),
[final] ).
cnf(i_0_11245,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X3)),X2)),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6199,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_11246,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,X2) = c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1))))))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6200]),
[final] ).
cnf(i_0_11247,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk209_6(X3,X4,X2,X5,X6,X1))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X1),X2),X5) != X4
| ~ hBOOL(hAPP(hAPP(c_member(X6),X3),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6201]),
[final] ).
cnf(i_0_11248,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),X6)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(X5,X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Ocomm__monoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6202]),
[final] ).
cnf(i_0_11249,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Ocomm__monoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6203]),
[final] ).
cnf(i_0_11250,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6204]),
[final] ).
cnf(i_0_11251,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),X6)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),X6),hAPP(c_Finite__Set_Ocard(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Ocomm__monoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6202]),
[final] ).
cnf(i_0_11252,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3) = c_Groups_Oone__class_Oone(X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Ocomm__monoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6203]),
[final] ).
cnf(i_0_11253,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3) = c_Groups_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6204]),
[final] ).
cnf(i_0_11254,plain,
( c_Complete__Lattice_OInf__class_OInf(X1,X2) = c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),c_Orderings_Oord__class_Oless__eq(X1)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6205]),
[final] ).
cnf(i_0_11255,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X6),X7)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X6)),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X5,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X5,tc_fun(X1,tc_HOL_Obool))),X2),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X4))),X7))),
inference(split_conjunct,[status(thm)],[i_0_6206]),
[final] ).
cnf(i_0_11256,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6),X7)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6)),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X5,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X5,tc_fun(X1,tc_HOL_Obool))),X2),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X4))),X7))),
inference(split_conjunct,[status(thm)],[i_0_6207]),
[final] ).
cnf(i_0_11257,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2)),c_Int_Onat))))) ),
inference(rw,[status(thm)],[i_0_6208,c_0_6169]),
[final] ).
cnf(i_0_11258,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Int_Onat))))) ),
inference(rw,[status(thm)],[i_0_6209,c_0_6169]),
[final] ).
cnf(i_0_11259,plain,
hAPP(c_Product__Type_Omap__pair(X5,X3,X2,X2,X6,c_Fun_Oid(X2)),hAPP(c_Product__Type_Omap__pair(X5,X5,X1,X2,c_Fun_Oid(X5),X4),X7)) = hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),hAPP(c_Product__Type_Omap__pair(X5,X3,X1,X1,X6,c_Fun_Oid(X1)),X7)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6210,c_0_6211]),c_0_6211]),c_0_6029]),c_0_6029]),
[final] ).
cnf(i_0_11260,plain,
hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X1,X2,X3,X4),X5),X6),X7) = c_New__DSequence_Oneg__bind(X1,X2,hAPP(hAPP(hAPP(X3,X5),X6),X7),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X4),X5)),X6)),X7)),
inference(split_conjunct,[status(thm)],[i_0_6212]),
[final] ).
cnf(i_0_11261,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X4))),X3)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3),esk313_4(X3,X1,X4,X2)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(c_Set_OCollect(X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6185]),
[final] ).
cnf(i_0_11262,plain,
( X1 = hAPP(hAPP(X2,X3),esk413_7(X1,X4,X3,X5,X2,X6,X7))
| hBOOL(hAPP(hAPP(c_member(X7),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X2,X5,hAPP(hAPP(c_Set_Oinsert(X7),X3),X4)),X1))
| ~ c_Finite__Set_Ofun__left__comm(X7,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6153]),
[final] ).
cnf(i_0_11263,plain,
( X1 = hAPP(hAPP(X2,X3),esk389_7(X3,X1,X4,X5,X2,X6,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X7),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X2,X5,X4),X1))
| ~ c_Finite__Set_Ofun__left__comm(X7,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6152]),
[final] ).
cnf(i_0_11264,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk460_5(X5,X4,X3,X2,X1)),esk460_5(X5,X4,X3,X2,X1))),X5))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olexord(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X2),X4))),c_List_Olexord(X1,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6213]),
[final] ).
cnf(i_0_11265,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X1,tc_HOL_Obool))),X2)))),c_member(X1)))),
inference(split_conjunct,[status(thm)],[i_0_6214]),
[final] ).
cnf(i_0_11266,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk381_5(X2,X3,X4,X5,X1)),esk382_5(X2,X3,X4,X5,X1))),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6215]),
[final] ).
cnf(i_0_11267,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk377_5(X2,X3,X4,X5,X1)),esk376_5(X2,X3,X4,X5,X1))),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6216]),
[final] ).
cnf(i_0_11268,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Omap(X4,X2),X5),X6)) = hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,X2),tc_fun(X4,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X4,X2),tc_fun(X4,tc_prod(X1,X2))),X1),c_COMBB(X2,tc_prod(X1,X2),X4)),c_Product__Type_OPair(X1,X2))),X5))),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X6)),
inference(split_conjunct,[status(thm)],[i_0_6217]),
[final] ).
cnf(i_0_11269,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6218,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11270,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Nat_OSuc,X2) ),
inference(rw,[status(thm)],[i_0_6219,c_0_6169]),
[final] ).
cnf(i_0_11271,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X1)))))
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) ),
inference(rw,[status(thm)],[i_0_6220,c_0_6169]),
[final] ).
cnf(i_0_11272,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk75_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk74_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk74_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6221]),
[final] ).
cnf(i_0_11273,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk73_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk72_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk72_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6222]),
[final] ).
cnf(i_0_11274,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk373_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk374_5(X2,X3,X4,X5,X1)),X2)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6223]),
[final] ).
cnf(i_0_11275,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk373_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk374_5(X2,X3,X4,X5,X1)),X2)))
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6223]),
[final] ).
cnf(i_0_11276,plain,
( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X2,X1)),X3),X4) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X2),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X2),c_Smallcheck_Osmall__class_Osmall(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X2),hAPP(c_COMBB(tc_prod(X2,X1),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X1),X3)),c_Product__Type_OPair(X2,X1)))),X4)),X4)
| ~ class_Smallcheck_Osmall(X1)
| ~ class_Smallcheck_Osmall(X2) ),
inference(split_conjunct,[status(thm)],[i_0_6224]),
[final] ).
cnf(i_0_11277,plain,
( hAPP(X1,esk75_3(X2,X1,X3)) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk74_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk74_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6221]),
[final] ).
cnf(i_0_11278,plain,
( hAPP(X1,esk73_3(X2,X1,X3)) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk72_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk72_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6222]),
[final] ).
cnf(i_0_11279,plain,
c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(split_conjunct,[status(thm)],[fact_Nitpick_OFrac__def]),
[final] ).
cnf(i_0_11280,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk286_6(X2,X3,X4,X5,X1,X6)),X5))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X6),hAPP(hAPP(c_COMBS(X1,tc_fun(X4,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X4,X6),tc_fun(tc_fun(X4,tc_HOL_Obool),X6),X1),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X6)),X2)),X3)),X5) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X1,X4),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,X6),X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ class_Groups_Ocomm__monoid__mult(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6186]),
[final] ).
cnf(i_0_11281,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk287_6(X2,X3,X4,X5,X1,X6)),X5))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),hAPP(hAPP(c_COMBS(X1,tc_fun(X4,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X4,X6),tc_fun(tc_fun(X4,tc_HOL_Obool),X6),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X6)),X2)),X3)),X5) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X1,X4),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,X6),X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ class_Groups_Ocomm__monoid__add(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6187]),
[final] ).
cnf(i_0_11282,plain,
( hAPP(X1,esk434_7(X2,X3,X4,X1,X5,X6,X7)) = hAPP(c_Option_Ooption_OSome(X6),X2)
| hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X7,c_Option_Ooption_ONone(X6),X1),hAPP(X4,X3)) != hAPP(c_Option_Ooption_OSome(X6),X2) ),
inference(rw,[status(thm)],[i_0_6225,c_0_6226]),
[final] ).
cnf(i_0_11283,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),esk434_7(X4,X2,X1,X5,X6,X7,X3))
| hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X7),X3,c_Option_Ooption_ONone(X7),X5),hAPP(X1,X2)) != hAPP(c_Option_Ooption_OSome(X7),X4) ),
inference(rw,[status(thm)],[i_0_6227,c_0_6226]),
[final] ).
cnf(i_0_11284,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4))),X4)),X5))
| ~ c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X5),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6184]),
[final] ).
cnf(i_0_11285,plain,
( hBOOL(hAPP(X1,esk313_4(X2,X3,X1,X4)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X1))),X2)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_OCollect(X4),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6185]),
[final] ).
cnf(i_0_11286,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X1),c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_6228]),
[final] ).
cnf(i_0_11287,plain,
hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X1,X2,X3,X4),X5),X6),X7) = c_New__DSequence_Opos__bind(X1,X2,hAPP(hAPP(hAPP(X3,X5),X6),X7),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X4),X5)),X6)),X7)),
inference(split_conjunct,[status(thm)],[i_0_6229]),
[final] ).
cnf(i_0_11288,plain,
( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X1),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,X1),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk18_5(X1,X2,X4,X5,X3)),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,esk18_5(X1,X2,X4,X5,X3)),c_Com_ORes))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X3,X5,X4)),X2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X1),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,X1),c_Com_ORes)))) ),
inference(split_conjunct,[status(thm)],[i_0_6230]),
[final] ).
cnf(i_0_11289,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6231]),
[final] ).
cnf(i_0_11290,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6232]),
[final] ).
cnf(i_0_11291,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6233]),
[final] ).
cnf(i_0_11292,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6234]),
[final] ).
cnf(i_0_11293,plain,
c_Nitpick_Oprod(X1,X2,X3,X4) = hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X4)))),
inference(split_conjunct,[status(thm)],[i_0_6235]),
[final] ).
cnf(i_0_11294,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X3)),hAPP(X2,X4)))
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X1,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6236]),
[final] ).
cnf(i_0_11295,plain,
( c_Orderings_Oorder_Omono(tc_Nat_Onat,X1,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X1,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_6237]),
[final] ).
cnf(i_0_11296,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6238,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11297,plain,
hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X4,X5,X6),hAPP(c_Product__Type_Omap__pair(X7,X1,X8,X3,X9,X10),X11)) = hAPP(c_Product__Type_Omap__pair(X7,X2,X8,X4,hAPP(c_Fun_Ocomp(X1,X2,X7,X5),X9),hAPP(c_Fun_Ocomp(X3,X4,X8,X6),X10)),X11),
inference(split_conjunct,[status(thm)],[i_0_6239]),
[final] ).
cnf(i_0_11298,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
inference(split_conjunct,[status(thm)],[i_0_6240]),
[final] ).
cnf(i_0_11299,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
inference(split_conjunct,[status(thm)],[i_0_6241]),
[final] ).
cnf(i_0_11300,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk241_6(X2,X3,X4,X5,X1,X6)),X5))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),hAPP(c_Fun_Ocomp(X2,X6,X1,X3),X4)),X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ class_Groups_Ocomm__monoid__add(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6242]),
[final] ).
cnf(i_0_11301,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk240_6(X2,X3,X4,X5,X1,X6)),X5))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),hAPP(c_Fun_Ocomp(X2,X6,X1,X3),X4)),X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ class_Groups_Ocomm__monoid__add(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6242]),
[final] ).
cnf(i_0_11302,plain,
( X1 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk19_5(X1,X2,X3,X4,X5)),hAPP(c_Natural_Ogetlocs,X2))),X5),hAPP(hAPP(c_Natural_Ogetlocs,esk19_5(X1,X2,X3,X4,X5)),c_Com_ORes))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X5,X4,X3)),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6243]),
[final] ).
cnf(i_0_11303,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk352_6(X2,X3,X4,X5,X6,X1)),X6))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X6),X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6123]),
[final] ).
cnf(i_0_11304,plain,
hAPP(c_Set_Oimage(X1,X2,hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),X3)),X4)),X5)),X6) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(c_Set_OCollect(X1),X3)))),hAPP(c_Set_Oimage(X1,X2,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X3))))),
inference(split_conjunct,[status(thm)],[i_0_6244]),
[final] ).
cnf(i_0_11305,plain,
hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),hAPP(c_Product__Type_Omap__pair(X3,X3,X5,X1,c_Fun_Oid(X3),X6),X7)) = hAPP(c_Product__Type_Omap__pair(X3,X3,X5,X2,c_Fun_Oid(X3),hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6)),X7),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6245,c_0_6029]),c_0_6029]),c_0_6029]),
[final] ).
cnf(i_0_11306,plain,
hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X5,X1,X3,X3,X6,c_Fun_Oid(X3)),X7)) = hAPP(c_Product__Type_Omap__pair(X5,X2,X3,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6),c_Fun_Oid(X3)),X7),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6246,c_0_6211]),c_0_6211]),c_0_6211]),
[final] ).
cnf(i_0_11307,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk360_6(X2,X3,X4,X5,X1,X6)),X4))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X6),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X6),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X6),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ class_Rings_Ocomm__semiring__1(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6124]),
[final] ).
cnf(i_0_11308,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_6247]),
[final] ).
cnf(i_0_11309,plain,
( hAPP(hAPP(hAPP(c_Natural_Oupdate,X1),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk9_6(X1,X4,X3,X5,X6,X2)),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X2,X6,X5),X3,X4,hAPP(hAPP(hAPP(c_Natural_Oupdate,X1),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6248]),
[final] ).
cnf(i_0_11310,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk359_6(X2,X3,X4,X5,X1,X6)),X5))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X4),X2),X5) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),X2),X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ class_Groups_Oab__semigroup__mult(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6249]),
[final] ).
cnf(i_0_11311,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6250,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11312,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6251,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11313,plain,
( hBOOL(hAPP(hAPP(X1,esk318_4(X2,X3,X1,X4)),X2))
| ~ c_Predicate_Opred__comp(X5,X6,X7,X4,X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6252]),
[final] ).
cnf(i_0_11314,plain,
( c_Wellfounded_Owf(X3,hAPP(c_Set_Oimage(tc_prod(X1,X1),tc_prod(X3,X3),c_Product__Type_Omap__pair(X1,X3,X1,X3,X4,X4)),X2))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_Fun_Oinj__on(X1,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_6253]),
[final] ).
cnf(i_0_11315,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk412_6(X2,X3,X4,X5,X1,X6)),X6))
| c_Fun_Oinj__on(X5,X4,X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X6),X2))
| X6 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6254]),
[final] ).
cnf(i_0_11316,plain,
( X1 = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk15_6(X1,X2,X3,X4,X5,X6)),c_Com_Ovname_OLoc(X6)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X6))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X6,X5,X4),X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_6255]),
[final] ).
cnf(i_0_11317,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk209_6(X2,X3,X4,X5,X1,X6)),X5))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6),hAPP(X4,X2)),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),X4),X5) != X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ class_Groups_Oordered__ab__group__add(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6201]),
[final] ).
cnf(i_0_11318,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X5,X1),X2),X4))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X5,X1),X3),X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk471_5(X3,X2,X4,X5,X1))),hAPP(X3,esk471_5(X3,X2,X4,X5,X1))))
| ~ class_Groups_Omonoid__add(X1)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6256]),
[final] ).
cnf(i_0_11319,plain,
( hBOOL(hAPP(hAPP(X1,X2),esk318_4(X3,X2,X4,X1)))
| ~ c_Predicate_Opred__comp(X5,X6,X7,X1,X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6252]),
[final] ).
cnf(i_0_11320,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X3),X4)))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk235_5(X3,X2,X4,X5,X1))),hAPP(X3,esk235_5(X3,X2,X4,X5,X1))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6257]),
[final] ).
cnf(i_0_11321,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X2),X4)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2),X4)))))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6258]),
[final] ).
cnf(i_0_11322,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk376_5(X2,X3,X4,X5,X1)),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6216]),
[final] ).
cnf(i_0_11323,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
inference(rw,[status(thm)],[i_0_6259,c_0_6169]),
[final] ).
cnf(i_0_11324,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
inference(rw,[status(thm)],[i_0_6260,c_0_6169]),
[final] ).
cnf(i_0_11325,plain,
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X4,hAPP(X3,X5)) = hAPP(X3,hAPP(c_Set_Oimage(X1,X1,X4),X5))
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| hAPP(X4,hAPP(hAPP(X2,esk305_5(X5,X4,X3,X2,X1)),esk306_5(X5,X4,X3,X2,X1))) != hAPP(hAPP(X2,hAPP(X4,esk305_5(X5,X4,X3,X2,X1))),hAPP(X4,esk306_5(X5,X4,X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6261]),
[final] ).
cnf(i_0_11326,plain,
( X3 = c_List_Olist_ONil(tc_List_Olist(X2))
| c_List_Otranspose(X2,X3) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk488_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6262,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_11327,plain,
( c_List_Otranspose(X2,X3) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk488_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6263,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_11328,plain,
( X2 = c_List_Olist_ONil(tc_List_Olist(X1))
| c_List_Otranspose(X1,X2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk488_3(X3,X1,X2))) != X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6264,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_11329,plain,
( c_List_Otranspose(X1,X2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))
| X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk488_3(X3,X1,X2))) != X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6265,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_11330,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6266,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11331,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk82_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk81_3(X1,X2,X3)),esk82_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,esk81_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),esk82_3(X1,X2,X3))))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6267,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11332,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Ocomm__monoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6268]),
[final] ).
cnf(i_0_11333,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6269]),
[final] ).
cnf(i_0_11334,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3) = c_Groups_Oone__class_Oone(X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Ocomm__monoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6268]),
[final] ).
cnf(i_0_11335,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3) = c_Groups_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6269]),
[final] ).
cnf(i_0_11336,plain,
hAPP(c_Fun_Ocomp(tc_prod(X1,X2),tc_prod(X3,X4),tc_prod(X5,X6),c_Product__Type_Omap__pair(X1,X3,X2,X4,X7,X8)),c_Product__Type_Omap__pair(X5,X1,X6,X2,X9,X10)) = c_Product__Type_Omap__pair(X5,X3,X6,X4,hAPP(c_Fun_Ocomp(X1,X3,X5,X7),X9),hAPP(c_Fun_Ocomp(X2,X4,X6,X8),X10)),
inference(split_conjunct,[status(thm)],[i_0_6270]),
[final] ).
cnf(i_0_11337,plain,
c_Product__Type_Omap__pair(X1,X2,X3,X4,hAPP(c_Fun_Ocomp(X5,X2,X1,X6),X7),hAPP(c_Fun_Ocomp(X8,X4,X3,X9),X10)) = hAPP(c_Fun_Ocomp(tc_prod(X5,X8),tc_prod(X2,X4),tc_prod(X1,X3),c_Product__Type_Omap__pair(X5,X2,X8,X4,X6,X9)),c_Product__Type_Omap__pair(X1,X5,X3,X8,X7,X10)),
inference(split_conjunct,[status(thm)],[i_0_6271]),
[final] ).
cnf(i_0_11338,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk454_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk454_4(X3,X4,X2,X1)))),X3))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_6272]),
[final] ).
cnf(i_0_11339,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk84_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk83_3(X1,X2,X3)),esk84_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(X1,esk83_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),esk84_3(X1,X2,X3))))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6273,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11340,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),esk446_5(X2,X3,X4,X5,X1)),X3)),c_List_Olistrel(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6274]),
[final] ).
cnf(i_0_11341,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6275,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11342,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk445_5(X2,X3,X4,X5,X1)),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6274]),
[final] ).
cnf(i_0_11343,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk385_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6276]),
[final] ).
cnf(i_0_11344,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk384_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6277]),
[final] ).
cnf(i_0_11345,plain,
c_Nitpick_Otimes__frac(X1,X2,X3) = hAPP(hAPP(c_Nitpick_Ofrac(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6278,c_0_6048]),c_0_6048]),c_0_6049]),c_0_6049]),
[final] ).
cnf(i_0_11346,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk371_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk372_5(X3,X4,X5,X2,X1)),X3)))
| X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6279]),
[final] ).
cnf(i_0_11347,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk371_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk372_5(X3,X4,X5,X2,X1)),X3)))
| X2 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6279]),
[final] ).
cnf(i_0_11348,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk383_5(X2,X3,X4,X5,X1)),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6280]),
[final] ).
cnf(i_0_11349,plain,
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6281,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11350,plain,
( c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6282,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11351,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk371_5(X2,X3,X4,X5,X1)),X4)),X2))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6279]),
[final] ).
cnf(i_0_11352,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk371_5(X2,X3,X4,X5,X1)),X4)),X2))
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6279]),
[final] ).
cnf(i_0_11353,plain,
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6283,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11354,plain,
( c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6284,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11355,plain,
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6285,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11356,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6286,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11357,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6287,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11358,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2)))) ),
inference(rw,[status(thm)],[i_0_6288,c_0_6169]),
[final] ).
cnf(i_0_11359,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2)))) ),
inference(rw,[status(thm)],[i_0_6289,c_0_6169]),
[final] ).
cnf(i_0_11360,plain,
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6290,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11361,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Relation_OImage(X1,X1,X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_6291]),
[final] ).
cnf(i_0_11362,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2)))
| ~ class_Rings_Osemiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6292,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11363,plain,
( c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6293,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11364,plain,
( c_Divides_OnegDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6294,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11365,plain,
( c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6295,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11366,plain,
( c_Divides_OposDivAlg(X1,X2) = hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6296,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11367,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2))) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6297,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11368,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3))
| ~ class_Rings_Oring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6298,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11369,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2))) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6299,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11370,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6300,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11371,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6301,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11372,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk271_5(X3,X4,X1,X5,X2)),X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6302]),
[final] ).
cnf(i_0_11373,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk237_5(X3,X4,X1,X5,X2)),X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6303]),
[final] ).
cnf(i_0_11374,plain,
( hAPP(c_List_Oset(tc_prod(X1,X2)),X3) = hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_Option_Ooption(X2),tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),c_Map_Omap__of(X1,X2,X3)))),c_Option_Ooption_OSome(X2))))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6304]),
[final] ).
cnf(i_0_11375,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X6),X1),hAPP(c_Set_Oimage(X5,X3,X2),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X3,X6,X5,X1),X2)),X4)
| hAPP(X1,hAPP(X2,esk240_6(X3,X1,X2,X4,X5,X6))) != c_Groups_Ozero__class_Ozero(X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
| ~ class_Groups_Ocomm__monoid__add(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6242]),
[final] ).
cnf(i_0_11376,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),hAPP(X3,X4)),X4))
| ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(X2,esk207_4(X4,X3,X2,X1)),esk208_4(X4,X3,X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk207_4(X4,X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk208_4(X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_6305]),
[final] ).
cnf(i_0_11377,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)),X5)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X1,X2,X3,X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X3),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5)))),
inference(rw,[status(thm)],[i_0_6306,c_0_6169]),
[final] ).
cnf(i_0_11378,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Code__Numeral_Oint__of,X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
| c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6307,c_0_6014]),c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11379,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2))
| ~ c_Fun_Oinj__on(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Equiv__Relations_Oquotient(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X2),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6308]),
[final] ).
cnf(i_0_11380,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),X1),X2),X4) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),X3),X2),X4)
| hAPP(X1,esk359_6(X2,X3,X1,X4,X5,X6)) != hAPP(X3,esk359_6(X2,X3,X1,X4,X5,X6))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
| ~ class_Groups_Oab__semigroup__mult(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6249]),
[final] ).
cnf(i_0_11381,plain,
( c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6),X4))
| X6 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(X4,esk412_6(X4,X3,X2,X1,X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6254]),
[final] ).
cnf(i_0_11382,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fimplies),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),X4))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Set_OCollect(X1)),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4))),
inference(split_conjunct,[status(thm)],[i_0_6309]),
[final] ).
cnf(i_0_11383,plain,
c_List_Osublist(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3),X4) = hAPP(hAPP(c_List_Oappend(X1),c_List_Osublist(X1,X2,X4)),c_List_Osublist(X1,X3,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),X4)))),
inference(split_conjunct,[status(thm)],[i_0_6310]),
[final] ).
cnf(i_0_11384,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk348_6(X1,X4,X3,X2,X5,X6)),esk349_6(X1,X4,X3,X2,X5,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,tc_fun(X6,tc_HOL_Obool)),X4),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6150]),
[final] ).
cnf(i_0_11385,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk428_6(X4,X5,X6,X1,X3,X2)),esk430_6(X4,X5,X6,X1,X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),hAPP(hAPP(c_Relation_Orel__comp(X2,X6,X3),X5),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6110]),
[final] ).
cnf(i_0_11386,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6311,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11387,plain,
( hAPP(X4,hAPP(c_Product__Type_Osnd(X3,X1),X5)) = hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X1),X5))
| hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),X5) != hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X6),X5) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6312,c_0_6029]),c_0_6029]),
[final] ).
cnf(i_0_11388,plain,
( hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X3),X5)) = hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X3),X5))
| hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),X5) != hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X6,c_Fun_Oid(X3)),X5) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6313,c_0_6211]),c_0_6211]),
[final] ).
cnf(i_0_11389,plain,
c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))) = hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(tc_prod(X1,X1),tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),tc_prod(X1,X1)),c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1)),c_fequal)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))))),
inference(rw,[status(thm)],[i_0_6314,c_0_6053]),
[final] ).
cnf(i_0_11390,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk346_6(X4,X5,X6,X3,X2,X1)),esk347_6(X4,X5,X6,X3,X2,X1))
| hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,tc_fun(X6,tc_HOL_Obool)),X4),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6125]),
[final] ).
cnf(i_0_11391,plain,
hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),hAPP(c_Product__Type_Omap__pair(X5,X3,X1,X1,X6,c_Fun_Oid(X1)),X7)) = hAPP(hAPP(c_Product__Type_OPair(X3,X2),hAPP(X6,hAPP(c_Product__Type_Ofst(X5,X1),X7))),hAPP(X4,hAPP(c_Product__Type_Osnd(X5,X1),X7))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6315,c_0_6211]),c_0_6029]),
[final] ).
cnf(i_0_11392,plain,
hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),X6),X7)) = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X5),X7))),hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X5),X7))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6316,c_0_6211]),c_0_6029]),
[final] ).
cnf(i_0_11393,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,X4),X5)) = c_List_Omap__filter(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X4)),hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3))),c_Option_Ooption_ONone(X2)),X5),
inference(split_conjunct,[status(thm)],[i_0_6317]),
[final] ).
cnf(i_0_11394,plain,
( hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)) = hAPP(c_Finite__Set_Ocard(X1),X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ c_Fun_Oinj__on(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Equiv__Relations_Oquotient(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_6318]),
[final] ).
cnf(i_0_11395,plain,
c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X3)),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X4)),hAPP(c_Set_OCollect(X1),X3))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X5)),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X3)))),
inference(split_conjunct,[status(thm)],[i_0_6319]),
[final] ).
cnf(i_0_11396,plain,
c_List_Omap__filter(X1,X2,X3,X4) = hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),X3)),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2)))),X4)),
inference(split_conjunct,[status(thm)],[i_0_6320]),
[final] ).
cnf(i_0_11397,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(X1,X1,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X1),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X1)),c_Nat_Osemiring__1__class_Oof__nat(X1))),X3))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6321]),
[final] ).
cnf(i_0_11398,plain,
( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6231]),
[final] ).
cnf(i_0_11399,plain,
( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6322]),
[final] ).
cnf(i_0_11400,plain,
( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6232]),
[final] ).
cnf(i_0_11401,plain,
( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6323]),
[final] ).
cnf(i_0_11402,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6233]),
[final] ).
cnf(i_0_11403,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6234]),
[final] ).
cnf(i_0_11404,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6231]),
[final] ).
cnf(i_0_11405,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6232]),
[final] ).
cnf(i_0_11406,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6233]),
[final] ).
cnf(i_0_11407,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6234]),
[final] ).
cnf(i_0_11408,plain,
( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X1,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk125_2(X2,X1))),hAPP(X2,esk126_2(X2,X1))))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6324]),
[final] ).
cnf(i_0_11409,plain,
( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X2,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),esk126_2(X1,X2)),esk125_2(X1,X2)))
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_6324]),
[final] ).
cnf(i_0_11410,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6240]),
[final] ).
cnf(i_0_11411,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6241]),
[final] ).
cnf(i_0_11412,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),esk125_2(X1,X2)),esk126_2(X1,X2)))
| c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X2,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_6324]),
[final] ).
cnf(i_0_11413,plain,
( c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6325]),
[final] ).
cnf(i_0_11414,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6326,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11415,plain,
( c_FunDef_Oreduction__pair(X1,X2)
| ~ c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6327]),
[final] ).
cnf(i_0_11416,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X2)))),
inference(rw,[status(thm)],[i_0_6328,c_0_6169]),
[final] ).
cnf(i_0_11417,plain,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6329,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11418,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X2)))),
inference(rw,[status(thm)],[i_0_6330,c_0_6169]),
[final] ).
cnf(i_0_11419,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk144_5(X3,X2,X4,X5,X1))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6331]),
[final] ).
cnf(i_0_11420,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Finite__Set_Ocard(X5),X4))),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk189_5(X3,X2,X4,X5,X1))),X3))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6332]),
[final] ).
cnf(i_0_11421,plain,
hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X2,X3)),c_Int_Onat)))),
inference(rw,[status(thm)],[i_0_6333,c_0_6169]),
[final] ).
cnf(i_0_11422,plain,
c_Product__Type_Omap__pair(X1,X2,X3,X4,X5,X6) = hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,tc_prod(X2,X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,X4),tc_fun(X3,tc_prod(X2,X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X2,X4)),tc_fun(tc_fun(X3,X4),tc_fun(X3,tc_prod(X2,X4))),X1),c_COMBB(X4,tc_prod(X2,X4),X3)),hAPP(hAPP(c_COMBB(X2,tc_fun(X4,tc_prod(X2,X4)),X1),c_Product__Type_OPair(X2,X4)),X5))),X6)),
inference(split_conjunct,[status(thm)],[i_0_6334]),
[final] ).
cnf(i_0_11423,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6335]),
[final] ).
cnf(i_0_11424,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk142_5(X3,X2,X4,X5,X1))),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6336]),
[final] ).
cnf(i_0_11425,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) = c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6337,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11426,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6338,c_0_6014]),c_0_6014]),c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11427,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin)) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6339,c_0_6014]),c_0_6014]),c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11428,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk459_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk459_4(X3,X4,X2,X1)))),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olexord(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6340]),
[final] ).
cnf(i_0_11429,plain,
( c_Predicate_Opred__comp(X6,X7,X8,X1,X4,X2,X5)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6252]),
[final] ).
cnf(i_0_11430,plain,
( c_Predicate_Opred__comp(X6,X7,X8,X1,X4,X2,X5)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6341]),
[final] ).
cnf(i_0_11431,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk459_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk459_4(X3,X4,X2,X1)))),X3))
| hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X4) = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olexord(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6340]),
[final] ).
cnf(i_0_11432,plain,
hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
inference(rw,[status(thm)],[i_0_6342,c_0_6100]),
[final] ).
cnf(i_0_11433,plain,
hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4))) = hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Set_OCollect(X1),X3)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),X4)),
inference(split_conjunct,[status(thm)],[i_0_6343]),
[final] ).
cnf(i_0_11434,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_6344]),
[final] ).
cnf(i_0_11435,plain,
c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(c_fequal,X3)))),hAPP(c_fequal,X4)))) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4),
inference(split_conjunct,[status(thm)],[i_0_6345]),
[final] ).
cnf(i_0_11436,plain,
c_HOL_OThe(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(c_fequal,X3)))),hAPP(c_fequal,X4)))) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4),
inference(split_conjunct,[status(thm)],[i_0_6346]),
[final] ).
cnf(i_0_11437,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6347,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11438,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1)),X4)),X5)),X6) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),hAPP(hAPP(c_COMBC(X3,tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_fun(tc_fun(X2,tc_HOL_Obool),X1),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1)),hAPP(c_COMBC(X2,X3,X1),X4))),X6)),X5)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6348]),
[final] ).
cnf(i_0_11439,plain,
hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4))) = hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Set_OCollect(X1),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_OCollect(X2),X4))),
inference(split_conjunct,[status(thm)],[i_0_6349]),
[final] ).
cnf(i_0_11440,plain,
( hAPP(c_Set_Oimage(X1,X3,X4),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X3,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_Set_Oinsert(X3)),X4)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6350]),
[final] ).
cnf(i_0_11441,plain,
hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
inference(rw,[status(thm)],[i_0_6351,c_0_6100]),
[final] ).
cnf(i_0_11442,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6352]),
[final] ).
cnf(i_0_11443,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2)),X3)),X2)) ),
inference(rw,[status(thm)],[i_0_6353,c_0_6053]),
[final] ).
cnf(i_0_11444,plain,
c_Relation_OId__on(X1,X2) = hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),c_fequal))),X2)),
inference(split_conjunct,[status(thm)],[i_0_6354]),
[final] ).
cnf(i_0_11445,plain,
c_Int_Oint__ge__less__than(X1) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(split_conjunct,[status(thm)],[i_0_6355]),
[final] ).
cnf(i_0_11446,plain,
hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),hAPP(hAPP(c_Product__Type_Oscomp(X1,X5,X6,tc_prod(X2,X3)),X7),X8)),X9) = hAPP(hAPP(c_Product__Type_Oscomp(X1,X5,X6,X4),X7),hAPP(hAPP(c_COMBC(X5,tc_fun(X2,tc_fun(X3,X4)),tc_fun(X6,X4)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X2,X3)),tc_fun(tc_fun(X2,tc_fun(X3,X4)),tc_fun(X6,X4)),X5),c_Product__Type_Oscomp(X6,X2,X3,X4)),X8)),X9)),
inference(split_conjunct,[status(thm)],[i_0_6356]),
[final] ).
cnf(i_0_11447,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk381_5(X3,X4,X5,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_6215]),
[final] ).
cnf(i_0_11448,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4)),X2)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X1)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X4),X2)),c_FunDef_Omax__weak)) ),
inference(split_conjunct,[status(thm)],[i_0_6357]),
[final] ).
cnf(i_0_11449,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4)),X2)),c_FunDef_Omax__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X1)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X4),X2)),c_FunDef_Omax__strict)) ),
inference(split_conjunct,[status(thm)],[i_0_6358]),
[final] ).
cnf(i_0_11450,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))) ),
inference(rw,[status(thm)],[i_0_6359,c_0_6169]),
[final] ).
cnf(i_0_11451,plain,
( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))) ),
inference(rw,[status(thm)],[i_0_6360,c_0_6169]),
[final] ).
cnf(i_0_11452,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBC(X2,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_HOL_Obool),X2),c_fequal),X3)),hAPP(X4,X5))),X5)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6361]),
[final] ).
cnf(i_0_11453,plain,
( hAPP(X1,esk240_6(X2,X3,X1,X4,X5,X6)) = hAPP(X1,esk241_6(X2,X3,X1,X4,X5,X6))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X5,X2,X1),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X2,X6,X5,X3),X1)),X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
| ~ class_Groups_Ocomm__monoid__add(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6242]),
[final] ).
cnf(i_0_11454,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),esk444_5(X3,X4,X2,X5,X1))),c_List_Olistrel(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),X4)),c_List_Olistrel(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6362]),
[final] ).
cnf(i_0_11455,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6363,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11456,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OWhile(X4,X5)),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_6364]),
[final] ).
cnf(i_0_11457,plain,
c_List_Osublist(X1,X2,X3) = hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X3)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))))),
inference(rw,[status(thm)],[i_0_6365,c_0_6135]),
[final] ).
cnf(i_0_11458,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk357_5(X3,X4,X5,X1,X2))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X4)),c_Wellfounded_Omax__ext(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6366]),
[final] ).
cnf(i_0_11459,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk443_5(X3,X4,X5,X2,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),X4)),c_List_Olistrel(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6362]),
[final] ).
cnf(i_0_11460,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
| ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6367]),
[final] ).
cnf(i_0_11461,plain,
( hAPP(c_Set_Oimage(tc_prod(X1,X6),tc_prod(X2,X7),c_Product__Type_Omap__pair(X1,X2,X6,X7,X3,X8)),hAPP(hAPP(c_Product__Type_OSigma(X1,X6),X4),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X1),X9))) = hAPP(hAPP(c_Product__Type_OSigma(X2,X7),X5),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X2),X10))
| hAPP(c_Set_Oimage(X1,X2,X3),X4) != X5
| hAPP(c_Set_Oimage(X6,X7,X8),X9) != X10 ),
inference(split_conjunct,[status(thm)],[i_0_6368]),
[final] ).
cnf(i_0_11462,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4))),c_FunDef_Omin__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X3)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),X4)),c_FunDef_Omin__weak)) ),
inference(split_conjunct,[status(thm)],[i_0_6369]),
[final] ).
cnf(i_0_11463,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4))),c_FunDef_Omin__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X3)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),X4)),c_FunDef_Omin__strict)) ),
inference(split_conjunct,[status(thm)],[i_0_6370]),
[final] ).
cnf(i_0_11464,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk281_5(X3,X4,X5,X2,X1),esk282_5(X3,X4,X5,X2,X1)),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6371]),
[final] ).
cnf(i_0_11465,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk279_5(X3,X4,X5,X2,X1),esk280_5(X3,X4,X5,X2,X1)),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6372]),
[final] ).
cnf(i_0_11466,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk462_4(X3,X4,X2,X1))),esk461_4(X3,X4,X2,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6373]),
[final] ).
cnf(i_0_11467,plain,
( hAPP(c_Set_Oimage(tc_prod(X1,X4),tc_prod(X2,X5),c_Product__Type_Omap__pair(X1,X2,X4,X5,X3,X6)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X4),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2,X5),tc_HOL_Obool))
| hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X4,X5,X6),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6374]),
[final] ).
cnf(i_0_11468,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3),X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6375]),
[final] ).
cnf(i_0_11469,plain,
( hAPP(c_Map_Omap__of(X2,X4,hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),tc_prod(X2,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,tc_prod(X2,X4)),hAPP(hAPP(c_COMBB(X2,tc_fun(X4,tc_prod(X2,X4)),X1),c_Product__Type_OPair(X2,X4)),X3))),X5)),hAPP(X3,X6)) = hAPP(c_Option_Ooption_OSome(X4),X7)
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| hAPP(c_Map_Omap__of(X1,X4,X5),X6) != hAPP(c_Option_Ooption_OSome(X4),X7) ),
inference(split_conjunct,[status(thm)],[i_0_6376]),
[final] ).
cnf(i_0_11470,plain,
( hAPP(c_Product__Type_Omap__pair(X2,X2,X3,X6,c_Fun_Oid(X2),X1),X4) = hAPP(c_Product__Type_Omap__pair(X2,X2,X3,X6,c_Fun_Oid(X2),X5),X4)
| hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)) != hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6377,c_0_6029]),c_0_6029]),
[final] ).
cnf(i_0_11471,plain,
( hAPP(c_Product__Type_Omap__pair(X2,X6,X3,X3,X1,c_Fun_Oid(X3)),X4) = hAPP(c_Product__Type_Omap__pair(X2,X6,X3,X3,X5,c_Fun_Oid(X3)),X4)
| hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)) != hAPP(X5,hAPP(c_Product__Type_Ofst(X2,X3),X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6378,c_0_6211]),c_0_6211]),
[final] ).
cnf(i_0_11472,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk383_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6280]),
[final] ).
cnf(i_0_11473,plain,
c_Nitpick_Ouminus__frac(X1,X2) = c_Nitpick_OAbs__Frac(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6379,c_0_6048]),c_0_6049]),
[final] ).
cnf(i_0_11474,plain,
hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Omap__pair(X1,X1,X3,X2,c_Fun_Oid(X1),X4),X5)) = hAPP(X4,hAPP(c_Product__Type_Osnd(X1,X3),X5)),
inference(rw,[status(thm)],[i_0_6380,c_0_6029]),
[final] ).
cnf(i_0_11475,plain,
hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X2,X2,X4,c_Fun_Oid(X2)),X5)) = hAPP(X4,hAPP(c_Product__Type_Ofst(X3,X2),X5)),
inference(rw,[status(thm)],[i_0_6381,c_0_6211]),
[final] ).
cnf(i_0_11476,plain,
hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6),X7)) = hAPP(X5,hAPP(c_Product__Type_Ofst(X3,X4),X7)),
inference(split_conjunct,[status(thm)],[i_0_6382]),
[final] ).
cnf(i_0_11477,plain,
hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6),X7)) = hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X4),X7)),
inference(split_conjunct,[status(thm)],[i_0_6383]),
[final] ).
cnf(i_0_11478,plain,
hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Omap__pair(X1,X1,X3,X2,c_Fun_Oid(X1),X4),X5)) = hAPP(c_Product__Type_Ofst(X1,X3),X5),
inference(rw,[status(thm)],[i_0_6384,c_0_6029]),
[final] ).
cnf(i_0_11479,plain,
hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X2,X2,X4,c_Fun_Oid(X2)),X5)) = hAPP(c_Product__Type_Osnd(X3,X2),X5),
inference(rw,[status(thm)],[i_0_6385,c_0_6211]),
[final] ).
cnf(i_0_11480,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),esk281_5(X2,X3,X4,X5,X1)),esk282_5(X2,X3,X4,X5,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6371]),
[final] ).
cnf(i_0_11481,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),esk279_5(X2,X3,X4,X5,X1)),esk280_5(X2,X3,X4,X5,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6372]),
[final] ).
cnf(i_0_11482,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olexord(X1,X4)))
| X3 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk473_4(X2,X3,X4,X1)),esk472_4(X2,X3,X4,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6386]),
[final] ).
cnf(i_0_11483,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olexord(X1,X4)))
| X3 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk472_4(X2,X3,X4,X1)),esk473_4(X2,X3,X4,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6386]),
[final] ).
cnf(i_0_11484,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk385_5(X3,X4,X5,X2,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6276]),
[final] ).
cnf(i_0_11485,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk384_5(X3,X4,X5,X2,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6277]),
[final] ).
cnf(i_0_11486,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_6387]),
[final] ).
cnf(i_0_11487,plain,
c_Relation_OId__on(X1,X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X1),c_Set_Oinsert(tc_prod(X1,X1))),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_6388]),
[final] ).
cnf(i_0_11488,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),esk431_4(X1,X2,X3,X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk432_4(X1,X2,X3,X4)),esk433_4(X1,X2,X3,X4)))))
| hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6389]),
[final] ).
cnf(i_0_11489,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk373_5(X3,X4,X5,X2,X1))),X3))
| X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6223]),
[final] ).
cnf(i_0_11490,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk373_5(X3,X4,X5,X2,X1))),X3))
| X2 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6223]),
[final] ).
cnf(i_0_11491,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X3),c_Int_Onat))),
inference(rw,[status(thm)],[i_0_6390,c_0_6169]),
[final] ).
cnf(i_0_11492,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1)),c_Int_Onat)))),
inference(rw,[status(thm)],[i_0_6391,c_0_6169]),
[final] ).
cnf(i_0_11493,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1)),c_Int_Onat)))),
inference(rw,[status(thm)],[i_0_6392,c_0_6169]),
[final] ).
cnf(i_0_11494,plain,
hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X3),X4),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(X5,X1),X6),X7)),X8)) = hAPP(hAPP(c_List_Omap(tc_prod(X5,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,X3),X5),hAPP(c_COMBB(tc_prod(X1,X2),X3,X2),X4)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),X5),c_Product__Type_OPair(X1,X2)),X6)))),hAPP(hAPP(c_List_Ozip(X5,X2),X7),X8)),
inference(split_conjunct,[status(thm)],[i_0_6393]),
[final] ).
cnf(i_0_11495,plain,
c_List_Osublist(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X4) = hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X1)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))),c_List_Olist_ONil(X1))),c_List_Osublist(X1,X3,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X4)))),
inference(split_conjunct,[status(thm)],[i_0_6394]),
[final] ).
cnf(i_0_11496,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6395,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11497,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),X2),hAPP(c_Set_Oimage(X5,X1,X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X1,X6,X5,X2),X3)),X4)
| esk240_6(X1,X2,X3,X4,X5,X6) != esk241_6(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
| ~ class_Groups_Ocomm__monoid__add(X6) ),
inference(split_conjunct,[status(thm)],[i_0_6242]),
[final] ).
cnf(i_0_11498,plain,
c_Map_Odom(X1,X2,c_Fun_Ooverride__on(X1,tc_Option_Ooption(X2),X3,X4,X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),c_Map_Odom(X1,X2,X4)))))),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),c_Map_Odom(X1,X2,X4))))),
inference(split_conjunct,[status(thm)],[i_0_6396]),
[final] ).
cnf(i_0_11499,plain,
( hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),c_List_Otranspose(X1,X2)),X3)),X4) = hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X4)),X3)
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6397]),
[final] ).
cnf(i_0_11500,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6398,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11501,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6399,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11502,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6400,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11503,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6401,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11504,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6402,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11505,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6403,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11506,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6404,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11507,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6405,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11508,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6406,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11509,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk393_5(X3,X2,X4,X5,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X4),X2)),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6407]),
[final] ).
cnf(i_0_11510,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk141_5(X2,X3,X4,X5,X1)),hAPP(X3,esk140_5(X2,X3,X4,X5,X1))))
| hBOOL(hAPP(X2,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6408]),
[final] ).
cnf(i_0_11511,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6409,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11512,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X6))),c_Wellfounded_Omax__ext(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X6)),c_Wellfounded_Omax__ext(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6410]),
[final] ).
cnf(i_0_11513,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk290_5(X2,X3,X4,X1,X5)),hAPP(X2,esk289_5(X2,X3,X4,X1,X5))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),X4),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6411]),
[final] ).
cnf(i_0_11514,plain,
hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Omap(X5,X2),X6),X7)) = hAPP(c_List_Ofoldl(X1,X5,hAPP(hAPP(c_COMBC(X1,tc_fun(X5,X2),tc_fun(X5,X1)),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_fun(tc_fun(X5,X2),tc_fun(X5,X1)),X1),c_COMBB(X2,X1,X5)),X3)),X6),X4),X7),
inference(split_conjunct,[status(thm)],[i_0_6412]),
[final] ).
cnf(i_0_11515,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6)),X7) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X4),c_Relation_Orel__comp(X1,X2,X3)),X6)),X7)),
inference(split_conjunct,[status(thm)],[i_0_6413]),
[final] ).
cnf(i_0_11516,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))
| ~ c_FunDef_Oreduction__pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6327]),
[final] ).
cnf(i_0_11517,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_6414]),
[final] ).
cnf(i_0_11518,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X2)),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_6415]),
[final] ).
cnf(i_0_11519,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X3)),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6415]),
[final] ).
cnf(i_0_11520,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk432_4(X1,X2,X3,X4)),esk433_4(X1,X2,X3,X4)))
| hBOOL(hAPP(hAPP(hAPP(X1,esk431_4(X1,X2,X3,X4)),esk432_4(X1,X2,X3,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk433_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))
| hAPP(esk431_4(X1,X2,X3,X4),esk433_4(X1,X2,X3,X4)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6389]),
[final] ).
cnf(i_0_11521,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_6416]),
[final] ).
cnf(i_0_11522,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X4))
| ~ class_Groups_Oab__semigroup__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X2,X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6417]),
[final] ).
cnf(i_0_11523,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X9),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X6),hAPP(hAPP(c_Set_Oinsert(X4),X10),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X8)) = hAPP(hAPP(X8,X9),X10)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X4,X5,X6)
| ~ c_Equiv__Relations_Ocongruent2(X1,X4,tc_fun(X7,tc_HOL_Obool),X3,X6,X8)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X9),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X10),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6418]),
[final] ).
cnf(i_0_11524,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osublist(X1,X2,X3)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X3)))),
inference(split_conjunct,[status(thm)],[i_0_6419]),
[final] ).
cnf(i_0_11525,plain,
hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(X2,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(X2,tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_OCons(X1)),X3)),c_List_Olist_ONil(X1))),X4)) = hAPP(hAPP(c_List_Omap(X2,X1),X3),X4),
inference(rw,[status(thm)],[i_0_6420,c_0_6100]),
[final] ).
cnf(i_0_11526,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat),X2),hAPP(c_List_Onth(X1),X3))))),
inference(split_conjunct,[status(thm)],[i_0_6421]),
[final] ).
cnf(i_0_11527,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4)),X5)),c_Groups_Oone__class_Oone(X1)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6422]),
[final] ).
cnf(i_0_11528,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6423]),
[final] ).
cnf(i_0_11529,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk150_4(X2,X3,X4,X1))),X4) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk150_4(X2,X3,X4,X1)),X3))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_6424]),
[final] ).
cnf(i_0_11530,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X3)),c_Wellfounded_Omax__ext(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk358_4(X4,X3,X5,X1)),X2)),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6366]),
[final] ).
cnf(i_0_11531,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X3)),c_Wellfounded_Omax__ext(X1,X4)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk278_4(X4,X3,X5,X1)),X2)),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6425]),
[final] ).
cnf(i_0_11532,plain,
c_Map_Oran(X1,X2,X3) = hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3))),c_Option_Ooption_OSome(X2)))),
inference(split_conjunct,[status(thm)],[i_0_6426]),
[final] ).
cnf(i_0_11533,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X3,hAPP(c_Nat_OSuc,esk363_3(X3,X2,X1)))),hAPP(X3,esk363_3(X3,X2,X1)))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6427]),
[final] ).
cnf(i_0_11534,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X3,hAPP(c_Nat_OSuc,esk319_3(X2,X1,X3)))),hAPP(X3,esk319_3(X2,X1,X3)))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6428]),
[final] ).
cnf(i_0_11535,plain,
( c_Equiv__Relations_Ocongruent(X1,tc_fun(X7,tc_HOL_Obool),X3,hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X6),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X8))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X4,X5,X6)
| ~ c_Equiv__Relations_Ocongruent2(X1,X4,tc_fun(X7,tc_HOL_Obool),X3,X6,X8)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X9),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6429]),
[final] ).
cnf(i_0_11536,plain,
( c_Nitpick_Oless__eq__frac(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rw,[status(thm)],[i_0_6430,c_0_6049]),
[final] ).
cnf(i_0_11537,plain,
( c_Nitpick_Oless__frac(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rw,[status(thm)],[i_0_6431,c_0_6049]),
[final] ).
cnf(i_0_11538,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),hAPP(hAPP(X3,X6),X7)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6432]),
[final] ).
cnf(i_0_11539,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk162_5(X2,X3,X4,X5,X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6433]),
[final] ).
cnf(i_0_11540,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk188_5(X2,X3,X4,X5,X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6434]),
[final] ).
cnf(i_0_11541,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2))),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6435]),
[final] ).
cnf(i_0_11542,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2))),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6436]),
[final] ).
cnf(i_0_11543,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6437]),
[final] ).
cnf(i_0_11544,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6438]),
[final] ).
cnf(i_0_11545,plain,
( c_Nitpick_Ofold__graph_H(X6,X8,X1,X9,X7,hAPP(hAPP(X1,X2),X3))
| hAPP(hAPP(X1,X2),X3) != hAPP(hAPP(X1,X4),X5)
| ~ hBOOL(hAPP(hAPP(c_member(X6),X4),X7))
| ~ c_Nitpick_Ofold__graph_H(X6,X8,X1,X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X6),X4),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X5) ),
inference(split_conjunct,[status(thm)],[i_0_6089]),
[final] ).
cnf(i_0_11546,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X1),X2)),c_List_Olistrel1(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X6),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6423]),
[final] ).
cnf(i_0_11547,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2))),X3))
| ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6367]),
[final] ).
cnf(i_0_11548,plain,
( X2 = X3
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6439,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11549,plain,
( c_Nitpick_Ofold__graph_H(X1,X4,X5,X6,X3,hAPP(hAPP(X5,X2),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Nitpick_Ofold__graph_H(X1,X4,X5,X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X7) ),
inference(split_conjunct,[status(thm)],[i_0_6440]),
[final] ).
cnf(i_0_11550,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X3,esk391_5(X3,X4,X5,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_6441]),
[final] ).
cnf(i_0_11551,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X4)))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6442]),
[final] ).
cnf(i_0_11552,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6443,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11553,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk392_5(X3,X4,X5,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_6444]),
[final] ).
cnf(i_0_11554,plain,
hAPP(c_Set_Ovimage(X1,tc_prod(X2,X3),X4),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X5),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X6))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,hAPP(c_Fun_Ocomp(tc_prod(X2,X3),X2,X1,c_Product__Type_Ofst(X2,X3)),X4)),X5)),hAPP(c_Set_Ovimage(X1,X3,hAPP(c_Fun_Ocomp(tc_prod(X2,X3),X3,X1,c_Product__Type_Osnd(X2,X3)),X4)),X6)),
inference(split_conjunct,[status(thm)],[i_0_6445]),
[final] ).
cnf(i_0_11555,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6423]),
[final] ).
cnf(i_0_11556,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X7)),X8))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X1),tc_prod(X5,X1))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X1),tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X6),X2)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X7),X3))),c_Wellfounded_Olex__prod(X5,X1,X8,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6446]),
[final] ).
cnf(i_0_11557,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X4,tc_HOL_Obool)),X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(X1,esk396_5(X2,X1,X3,X4,X5)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6447]),
[final] ).
cnf(i_0_11558,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2))))),
inference(split_conjunct,[status(thm)],[i_0_6448]),
[final] ).
cnf(i_0_11559,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6449]),
[final] ).
cnf(i_0_11560,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,esk390_5(X3,X4,X5,X2,X1))))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6450]),
[final] ).
cnf(i_0_11561,plain,
( hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk214_5(X3,X2,X4,X5,X1))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4) != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6451]),
[final] ).
cnf(i_0_11562,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6452,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11563,plain,
( hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(X1,esk431_4(X1,X2,X3,X4)),esk432_4(X1,X2,X3,X4)),esk433_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6389]),
[final] ).
cnf(i_0_11564,plain,
hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5) = c_HOL_OThe(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4)),X5))),
inference(split_conjunct,[status(thm)],[i_0_6453]),
[final] ).
cnf(i_0_11565,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6454,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11566,plain,
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X3,X2)),X4,esk17_6(X5,X4,X2,X3,X1,X6))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X6,X1,X3),X2,X4,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X5),hAPP(c_Natural_Ogetlocs,X2))),X6),hAPP(hAPP(c_Natural_Ogetlocs,X5),c_Com_ORes))) ),
inference(split_conjunct,[status(thm)],[i_0_6120]),
[final] ).
cnf(i_0_11567,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk463_4(X2,X3,X4,X1)),esk464_4(X2,X3,X4,X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel1(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6455]),
[final] ).
cnf(i_0_11568,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(X2,X4),X1),X6),c_Sum__Type_OPlus(X2,X4,X3,X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_Fun_Ocomp(tc_sum(X2,X4),X1,X2,X6),c_Sum__Type_OInl(X2,X4))),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),hAPP(c_Fun_Ocomp(tc_sum(X2,X4),X1,X4,X6),c_Sum__Type_OInr(X4,X2))),X5))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6456]),
[final] ).
cnf(i_0_11569,plain,
( X7 = X6
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6457]),
[final] ).
cnf(i_0_11570,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Ominus__class_Ominus(X1)),X3)),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6458]),
[final] ).
cnf(i_0_11571,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Oplus__class_Oplus(X1)),X3)),X4)),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6459]),
[final] ).
cnf(i_0_11572,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X2),c_Set_OPow(X1)),X4))),hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))),
inference(split_conjunct,[status(thm)],[i_0_6460]),
[final] ).
cnf(i_0_11573,plain,
( X1 = X2
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X1),hAPP(hAPP(c_List_Olist_OCons(X5),X3),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X2),hAPP(hAPP(c_List_Olist_OCons(X5),X4),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6423]),
[final] ).
cnf(i_0_11574,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk357_5(X2,X3,X4,X1,X5)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6366]),
[final] ).
cnf(i_0_11575,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3,X5),tc_prod(X3,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3,X5),tc_prod(X3,X5)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X1),X6)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X2),X7))),c_Wellfounded_Olex__prod(X3,X5,X4,X8))) ),
inference(split_conjunct,[status(thm)],[i_0_6446]),
[final] ).
cnf(i_0_11576,plain,
c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[fact_min__weak__def]),
[final] ).
cnf(i_0_11577,plain,
c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[fact_max__weak__def]),
[final] ).
cnf(i_0_11578,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6461]),
[final] ).
cnf(i_0_11579,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6462]),
[final] ).
cnf(i_0_11580,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X4)),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),X4)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6463]),
[final] ).
cnf(i_0_11581,plain,
c_Int_Oint__ge__less__than2(X1) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(split_conjunct,[status(thm)],[i_0_6464]),
[final] ).
cnf(i_0_11582,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk270_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,c_Groups_Otimes__class_Otimes(X5)),X2),c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,c_Groups_Otimes__class_Otimes(X5)),X2),c_Groups_Oone__class_Oone(X5)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,c_Groups_Otimes__class_Otimes(X5)),X2),c_Groups_Oone__class_Oone(X5)),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6465]),
[final] ).
cnf(i_0_11583,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6466]),
[final] ).
cnf(i_0_11584,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6467]),
[final] ).
cnf(i_0_11585,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_Set_OCollect(X1),X3)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)))),X3)),
inference(split_conjunct,[status(thm)],[i_0_6468]),
[final] ).
cnf(i_0_11586,plain,
( c_Nitpick_Oof__frac(X2,X1,X3) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X2,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X2)),X3))),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X2,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X2)),X3)))
| ~ class_Rings_Oring__1(X1)
| ~ class_Rings_Oinverse(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6469,c_0_6048]),c_0_6049]),
[final] ).
cnf(i_0_11587,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))) ),
inference(split_conjunct,[status(thm)],[i_0_6470]),
[final] ).
cnf(i_0_11588,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X5),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X6)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X7)),X2))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X7),X2))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X5,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X7)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6471]),
[final] ).
cnf(i_0_11589,plain,
c_Random__Sequence_Omap(X1,X2,X3,X4) = c_Random__Sequence_Obind(X1,X2,X4,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X1,c_Random__Sequence_Osingle(X2)),X3)),
inference(split_conjunct,[status(thm)],[i_0_6472]),
[final] ).
cnf(i_0_11590,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk251_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Fields_Ofield(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6473]),
[final] ).
cnf(i_0_11591,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X5),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X6)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X7)),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X7),X2))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X5,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X7))) ),
inference(split_conjunct,[status(thm)],[i_0_6474]),
[final] ).
cnf(i_0_11592,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X1)),X4)),X5)),X6) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X2,X3),X1),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),X4)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X5)))
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6475]),
[final] ).
cnf(i_0_11593,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1)),X4)),X5)),X6) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X2,X3),X1),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),X4)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X5)))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6476]),
[final] ).
cnf(i_0_11594,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6437]),
[final] ).
cnf(i_0_11595,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6438]),
[final] ).
cnf(i_0_11596,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X3,X2))),esk18_5(X4,X2,X3,X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X5,X1,X3)),X2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X4),hAPP(c_Natural_Ogetlocs,X2))),X5),hAPP(hAPP(c_Natural_Ogetlocs,X4),c_Com_ORes)))) ),
inference(split_conjunct,[status(thm)],[i_0_6230]),
[final] ).
cnf(i_0_11597,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk426_4(X3,X4,X1,X2)),esk427_4(X3,X4,X1,X2))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),X4),hAPP(c_Relation_Oconverse(X1,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6477]),
[final] ).
cnf(i_0_11598,plain,
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X3,X2)),X4,esk20_6(X5,X4,X2,X3,X1,X6))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X6,X1,X3),X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_6121]),
[final] ).
cnf(i_0_11599,plain,
( c_Fun_Oinj__on(tc_prod(X1,X5),tc_prod(X2,X6),c_Product__Type_Omap__pair(X1,X2,X5,X6,X3,X7),hAPP(hAPP(c_Product__Type_OSigma(X1,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X1),X8)))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X5,X6,X7,X8) ),
inference(split_conjunct,[status(thm)],[i_0_6478]),
[final] ).
cnf(i_0_11600,plain,
( c_Natural_Oevaln(X1,hAPP(hAPP(hAPP(c_Natural_Oupdate,X2),c_Com_Ovname_OLoc(X3)),hAPP(X4,X2)),X5,esk9_6(X6,X5,X2,X1,X4,X3))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X3,X4,X1),X2,X5,hAPP(hAPP(hAPP(c_Natural_Oupdate,X6),c_Com_Ovname_OLoc(X3)),hAPP(hAPP(c_Natural_Ogetlocs,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6248]),
[final] ).
cnf(i_0_11601,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X4)),X2))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X4),X2))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6479]),
[final] ).
cnf(i_0_11602,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X3)),hAPP(X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk38_4(X4,X3,X2,X1))),hAPP(X2,hAPP(c_Nat_OSuc,esk38_4(X4,X3,X2,X1)))))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6480]),
[final] ).
cnf(i_0_11603,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X4)),hAPP(X2,X3)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk37_4(X3,X4,X2,X1))),hAPP(X2,hAPP(c_Nat_OSuc,esk37_4(X3,X4,X2,X1)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6481]),
[final] ).
cnf(i_0_11604,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(X4,X1)),hAPP(X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(X4,esk38_4(X2,X1,X4,X3))),hAPP(X4,hAPP(c_Nat_OSuc,esk38_4(X2,X1,X4,X3)))))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_6480]),
[final] ).
cnf(i_0_11605,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk274_5(X2,X3,X1,X4,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Oran(X1,X5,c_Map_Orestrict__map(X1,X5,X3,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6482]),
[final] ).
cnf(i_0_11606,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4)),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X2))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6483]),
[final] ).
cnf(i_0_11607,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X3)),X4)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X3,tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),hAPP(X4,X1)),hAPP(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ class_Groups_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_6484]),
[final] ).
cnf(i_0_11608,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),X5))))
| c_Map_Omap__upds(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X6),X2),hAPP(c_Option_Ooption_OSome(X3),X7)),X5,X4) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__upds(X1,X3,X6,X5,X4)),X2),hAPP(c_Option_Ooption_OSome(X3),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6485]),
[final] ).
cnf(i_0_11609,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,tc_prod(X1,X2),esk283_4(X3,X4,X1,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X3))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X3))),
inference(split_conjunct,[status(thm)],[i_0_6486]),
[final] ).
cnf(i_0_11610,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X4)))
| ~ class_Groups_Oab__semigroup__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6487]),
[final] ).
cnf(i_0_11611,plain,
hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X1,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X1,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),X4))) = hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),c_Product__Type_Osnd(X1,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X4)))),
inference(split_conjunct,[status(thm)],[i_0_6488]),
[final] ).
cnf(i_0_11612,plain,
hAPP(c_Fun_Ocomp(tc_prod(X1,X2),X1,tc_prod(X3,X4),c_Product__Type_Ofst(X1,X2)),c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6)) = hAPP(c_Fun_Ocomp(X3,X1,tc_prod(X3,X4),X5),c_Product__Type_Ofst(X3,X4)),
inference(split_conjunct,[status(thm)],[i_0_6489]),
[final] ).
cnf(i_0_11613,plain,
hAPP(c_Fun_Ocomp(tc_prod(X1,X2),X2,tc_prod(X3,X4),c_Product__Type_Osnd(X1,X2)),c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6)) = hAPP(c_Fun_Ocomp(X4,X2,tc_prod(X3,X4),X6),c_Product__Type_Osnd(X3,X4)),
inference(split_conjunct,[status(thm)],[i_0_6490]),
[final] ).
cnf(i_0_11614,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool))),X5)),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)),X6),
inference(split_conjunct,[status(thm)],[i_0_6491]),
[final] ).
cnf(i_0_11615,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool))),X5)),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)),X6),
inference(split_conjunct,[status(thm)],[i_0_6492]),
[final] ).
cnf(i_0_11616,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool))),X5)),X6)),
inference(split_conjunct,[status(thm)],[i_0_6493]),
[final] ).
cnf(i_0_11617,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X5)),X6)),
inference(split_conjunct,[status(thm)],[i_0_6494]),
[final] ).
cnf(i_0_11618,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X5)),X6)),
inference(split_conjunct,[status(thm)],[i_0_6495]),
[final] ).
cnf(i_0_11619,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X6,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(X5,X2),X7)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X6,X3),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6496]),
[final] ).
cnf(i_0_11620,plain,
( c_Natural_Oevaln(X1,hAPP(hAPP(hAPP(c_Natural_Oupdate,X2),c_Com_Ovname_OLoc(X3)),hAPP(X4,X2)),X5,esk15_6(X6,X5,X2,X1,X4,X3))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X3,X4,X1),X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_6255]),
[final] ).
cnf(i_0_11621,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X3)),X4)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X3,tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(X3)
| ~ class_Groups_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_6484]),
[final] ).
cnf(i_0_11622,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),esk435_6(X2,X1,X4,X5,X6,X3))
| hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X3,c_Option_Ooption_ONone(X6),X4),hAPP(X1,X2)) != c_Option_Ooption_ONone(X6) ),
inference(rw,[status(thm)],[i_0_6497,c_0_6226]),
[final] ).
cnf(i_0_11623,plain,
( hAPP(X3,X2) = c_Option_Ooption_ONone(X6)
| hAPP(X1,esk435_6(X2,X3,X1,X4,X5,X6)) = c_Option_Ooption_ONone(X5)
| hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5),X6,c_Option_Ooption_ONone(X5),X1),hAPP(X3,X2)) != c_Option_Ooption_ONone(X5) ),
inference(rw,[status(thm)],[i_0_6498,c_0_6226]),
[final] ).
cnf(i_0_11624,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X2)),X3))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6415]),
[final] ).
cnf(i_0_11625,plain,
( hAPP(hAPP(X6,X7),X9) = hAPP(hAPP(X6,X8),X10)
| ~ c_Equiv__Relations_Ocongruent2(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X7),X8)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X9),X10)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6499]),
[final] ).
cnf(i_0_11626,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk424_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(c_Set_OCollect(X1),X3))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6500]),
[final] ).
cnf(i_0_11627,plain,
( c_Map_Omap__upds(X1,X3,X5,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))),X4) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__upds(X1,X3,X5,X2,X4)),X6),hAPP(c_Option_Ooption_OSome(X3),hAPP(hAPP(c_List_Onth(X3),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6501]),
[final] ).
cnf(i_0_11628,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk151_3(X2,X3,X1))),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6502]),
[final] ).
cnf(i_0_11629,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),
inference(split_conjunct,[status(thm)],[i_0_6503]),
[final] ).
cnf(i_0_11630,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X3))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6504]),
[final] ).
cnf(i_0_11631,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3)),X2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6504]),
[final] ).
cnf(i_0_11632,plain,
( hAPP(hAPP(hAPP(c_Natural_Oupdate,X1),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk8_5(X1,X3,X4,X5,X2)),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X2,X5,X4)),X3),hAPP(hAPP(hAPP(c_Natural_Oupdate,X1),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6505]),
[final] ).
cnf(i_0_11633,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk443_5(X3,X1,X4,X5,X2)),esk444_5(X3,X1,X4,X5,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4)),X1)),c_List_Olistrel(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6362]),
[final] ).
cnf(i_0_11634,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2),
inference(split_conjunct,[status(thm)],[i_0_6506]),
[final] ).
cnf(i_0_11635,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk387_4(X2,X3,X4,X1)),X3)),c_Transitive__Closure_Ortrancl(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
inference(rw,[status(thm)],[i_0_6507,c_0_6062]),
[final] ).
cnf(i_0_11636,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk471_5(X2,X3,X4,X1,X5)),hAPP(c_List_Oset(X1),X4)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X1,X5),X3),X4))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X1,X5),X2),X4))))
| ~ class_Groups_Omonoid__add(X5)
| ~ class_Groups_Oordered__ab__semigroup__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6256]),
[final] ).
cnf(i_0_11637,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk386_4(X2,X3,X4,X1)),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
inference(rw,[status(thm)],[i_0_6508,c_0_6062]),
[final] ).
cnf(i_0_11638,plain,
hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X4,X5,X6),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X7),X8)) = hAPP(hAPP(c_Product__Type_OPair(X2,X4),hAPP(X5,X7)),hAPP(X6,X8)),
inference(split_conjunct,[status(thm)],[i_0_6509]),
[final] ).
cnf(i_0_11639,plain,
hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X5),X6)) = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,X5)),X6),
inference(rw,[status(thm)],[i_0_6510,c_0_6211]),
[final] ).
cnf(i_0_11640,plain,
hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X6)) = hAPP(hAPP(c_Product__Type_OPair(X3,X2),X5),hAPP(X4,X6)),
inference(rw,[status(thm)],[i_0_6511,c_0_6029]),
[final] ).
cnf(i_0_11641,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
| X5 != X6 ),
inference(split_conjunct,[status(thm)],[i_0_6423]),
[final] ).
cnf(i_0_11642,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6461]),
[final] ).
cnf(i_0_11643,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6462]),
[final] ).
cnf(i_0_11644,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk162_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Ocomm__monoid__add(X5)
| ~ class_Groups_Oordered__ab__semigroup__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6433]),
[final] ).
cnf(i_0_11645,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk188_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Oordered__comm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6434]),
[final] ).
cnf(i_0_11646,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6435]),
[final] ).
cnf(i_0_11647,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6436]),
[final] ).
cnf(i_0_11648,plain,
hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X2,c_COMBI(X1),c_COMBI(X2)),X3) = X3,
inference(split_conjunct,[status(thm)],[i_0_6512]),
[final] ).
cnf(i_0_11649,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk123_5(X1,X2,X3,X4,X5)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6513]),
[final] ).
cnf(i_0_11650,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk121_5(X1,X2,X3,X4,X5)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6514]),
[final] ).
cnf(i_0_11651,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| c_Map_Omap__upds(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),hAPP(c_Option_Ooption_OSome(X4),X6)),X3,X7) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Omap__upds(X1,X4,X5,X3,X7)),X2),hAPP(c_Option_Ooption_OSome(X4),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6515]),
[final] ).
cnf(i_0_11652,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk124_5(X1,X2,X3,X4,X5)),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6513]),
[final] ).
cnf(i_0_11653,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk122_5(X1,X2,X3,X4,X5)),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6514]),
[final] ).
cnf(i_0_11654,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk189_5(X2,X3,X4,X1,X5)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(c_Finite__Set_Ocard(X1),X4))),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add(X5)
| ~ class_Rings_Osemiring__1(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6332]),
[final] ).
cnf(i_0_11655,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk119_5(X1,X2,X3,X4,X5)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6516]),
[final] ).
cnf(i_0_11656,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk117_5(X1,X2,X3,X4,X5)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6517]),
[final] ).
cnf(i_0_11657,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk144_5(X2,X3,X4,X1,X5)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6331]),
[final] ).
cnf(i_0_11658,plain,
( hAPP(hAPP(X3,hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X7),X8))),hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X7),X8))) = hAPP(hAPP(X3,hAPP(X6,X7)),hAPP(X6,X8))
| ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X8)) ),
inference(split_conjunct,[status(thm)],[i_0_6518]),
[final] ).
cnf(i_0_11659,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk253_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6519]),
[final] ).
cnf(i_0_11660,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk252_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6520]),
[final] ).
cnf(i_0_11661,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk255_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Ocomm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6521]),
[final] ).
cnf(i_0_11662,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk254_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Ocomm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6522]),
[final] ).
cnf(i_0_11663,plain,
hAPP(c_Relation_OImage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2))),hAPP(c_Product__Type_OPair(X1,X2),X4))),X3)),
inference(split_conjunct,[status(thm)],[i_0_6523]),
[final] ).
cnf(i_0_11664,plain,
( X1 = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk14_5(X1,X2,X3,X4,X5)),c_Com_Ovname_OLoc(X5)),hAPP(hAPP(c_Natural_Ogetlocs,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X5,X4,X3)),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6524]),
[final] ).
cnf(i_0_11665,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk120_5(X1,X2,X3,X4,X5)),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6516]),
[final] ).
cnf(i_0_11666,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk118_5(X1,X2,X3,X4,X5)),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6517]),
[final] ).
cnf(i_0_11667,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X4),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6423]),
[final] ).
cnf(i_0_11668,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk445_5(X3,X4,X5,X1,X2)),esk446_5(X3,X4,X5,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4))),c_List_Olistrel(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6274]),
[final] ).
cnf(i_0_11669,plain,
hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X1)),c_List_Otranspose(X1,X2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2)),
inference(rw,[status(thm)],[i_0_6525,c_0_6070]),
[final] ).
cnf(i_0_11670,plain,
( hAPP(X6,X7) = hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X8),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
| ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X8),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6526]),
[final] ).
cnf(i_0_11671,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk127_5(X2,X3,X1,X4,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6527]),
[final] ).
cnf(i_0_11672,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk168_5(X3,X4,X5,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6528]),
[final] ).
cnf(i_0_11673,plain,
( hAPP(X6,hAPP(hAPP(c_Set_Oinsert(X2),X8),X7)) = hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X8),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
| ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6529]),
[final] ).
cnf(i_0_11674,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk140_5(X2,X3,X4,X1,X5)),X4))
| hBOOL(hAPP(X2,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6408]),
[final] ).
cnf(i_0_11675,plain,
( hAPP(c_Fun_Othe__inv__into(X4,X2,X6,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X7) = hAPP(hAPP(c_Fun_Ocomp(X1,X4,X2,c_Fun_Othe__inv__into(X4,X1,X6,X5)),c_Fun_Othe__inv__into(X1,X2,hAPP(c_Set_Oimage(X4,X1,X5),X6),X3)),X7)
| ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(c_Set_Oimage(X4,X1,X5),X6))
| ~ c_Fun_Oinj__on(X4,X1,X5,X6)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X1,X5),X6)))) ),
inference(split_conjunct,[status(thm)],[i_0_6530]),
[final] ).
cnf(i_0_11676,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk393_5(X2,X3,X4,X1,X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X5),X4),X3)),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| ~ class_Orderings_Olinorder(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6407]),
[final] ).
cnf(i_0_11677,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk168_5(X2,X3,X1,X4,X5)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6528]),
[final] ).
cnf(i_0_11678,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk235_5(X2,X3,X4,X1,X5)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Ocomm__monoid__add(X5)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6257]),
[final] ).
cnf(i_0_11679,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6531,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11680,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk228_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6532]),
[final] ).
cnf(i_0_11681,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk227_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6533]),
[final] ).
cnf(i_0_11682,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk230_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Ocomm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6534]),
[final] ).
cnf(i_0_11683,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk229_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Ocomm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6535]),
[final] ).
cnf(i_0_11684,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,X2)))
| esk381_5(X1,X2,X3,X4,X5) != esk382_5(X1,X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_6215]),
[final] ).
cnf(i_0_11685,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,X2)))
| esk377_5(X1,X2,X3,X4,X5) != esk376_5(X1,X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_6216]),
[final] ).
cnf(i_0_11686,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__eq__frac(X1,X2,X3) ),
inference(rw,[status(thm)],[i_0_6536,c_0_6049]),
[final] ).
cnf(i_0_11687,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__frac(X1,X2,X3) ),
inference(rw,[status(thm)],[i_0_6537,c_0_6049]),
[final] ).
cnf(i_0_11688,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk138_5(X2,X3,X4,X5,X1)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6538]),
[final] ).
cnf(i_0_11689,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk139_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| hBOOL(hAPP(X2,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X7),hAPP(X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6408]),
[final] ).
cnf(i_0_11690,plain,
( hBOOL(hAPP(hAPP(X1,esk138_5(X2,X1,X3,X4,X5)),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X4,tc_HOL_Obool)),X3),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6538]),
[final] ).
cnf(i_0_11691,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X3,X5,X6)),X2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X1),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,X1),c_Com_ORes))))
| hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X1),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,X1),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X4),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,X4),c_Com_ORes))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X5)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X6,X2))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6230]),
[final] ).
cnf(i_0_11692,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk289_5(X2,X3,X4,X5,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X5)),X4),hAPP(hAPP(c_Product__Type_OSigma(X1,X5),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6411]),
[final] ).
cnf(i_0_11693,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk391_5(X2,X3,X1,X4,X5)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6441]),
[final] ).
cnf(i_0_11694,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool)),X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6539]),
[final] ).
cnf(i_0_11695,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X5),X3))),
inference(split_conjunct,[status(thm)],[i_0_6540]),
[final] ).
cnf(i_0_11696,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X5),X3))),
inference(split_conjunct,[status(thm)],[i_0_6541]),
[final] ).
cnf(i_0_11697,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X6))),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7)))),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6542]),
[final] ).
cnf(i_0_11698,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk271_5(X2,X3,X1,X4,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6302]),
[final] ).
cnf(i_0_11699,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk237_5(X2,X3,X1,X4,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6303]),
[final] ).
cnf(i_0_11700,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_Int_Ointrel)) ),
inference(split_conjunct,[status(thm)],[i_0_6543]),
[final] ).
cnf(i_0_11701,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Recdef_Osame__fst(X7,X3,X1,X6)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6544]),
[final] ).
cnf(i_0_11702,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk142_5(X2,X3,X4,X1,X5)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5),X4),X3)),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6336]),
[final] ).
cnf(i_0_11703,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk392_5(X2,X3,X1,X4,X5)),X3))
| hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6444]),
[final] ).
cnf(i_0_11704,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk143_5(X3,X4,X5,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1),X4),X3)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6545]),
[final] ).
cnf(i_0_11705,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X5),X2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X5),X1))))
| ~ hBOOL(hAPP(X1,esk424_5(X1,X2,X3,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6500]),
[final] ).
cnf(i_0_11706,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X1),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Wellfounded_Olex__prod(X7,X3,X8,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6446]),
[final] ).
cnf(i_0_11707,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X5),tc_prod(X1,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X5),tc_prod(X1,X5)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X2),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X3),X7))),c_Wellfounded_Olex__prod(X1,X5,X4,X8)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6446]),
[final] ).
cnf(i_0_11708,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk396_5(X2,X3,X4,X5,X1)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6447]),
[final] ).
cnf(i_0_11709,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk143_5(X2,X3,X1,X4,X5)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5),X3),X2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| ~ class_Orderings_Olinorder(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6545]),
[final] ).
cnf(i_0_11710,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X6,tc_prod(X1,X2)),X7),X8)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X6,X3),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X1,X2)),tc_fun(X6,X3),X5),hAPP(c_COMBB(tc_prod(X1,X2),X3,X6),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4))),X7)),X8),
inference(split_conjunct,[status(thm)],[i_0_6546]),
[final] ).
cnf(i_0_11711,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6547,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11712,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
| ~ class_Rings_Oring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6548,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11713,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6549,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11714,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk233_4(X1,X3,X4,X2)),esk234_4(X1,X3,X4,X2))))
| ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6550]),
[final] ).
cnf(i_0_11715,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X4,X1,X3)),c_List_Olist_Olist__size(X4,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,esk477_4(X2,X1,X3,X4))),hAPP(X2,esk477_4(X2,X1,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_6551]),
[final] ).
cnf(i_0_11716,plain,
c_Fun_Oinj__on(tc_fun(X1,X2),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,X2)),c_Set_OCollect(tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,X2)),c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool)),hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_6552]),
[final] ).
cnf(i_0_11717,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6553,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11718,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6554,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11719,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6555,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11720,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6556,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11721,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X1) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6557,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11722,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk276_5(X2,X3,X4,X1,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3))
| ~ c_Wellfounded_Omax__extp(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6558]),
[final] ).
cnf(i_0_11723,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),
inference(split_conjunct,[status(thm)],[i_0_6559]),
[final] ).
cnf(i_0_11724,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),
inference(split_conjunct,[status(thm)],[i_0_6560]),
[final] ).
cnf(i_0_11725,plain,
( hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X7),X8)) = hAPP(hAPP(X3,hAPP(X6,X7)),hAPP(X6,X8))
| ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X8))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X7),X8) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6561]),
[final] ).
cnf(i_0_11726,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk390_5(X2,X3,X1,X4,X5)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X5),X3),X2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6450]),
[final] ).
cnf(i_0_11727,plain,
( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,X3)),X2),X6) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X2),X6)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6562]),
[final] ).
cnf(i_0_11728,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk214_5(X2,X3,X4,X1,X5)),X4))
| hAPP(X3,X2) = c_Groups_Ozero__class_Ozero(X5)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4) != c_Groups_Ozero__class_Ozero(X5)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Groups_Oordered__ab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6451]),
[final] ).
cnf(i_0_11729,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6563]),
[final] ).
cnf(i_0_11730,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6564]),
[final] ).
cnf(i_0_11731,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),X6))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Relation_OImage(X2,X1,X3)),X6)))),
inference(split_conjunct,[status(thm)],[i_0_6565]),
[final] ).
cnf(i_0_11732,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6466]),
[final] ).
cnf(i_0_11733,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6467]),
[final] ).
cnf(i_0_11734,plain,
( hAPP(hAPP(X3,hAPP(X6,X8)),hAPP(X6,X7)) = hAPP(X6,X7)
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X8),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6566]),
[final] ).
cnf(i_0_11735,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk42_4(X3,X2,X4,X1))),hAPP(X3,esk42_4(X3,X2,X4,X1))))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6567]),
[final] ).
cnf(i_0_11736,plain,
hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),X6) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X5),X6),
inference(split_conjunct,[status(thm)],[i_0_6568]),
[final] ).
cnf(i_0_11737,plain,
( hAPP(X6,X7) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X5),X4),X7)
| ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6569]),
[final] ).
cnf(i_0_11738,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk436_5(X2,X3,X4,X5,X1)),hAPP(c_List_Oset(X1),X3)))
| hAPP(hAPP(c_List_Omap(X1,X5),X4),X3) = hAPP(hAPP(c_List_Omap(X1,X5),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6570]),
[final] ).
cnf(i_0_11739,plain,
( hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X7),X8)) = hAPP(hAPP(X3,hAPP(X6,X7)),hAPP(X6,X8))
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X8)) ),
inference(split_conjunct,[status(thm)],[i_0_6571]),
[final] ).
cnf(i_0_11740,plain,
( c_Equiv__Relations_Ocongruent(X4,X5,X6,hAPP(X7,X8))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_Equiv__Relations_Ocongruent2(X1,X4,X5,X3,X6,X7)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X8),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6572]),
[final] ).
cnf(i_0_11741,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk458_5(X3,X4,X1,X5,X2)),X3)
| hAPP(hAPP(c_List_Oappend(X2),esk457_5(X3,X4,X1,X5,X2)),X1) = X3
| hAPP(hAPP(c_List_Oappend(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6573]),
[final] ).
cnf(i_0_11742,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X8),X7))
| hAPP(X6,hAPP(hAPP(c_Set_Oinsert(X2),X8),X7)) = hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))
| ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6574]),
[final] ).
cnf(i_0_11743,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk269_4(X3,X1,X4,X2)),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X4)),hAPP(c_Finite__Set_Ocard(X1),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6575]),
[final] ).
cnf(i_0_11744,plain,
( hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7)) = hAPP(X6,X7)
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X8),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6576]),
[final] ).
cnf(i_0_11745,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X3,X2))),esk19_5(X4,X2,X3,X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X5,X1,X3)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6243]),
[final] ).
cnf(i_0_11746,plain,
( hAPP(X6,hAPP(hAPP(c_Set_Oinsert(X2),X8),X7)) = hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6577]),
[final] ).
cnf(i_0_11747,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_6578]),
[final] ).
cnf(i_0_11748,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_6579]),
[final] ).
cnf(i_0_11749,plain,
( hAPP(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = X4
| ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_6580]),
[final] ).
cnf(i_0_11750,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
inference(split_conjunct,[status(thm)],[fact_max__rpair__set]),
[final] ).
cnf(i_0_11751,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
inference(split_conjunct,[status(thm)],[fact_min__rpair__set]),
[final] ).
cnf(i_0_11752,plain,
( hAPP(hAPP(X3,X7),X7) = X7
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_6581]),
[final] ).
cnf(i_0_11753,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X1)),c_FunDef_Omax__strict))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6582]),
[final] ).
cnf(i_0_11754,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6563]),
[final] ).
cnf(i_0_11755,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6564]),
[final] ).
cnf(i_0_11756,plain,
hAPP(c_List_Oset(X1),hAPP(c_List_Ofilter(X1,X2),X3)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(c_List_Oset(X1),X3)))),X2)),
inference(split_conjunct,[status(thm)],[i_0_6583]),
[final] ).
cnf(i_0_11757,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X3)),X1)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X1,esk100_3(X2,X3,X1))),hAPP(X3,esk100_3(X2,X3,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_6584]),
[final] ).
cnf(i_0_11758,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk268_4(X3,X1,X2,X4)),X4)),X3))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X1,X2,X5),X3) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_6585]),
[final] ).
cnf(i_0_11759,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk324_4(X4,X3,X2,X1)),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6586]),
[final] ).
cnf(i_0_11760,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk323_4(X4,X3,X2,X1)),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6587]),
[final] ).
cnf(i_0_11761,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X1)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6588]),
[final] ).
cnf(i_0_11762,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) ),
inference(split_conjunct,[status(thm)],[i_0_6589]),
[final] ).
cnf(i_0_11763,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) ),
inference(split_conjunct,[status(thm)],[i_0_6590]),
[final] ).
cnf(i_0_11764,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) ),
inference(split_conjunct,[status(thm)],[i_0_6591]),
[final] ).
cnf(i_0_11765,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6592]),
[final] ).
cnf(i_0_11766,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6593]),
[final] ).
cnf(i_0_11767,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6594]),
[final] ).
cnf(i_0_11768,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5),
inference(split_conjunct,[status(thm)],[i_0_6595]),
[final] ).
cnf(i_0_11769,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5),
inference(split_conjunct,[status(thm)],[i_0_6596]),
[final] ).
cnf(i_0_11770,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5),
inference(split_conjunct,[status(thm)],[i_0_6597]),
[final] ).
cnf(i_0_11771,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X4)),X5)),
inference(split_conjunct,[status(thm)],[i_0_6598]),
[final] ).
cnf(i_0_11772,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X4)),X5)),
inference(split_conjunct,[status(thm)],[i_0_6599]),
[final] ).
cnf(i_0_11773,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool))),X4)),X5)),
inference(split_conjunct,[status(thm)],[i_0_6600]),
[final] ).
cnf(i_0_11774,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X6),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X6),X3),X7)),hAPP(hAPP(c_Product__Type_OSigma(X1,X6),X4),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X1),X8))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X6),tc_HOL_Obool)),X7),hAPP(hAPP(c_Product__Type_OSigma(X2,X6),X5),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X2),X8)))) ),
inference(split_conjunct,[status(thm)],[i_0_6601]),
[final] ).
cnf(i_0_11775,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk124_5(X2,X3,X4,X5,X1)),esk123_5(X2,X3,X4,X5,X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6513]),
[final] ).
cnf(i_0_11776,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk122_5(X2,X3,X4,X5,X1)),esk121_5(X2,X3,X4,X5,X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6514]),
[final] ).
cnf(i_0_11777,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6602]),
[final] ).
cnf(i_0_11778,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olexord(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6603]),
[final] ).
cnf(i_0_11779,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olex(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6604]),
[final] ).
cnf(i_0_11780,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_6605]),
[final] ).
cnf(i_0_11781,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_6606]),
[final] ).
cnf(i_0_11782,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_6607]),
[final] ).
cnf(i_0_11783,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X5)))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6608]),
[final] ).
cnf(i_0_11784,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6609]),
[final] ).
cnf(i_0_11785,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6610]),
[final] ).
cnf(i_0_11786,plain,
( hAPP(hAPP(X5,hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),X3),X7)),X8)),X6) = hAPP(hAPP(X3,hAPP(hAPP(X5,X7),X6)),hAPP(hAPP(X5,X8),X6))
| ~ c_Finite__Set_Ofolding__image(X1,X2,X3,X4,X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6611]),
[final] ).
cnf(i_0_11787,plain,
( hBOOL(hAPP(X1,X6))
| ~ hBOOL(hAPP(X1,esk141_5(X1,X2,X3,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X5,tc_HOL_Obool)),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6408]),
[final] ).
cnf(i_0_11788,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X4)),c_List_Olexord(X2,X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))
| hAPP(hAPP(c_List_Otake(X2),X1),X3) != hAPP(hAPP(c_List_Otake(X2),X1),X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Onth(X2),X4),X1))),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6340]),
[final] ).
cnf(i_0_11789,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6612,c_0_6062]),c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_11790,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6613]),
[final] ).
cnf(i_0_11791,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)))),
inference(split_conjunct,[status(thm)],[i_0_6614]),
[final] ).
cnf(i_0_11792,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2)),
inference(split_conjunct,[status(thm)],[i_0_6615]),
[final] ).
cnf(i_0_11793,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk120_5(X2,X3,X4,X5,X1)),esk119_5(X2,X3,X4,X5,X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6516]),
[final] ).
cnf(i_0_11794,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk118_5(X2,X3,X4,X5,X1)),esk117_5(X2,X3,X4,X5,X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6517]),
[final] ).
cnf(i_0_11795,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X5,X1,X3)),X2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X4),hAPP(c_Natural_Ogetlocs,X2))),X5),hAPP(hAPP(c_Natural_Ogetlocs,X4),c_Com_ORes))))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X3,X2))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6616]),
[final] ).
cnf(i_0_11796,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_6617]),
[final] ).
cnf(i_0_11797,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5)))),
inference(split_conjunct,[status(thm)],[i_0_6618]),
[final] ).
cnf(i_0_11798,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6619,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_11799,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6620,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_11800,plain,
( c_Map_Orestrict__map(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),X6),X3) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X2),X6)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6621]),
[final] ).
cnf(i_0_11801,plain,
hAPP(c_Set_OCollect(tc_Nat_Onat),X1) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X1),c_Int_Onat)))),
inference(split_conjunct,[status(thm)],[i_0_6622]),
[final] ).
cnf(i_0_11802,plain,
c_List_Olenlex(X1,X2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X1)),tc_List_Olist(X1)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X1),c_Wellfounded_Oless__than,c_List_Olex(X1,X2))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_List_Olist(X1),tc_prod(tc_Nat_Onat,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X1),tc_prod(tc_Nat_Onat,tc_List_Olist(X1))),tc_List_Olist(X1)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X1))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_COMBI(tc_List_Olist(X1)))),
inference(split_conjunct,[status(thm)],[i_0_6623]),
[final] ).
cnf(i_0_11803,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X6,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X7))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != hAPP(hAPP(c_Set_Oinsert(X1),X4),X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X6,X4,X5),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6372]),
[final] ).
cnf(i_0_11804,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),hAPP(hAPP(hAPP(c_Natural_Oupdate,X2),c_Com_Ovname_OLoc(X3)),hAPP(X4,X2))),esk8_5(X5,X2,X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X3,X4,X1)),X2),hAPP(hAPP(hAPP(c_Natural_Oupdate,X5),c_Com_Ovname_OLoc(X3)),hAPP(hAPP(c_Natural_Ogetlocs,X2),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_6505]),
[final] ).
cnf(i_0_11805,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6589]),
[final] ).
cnf(i_0_11806,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6590]),
[final] ).
cnf(i_0_11807,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X4)),X5)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6591]),
[final] ).
cnf(i_0_11808,plain,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk294_3(X2,X3,X1)),esk294_3(X2,X3,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6624]),
[final] ).
cnf(i_0_11809,plain,
( c_Relation_Orefl__on(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk293_3(X2,X3,X1)),esk293_3(X2,X3,X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_6625]),
[final] ).
cnf(i_0_11810,plain,
( c_Map_Omap__of(X1,X3,hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X3)),hAPP(hAPP(c_COMBS(X1,X3,tc_prod(X1,X3)),c_Product__Type_OPair(X1,X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X3),X3,X1),c_Option_Othe(X3)),X4))),X2)) = X4
| hAPP(c_List_Oset(X1),X2) != c_Map_Odom(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6626]),
[final] ).
cnf(i_0_11811,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),
inference(split_conjunct,[status(thm)],[i_0_6627]),
[final] ).
cnf(i_0_11812,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),
inference(split_conjunct,[status(thm)],[i_0_6628]),
[final] ).
cnf(i_0_11813,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk386_4(X3,X4,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))) ),
inference(rw,[status(thm)],[i_0_6629,c_0_6062]),
[final] ).
cnf(i_0_11814,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6609]),
[final] ).
cnf(i_0_11815,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6610]),
[final] ).
cnf(i_0_11816,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olistrel(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_List_Olistrel(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6630]),
[final] ).
cnf(i_0_11817,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk289_5(X4,X5,X1,X3,X2)),esk290_5(X4,X5,X1,X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X5),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6411]),
[final] ).
cnf(i_0_11818,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk387_4(X3,X4,X2,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))) ),
inference(rw,[status(thm)],[i_0_6631,c_0_6062]),
[final] ).
cnf(i_0_11819,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,X3,X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6632]),
[final] ).
cnf(i_0_11820,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk281_5(X4,X3,X2,X5,X1)),esk282_5(X4,X3,X2,X5,X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6371]),
[final] ).
cnf(i_0_11821,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk279_5(X4,X3,X2,X5,X1)),esk280_5(X4,X3,X2,X5,X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6372]),
[final] ).
cnf(i_0_11822,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X4,c_Groups_Otimes__class_Otimes(X5)),X1),c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X4,c_Groups_Otimes__class_Otimes(X5)),X1),c_Groups_Oone__class_Oone(X5)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X4,c_Groups_Otimes__class_Otimes(X5)),X1),c_Groups_Oone__class_Oone(X5)),X2))
| hAPP(X1,esk270_5(X1,X2,X3,X4,X5)) != c_Groups_Oone__class_Oone(X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6465]),
[final] ).
cnf(i_0_11823,plain,
c_Map_Odom(X1,X2,X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2)))),
inference(split_conjunct,[status(thm)],[i_0_6633]),
[final] ).
cnf(i_0_11824,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olex(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6604]),
[final] ).
cnf(i_0_11825,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6634,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11826,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6635,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11827,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6602]),
[final] ).
cnf(i_0_11828,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ),
inference(split_conjunct,[status(thm)],[i_0_6636]),
[final] ).
cnf(i_0_11829,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_6637]),
[final] ).
cnf(i_0_11830,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
inference(split_conjunct,[status(thm)],[i_0_6638]),
[final] ).
cnf(i_0_11831,plain,
( hBOOL(hAPP(X1,X7))
| ~ hBOOL(hAPP(X1,esk139_5(X1,X2,X3,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X6),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X7),hAPP(X2,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6408]),
[final] ).
cnf(i_0_11832,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X5) = X6
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6639]),
[final] ).
cnf(i_0_11833,plain,
( X5 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6640]),
[final] ).
cnf(i_0_11834,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6641]),
[final] ).
cnf(i_0_11835,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastLessThan(X4,X5,X1,X6,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6642]),
[final] ).
cnf(i_0_11836,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X5,X6,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6643]),
[final] ).
cnf(i_0_11837,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastLessThan(X4,X1,X5,X2,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6642]),
[final] ).
cnf(i_0_11838,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X5,X1,X2,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6643]),
[final] ).
cnf(i_0_11839,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X1),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X3)
| hAPP(X1,esk236_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk236_5(X2,X1,X3,X4,X5))
| ~ c_Nat__Transfer_Onat__set(X3)
| X4 != X3
| ~ class_Groups_Ocomm__monoid__add(X5)
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6644]),
[final] ).
cnf(i_0_11840,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X3)
| hAPP(X1,esk131_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk131_5(X2,X1,X3,X4,X5))
| ~ c_Nat__Transfer_Onat__set(X3)
| X4 != X3
| ~ class_Groups_Ocomm__monoid__add(X5)
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6645]),
[final] ).
cnf(i_0_11841,plain,
( hAPP(hAPP(c_List_Omap(X5,X4),X1),X3) = hAPP(hAPP(c_List_Omap(X5,X4),X2),X3)
| hAPP(X1,esk436_5(X2,X3,X1,X4,X5)) != hAPP(X2,esk436_5(X2,X3,X1,X4,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6570]),
[final] ).
cnf(i_0_11842,plain,
c_Random_Oselect__weight(X1,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2)) = c_Random_Oselect__weight(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_6646]),
[final] ).
cnf(i_0_11843,plain,
c_Random_Opick(X1,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2)) = c_Random_Opick(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_6647]),
[final] ).
cnf(i_0_11844,plain,
( hBOOL(hAPP(X1,esk424_5(X2,X1,X3,X4,X5)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X5),X1))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X5),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6500]),
[final] ).
cnf(i_0_11845,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6648,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11846,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6649,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11847,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),c_Map_Omap__add(X2,X1,X3,c_Map_Omap__of(X2,X1,X4))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[i_0_6650]),
[final] ).
cnf(i_0_11848,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4)))),
inference(split_conjunct,[status(thm)],[i_0_6651]),
[final] ).
cnf(i_0_11849,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4)))),
inference(split_conjunct,[status(thm)],[i_0_6652]),
[final] ).
cnf(i_0_11850,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Rings_Oinverse__class_Odivide(X1)),X4)),X5)),X3) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6653]),
[final] ).
cnf(i_0_11851,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4)),X5)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6654]),
[final] ).
cnf(i_0_11852,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Oplus__class_Oplus(X1)),X4)),X5)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6655]),
[final] ).
cnf(i_0_11853,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(c_List_Oset(X3),X4)))
| c_Map_Omap__of(X3,X1,hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2)) = c_Map_Omap__of(X3,X1,hAPP(hAPP(c_List_Ozip(X3,X1),X4),X5))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X1)),c_Map_Omap__of(X3,X1,hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2))),X6),hAPP(c_Option_Ooption_OSome(X1),X7)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X1)),c_Map_Omap__of(X3,X1,hAPP(hAPP(c_List_Ozip(X3,X1),X4),X5))),X6),hAPP(c_Option_Ooption_OSome(X1),X8)) ),
inference(split_conjunct,[status(thm)],[i_0_6656]),
[final] ).
cnf(i_0_11854,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6657]),
[final] ).
cnf(i_0_11855,plain,
hAPP(c_List_Orotate1(X1),X2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)))),X2),
inference(split_conjunct,[status(thm)],[i_0_6658]),
[final] ).
cnf(i_0_11856,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X4)),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X5))
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6659]),
[final] ).
cnf(i_0_11857,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Ominus__class_Ominus(X1)),X3)),X4)),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X5))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6660]),
[final] ).
cnf(i_0_11858,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Oplus__class_Oplus(X1)),X3)),X4)),X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6661]),
[final] ).
cnf(i_0_11859,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X5))),X4))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6662]),
[final] ).
cnf(i_0_11860,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olistrel1(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6602]),
[final] ).
cnf(i_0_11861,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olexord(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6603]),
[final] ).
cnf(i_0_11862,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olex(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6604]),
[final] ).
cnf(i_0_11863,plain,
c_Random_Oselect__weight(X1,X2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_6663]),
[final] ).
cnf(i_0_11864,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),esk458_5(X3,X4,X5,X2,X1)) = X4
| hAPP(hAPP(c_List_Oappend(X1),esk457_5(X3,X4,X5,X2,X1)),X5) = X3
| hAPP(hAPP(c_List_Oappend(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6573]),
[final] ).
cnf(i_0_11865,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk458_5(X3,X4,X1,X5,X2)),X3)
| X5 = hAPP(hAPP(c_List_Oappend(X2),X4),esk457_5(X3,X4,X1,X5,X2))
| hAPP(hAPP(c_List_Oappend(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6573]),
[final] ).
cnf(i_0_11866,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Set_Oinsert(X2),X5),X6))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Set_Oinsert(X2),X5),X6)))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X6)))),
inference(split_conjunct,[status(thm)],[i_0_6664]),
[final] ).
cnf(i_0_11867,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),X5) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Rings_Oinverse__class_Odivide(X1)),X3)),X5)),X4)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6665]),
[final] ).
cnf(i_0_11868,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),X5) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X5)),X4)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6666]),
[final] ).
cnf(i_0_11869,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),hAPP(hAPP(hAPP(c_Natural_Oupdate,X2),c_Com_Ovname_OLoc(X3)),hAPP(X4,X2))),esk14_5(X5,X2,X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X3,X4,X1)),X2),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6524]),
[final] ).
cnf(i_0_11870,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X5))),X4))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6667]),
[final] ).
cnf(i_0_11871,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X5)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X5)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_6668]),
[final] ).
cnf(i_0_11872,plain,
hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(c_List_Orev(X1),X3)) = hAPP(c_List_Orev(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))),c_List_Orotate1(X1)),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6669,c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_11873,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6671]),
[final] ).
cnf(i_0_11874,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6672,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_11875,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6673,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_11876,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))
| ~ c_FunDef_Oreduction__pair(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))
| ~ c_Wellfounded_Owf(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6674]),
[final] ).
cnf(i_0_11877,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))),
inference(split_conjunct,[status(thm)],[i_0_6675]),
[final] ).
cnf(i_0_11878,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X3,X4),X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X1,hAPP(c_Relation_Oconverse(X1,X3),X4)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X5))))) ),
inference(split_conjunct,[status(thm)],[i_0_6676]),
[final] ).
cnf(i_0_11879,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6677,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_11880,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6678,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_11881,plain,
hAPP(c_Set_Oimage(X1,X2,X3),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Set_Oinsert(X2)),X3)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_6679]),
[final] ).
cnf(i_0_11882,plain,
( hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,X3,tc_HOL_Obool),c_fequal),X2))),X1)) = hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6680]),
[final] ).
cnf(i_0_11883,plain,
hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),tc_sum(X3,X4),hAPP(c_Option_Omap(X1,X2),X5)),c_Sum__Type_Osum_Osum__case(X3,tc_Option_Ooption(X1),X4,X6,X7)) = c_Sum__Type_Osum_Osum__case(X3,tc_Option_Ooption(X2),X4,hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),X3,hAPP(c_Option_Omap(X1,X2),X5)),X6),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),X4,hAPP(c_Option_Omap(X1,X2),X5)),X7)),
inference(split_conjunct,[status(thm)],[i_0_6681]),
[final] ).
cnf(i_0_11884,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_6682]),
[final] ).
cnf(i_0_11885,plain,
hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),X3,hAPP(c_Option_Omap(X1,X2),X4)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X1)),X5),X6),hAPP(c_Option_Ooption_OSome(X1),X7))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X2)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),X3,hAPP(c_Option_Omap(X1,X2),X4)),X5)),X6),hAPP(c_Option_Ooption_OSome(X2),hAPP(X4,X7))),
inference(split_conjunct,[status(thm)],[i_0_6683]),
[final] ).
cnf(i_0_11886,plain,
( hBOOL(hAPP(X1,X2))
| hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,X3,tc_HOL_Obool),c_fequal),X2))),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6680]),
[final] ).
cnf(i_0_11887,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6684]),
[final] ).
cnf(i_0_11888,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6685]),
[final] ).
cnf(i_0_11889,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3))),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))),
inference(split_conjunct,[status(thm)],[i_0_6686]),
[final] ).
cnf(i_0_11890,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5)))),
inference(split_conjunct,[status(thm)],[i_0_6687]),
[final] ).
cnf(i_0_11891,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))),
inference(split_conjunct,[status(thm)],[i_0_6688]),
[final] ).
cnf(i_0_11892,plain,
( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X2))
| ~ hBOOL(hAPP(X1,esk423_2(X2,X1)))
| ~ hBOOL(hAPP(X2,esk423_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6689]),
[final] ).
cnf(i_0_11893,plain,
hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X7),hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Omap(X4,X1),X5),X6))) = hAPP(c_List_Ofoldl(X2,X4,hAPP(c_COMBC(X4,X2,X2),hAPP(c_Fun_Ocomp(X1,tc_fun(X2,X2),X4,X3),X5)),X7),hAPP(c_List_Orev(X4),X6)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6690,c_0_6070]),c_0_6070]),
[final] ).
cnf(i_0_11894,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6691]),
[final] ).
cnf(i_0_11895,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6692]),
[final] ).
cnf(i_0_11896,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_6543]),
[final] ).
cnf(i_0_11897,plain,
( hBOOL(hAPP(X1,esk423_2(X2,X1)))
| hBOOL(hAPP(X2,esk423_2(X2,X1)))
| hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6689]),
[final] ).
cnf(i_0_11898,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk423_2(X1,X2)))
| hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6689]),
[final] ).
cnf(i_0_11899,plain,
c_List_Olists(X1,X2) = hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2)),
inference(split_conjunct,[status(thm)],[i_0_6693]),
[final] ).
cnf(i_0_11900,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X5)),hAPP(hAPP(c_List_Oappend(X1),X3),X6))),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
| X5 != X6 ),
inference(split_conjunct,[status(thm)],[i_0_6694]),
[final] ).
cnf(i_0_11901,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X1),X4)),hAPP(hAPP(c_List_Oappend(X3),X2),X5))),c_List_Olistrel1(X3,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olistrel1(X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6694]),
[final] ).
cnf(i_0_11902,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olistrel1(X3,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olistrel1(X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6602]),
[final] ).
cnf(i_0_11903,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olexord(X3,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olexord(X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6603]),
[final] ).
cnf(i_0_11904,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olex(X3,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olex(X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6604]),
[final] ).
cnf(i_0_11905,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),X2)),hAPP(hAPP(c_List_Oappend(X1),X5),X3))),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6695]),
[final] ).
cnf(i_0_11906,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3))),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6696]),
[final] ).
cnf(i_0_11907,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk465_4(X3,X1,X4,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk464_4(X3,X1,X4,X2)),esk466_4(X3,X1,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X4),X1)),c_List_Olistrel1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6455]),
[final] ).
cnf(i_0_11908,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk465_4(X3,X4,X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk463_4(X3,X4,X1,X2)),esk466_4(X3,X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),X4)),c_List_Olistrel1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6455]),
[final] ).
cnf(i_0_11909,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))) ),
inference(rw,[status(thm)],[i_0_6697,c_0_6062]),
[final] ).
cnf(i_0_11910,plain,
c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1))),
inference(split_conjunct,[status(thm)],[i_0_6698]),
[final] ).
cnf(i_0_11911,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,tc_Option_Ooption(X1)),X3),X4),hAPP(c_Option_Ooption_OSome(X1),X5))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[i_0_6699]),
[final] ).
cnf(i_0_11912,plain,
( X1 = X2
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olex(X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6604]),
[final] ).
cnf(i_0_11913,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)),X6) = hAPP(hAPP(c_List_Omap(tc_prod(X3,X2),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X2,tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),X3),c_Product__Type_OPair(X1,X2)),X4))),hAPP(hAPP(c_List_Ozip(X3,X2),X5),X6)),
inference(split_conjunct,[status(thm)],[i_0_6700]),
[final] ).
cnf(i_0_11914,plain,
c_Wellfounded_Omlex__prod(X1,X2,X3) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X1),X1),c_Wellfounded_Olex__prod(tc_Nat_Onat,X1,c_Wellfounded_Oless__than,X3)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(tc_Nat_Onat,X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,tc_prod(tc_Nat_Onat,X1)),X1),c_Product__Type_OPair(tc_Nat_Onat,X1)),X2)),c_COMBI(X1))),
inference(split_conjunct,[status(thm)],[i_0_6701]),
[final] ).
cnf(i_0_11915,plain,
( hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),esk232_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk231_3(X1,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6702]),
[final] ).
cnf(i_0_11916,plain,
( X1 = X2
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X5),X2),X4))),c_List_Olistrel1(X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6602]),
[final] ).
cnf(i_0_11917,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Onth(X2),X4),X1))),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X4)),c_List_Olistrel(X2,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6272]),
[final] ).
cnf(i_0_11918,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6703]),
[final] ).
cnf(i_0_11919,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk331_3(X2,X3,X1)),X2))
| c_Relation_Orefl__on(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk332_3(X2,X3,X1)),esk332_3(X2,X3,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6138]),
[final] ).
cnf(i_0_11920,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = hAPP(hAPP(c_HOL_OLet(X2,X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Otimes__class_Otimes(X2)),hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)))),c_COMBI(X2)))
| ~ class_Int_Onumber__ring(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6704,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_11921,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X6)),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X6),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6705]),
[final] ).
cnf(i_0_11922,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X6)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X6)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6706]),
[final] ).
cnf(i_0_11923,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3)),hAPP(c_Set_OPow(X2),X4))),hAPP(c_Set_OPow(X1),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6707]),
[final] ).
cnf(i_0_11924,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X6)),c_List_Olistrel1(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| X6 != hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_6373]),
[final] ).
cnf(i_0_11925,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X1,X2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6708]),
[final] ).
cnf(i_0_11926,plain,
hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X6),hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Oappend(X1),X4),X5))) = hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X6),hAPP(c_List_Orev(X1),X5))),hAPP(c_List_Orev(X1),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6709,c_0_6070]),c_0_6070]),c_0_6070]),
[final] ).
cnf(i_0_11927,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Product__Type_Ofst(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X1,X2),X3))),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),X1),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X1)),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6710]),
[final] ).
cnf(i_0_11928,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6711]),
[final] ).
cnf(i_0_11929,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_List_Oset(X1),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3))),X2)),
inference(split_conjunct,[status(thm)],[i_0_6712]),
[final] ).
cnf(i_0_11930,plain,
hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Ofilter(X1,X3),X4)) = hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3)),X2)),X4),
inference(split_conjunct,[status(thm)],[i_0_6713]),
[final] ).
cnf(i_0_11931,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4))),hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))),
inference(split_conjunct,[status(thm)],[i_0_6714]),
[final] ).
cnf(i_0_11932,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4))),hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)))),
inference(split_conjunct,[status(thm)],[i_0_6715]),
[final] ).
cnf(i_0_11933,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6716]),
[final] ).
cnf(i_0_11934,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk474_3(X2,X3,X1)),esk474_3(X2,X3,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olexord(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6717]),
[final] ).
cnf(i_0_11935,plain,
c_Finite__Set_Ofun__left__comm__idem(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_6718]),
[final] ).
cnf(i_0_11936,plain,
( c_Nitpick_Ofold__graph_H(X2,X7,X3,X6,X1,hAPP(hAPP(X3,X4),X5))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(X3,X4),X5) != X6 ),
inference(split_conjunct,[status(thm)],[i_0_6089]),
[final] ).
cnf(i_0_11937,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6719,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6169]),c_0_6169]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_11938,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6720]),
[final] ).
cnf(i_0_11939,plain,
( hAPP(X1,esk251_5(X1,X2,X3,X4,X5)) = c_Groups_Ozero__class_Ozero(X5)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
| ~ class_Fields_Ofield(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6473]),
[final] ).
cnf(i_0_11940,plain,
hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,X3),tc_prod(X1,X2)),X5),hAPP(hAPP(c_COMBB(X1,X4,tc_prod(X1,X2)),X6),c_Product__Type_Ofst(X1,X2)))),c_Product__Type_Osnd(X1,X2)) = hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,X3),X1),X5),X6)),
inference(split_conjunct,[status(thm)],[i_0_6721]),
[final] ).
cnf(i_0_11941,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk459_4(X1,X2,X3,X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olexord(X4,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6340]),
[final] ).
cnf(i_0_11942,plain,
( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X5),X3),c_List_Oremove1(X2,X3,X4)) = X4
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X4)))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X5),X4))
| hAPP(c_List_Ohd(X2),hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_fequal,hAPP(X5,X3))),X5)),X4)) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_6722]),
[final] ).
cnf(i_0_11943,plain,
c_Sum__Type_Osum_Osum__rec(X1,X2,X3,X4,X5,hAPP(c_Sum__Type_OInl(X1,X3),X6)) = hAPP(X4,X6),
inference(split_conjunct,[status(thm)],[i_0_6723]),
[final] ).
cnf(i_0_11944,plain,
c_Sum__Type_Osum_Osum__rec(X1,X2,X3,X4,X5,hAPP(c_Sum__Type_OInr(X3,X1),X6)) = hAPP(X5,X6),
inference(split_conjunct,[status(thm)],[i_0_6724]),
[final] ).
cnf(i_0_11945,plain,
( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),c_Int_Ointrel)) ),
inference(split_conjunct,[status(thm)],[i_0_6725]),
[final] ).
cnf(i_0_11946,plain,
( hAPP(X1,esk274_5(X2,X1,X3,X4,X5)) = hAPP(c_Option_Ooption_OSome(X5),X4)
| ~ hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Oran(X3,X5,c_Map_Orestrict__map(X3,X5,X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6482]),
[final] ).
cnf(i_0_11947,plain,
c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4),
inference(split_conjunct,[status(thm)],[i_0_6726]),
[final] ).
cnf(i_0_11948,plain,
c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4),
inference(split_conjunct,[status(thm)],[i_0_6727]),
[final] ).
cnf(i_0_11949,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(X4,X1,X2,hAPP(hAPP(c_Set_Oinsert(X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6728]),
[final] ).
cnf(i_0_11950,plain,
c_Product__Type_Omap__pair(X1,X1,X2,X2,c_Fun_Oid(X1),c_Fun_Oid(X2)) = c_Fun_Oid(tc_prod(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_6729]),
[final] ).
cnf(i_0_11951,plain,
c_Product__Type_Omap__pair(X1,X1,X2,X2,c_Fun_Oid(X1),c_Fun_Oid(X2)) = c_Fun_Oid(tc_prod(X1,X2)),
inference(rw,[status(thm)],[i_0_6730,c_0_6211]),
[final] ).
cnf(i_0_11952,plain,
c_Product__Type_Omap__pair(X1,X1,X2,X2,c_COMBI(X1),c_COMBI(X2)) = c_Fun_Oid(tc_prod(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_6731]),
[final] ).
cnf(i_0_11953,plain,
c_Product__Type_Omap__pair(X2,X2,X1,X1,c_Fun_Oid(X2),c_Fun_Oid(X1)) = c_Fun_Oid(tc_prod(X2,X1)),
inference(rw,[status(thm)],[i_0_6732,c_0_6029]),
[final] ).
cnf(i_0_11954,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X5,X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),X4)))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6733]),
[final] ).
cnf(i_0_11955,plain,
c_Divides_OnegateSnd = c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
inference(rw,[status(thm)],[i_0_6734,c_0_6029]),
[final] ).
cnf(i_0_11956,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6735]),
[final] ).
cnf(i_0_11957,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6716]),
[final] ).
cnf(i_0_11958,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X5),X3),X6)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X5),X4),X7)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X5),tc_HOL_Obool)),X6),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6736]),
[final] ).
cnf(i_0_11959,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6737]),
[final] ).
cnf(i_0_11960,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5)),X6))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6738]),
[final] ).
cnf(i_0_11961,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_Oimage(X2,X4,hAPP(hAPP(c_COMBB(X1,X4,X2),X5),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[i_0_6739]),
[final] ).
cnf(i_0_11962,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)))),
inference(split_conjunct,[status(thm)],[i_0_6740]),
[final] ).
cnf(i_0_11963,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6716]),
[final] ).
cnf(i_0_11964,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olists(X1,X3)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_List_Olist(X1)),c_List_Olists(X1,X3)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_6741]),
[final] ).
cnf(i_0_11965,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X4,c_Groups_Otimes__class_Otimes(X1)),X6),X7),hAPP(c_Set_Oimage(X2,X4,X5),X3)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Fun_Ocomp(X4,X1,X2,X6),X5)),X7),X3)
| ~ class_Groups_Oab__semigroup__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ c_Fun_Oinj__on(X2,X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6742]),
[final] ).
cnf(i_0_11966,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6743]),
[final] ).
cnf(i_0_11967,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olex(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X6) ),
inference(split_conjunct,[status(thm)],[i_0_6604]),
[final] ).
cnf(i_0_11968,plain,
( c_Map_Orestrict__map(X1,X3,c_Map_Omap__upds(X1,X3,X6,X2,X4),X5) = c_Map_Omap__upds(X1,X3,c_Map_Orestrict__map(X1,X3,X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(c_List_Oset(X1),X2))),X2,X4)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6744]),
[final] ).
cnf(i_0_11969,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk418_4(X2,X3,X4,X1)),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6745]),
[final] ).
cnf(i_0_11970,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk414_4(X2,X3,X4,X1)),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6746]),
[final] ).
cnf(i_0_11971,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk459_4(X1,X2,X3,X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2))))
| hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olexord(X4,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6340]),
[final] ).
cnf(i_0_11972,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6747,c_0_6053]),c_0_6062]),
[final] ).
cnf(i_0_11973,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6748]),
[final] ).
cnf(i_0_11974,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| X5 != X6 ),
inference(split_conjunct,[status(thm)],[i_0_6602]),
[final] ).
cnf(i_0_11975,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X5))),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6749]),
[final] ).
cnf(i_0_11976,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6603]),
[final] ).
cnf(i_0_11977,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6750,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_11978,plain,
( c_Groups_Oone__class_Oone(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6751,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_11979,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X5)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6676]),
[final] ).
cnf(i_0_11980,plain,
( hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,X1),c_List_Onth(X1)),X3)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_List_Otranspose(X1,X2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X3)
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6752]),
[final] ).
cnf(i_0_11981,plain,
c_Hilbert__Choice_OEps(tc_prod(X1,X2),X3) = c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))),
inference(split_conjunct,[status(thm)],[i_0_6753]),
[final] ).
cnf(i_0_11982,plain,
c_HOL_OThe(tc_prod(X1,X2),X3) = c_HOL_OThe(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))),
inference(split_conjunct,[status(thm)],[i_0_6754]),
[final] ).
cnf(i_0_11983,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSemi(X4,X6)),X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X6),X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_6755]),
[final] ).
cnf(i_0_11984,plain,
( c_Relation_Ototal__on(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk370_3(X2,X3,X1)),esk369_3(X2,X3,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6756]),
[final] ).
cnf(i_0_11985,plain,
( c_Relation_Ototal__on(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk369_3(X2,X3,X1)),esk370_3(X2,X3,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6756]),
[final] ).
cnf(i_0_11986,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4,X1))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6757]),
[final] ).
cnf(i_0_11987,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| c_Smallcheck_Osmall_H(X3,X1,X2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X3,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X3,X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X3),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6758]),
[final] ).
cnf(i_0_11988,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),c_Transitive__Closure_Ortrancl(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
| ~ c_Relation_Osingle__valued(X1,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6759]),
[final] ).
cnf(i_0_11989,plain,
( c_FunDef_Oreduction__pair(X1,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6760]),
[final] ).
cnf(i_0_11990,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6761]),
[final] ).
cnf(i_0_11991,plain,
c_Random_Oselect(X1,X2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X1),X2)),c_Code__Numeral_Onat__of))),
inference(split_conjunct,[status(thm)],[i_0_6762]),
[final] ).
cnf(i_0_11992,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X1,X2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6763]),
[final] ).
cnf(i_0_11993,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6764]),
[final] ).
cnf(i_0_11994,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6716]),
[final] ).
cnf(i_0_11995,plain,
c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X3),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_Option_Ooption(X3),tc_Option_Ooption(X2)),X1),c_Option_Omap(X3,X2)),X4)),X5)) = c_Map_Odom(X1,X3,X5),
inference(split_conjunct,[status(thm)],[i_0_6765]),
[final] ).
cnf(i_0_11996,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk233_4(X2,X3,X4,X1)),esk234_4(X2,X3,X4,X1)))
| ~ hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6550]),
[final] ).
cnf(i_0_11997,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5456]),
[final] ).
cnf(i_0_11998,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk358_4(X2,X3,X4,X1)),X4))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6366]),
[final] ).
cnf(i_0_11999,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk278_4(X2,X3,X4,X1)),X4))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6425]),
[final] ).
cnf(i_0_12000,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(rw,[status(thm)],[i_0_6766,c_0_6062]),
[final] ).
cnf(i_0_12001,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(rw,[status(thm)],[i_0_6767,c_0_6062]),
[final] ).
cnf(i_0_12002,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6768]),
[final] ).
cnf(i_0_12003,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6748]),
[final] ).
cnf(i_0_12004,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5456]),
[final] ).
cnf(i_0_12005,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5456]),
[final] ).
cnf(i_0_12006,plain,
hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_6769]),
[final] ).
cnf(i_0_12007,plain,
( c_Map_Omap__upds(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X6),X2),hAPP(c_Option_Ooption_OSome(X3),X7)),X5,X4) = c_Map_Omap__upds(X1,X3,X6,X5,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_6485]),
[final] ).
cnf(i_0_12008,plain,
( hBOOL(hAPP(hAPP(X1,X2),esk276_5(X3,X4,X1,X5,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X2),X4))
| ~ c_Wellfounded_Omax__extp(X5,X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6558]),
[final] ).
cnf(i_0_12009,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = hAPP(hAPP(c_HOL_OLet(X2,X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Otimes__class_Otimes(X2)),hAPP(c_Groups_Otimes__class_Otimes(X2),X3))),c_COMBI(X2)))
| ~ class_Int_Onumber__ring(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6770,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12010,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Groups_Omonoid__mult(X1)
| ~ class_Int_Onumber(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6771,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12011,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5456]),
[final] ).
cnf(i_0_12012,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(rw,[status(thm)],[i_0_6772,c_0_6062]),
[final] ).
cnf(i_0_12013,plain,
( c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X5)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5))),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4))) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6773]),
[final] ).
cnf(i_0_12014,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6774]),
[final] ).
cnf(i_0_12015,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk328_4(X4,X3,X2,X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6775]),
[final] ).
cnf(i_0_12016,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk327_4(X4,X3,X2,X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6776]),
[final] ).
cnf(i_0_12017,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3))),hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))),
inference(split_conjunct,[status(thm)],[i_0_6777]),
[final] ).
cnf(i_0_12018,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3)),X4)),X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6778]),
[final] ).
cnf(i_0_12019,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6779,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12020,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_Random_Opick(X2,X3),X1)),hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X2),X2),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X2)),X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X2),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2)),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_6780]),
[final] ).
cnf(i_0_12021,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X3)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6781]),
[final] ).
cnf(i_0_12022,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X3)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_5456]),
[final] ).
cnf(i_0_12023,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6781]),
[final] ).
cnf(i_0_12024,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5456]),
[final] ).
cnf(i_0_12025,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X6),X3),X7)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X6),X5),X8)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X6)),hAPP(hAPP(c_Product__Type_OPair(X2,X6),X4),X7)),X8)) ),
inference(split_conjunct,[status(thm)],[i_0_6782]),
[final] ).
cnf(i_0_12026,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olinorder__class_Oinsort__insert__key(X2,X1,X3,X5,X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6783]),
[final] ).
cnf(i_0_12027,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk136_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(hAPP(c_member(X1),esk135_4(X2,X3,X4,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(X2,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6784]),
[final] ).
cnf(i_0_12028,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6785,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12029,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk134_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(hAPP(c_member(X1),esk133_4(X2,X3,X4,X1)),X4))
| hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6786]),
[final] ).
cnf(i_0_12030,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6787,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12031,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6788,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12032,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(X2)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6789,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12033,plain,
( X1 = hAPP(c_Nat_OSuc,esk374_5(X2,X1,X3,X4,X5))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6223]),
[final] ).
cnf(i_0_12034,plain,
( X1 = hAPP(c_Nat_OSuc,esk372_5(X2,X1,X3,X4,X5))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6279]),
[final] ).
cnf(i_0_12035,plain,
( X1 = hAPP(c_Nat_OSuc,esk374_5(X2,X1,X3,X4,X5))
| X4 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6223]),
[final] ).
cnf(i_0_12036,plain,
( X1 = hAPP(c_Nat_OSuc,esk372_5(X2,X1,X3,X4,X5))
| X4 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6279]),
[final] ).
cnf(i_0_12037,plain,
( hBOOL(hAPP(hAPP(hAPP(X5,X8),X6),X7))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X8),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6077]),
[final] ).
cnf(i_0_12038,plain,
( hBOOL(hAPP(hAPP(hAPP(X5,X8),X6),X7))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X8),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6790]),
[final] ).
cnf(i_0_12039,plain,
( hBOOL(hAPP(hAPP(hAPP(X5,X8),X6),X7))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X8),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6791]),
[final] ).
cnf(i_0_12040,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6792,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12041,plain,
( c_Natural_Oevaln(c_Com_Ocom_OCall(X3,X5,X6),X2,X7,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X1),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,X1),c_Com_ORes)))
| hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X1),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,X1),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X4),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,X4),c_Com_ORes))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X5),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X6,X2)),X7,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6120]),
[final] ).
cnf(i_0_12042,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6793,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12043,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),X1)),c_Wellfounded_Omax__ext(X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6366]),
[final] ).
cnf(i_0_12044,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6794,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12045,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6795,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12046,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6366]),
[final] ).
cnf(i_0_12047,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Omax__ext(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6366]),
[final] ).
cnf(i_0_12048,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6796,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12049,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6797,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12050,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),c_Int_Ointrel))
| hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_6725]),
[final] ).
cnf(i_0_12051,plain,
hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6798,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12052,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X4)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5456]),
[final] ).
cnf(i_0_12053,plain,
( hAPP(hAPP(c_List_Otake(X1),esk459_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk459_4(X2,X3,X4,X1)),X3)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olexord(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6340]),
[final] ).
cnf(i_0_12054,plain,
( hBOOL(hAPP(hAPP(c_member(X6),X3),c_SetInterval_Oord_OatLeastLessThan(X6,X1,X4,X2,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6642]),
[final] ).
cnf(i_0_12055,plain,
( hBOOL(hAPP(hAPP(c_member(X6),X3),c_SetInterval_Oord_OgreaterThanAtMost(X6,X4,X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6643]),
[final] ).
cnf(i_0_12056,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X1),X5),X6),X7)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)),X6),hAPP(X4,X7)),
inference(split_conjunct,[status(thm)],[i_0_6799]),
[final] ).
cnf(i_0_12057,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Ofinite__psubset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6774]),
[final] ).
cnf(i_0_12058,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6800,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12059,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),X1),c_member(X2)),X3)),X4)),
inference(split_conjunct,[status(thm)],[i_0_6801]),
[final] ).
cnf(i_0_12060,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Oappend(X2),X4),X5)) = hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),X3)),X4)),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),X3)),X5)),
inference(split_conjunct,[status(thm)],[i_0_6802]),
[final] ).
cnf(i_0_12061,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk236_5(X1,X2,X3,X4,X5)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X1),X3)
| ~ c_Nat__Transfer_Onat__set(X3)
| X4 != X3
| ~ class_Groups_Ocomm__monoid__add(X5)
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6644]),
[final] ).
cnf(i_0_12062,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk131_5(X1,X2,X3,X4,X5)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X3)
| ~ c_Nat__Transfer_Onat__set(X3)
| X4 != X3
| ~ class_Groups_Ocomm__monoid__add(X5)
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6645]),
[final] ).
cnf(i_0_12063,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),hAPP(c_Relation_Oconverse(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,hAPP(c_Relation_Oconverse(X1,X1),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_6803]),
[final] ).
cnf(i_0_12064,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,hAPP(c_Relation_Oconverse(X1,X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),hAPP(c_Relation_Oconverse(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_6803]),
[final] ).
cnf(i_0_12065,plain,
c_List_Omap__filter(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X2),X2,c_List_Omap__filter(X1,X2,X3,X5),hAPP(hAPP(c_COMBC(X2,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olist_OCons(X2)),c_List_Omap__filter(X1,X2,X3,X5))),hAPP(X3,X4)),
inference(split_conjunct,[status(thm)],[i_0_6804]),
[final] ).
cnf(i_0_12066,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),esk458_5(X3,X4,X5,X2,X1)) = X4
| X2 = hAPP(hAPP(c_List_Oappend(X1),X4),esk457_5(X3,X4,X5,X2,X1))
| hAPP(hAPP(c_List_Oappend(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6573]),
[final] ).
cnf(i_0_12067,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk455_5(X3,X4,X1,X5,X2)),X3)
| hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1) = X3
| hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6805]),
[final] ).
cnf(i_0_12068,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk456_5(X2,X3,X4,X5,X1)),X4) = X2
| X4 = hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)
| hAPP(hAPP(c_List_Oappend(X1),X5),X4) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_6806]),
[final] ).
cnf(i_0_12069,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk442_4(X2,X3,X4,X1)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X4),X3))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel(X1,X2)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6085]),
[final] ).
cnf(i_0_12070,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk205_2(X2,X1)),esk206_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk205_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk206_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_6807]),
[final] ).
cnf(i_0_12071,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk203_2(X2,X1)),esk204_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk203_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk204_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_6808]),
[final] ).
cnf(i_0_12072,plain,
( c_Hoare__Mirabelle_Otriple__valid(X5,X4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(X1,esk200_4(X1,X2,X3,X4)),esk202_4(X1,X2,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6809]),
[final] ).
cnf(i_0_12073,plain,
c_Map_Omap__of(X1,X2,hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X2)),hAPP(hAPP(c_COMBS(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),X3)),X4)) = c_Map_Orestrict__map(X1,X2,hAPP(c_Fun_Ocomp(X2,tc_Option_Ooption(X2),X1,c_Option_Ooption_OSome(X2)),X3),hAPP(c_List_Oset(X1),X4)),
inference(split_conjunct,[status(thm)],[i_0_6810]),
[final] ).
cnf(i_0_12074,plain,
( hAPP(c_Finite__Set_Ocard(tc_prod(X4,X1)),hAPP(hAPP(c_Product__Type_OSigma(X4,X1),X3),X2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X1)),X2)),X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk288_4(X2,X1,X3,X4))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6811]),
[final] ).
cnf(i_0_12075,plain,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)),
inference(split_conjunct,[status(thm)],[i_0_6812]),
[final] ).
cnf(i_0_12076,plain,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)),
inference(split_conjunct,[status(thm)],[i_0_6813]),
[final] ).
cnf(i_0_12077,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X1,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6814]),
[final] ).
cnf(i_0_12078,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk456_5(X2,X3,X4,X5,X1)),X4) = X2
| X5 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X5),X4) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_6806]),
[final] ).
cnf(i_0_12079,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk455_5(X3,X4,X1,X5,X2)),X3)
| X4 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6805]),
[final] ).
cnf(i_0_12080,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),X2))
| ~ class_Groups_Oab__semigroup__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk300_2(X2,X1)),esk301_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk300_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk301_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_6815]),
[final] ).
cnf(i_0_12081,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2))),c_COMBI(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6816,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12082,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6817]),
[final] ).
cnf(i_0_12083,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6671]),
[final] ).
cnf(i_0_12084,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6818]),
[final] ).
cnf(i_0_12085,plain,
( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Olinorder__class_Oinsort__insert__key(X2,X1,X4,X5,X3)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6819]),
[final] ).
cnf(i_0_12086,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2))
| hAPP(X1,esk253_5(X1,X2,X3,X4,X5)) != c_Groups_Oone__class_Oone(X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6519]),
[final] ).
cnf(i_0_12087,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2))
| hAPP(X1,esk252_5(X1,X2,X3,X4,X5)) != c_Groups_Oone__class_Oone(X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6520]),
[final] ).
cnf(i_0_12088,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X2))
| hAPP(X1,esk255_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
| ~ class_Groups_Ocomm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6521]),
[final] ).
cnf(i_0_12089,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X2))
| hAPP(X1,esk254_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
| ~ class_Groups_Ocomm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6522]),
[final] ).
cnf(i_0_12090,plain,
( hAPP(hAPP(c_List_Onth(tc_List_Olist(X2)),c_List_Otranspose(X2,X3)),X1) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),X2),hAPP(hAPP(c_COMBC(tc_List_Olist(X2),tc_Nat_Onat,X2),c_List_Onth(X2)),X1)),hAPP(c_List_Ofilter(tc_List_Olist(X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X2)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Nat_Osize__class_Osize(tc_List_Olist(X2)))),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),c_List_Otranspose(X2,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_6820]),
[final] ).
cnf(i_0_12091,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_OPow(X1),X2)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6821]),
[final] ).
cnf(i_0_12092,plain,
( hAPP(hAPP(c_List_Otake(X1),esk459_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk459_4(X2,X3,X4,X1)),X3)
| hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),X3) = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olexord(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6340]),
[final] ).
cnf(i_0_12093,plain,
( hAPP(c_Finite__Set_Ocard(X1),X4) = hAPP(c_Finite__Set_Ocard(X2),X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))
| ~ c_Fun_Oinj__on(X2,X1,X6,X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X6),X5)),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6822]),
[final] ).
cnf(i_0_12094,plain,
c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)) = c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),tc_prod(X1,X2)),X3),c_Product__Type_Ofst(X1,X2))),c_Product__Type_Osnd(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_6823]),
[final] ).
cnf(i_0_12095,plain,
c_HOL_OThe(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)) = c_HOL_OThe(tc_prod(X1,X2),hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),tc_prod(X1,X2)),X3),c_Product__Type_Ofst(X1,X2))),c_Product__Type_Osnd(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_6824]),
[final] ).
cnf(i_0_12096,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X5))
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6825]),
[final] ).
cnf(i_0_12097,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X5))
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6826]),
[final] ).
cnf(i_0_12098,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6827]),
[final] ).
cnf(i_0_12099,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk462_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olistrel1(X4,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6373]),
[final] ).
cnf(i_0_12100,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_4(X1,X2,X3,X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6122]),
[final] ).
cnf(i_0_12101,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X4))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6828]),
[final] ).
cnf(i_0_12102,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6829,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_12103,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_Fun_Ocomp(X1,X1,X2,c_Groups_Ouminus__class_Ouminus(X1)),X3)),X4))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6830]),
[final] ).
cnf(i_0_12104,plain,
( hBOOL(hAPP(hAPP(c_member(X4),esk133_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,esk134_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6786]),
[final] ).
cnf(i_0_12105,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk134_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(X2,esk133_4(X2,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6786]),
[final] ).
cnf(i_0_12106,plain,
c_New__Random__Sequence_Oneg__map(X1,X2,X3,X4) = c_New__Random__Sequence_Oneg__bind(X1,X2,X4,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X1,c_New__Random__Sequence_Oneg__single(X2)),X3)),
inference(split_conjunct,[status(thm)],[i_0_6831]),
[final] ).
cnf(i_0_12107,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6832]),
[final] ).
cnf(i_0_12108,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6833]),
[final] ).
cnf(i_0_12109,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))),c_Groups_Ozero__class_Ozero(X2)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_6834]),
[final] ).
cnf(i_0_12110,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1))),c_Groups_Ozero__class_Ozero(X2)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_6834]),
[final] ).
cnf(i_0_12111,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),X2))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk257_2(X2,X1)),esk258_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk257_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk258_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_6835]),
[final] ).
cnf(i_0_12112,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk196_2(X2,X1)),esk197_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk196_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk197_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_6836]),
[final] ).
cnf(i_0_12113,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk194_2(X2,X1)),esk195_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk194_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk195_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_6837]),
[final] ).
cnf(i_0_12114,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),X2))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk192_2(X2,X1)),esk193_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk192_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk193_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_6838]),
[final] ).
cnf(i_0_12115,plain,
( ~ class_Rings_Olinordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6839]),
[final] ).
cnf(i_0_12116,plain,
( hAPP(hAPP(X5,X8),hAPP(c_Set_Oimage(X2,X2,X7),X6)) = hAPP(hAPP(X5,hAPP(c_Fun_Ocomp(X2,X1,X2,X8),X7)),X6)
| ~ c_Finite__Set_Ofolding__image(X1,X2,X3,X4,X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6))
| ~ c_Fun_Oinj__on(X2,X2,X7,X6) ),
inference(split_conjunct,[status(thm)],[i_0_6840]),
[final] ).
cnf(i_0_12117,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk418_4(X2,X3,X4,X1)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6745]),
[final] ).
cnf(i_0_12118,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk414_4(X2,X3,X4,X1)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6746]),
[final] ).
cnf(i_0_12119,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_List_Otranspose(X1,X2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X3))
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6841]),
[final] ).
cnf(i_0_12120,plain,
( hBOOL(hAPP(hAPP(c_member(X6),hAPP(hAPP(X7,X3),X4)),hAPP(c_Set_Oimage(tc_prod(X1,X2),X6,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X6),X7)),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6842]),
[final] ).
cnf(i_0_12121,plain,
( hAPP(c_Map_Omap__of(X1,X2,X5),X3) = hAPP(c_Option_Ooption_OSome(X2),esk439_5(X5,X4,X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6843]),
[final] ).
cnf(i_0_12122,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),hAPP(c_List_Ofilter(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4)),X5)),
inference(split_conjunct,[status(thm)],[i_0_6844]),
[final] ).
cnf(i_0_12123,plain,
( c_Smallcheck_Osmall_H(X3,X1,X2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X3),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6758]),
[final] ).
cnf(i_0_12124,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),hAPP(c_Relation_OField(X1),X2)),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_Relation_OField(X1),X2))))),
inference(rw,[status(thm)],[i_0_6845,c_0_6062]),
[final] ).
cnf(i_0_12125,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X5),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_6846]),
[final] ).
cnf(i_0_12126,plain,
( hBOOL(hAPP(hAPP(X3,X5),X6))
| hBOOL(hAPP(hAPP(X4,X5),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6847]),
[final] ).
cnf(i_0_12127,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)),X3))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3),
inference(split_conjunct,[status(thm)],[i_0_6848]),
[final] ).
cnf(i_0_12128,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6849]),
[final] ).
cnf(i_0_12129,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2)
| hAPP(X1,esk228_5(X1,X2,X3,X4,X5)) != c_Groups_Oone__class_Oone(X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6532]),
[final] ).
cnf(i_0_12130,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)
| hAPP(X1,esk227_5(X1,X2,X3,X4,X5)) != c_Groups_Oone__class_Oone(X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
| ~ class_Groups_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6533]),
[final] ).
cnf(i_0_12131,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X3)
| hAPP(X1,esk230_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
| ~ class_Groups_Ocomm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6534]),
[final] ).
cnf(i_0_12132,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X2)
| hAPP(X1,esk229_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
| ~ class_Groups_Ocomm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_6535]),
[final] ).
cnf(i_0_12133,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(hAPP(c_Relation_Orel__comp(X3,X3,X3),X4),c_Transitive__Closure_Ortrancl(X3,X4)))) ),
inference(rw,[status(thm)],[i_0_6850,c_0_6062]),
[final] ).
cnf(i_0_12134,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))) ),
inference(rw,[status(thm)],[i_0_6851,c_0_6062]),
[final] ).
cnf(i_0_12135,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X3)),
inference(split_conjunct,[status(thm)],[i_0_6852]),
[final] ).
cnf(i_0_12136,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X3)),
inference(split_conjunct,[status(thm)],[i_0_6853]),
[final] ).
cnf(i_0_12137,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6854]),
[final] ).
cnf(i_0_12138,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6854]),
[final] ).
cnf(i_0_12139,plain,
( hBOOL(hAPP(hAPP(X3,X5),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6855]),
[final] ).
cnf(i_0_12140,plain,
( hBOOL(hAPP(hAPP(X4,X5),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6856]),
[final] ).
cnf(i_0_12141,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk492_3(X2,X3,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2))))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)
| hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) != hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6857,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_12142,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk491_3(X3,X2,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3))))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)
| hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) != hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6858,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_12143,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6859,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12144,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6860,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12145,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6861,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12146,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6862,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12147,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X5))),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X5))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6703]),
[final] ).
cnf(i_0_12148,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6863]),
[final] ).
cnf(i_0_12149,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6864]),
[final] ).
cnf(i_0_12150,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6865]),
[final] ).
cnf(i_0_12151,plain,
( hAPP(c_Fun_Ocomp(X5,X6,X7,X8),hAPP(c_Fun_Ocomp(X9,X5,X7,X10),X11)) = hAPP(c_Fun_Ocomp(X9,X6,X7,hAPP(c_Fun_Ocomp(X5,X6,X9,X8),X10)),X11)
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6866]),
[final] ).
cnf(i_0_12152,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6867]),
[final] ).
cnf(i_0_12153,plain,
hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(split_conjunct,[status(thm)],[i_0_6868]),
[final] ).
cnf(i_0_12154,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6869]),
[final] ).
cnf(i_0_12155,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6870]),
[final] ).
cnf(i_0_12156,plain,
hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(c_List_Ofilter(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4)),X5)),
inference(split_conjunct,[status(thm)],[i_0_6871]),
[final] ).
cnf(i_0_12157,plain,
( c_Wellfounded_OwfP(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Predicate_ODomainP(X1,X1,hAPP(X2,esk343_3(X3,X2,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X2,esk344_3(X3,X2,X1)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Wellfounded_OwfP(X1,hAPP(X2,esk342_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6872]),
[final] ).
cnf(i_0_12158,plain,
c_List_Opartition(X1,X2,X3) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot),X2)),X3)),
inference(split_conjunct,[status(thm)],[i_0_6873]),
[final] ).
cnf(i_0_12159,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk147_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk148_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk147_3(X1,X2,X3)),esk148_3(X1,X2,X3)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6874]),
[final] ).
cnf(i_0_12160,plain,
c_Map_Omap__add(X1,X2,X3,c_Map_Omap__upds(X1,X2,X4,X5,X6)) = c_Map_Omap__upds(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5,X6),
inference(split_conjunct,[status(thm)],[i_0_6875]),
[final] ).
cnf(i_0_12161,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X1),X2)),c_Transitive__Closure_Ortrancl(X1,X2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
inference(rw,[status(thm)],[i_0_6876,c_0_6062]),
[final] ).
cnf(i_0_12162,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6877]),
[final] ).
cnf(i_0_12163,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6870]),
[final] ).
cnf(i_0_12164,plain,
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,esk134_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(X1,esk133_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6786]),
[final] ).
cnf(i_0_12165,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3),
inference(split_conjunct,[status(thm)],[i_0_6878]),
[final] ).
cnf(i_0_12166,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4))),X5)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6879]),
[final] ).
cnf(i_0_12167,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X5)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))))
| c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6728]),
[final] ).
cnf(i_0_12168,plain,
( X1 = hAPP(hAPP(c_List_Olist__update(X2,X3),esk462_4(X4,X1,X3,X2)),esk461_4(X4,X1,X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X1)),c_List_Olistrel1(X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6373]),
[final] ).
cnf(i_0_12169,plain,
( hBOOL(hAPP(X1,esk136_4(X1,X2,X3,X4)))
| hBOOL(hAPP(hAPP(c_member(X4),esk135_4(X1,X2,X3,X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))
| ~ hBOOL(hAPP(X1,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6784]),
[final] ).
cnf(i_0_12170,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk136_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(X2,esk135_4(X2,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(X2,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6784]),
[final] ).
cnf(i_0_12171,plain,
c_Map_Odom(X1,X2,c_Map_Omap__upds(X1,X2,X3,X4,X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)),X4))),c_Map_Odom(X1,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_6880]),
[final] ).
cnf(i_0_12172,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)) = hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2)),
inference(rw,[status(thm)],[i_0_6881,c_0_6070]),
[final] ).
cnf(i_0_12173,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk368_3(X3,X2,X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))) ),
inference(rw,[status(thm)],[i_0_6882,c_0_6062]),
[final] ).
cnf(i_0_12174,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X2),X1)),c_List_Olexord(X4,X3)))
| X2 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X1),X2)),c_List_Olexord(X4,X3)))
| esk472_4(X1,X2,X3,X4) != esk473_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6386]),
[final] ).
cnf(i_0_12175,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6716]),
[final] ).
cnf(i_0_12176,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),hAPP(c_List_Oset(X2),X3)),X4) = hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4)),c_Orderings_Otop__class_Otop(X1)),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6883]),
[final] ).
cnf(i_0_12177,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),hAPP(c_List_Oset(X2),X3)),X4) = hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__sup__class_Osup(X1)),X4)),c_Orderings_Obot__class_Obot(X1)),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6884]),
[final] ).
cnf(i_0_12178,plain,
hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Oappend(tc_List_Olist(X1)),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6885,c_0_6100]),c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_12179,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X3),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk340_4(X2,X1,X3,X4))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6886]),
[final] ).
cnf(i_0_12180,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X3),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk161_4(X2,X1,X3,X4))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6887]),
[final] ).
cnf(i_0_12181,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X6),X7)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X6),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(tc_prod(X1,X3),tc_HOL_Obool),X5),hAPP(c_Relation_Orel__comp(X1,X2,X3),X4)),X7)),
inference(split_conjunct,[status(thm)],[i_0_6888]),
[final] ).
cnf(i_0_12182,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4),hAPP(c_Fun_Ocomp(X5,X1,X3,X6),X7)) = hAPP(c_Fun_Ocomp(X5,X2,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6)),X7),
inference(split_conjunct,[status(thm)],[i_0_6889]),
[final] ).
cnf(i_0_12183,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X4))))
| hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6890]),
[final] ).
cnf(i_0_12184,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6748]),
[final] ).
cnf(i_0_12185,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X4)),hAPP(hAPP(c_Relation_Oinv__image(X1,X6),X5),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,X3)),hAPP(X2,X4))),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6891]),
[final] ).
cnf(i_0_12186,plain,
( hAPP(X4,X5) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(X3,X6))
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6892]),
[final] ).
cnf(i_0_12187,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,X3),X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_6893]),
[final] ).
cnf(i_0_12188,plain,
hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1),X1,hAPP(c_List_Otl(X1),X3),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1)),X3))),X2),
inference(split_conjunct,[status(thm)],[i_0_6894]),
[final] ).
cnf(i_0_12189,plain,
c_New__Random__Sequence_Opos__map(X1,X2,X3,X4) = c_New__Random__Sequence_Opos__bind(X1,X2,X4,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X1,c_New__Random__Sequence_Opos__single(X2)),X3)),
inference(split_conjunct,[status(thm)],[i_0_6895]),
[final] ).
cnf(i_0_12190,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X4))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4))))
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_6896]),
[final] ).
cnf(i_0_12191,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk454_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olistrel(X4,X1)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_6272]),
[final] ).
cnf(i_0_12192,plain,
( hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X6),X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(X3,X6))
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6897]),
[final] ).
cnf(i_0_12193,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),hAPP(hAPP(c_List_Onth(X1),X2),X4)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X4),X3)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6898]),
[final] ).
cnf(i_0_12194,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4))),hAPP(c_Finite__Set_Ocard(X2),X4)))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6899]),
[final] ).
cnf(i_0_12195,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk288_4(X2,X3,X4,X1)),X4))
| hAPP(c_Finite__Set_Ocard(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X4),X2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X3)),X2)),X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6811]),
[final] ).
cnf(i_0_12196,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X2,X6,X5)),X3),hAPP(hAPP(hAPP(c_Natural_Oupdate,X1),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2))))
| hAPP(hAPP(hAPP(c_Natural_Oupdate,X1),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,X4),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X5),hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),c_Com_Ovname_OLoc(X2)),hAPP(X6,X3))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6505]),
[final] ).
cnf(i_0_12197,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(rw,[status(thm)],[i_0_6900,c_0_6062]),
[final] ).
cnf(i_0_12198,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(rw,[status(thm)],[i_0_6901,c_0_6062]),
[final] ).
cnf(i_0_12199,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X6)),hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X5)),X8)) = hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X5)),hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X6)),X8))
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6902]),
[final] ).
cnf(i_0_12200,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X6,X2)),hAPP(X6,X3))),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(X4,X1),X5),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6891]),
[final] ).
cnf(i_0_12201,plain,
( hAPP(c_Map_Omap__of(X1,X2,X3),X4) = hAPP(c_Option_Ooption_OSome(X2),X5)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6903]),
[final] ).
cnf(i_0_12202,plain,
( hAPP(c_Map_Omap__of(X1,X2,X5),X3) = hAPP(c_Option_Ooption_OSome(X2),X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),X5)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6904]),
[final] ).
cnf(i_0_12203,plain,
( hAPP(c_Option_Ooption_OSome(X2),X4) = hAPP(c_Map_Omap__of(X1,X2,X5),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),X5)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6905]),
[final] ).
cnf(i_0_12204,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk77_4(X2,X3,X4,X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_4(X2,X3,X4,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6122]),
[final] ).
cnf(i_0_12205,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk76_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6122]),
[final] ).
cnf(i_0_12206,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X1)),hAPP(hAPP(c_Product__Type_OSigma(X4,X1),X3),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk285_4(X2,X1,X3,X4))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6906]),
[final] ).
cnf(i_0_12207,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4))),X3))
| ~ class_Rings_Olinordered__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),X6) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6907]),
[final] ).
cnf(i_0_12208,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4))),X3))
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),X6) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6908]),
[final] ).
cnf(i_0_12209,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk170_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6909]),
[final] ).
cnf(i_0_12210,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Wellfounded_Omax__extp(X1,X4,X5,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,esk277_4(X3,X5,X4,X1)),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6558]),
[final] ).
cnf(i_0_12211,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X3,X7)),hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X4,X5)),X8)) = hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X4,X5)),hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X3,X7)),X8))
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6910]),
[final] ).
cnf(i_0_12212,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X8)),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| X5 != hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X7))
| X8 != hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6911]),
[final] ).
cnf(i_0_12213,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(rw,[status(thm)],[i_0_6912,c_0_6062]),
[final] ).
cnf(i_0_12214,plain,
( X1 = X2
| c_Sum__Type_Osum_Osum__case(X3,X4,X5,X1,X6) != c_Sum__Type_Osum_Osum__case(X3,X4,X5,X2,X7) ),
inference(split_conjunct,[status(thm)],[i_0_6913]),
[final] ).
cnf(i_0_12215,plain,
( X1 = X2
| c_Sum__Type_Osum_Osum__case(X3,X4,X5,X6,X1) != c_Sum__Type_Osum_Osum__case(X3,X4,X5,X7,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6913]),
[final] ).
cnf(i_0_12216,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X3)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(cn,[status(thm)],[i_0_6914]),
[final] ).
cnf(i_0_12217,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(cn,[status(thm)],[i_0_6915]),
[final] ).
cnf(i_0_12218,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk417_4(X2,X3,X4,X1)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2),X4)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6916]),
[final] ).
cnf(i_0_12219,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk415_4(X2,X3,X4,X1)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X2),X4)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6917]),
[final] ).
cnf(i_0_12220,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6774]),
[final] ).
cnf(i_0_12221,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X4))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6918]),
[final] ).
cnf(i_0_12222,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6919]),
[final] ).
cnf(i_0_12223,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6919]),
[final] ).
cnf(i_0_12224,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X7)),X8)) = hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X7)),hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),X8))
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6920]),
[final] ).
cnf(i_0_12225,plain,
( X1 = hAPP(c_Set_Oimage(X2,X3,X4),esk127_5(X5,X4,X2,X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X2,X3,X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6527]),
[final] ).
cnf(i_0_12226,plain,
( X1 = hAPP(X2,esk266_5(X1,X2,X3,X4,X5))
| hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_Set_Oimage(X4,X3,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| X1 != hAPP(X2,X5)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_6921]),
[final] ).
cnf(i_0_12227,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)))
| ~ class_Groups_Oab__group__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6922]),
[final] ).
cnf(i_0_12228,plain,
( hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)) = hAPP(hAPP(c_List_Olist__update(X2,hAPP(c_List_Orev(X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6923]),
[final] ).
cnf(i_0_12229,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(X2),esk256_4(X1,X3,X4,X2))))
| ~ c_Equiv__Relations_Oequiv(X2,X4,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6924]),
[final] ).
cnf(i_0_12230,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
| c_Groups_Oone__class_Oone(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6925,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12231,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6926,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12232,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X2)),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2))),hAPP(c_Set_OCollect(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_6927]),
[final] ).
cnf(i_0_12233,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6928]),
[final] ).
cnf(i_0_12234,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6929]),
[final] ).
cnf(i_0_12235,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk378_3(X3,X2,X1)),esk380_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6930]),
[final] ).
cnf(i_0_12236,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk378_3(X3,X2,X1)),esk379_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6930]),
[final] ).
cnf(i_0_12237,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk320_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk320_2(X2,X1),X3))),X2))
| c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6428]),
[final] ).
cnf(i_0_12238,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6931]),
[final] ).
cnf(i_0_12239,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6932]),
[final] ).
cnf(i_0_12240,plain,
c_Product__Type_Oprod_Oprod__size(X1,X2,X3,X4,X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X3,hAPP(c_Product__Type_Ofst(X1,X2),X5))),hAPP(X4,hAPP(c_Product__Type_Osnd(X1,X2),X5)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_6933]),
[final] ).
cnf(i_0_12241,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X4))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6934]),
[final] ).
cnf(i_0_12242,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk172_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6935]),
[final] ).
cnf(i_0_12243,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6936]),
[final] ).
cnf(i_0_12244,plain,
( X4 = X5
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X7),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X6),X7)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6937]),
[final] ).
cnf(i_0_12245,plain,
( X5 = X6
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))
| ~ c_Equiv__Relations_Oequiv(X1,X7,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6938]),
[final] ).
cnf(i_0_12246,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk66_3(X2,X3,X1)),X3)),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6939]),
[final] ).
cnf(i_0_12247,plain,
( hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,tc_HOL_Obool,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6940]),
[final] ).
cnf(i_0_12248,plain,
( hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,tc_HOL_Obool,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6941]),
[final] ).
cnf(i_0_12249,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Set_Ovimage(X1,X2,X3)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_Oinsert(X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_6942]),
[final] ).
cnf(i_0_12250,plain,
hAPP(c_Relation_OImage(X1,X2,X3),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Relation_OImage(X1,X2,X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_6943]),
[final] ).
cnf(i_0_12251,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk171_4(X1,X2,X3,X4)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6909]),
[final] ).
cnf(i_0_12252,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6944]),
[final] ).
cnf(i_0_12253,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6945]),
[final] ).
cnf(i_0_12254,plain,
( c_Map_Omap__of(X1,X2,X3) = c_Map_Omap__of(X1,X2,X4)
| hAPP(c_List_Oset(tc_prod(X1,X2)),X3) != hAPP(c_List_Oset(tc_prod(X1,X2)),X4)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6946]),
[final] ).
cnf(i_0_12255,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X8,tc_HOL_Obool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6090]),
[final] ).
cnf(i_0_12256,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X8,tc_HOL_Obool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6947]),
[final] ).
cnf(i_0_12257,plain,
( hAPP(c_List_Oset(tc_prod(X1,X2)),X3) = hAPP(c_List_Oset(tc_prod(X1,X2)),X4)
| c_Map_Omap__of(X1,X2,X3) != c_Map_Omap__of(X1,X2,X4)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6946]),
[final] ).
cnf(i_0_12258,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X3)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6781]),
[final] ).
cnf(i_0_12259,plain,
( hBOOL(hAPP(hAPP(hAPP(X4,X5),X6),X7))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_6948]),
[final] ).
cnf(i_0_12260,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6928]),
[final] ).
cnf(i_0_12261,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6929]),
[final] ).
cnf(i_0_12262,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X4),X5)),X6) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X6)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X5),X6)),
inference(split_conjunct,[status(thm)],[i_0_6949]),
[final] ).
cnf(i_0_12263,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X5)) = hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X5)),X4),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6950]),
[final] ).
cnf(i_0_12264,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X5)) = hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__sup__class_Osup(X1)),X5)),X4),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6951]),
[final] ).
cnf(i_0_12265,plain,
( X1 = X2
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X1),X6)),X2),X7) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X7)),X1),X6) ),
inference(split_conjunct,[status(thm)],[i_0_6952]),
[final] ).
cnf(i_0_12266,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6953]),
[final] ).
cnf(i_0_12267,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6954]),
[final] ).
cnf(i_0_12268,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6955]),
[final] ).
cnf(i_0_12269,plain,
( hAPP(c_Set_Oimage(X2,X1,esk267_4(X5,X2,X1,X4)),X5) = X4
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6585]),
[final] ).
cnf(i_0_12270,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_5456]),
[final] ).
cnf(i_0_12271,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6956]),
[final] ).
cnf(i_0_12272,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6957]),
[final] ).
cnf(i_0_12273,plain,
( c_Map_Omap__upds(X1,X4,X6,X2,hAPP(hAPP(c_List_Olist__update(X4,X5),X3),X7)) = c_Map_Omap__upds(X1,X4,X6,X2,X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6958]),
[final] ).
cnf(i_0_12274,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))
| ~ c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_6959]),
[final] ).
cnf(i_0_12275,plain,
( hBOOL(hAPP(c_Predicate_OPowp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6821]),
[final] ).
cnf(i_0_12276,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X5),X4))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(X2,X1,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6773]),
[final] ).
cnf(i_0_12277,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))),X3))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6960]),
[final] ).
cnf(i_0_12278,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6))),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X6))
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6825]),
[final] ).
cnf(i_0_12279,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6))),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X6))
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6826]),
[final] ).
cnf(i_0_12280,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6961]),
[final] ).
cnf(i_0_12281,plain,
( hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(c_fequal,X2))),X1)) = hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6962]),
[final] ).
cnf(i_0_12282,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk417_4(X3,X2,X4,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6916]),
[final] ).
cnf(i_0_12283,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk415_4(X3,X2,X4,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6917]),
[final] ).
cnf(i_0_12284,plain,
hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3) = hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),hAPP(hAPP(c_List_Otake(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),
inference(rw,[status(thm)],[i_0_6963,c_0_6670]),
[final] ).
cnf(i_0_12285,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk173_4(X1,X2,X3,X4)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6935]),
[final] ).
cnf(i_0_12286,plain,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
inference(rw,[status(thm)],[i_0_6964,c_0_6062]),
[final] ).
cnf(i_0_12287,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_6965]),
[final] ).
cnf(i_0_12288,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(c_List_Oset(tc_prod(X1,X4)),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X6)))) ),
inference(split_conjunct,[status(thm)],[i_0_6966]),
[final] ).
cnf(i_0_12289,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X1)),hAPP(hAPP(c_Product__Type_OPair(X4,X1),X5),X2)),hAPP(c_List_Oset(tc_prod(X4,X1)),hAPP(hAPP(c_List_Ozip(X4,X1),X6),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_6966]),
[final] ).
cnf(i_0_12290,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6)))) ),
inference(split_conjunct,[status(thm)],[i_0_6967]),
[final] ).
cnf(i_0_12291,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6)))) ),
inference(split_conjunct,[status(thm)],[i_0_6968]),
[final] ).
cnf(i_0_12292,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X6))),hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6))) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6969]),
[final] ).
cnf(i_0_12293,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6931]),
[final] ).
cnf(i_0_12294,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6932]),
[final] ).
cnf(i_0_12295,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6970]),
[final] ).
cnf(i_0_12296,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6971]),
[final] ).
cnf(i_0_12297,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))
| c_Map_Omap__add(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X5),X2),hAPP(c_Option_Ooption_OSome(X3),X6)),X4) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__add(X1,X3,X5,X4)),X2),hAPP(c_Option_Ooption_OSome(X3),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6972]),
[final] ).
cnf(i_0_12298,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X4) = hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4)),c_Orderings_Otop__class_Otop(X1)),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6973]),
[final] ).
cnf(i_0_12299,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X4) = hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__sup__class_Osup(X1)),X4)),c_Orderings_Obot__class_Obot(X1)),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6974]),
[final] ).
cnf(i_0_12300,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6975]),
[final] ).
cnf(i_0_12301,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6976]),
[final] ).
cnf(i_0_12302,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6977,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_12303,plain,
( X5 = X6
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6978]),
[final] ).
cnf(i_0_12304,plain,
( X5 = X6
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6930]),
[final] ).
cnf(i_0_12305,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X3,X4,X1)),X2),hAPP(hAPP(hAPP(c_Natural_Oupdate,X5),c_Com_Ovname_OLoc(X3)),hAPP(hAPP(c_Natural_Ogetlocs,X2),X3))))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),hAPP(hAPP(hAPP(c_Natural_Oupdate,X2),c_Com_Ovname_OLoc(X3)),hAPP(X4,X2))),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6979]),
[final] ).
cnf(i_0_12306,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X2)),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),hAPP(c_Set_OCollect(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_6980]),
[final] ).
cnf(i_0_12307,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),hAPP(c_Set_OCollect(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_6981]),
[final] ).
cnf(i_0_12308,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk419_3(X3,X1,X4))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ c_Wellfounded_Owf(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6982]),
[final] ).
cnf(i_0_12309,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6983,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12310,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6984,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12311,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6985,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12312,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6986,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12313,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6781]),
[final] ).
cnf(i_0_12314,plain,
( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,X3)),X2),c_Option_Ooption_ONone(X4)) = c_Map_Orestrict__map(X1,X4,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6987]),
[final] ).
cnf(i_0_12315,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk294_3(X2,X3,X1)),X2))
| c_Relation_Orefl__on(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_6624]),
[final] ).
cnf(i_0_12316,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk293_3(X2,X3,X1)),X3))
| c_Relation_Orefl__on(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_6625]),
[final] ).
cnf(i_0_12317,plain,
( hBOOL(hAPP(hAPP(X1,esk200_4(X2,X3,X1,X4)),esk201_4(X2,X3,X1,X4)))
| c_Hoare__Mirabelle_Otriple__valid(X5,X4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6809]),
[final] ).
cnf(i_0_12318,plain,
( hBOOL(hAPP(X1,X2))
| hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(c_fequal,X2))),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6962]),
[final] ).
cnf(i_0_12319,plain,
c_Nitpick_Oint__lcm(X1,X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))))),
inference(rw,[status(thm)],[i_0_6988,c_0_6989]),
[final] ).
cnf(i_0_12320,plain,
hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X6),hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))) = hAPP(hAPP(X3,X4),hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X6),hAPP(c_List_Orev(X1),X5))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6990,c_0_6070]),c_0_6070]),
[final] ).
cnf(i_0_12321,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X4,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6331]),
[final] ).
cnf(i_0_12322,plain,
c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
inference(split_conjunct,[status(thm)],[fact_pred__nat__def]),
[final] ).
cnf(i_0_12323,plain,
( hAPP(c_Map_Omap__of(X1,X4,hAPP(hAPP(c_List_Ozip(X1,X4),X3),X5)),X2) = hAPP(c_Option_Ooption_OSome(X4),esk441_5(X2,X5,X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5) ),
inference(split_conjunct,[status(thm)],[i_0_6991]),
[final] ).
cnf(i_0_12324,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_6992]),
[final] ).
cnf(i_0_12325,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6993]),
[final] ).
cnf(i_0_12326,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6994]),
[final] ).
cnf(i_0_12327,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1),X3)),X4)),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6995]),
[final] ).
cnf(i_0_12328,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,X3),X5)),hAPP(c_Relation_OImage(X1,X2,X4),X6)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6996]),
[final] ).
cnf(i_0_12329,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_12330,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6998]),
[final] ).
cnf(i_0_12331,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6999]),
[final] ).
cnf(i_0_12332,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7000]),
[final] ).
cnf(i_0_12333,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),hAPP(hAPP(c_Relation_Orel__comp(X2,X2,X2),X4),c_Transitive__Closure_Ortrancl(X2,X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X4))) ),
inference(rw,[status(thm)],[i_0_7001,c_0_6062]),
[final] ).
cnf(i_0_12334,plain,
hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1)))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))) = hAPP(hAPP(c_Product__Type_OSigma(X2,X1),X4),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_7002]),
[final] ).
cnf(i_0_12335,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),c_Int_OMin))),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7003,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6169]),c_0_6169]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12336,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7004]),
[final] ).
cnf(i_0_12337,plain,
( hAPP(X1,esk77_4(X2,X1,X3,X4)) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_4(X2,X1,X3,X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6122]),
[final] ).
cnf(i_0_12338,plain,
( c_Natural_Oevaln(c_Com_Ocom_OCall(X6,X1,X3),X2,X4,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X5),hAPP(c_Natural_Ogetlocs,X2))),X6),hAPP(hAPP(c_Natural_Ogetlocs,X5),c_Com_ORes)))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X3,X2)),X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7005]),
[final] ).
cnf(i_0_12339,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_OImage(X3,X1,X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_7006]),
[final] ).
cnf(i_0_12340,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_12341,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(c_List_Oset(tc_prod(X3,X3)),hAPP(hAPP(c_List_Ozip(X3,X3),X4),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_6965]),
[final] ).
cnf(i_0_12342,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk88_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk89_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk89_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7007]),
[final] ).
cnf(i_0_12343,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk180_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7008]),
[final] ).
cnf(i_0_12344,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))),c_Divides_Odiv__class_Omod(X1,X3,X2))),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7009]),
[final] ).
cnf(i_0_12345,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_Set_Oimage(X4,X3,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| esk266_5(X1,X2,X3,X4,X5) != X5
| X1 != hAPP(X2,X5)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_6921]),
[final] ).
cnf(i_0_12346,plain,
c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X6),X7)) = c_Map_Omap__upds(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X6)),X5,X7),
inference(split_conjunct,[status(thm)],[i_0_7010]),
[final] ).
cnf(i_0_12347,plain,
( X2 = hAPP(hAPP(c_List_Olist_OCons(X1),esk469_3(X3,X2,X1)),esk470_3(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olexord(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7011]),
[final] ).
cnf(i_0_12348,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_Set_Ovimage(X2,X1,X3),X4))),X4)),
inference(split_conjunct,[status(thm)],[i_0_7012]),
[final] ).
cnf(i_0_12349,plain,
( X4 = X5
| ~ class_Orderings_Olinorder(X1)
| ~ c_Fun_Oinj__on(X2,X1,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_List_Oset(X2),X4)),hAPP(c_List_Oset(X2),X5)))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5)))
| hAPP(c_List_Oset(X2),X4) != hAPP(c_List_Oset(X2),X5) ),
inference(split_conjunct,[status(thm)],[i_0_7013]),
[final] ).
cnf(i_0_12350,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))
| hAPP(c_Map_Omap__of(X1,X2,X3),X4) != hAPP(c_Option_Ooption_OSome(X2),X5)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6904]),
[final] ).
cnf(i_0_12351,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),hAPP(c_List_Oset(tc_prod(X3,X1)),X4)))
| hAPP(c_Option_Ooption_OSome(X1),X2) != hAPP(c_Map_Omap__of(X3,X1,X4),X5)
| ~ hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(tc_prod(X3,X1),X3),c_Product__Type_Ofst(X3,X1)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6905]),
[final] ).
cnf(i_0_12352,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk26_5(X3,X4,X5,X2,X1),X4,X3)
| ~ hBOOL(hAPP(X1,X5))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X5,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7014]),
[final] ).
cnf(i_0_12353,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk10_5(X3,X4,X5,X2,X1),X4,X3)
| ~ hBOOL(hAPP(X1,X5))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X5,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7015]),
[final] ).
cnf(i_0_12354,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7016]),
[final] ).
cnf(i_0_12355,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_7017]),
[final] ).
cnf(i_0_12356,plain,
( hBOOL(hAPP(X1,esk136_4(X1,X2,X3,X4)))
| hBOOL(hAPP(X1,esk135_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))
| ~ hBOOL(hAPP(X1,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6784]),
[final] ).
cnf(i_0_12357,plain,
hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Oappend(X2),X5),X6)) = hAPP(c_List_Ofoldl(X1,X2,X3,hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5)),X6),
inference(split_conjunct,[status(thm)],[i_0_7018]),
[final] ).
cnf(i_0_12358,plain,
( c_Natural_Oevaln(X1,X2,X3,esk26_5(X4,X3,X2,X1,X5))
| ~ hBOOL(hAPP(X5,X2))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7014]),
[final] ).
cnf(i_0_12359,plain,
( c_Natural_Oevaln(X1,X2,X3,esk10_5(X4,X3,X2,X1,X5))
| ~ hBOOL(hAPP(X5,X2))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7015]),
[final] ).
cnf(i_0_12360,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7019]),
[final] ).
cnf(i_0_12361,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)),X5) = hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X5))),hAPP(hAPP(c_List_Ozip(X1,X2),X4),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X5))),
inference(split_conjunct,[status(thm)],[i_0_7020]),
[final] ).
cnf(i_0_12362,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk26_5(X3,X4,X5,X2,X1),X4,X3)
| X3 = X5
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X5,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7014]),
[final] ).
cnf(i_0_12363,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk10_5(X3,X4,X5,X2,X1),X4,X3)
| X3 = X5
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X5,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7015]),
[final] ).
cnf(i_0_12364,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7021]),
[final] ).
cnf(i_0_12365,plain,
( c_Natural_Oevaln(X1,X2,X3,esk26_5(X4,X3,X2,X1,X5))
| X4 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7014]),
[final] ).
cnf(i_0_12366,plain,
( c_Natural_Oevaln(X1,X2,X3,esk10_5(X4,X3,X2,X1,X5))
| X4 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7015]),
[final] ).
cnf(i_0_12367,plain,
( c_Natural_Oevaln(X1,esk6_5(X2,X3,X4,X1,X5),X3,X2)
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X5,X1),X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7022]),
[final] ).
cnf(i_0_12368,plain,
( c_Natural_Oevaln(X1,esk4_5(X2,X3,X4,X1,X5),X3,X2)
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X5,X1),X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7023]),
[final] ).
cnf(i_0_12369,plain,
( c_Natural_Oevaln(X1,X2,X3,esk6_5(X4,X3,X2,X5,X1))
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7022]),
[final] ).
cnf(i_0_12370,plain,
( c_Natural_Oevaln(X1,X2,X3,esk4_5(X4,X3,X2,X5,X1))
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7023]),
[final] ).
cnf(i_0_12371,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))) ),
inference(rw,[status(thm)],[i_0_7024,c_0_6062]),
[final] ).
cnf(i_0_12372,plain,
( X1 = hAPP(c_Relation_OImage(X2,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),esk242_4(X3,X4,X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7025]),
[final] ).
cnf(i_0_12373,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X2,X1)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7026,c_0_7027]),c_0_7027]),
[final] ).
cnf(i_0_12374,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7028,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12375,plain,
c_Map_Omap__add(X1,X2,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X4),X5),hAPP(c_Option_Ooption_OSome(X2),X6))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__add(X1,X2,X3,X4)),X5),hAPP(c_Option_Ooption_OSome(X2),X6)),
inference(split_conjunct,[status(thm)],[i_0_7029]),
[final] ).
cnf(i_0_12376,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6999]),
[final] ).
cnf(i_0_12377,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7000]),
[final] ).
cnf(i_0_12378,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk107_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7030]),
[final] ).
cnf(i_0_12379,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk113_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7031]),
[final] ).
cnf(i_0_12380,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk171_4(X2,X3,X4,X1)),esk170_4(X2,X3,X4,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6909]),
[final] ).
cnf(i_0_12381,plain,
( hAPP(hAPP(c_List_Oappend(X1),X3),X4) = hAPP(hAPP(c_List_Oappend(X1),X2),X5)
| hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3) != X2
| hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4) != X5
| X3 != hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)
| X4 != hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)),X5) ),
inference(split_conjunct,[status(thm)],[i_0_7032]),
[final] ).
cnf(i_0_12382,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7033]),
[final] ).
cnf(i_0_12383,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7034]),
[final] ).
cnf(i_0_12384,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7035]),
[final] ).
cnf(i_0_12385,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7036,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12386,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OPls)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7037,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12387,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OPls)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7038,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12388,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7039,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12389,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7040,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12390,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X6,tc_HOL_Obool))),X1),X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7041]),
[final] ).
cnf(i_0_12391,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_OImage(X1,X2,X5),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7006]),
[final] ).
cnf(i_0_12392,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5)))
| hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7042]),
[final] ).
cnf(i_0_12393,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk186_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7043]),
[final] ).
cnf(i_0_12394,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X5))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7044]),
[final] ).
cnf(i_0_12395,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))
| ~ c_Equiv__Relations_Oequiv(X3,X7,X6) ),
inference(split_conjunct,[status(thm)],[i_0_6938]),
[final] ).
cnf(i_0_12396,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X1),tc_HOL_Obool),X3),c_Relation_Oconverse(X1,X2)),X5)),
inference(split_conjunct,[status(thm)],[i_0_7045]),
[final] ).
cnf(i_0_12397,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X1),tc_HOL_Obool),X3),c_Relation_Oconverse(X1,X2)),X5)),
inference(split_conjunct,[status(thm)],[i_0_7046]),
[final] ).
cnf(i_0_12398,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5))),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6879]),
[final] ).
cnf(i_0_12399,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk422_3(X2,X1,X3)),X3)),X2))
| c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk420_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6982]),
[final] ).
cnf(i_0_12400,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))),c_Groups_Ozero__class_Ozero(X2)))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_6834]),
[final] ).
cnf(i_0_12401,plain,
X1 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk238_1(X1)),esk239_1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_7047]),
[final] ).
cnf(i_0_12402,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk167_4(X2,X3,X1,X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7048]),
[final] ).
cnf(i_0_12403,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk181_4(X1,X2,X3,X4)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7008]),
[final] ).
cnf(i_0_12404,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7049]),
[final] ).
cnf(i_0_12405,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(c_Fun_Ocomp(X4,tc_fun(X2,X3),X1,X5),X6)),X7) = hAPP(hAPP(X5,hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X2),X7))),hAPP(c_Product__Type_Osnd(X1,X2),X7)),
inference(split_conjunct,[status(thm)],[i_0_7050]),
[final] ).
cnf(i_0_12406,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
| ~ class_Rings_Olinordered__idom(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7051,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12407,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
| ~ class_Rings_Olinordered__idom(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7052,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12408,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7053]),
[final] ).
cnf(i_0_12409,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7054]),
[final] ).
cnf(i_0_12410,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk330_4(X2,X3,X4,X1)),X4))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6160]),
[final] ).
cnf(i_0_12411,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X2,c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)) = c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_Set_Oimage(X1,X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk217_3(X3,X2,X1)),esk218_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk217_3(X3,X2,X1))),hAPP(X2,esk218_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7055]),
[final] ).
cnf(i_0_12412,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X2,c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)) = c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_Oimage(X1,X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk215_3(X3,X2,X1)),esk216_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk215_3(X3,X2,X1))),hAPP(X2,esk216_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7056]),
[final] ).
cnf(i_0_12413,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6877]),
[final] ).
cnf(i_0_12414,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X5))
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7057]),
[final] ).
cnf(i_0_12415,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7058,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12416,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7059,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12417,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7060,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12418,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7061,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12419,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7062]),
[final] ).
cnf(i_0_12420,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7063]),
[final] ).
cnf(i_0_12421,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7049]),
[final] ).
cnf(i_0_12422,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_Relation_Oconverse(X2,X1),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7064]),
[final] ).
cnf(i_0_12423,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_Relation_Oconverse(X2,X1),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7065]),
[final] ).
cnf(i_0_12424,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk340_4(X2,X3,X4,X1)),X4))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X4),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6886]),
[final] ).
cnf(i_0_12425,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk161_4(X2,X3,X4,X1)),X4))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X4),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6887]),
[final] ).
cnf(i_0_12426,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7066]),
[final] ).
cnf(i_0_12427,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7067]),
[final] ).
cnf(i_0_12428,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7068]),
[final] ).
cnf(i_0_12429,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7067]),
[final] ).
cnf(i_0_12430,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7069]),
[final] ).
cnf(i_0_12431,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7070]),
[final] ).
cnf(i_0_12432,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7071]),
[final] ).
cnf(i_0_12433,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X2,hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3)) = hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Set_Oimage(X1,X1,X2),X3))
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk302_3(X3,X2,X1)),esk303_3(X3,X2,X1))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,esk302_3(X3,X2,X1))),hAPP(X2,esk303_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7072]),
[final] ).
cnf(i_0_12434,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(c_Set_Oimage(X2,X2,X4),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_Fun_Ocomp(X2,X1,X2,X5),X4)),X3)
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ c_Fun_Oinj__on(X2,X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7073]),
[final] ).
cnf(i_0_12435,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(c_Set_Oimage(X2,X2,X4),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_Fun_Ocomp(X2,X1,X2,X5),X4)),X3)
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ c_Fun_Oinj__on(X2,X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7074]),
[final] ).
cnf(i_0_12436,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk354_3(X2,X3,X1)),X3)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7075]),
[final] ).
cnf(i_0_12437,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk353_3(X2,X3,X1)),X3)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7076]),
[final] ).
cnf(i_0_12438,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk275_3(X2,X3,X1)),X3)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7077]),
[final] ).
cnf(i_0_12439,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7078]),
[final] ).
cnf(i_0_12440,plain,
hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4),X5) = c_Nat_Onat_Onat__case(tc_List_Olist(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_List_Olist(X1),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X1),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X1,tc_List_Olist(X1)),c_List_Olist__update(X1,X3)),X5)),X4),
inference(split_conjunct,[status(thm)],[i_0_7079]),
[final] ).
cnf(i_0_12441,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk477_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X1,X3,X4)),c_List_Olist_Olist__size(X1,X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6551]),
[final] ).
cnf(i_0_12442,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X1,X2),X3,X2),X4)),c_Product__Type_OPair(X1,X2))) = X4,
inference(split_conjunct,[status(thm)],[i_0_7080]),
[final] ).
cnf(i_0_12443,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk105_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7081]),
[final] ).
cnf(i_0_12444,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk115_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7082]),
[final] ).
cnf(i_0_12445,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk173_4(X2,X3,X4,X1)),esk172_4(X2,X3,X4,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6935]),
[final] ).
cnf(i_0_12446,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
| c_Partial__Function_Oflat__lub(X1,X3,X2) = c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_7083]),
[final] ).
cnf(i_0_12447,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk137_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3))
| ~ hBOOL(hAPP(X2,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6784]),
[final] ).
cnf(i_0_12448,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk137_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ hBOOL(hAPP(X2,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6784]),
[final] ).
cnf(i_0_12449,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk478_4(X1,X2,X3,X4)),X4))
| hAPP(hAPP(c_List_Otake(X3),X4),X2) = hAPP(hAPP(c_List_Otake(X3),X4),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7084]),
[final] ).
cnf(i_0_12450,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7085]),
[final] ).
cnf(i_0_12451,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[fact_One__int__def]),
[final] ).
cnf(i_0_12452,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[fact_Zero__int__def]),
[final] ).
cnf(i_0_12453,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(c_Product__Type_Osnd(X4,X5),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X3),X2))),hAPP(c_Product__Type_Ofst(X4,X5),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X3),X2))))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7086]),
[final] ).
cnf(i_0_12454,plain,
( c_Fun_Oinj__on(X3,X2,X4,hAPP(c_Set_Oimage(X1,X3,X5),X6))
| ~ c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6)
| ~ c_Fun_Oinj__on(X1,X3,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_7087]),
[final] ).
cnf(i_0_12455,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk242_4(X2,X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7025]),
[final] ).
cnf(i_0_12456,plain,
( hAPP(c_Set_Oimage(X1,X4,hAPP(c_Fun_Ocomp(X2,X4,X1,X5),X3)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X2,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7088]),
[final] ).
cnf(i_0_12457,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk77_4(X2,X3,X4,X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk76_4(X2,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6122]),
[final] ).
cnf(i_0_12458,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_7089]),
[final] ).
cnf(i_0_12459,plain,
( hBOOL(hAPP(X4,X2))
| hBOOL(hAPP(hAPP(c_member(X1),esk132_4(X4,X3,X5,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6786]),
[final] ).
cnf(i_0_12460,plain,
( hBOOL(hAPP(X4,X2))
| hBOOL(hAPP(hAPP(c_member(X1),esk132_4(X4,X5,X3,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6786]),
[final] ).
cnf(i_0_12461,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X1),X6),hAPP(c_Set_Oimage(X2,X3,X4),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_Fun_Ocomp(X3,X1,X2,X6),X4)),X5)
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ c_Fun_Oinj__on(X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7090]),
[final] ).
cnf(i_0_12462,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X6),hAPP(c_Set_Oimage(X2,X3,X4),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_Fun_Ocomp(X3,X1,X2,X6),X4)),X5)
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ c_Fun_Oinj__on(X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7091]),
[final] ).
cnf(i_0_12463,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7092]),
[final] ).
cnf(i_0_12464,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7093]),
[final] ).
cnf(i_0_12465,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk233_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6550]),
[final] ).
cnf(i_0_12466,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk114_4(X1,X2,X3,X4)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7031]),
[final] ).
cnf(i_0_12467,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk108_4(X1,X2,X3,X4)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7030]),
[final] ).
cnf(i_0_12468,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),hAPP(c_List_Olexn(X1,X5),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7094]),
[final] ).
cnf(i_0_12469,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X2)),hAPP(c_List_Olexn(X1,X5),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7094]),
[final] ).
cnf(i_0_12470,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6928]),
[final] ).
cnf(i_0_12471,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6929]),
[final] ).
cnf(i_0_12472,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),hAPP(c_Relation_Oconverse(X1,X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7064]),
[final] ).
cnf(i_0_12473,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),hAPP(c_Relation_Oconverse(X1,X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7095]),
[final] ).
cnf(i_0_12474,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk25_4(X3,X4,X2,X1)),X3))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7096]),
[final] ).
cnf(i_0_12475,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk12_4(X3,X4,X2,X1)),X3))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7097]),
[final] ).
cnf(i_0_12476,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X6)),
inference(split_conjunct,[status(thm)],[i_0_7098]),
[final] ).
cnf(i_0_12477,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X4)),hAPP(c_Finite__Set_Ocard(X2),X5)))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6575]),
[final] ).
cnf(i_0_12478,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7099,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12479,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk187_4(X1,X2,X3,X4)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7043]),
[final] ).
cnf(i_0_12480,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_7100]),
[final] ).
cnf(i_0_12481,plain,
( c_List_Otranspose(X1,c_List_Otranspose(X1,X2)) = c_List_OtakeWhile(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1))),X2)
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7101]),
[final] ).
cnf(i_0_12482,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X2,c_Big__Operators_Olattice__class_OInf__fin(X1,X3)) = c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))
| ~ class_Lattices_Olattice(X1)
| hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk261_3(X3,X2,X1)),esk262_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,esk261_3(X3,X2,X1))),hAPP(X2,esk262_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7102]),
[final] ).
cnf(i_0_12483,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X2,c_Big__Operators_Olinorder__class_OMin(X1,X3)) = c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk221_3(X3,X2,X1)),esk222_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk221_3(X3,X2,X1))),hAPP(X2,esk222_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7103]),
[final] ).
cnf(i_0_12484,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X2,c_Big__Operators_Olinorder__class_OMax(X1,X3)) = c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))
| ~ class_Orderings_Olinorder(X1)
| hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk219_3(X3,X2,X1)),esk220_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk219_3(X3,X2,X1))),hAPP(X2,esk220_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7104]),
[final] ).
cnf(i_0_12485,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X2,c_Big__Operators_Olattice__class_OSup__fin(X1,X3)) = c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))
| ~ class_Lattices_Olattice(X1)
| hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk225_3(X3,X2,X1)),esk226_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,esk225_3(X3,X2,X1))),hAPP(X2,esk226_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7105]),
[final] ).
cnf(i_0_12486,plain,
( hBOOL(hAPP(X3,esk112_2(X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,esk109_2(X3,X2)))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X3,X2)),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7106]),
[final] ).
cnf(i_0_12487,plain,
( X2 = c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7107]),
[final] ).
cnf(i_0_12488,plain,
c_Set_Othe__elem(X1,X2) = c_HOL_OThe(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),hAPP(c_fequal,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_7108]),
[final] ).
cnf(i_0_12489,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6931]),
[final] ).
cnf(i_0_12490,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6932]),
[final] ).
cnf(i_0_12491,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk375_2(X2,X1)),esk375_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
inference(rw,[status(thm)],[i_0_7109,c_0_6062]),
[final] ).
cnf(i_0_12492,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk365_2(X2,X1)),esk365_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
inference(rw,[status(thm)],[i_0_7110,c_0_6062]),
[final] ).
cnf(i_0_12493,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel1(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_7111]),
[final] ).
cnf(i_0_12494,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olex(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_7112]),
[final] ).
cnf(i_0_12495,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk256_4(X2,X3,X4,X1)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(X1),X4)))
| ~ c_Equiv__Relations_Oequiv(X1,X4,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6924]),
[final] ).
cnf(i_0_12496,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7021]),
[final] ).
cnf(i_0_12497,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
| ~ c_Nat__Transfer_Onat__set(X2)
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7113]),
[final] ).
cnf(i_0_12498,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
| ~ c_Nat__Transfer_Onat__set(X2)
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7114]),
[final] ).
cnf(i_0_12499,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk25_4(X3,X4,X2,X1)),X3))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7096]),
[final] ).
cnf(i_0_12500,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk12_4(X3,X4,X2,X1)),X3))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7097]),
[final] ).
cnf(i_0_12501,plain,
( hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X4)),X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7115]),
[final] ).
cnf(i_0_12502,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_7116]),
[final] ).
cnf(i_0_12503,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7117]),
[final] ).
cnf(i_0_12504,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7118]),
[final] ).
cnf(i_0_12505,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4),X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7119]),
[final] ).
cnf(i_0_12506,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X4),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7120]),
[final] ).
cnf(i_0_12507,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6999]),
[final] ).
cnf(i_0_12508,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6999]),
[final] ).
cnf(i_0_12509,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7000]),
[final] ).
cnf(i_0_12510,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7000]),
[final] ).
cnf(i_0_12511,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X5),X4))),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7121]),
[final] ).
cnf(i_0_12512,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X5))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X5))))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_7122]),
[final] ).
cnf(i_0_12513,plain,
( hAPP(c_Set_Oimage(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X4),X5),X2),X6)),X3) = hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(c_Set_Oimage(X1,X4,X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7123]),
[final] ).
cnf(i_0_12514,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),
inference(split_conjunct,[status(thm)],[i_0_7124]),
[final] ).
cnf(i_0_12515,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),
inference(split_conjunct,[status(thm)],[i_0_7125]),
[final] ).
cnf(i_0_12516,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))),
inference(split_conjunct,[status(thm)],[i_0_7126]),
[final] ).
cnf(i_0_12517,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X4)),hAPP(c_Finite__Set_Ocard(X2),X5)))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7127]),
[final] ).
cnf(i_0_12518,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk355_4(X2,X3,X1,X4)),X3))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X1,c_Groups_Otimes__class_Otimes(X4)),X2),c_Groups_Oone__class_Oone(X4)),X3) = c_Groups_Oone__class_Oone(X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Ocomm__monoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[i_0_7128]),
[final] ).
cnf(i_0_12519,plain,
c_Sum__Type_Osum_Osum__case(X1,X2,X3,hAPP(hAPP(c_COMBB(tc_sum(X1,X3),X2,X1),X4),c_Sum__Type_OInl(X1,X3)),hAPP(hAPP(c_COMBB(tc_sum(X1,X3),X2,X3),X4),c_Sum__Type_OInr(X3,X1))) = X4,
inference(split_conjunct,[status(thm)],[i_0_7129]),
[final] ).
cnf(i_0_12520,plain,
hAPP(c_Sum__Type_Osum_Osum__case(X1,X2,X3,hAPP(c_COMBK(X2,X1),X4),hAPP(c_COMBK(X2,X3),X4)),X5) = X4,
inference(split_conjunct,[status(thm)],[i_0_7130]),
[final] ).
cnf(i_0_12521,plain,
( hAPP(c_Map_Omap__of(X1,X2,hAPP(c_List_Ofilter(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X6)),X3)),X4) = hAPP(c_Option_Ooption_OSome(X2),X5)
| hAPP(c_Map_Omap__of(X1,X2,X3),X4) != hAPP(c_Option_Ooption_OSome(X2),X5)
| ~ hBOOL(hAPP(hAPP(X6,X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7131]),
[final] ).
cnf(i_0_12522,plain,
( X2 = c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7132]),
[final] ).
cnf(i_0_12523,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,X1),X1,X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1),X5)),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),X1,X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3)),hAPP(c_COMBC(X2,X4,X1),X6)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7133]),
[final] ).
cnf(i_0_12524,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,X1),X1,X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1),X5)),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),X1,X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3)),hAPP(c_COMBC(X2,X4,X1),X6)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7134]),
[final] ).
cnf(i_0_12525,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olistrel1(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_7135]),
[final] ).
cnf(i_0_12526,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olexord(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_7136]),
[final] ).
cnf(i_0_12527,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olex(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_7137]),
[final] ).
cnf(i_0_12528,plain,
( hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7138]),
[final] ).
cnf(i_0_12529,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk213_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),X2),X3) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X1),c_Int_Onat),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7139]),
[final] ).
cnf(i_0_12530,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk169_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),X2),X3) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X1),c_Int_Onat),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7140]),
[final] ).
cnf(i_0_12531,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7141]),
[final] ).
cnf(i_0_12532,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6272]),
[final] ).
cnf(i_0_12533,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7142]),
[final] ).
cnf(i_0_12534,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6085]),
[final] ).
cnf(i_0_12535,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6870]),
[final] ).
cnf(i_0_12536,plain,
( hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_List_Orev(X1),X3)))
| ~ class_Groups_Omonoid__add(X1) ),
inference(rw,[status(thm)],[i_0_7143,c_0_6070]),
[final] ).
cnf(i_0_12537,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
| hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_6340]),
[final] ).
cnf(i_0_12538,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) ),
inference(rw,[status(thm)],[i_0_7144,c_0_6053]),
[final] ).
cnf(i_0_12539,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6928]),
[final] ).
cnf(i_0_12540,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6929]),
[final] ).
cnf(i_0_12541,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7062]),
[final] ).
cnf(i_0_12542,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7063]),
[final] ).
cnf(i_0_12543,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2)),X4)),
inference(split_conjunct,[status(thm)],[i_0_7145]),
[final] ).
cnf(i_0_12544,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk184_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| X4 = X2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3) != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7146]),
[final] ).
cnf(i_0_12545,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk182_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| X4 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3) != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7147]),
[final] ).
cnf(i_0_12546,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk455_5(X3,X4,X5,X2,X1)) = X4
| hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) = X3
| hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6805]),
[final] ).
cnf(i_0_12547,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk456_5(X4,X3,X5,X1,X2))
| X5 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
| hAPP(hAPP(c_List_Oappend(X2),X1),X5) != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_6806]),
[final] ).
cnf(i_0_12548,plain,
hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X5) = c_HOL_OThe(X2,c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5)),
inference(split_conjunct,[status(thm)],[i_0_7148]),
[final] ).
cnf(i_0_12549,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk86_3(X3,X2,X1)),esk87_3(X3,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_7149]),
[final] ).
cnf(i_0_12550,plain,
( hAPP(c_Map_Omap__of(X1,X2,X3),X4) != c_Option_Ooption_ONone(X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_7150]),
[final] ).
cnf(i_0_12551,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X2,X3,tc_HOL_Obool,X1),X4),X5))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7151]),
[final] ).
cnf(i_0_12552,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk116_4(X1,X2,X3,X4)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7082]),
[final] ).
cnf(i_0_12553,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk106_4(X1,X2,X3,X4)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7081]),
[final] ).
cnf(i_0_12554,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk285_4(X2,X3,X4,X1)),X4))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X4),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6906]),
[final] ).
cnf(i_0_12555,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7152]),
[final] ).
cnf(i_0_12556,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk410_4(X2,X3,X1,X4)),X4))
| c_Fun_Oinj__on(X1,X3,X2,c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7153]),
[final] ).
cnf(i_0_12557,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X5),X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_6959]),
[final] ).
cnf(i_0_12558,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7154,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12559,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk111_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk109_2(X1,X2)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X1,X2)),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7106]),
[final] ).
cnf(i_0_12560,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7155,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12561,plain,
( c_Nitpick_Orefl_H(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk175_2(X2,X1)),esk175_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7156]),
[final] ).
cnf(i_0_12562,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk69_3(X2,X1,X3)),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7157]),
[final] ).
cnf(i_0_12563,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk65_3(X2,X1,X3)),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7158]),
[final] ).
cnf(i_0_12564,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk455_5(X3,X4,X5,X2,X1)) = X4
| X4 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_6805]),
[final] ).
cnf(i_0_12565,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk456_5(X4,X3,X5,X1,X2))
| X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),X1),X5) != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_6806]),
[final] ).
cnf(i_0_12566,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7159,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12567,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),X7)) = hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),X7)
| ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7160]),
[final] ).
cnf(i_0_12568,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X7,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OPair(X6,X7),X4),X5))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7161]),
[final] ).
cnf(i_0_12569,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| hAPP(c_Map_Omap__upds(X1,X4,X5,X3,X6),X2) = hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7162]),
[final] ).
cnf(i_0_12570,plain,
hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))) = c_List_Oset__Cons(X1,hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_7163]),
[final] ).
cnf(i_0_12571,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat),X3),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X4))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))),X3),
inference(split_conjunct,[status(thm)],[i_0_7164]),
[final] ).
cnf(i_0_12572,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7165,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12573,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7166,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12574,plain,
( c_Map_Omap__upds(X1,X3,X5,hAPP(hAPP(c_List_Oappend(X1),X2),X6),X4) = c_Map_Omap__upds(X1,X3,X5,X2,X4)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_7167]),
[final] ).
cnf(i_0_12575,plain,
( c_Map_Omap__upds(X1,X3,X5,X2,hAPP(hAPP(c_List_Oappend(X3),X4),X6)) = c_Map_Omap__upds(X1,X3,X5,X2,X4)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_7168]),
[final] ).
cnf(i_0_12576,plain,
( X1 = hAPP(c_Option_Ooption_OSome(X2),esk437_5(X3,X1,X4,X5,X2))
| hAPP(hAPP(c_Option_Omap(X2,X5),X4),X1) != hAPP(c_Option_Ooption_OSome(X5),X3) ),
inference(split_conjunct,[status(thm)],[i_0_7169]),
[final] ).
cnf(i_0_12577,plain,
( hAPP(c_Fun_Ooverride__on(X1,X4,X5,X6,X3),X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7170]),
[final] ).
cnf(i_0_12578,plain,
( hAPP(c_Fun_Ooverride__on(X1,X4,X5,X6,X3),X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7171]),
[final] ).
cnf(i_0_12579,plain,
( hAPP(X1,esk437_5(X2,X3,X1,X4,X5)) = X2
| hAPP(hAPP(c_Option_Omap(X5,X4),X1),X3) != hAPP(c_Option_Ooption_OSome(X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_7169]),
[final] ).
cnf(i_0_12580,plain,
c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),X5)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X5)),X4),hAPP(X3,X4)),
inference(split_conjunct,[status(thm)],[i_0_7172]),
[final] ).
cnf(i_0_12581,plain,
( c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X2,X1)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(rw,[status(thm)],[i_0_7173,c_0_7027]),
[final] ).
cnf(i_0_12582,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X5),hAPP(hAPP(c_List_Oappend(X2),X5),X1))),c_List_Olexord(X2,X6)))
| X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_7174]),
[final] ).
cnf(i_0_12583,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,X3)),X2),c_Option_Ooption_ONone(X4)) = c_Map_Orestrict__map(X1,X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6987]),
[final] ).
cnf(i_0_12584,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X4))))
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[i_0_7175]),
[final] ).
cnf(i_0_12585,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk147_3(X1,X2,X3)),esk148_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6874]),
[final] ).
cnf(i_0_12586,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk88_3(X1,X2,X3)),esk89_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7007]),
[final] ).
cnf(i_0_12587,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk83_3(X1,X2,X3)),esk84_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5289]),
[final] ).
cnf(i_0_12588,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk81_3(X1,X2,X3)),esk82_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5286]),
[final] ).
cnf(i_0_12589,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk90_3(X1,X2,X3)),esk91_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7176]),
[final] ).
cnf(i_0_12590,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),hAPP(c_Set_Oimage(X1,X2,X3),X4)))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7177]),
[final] ).
cnf(i_0_12591,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),esk5_4(X2,X3,X1,X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X4,X1)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7178]),
[final] ).
cnf(i_0_12592,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),esk2_4(X2,X3,X1,X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X4,X1)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7179]),
[final] ).
cnf(i_0_12593,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),hAPP(c_Set_Oimage(X1,X2,X3),X6))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7180]),
[final] ).
cnf(i_0_12594,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),hAPP(c_Set_Oimage(X1,X2,X3),X6))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7181]),
[final] ).
cnf(i_0_12595,plain,
( hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3)))),X2) = c_List_Osublist(X1,X2,X3)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7182]),
[final] ).
cnf(i_0_12596,plain,
hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5) = hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(c_COMBC(X1,X2,X1),X3)),X4),hAPP(c_List_Orev(X2),hAPP(c_List_Orev(X2),X5))),
inference(rw,[status(thm)],[i_0_7183,c_0_6070]),
[final] ).
cnf(i_0_12597,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk368_3(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),X2),hAPP(hAPP(c_Relation_Orel__comp(X3,X3,X3),X1),c_Transitive__Closure_Ortrancl(X3,X1)))) ),
inference(rw,[status(thm)],[i_0_7184,c_0_6062]),
[final] ).
cnf(i_0_12598,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Int_Oint),X1),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X3),c_Int_Onat),X1)),X2))
| ~ c_Nat__Transfer_Ois__nat(hAPP(X1,esk213_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7139]),
[final] ).
cnf(i_0_12599,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Int_Oint),X1),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X3),c_Int_Onat),X1)),X2))
| ~ c_Nat__Transfer_Ois__nat(hAPP(X1,esk169_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7140]),
[final] ).
cnf(i_0_12600,plain,
( hAPP(c_Set_Oimage(X1,X1,X3),X2) = X2
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X1,X3),X2)),X2))
| ~ c_Fun_Oinj__on(X1,X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7185]),
[final] ).
cnf(i_0_12601,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Fun_Ooverride__on(X1,X4,X5,X6,X3),X2) = hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7170]),
[final] ).
cnf(i_0_12602,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Fun_Ooverride__on(X1,X4,X5,X6,X3),X2) = hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7186]),
[final] ).
cnf(i_0_12603,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6999]),
[final] ).
cnf(i_0_12604,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7000]),
[final] ).
cnf(i_0_12605,plain,
( c_List_Olinorder__class_Oinsort__insert__key(X4,X1,X2,X3,X5) = X5
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(c_List_Oset(X4),X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_7187]),
[final] ).
cnf(i_0_12606,plain,
( hAPP(c_List_Oset(X1),c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7188]),
[final] ).
cnf(i_0_12607,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk334_4(X2,X3,X4,X1)),X3))
| c_Equiv__Relations_Ocongruent(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6184]),
[final] ).
cnf(i_0_12608,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_12609,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,X2)),c_List_Olistrel(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
| ~ c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_7189]),
[final] ).
cnf(i_0_12610,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7190,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12611,plain,
( hAPP(hAPP(X3,X4),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,X6),X4),X7),X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ c_Big__Operators_Ocomm__monoid__big(X5,X1,X6,X7,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7191]),
[final] ).
cnf(i_0_12612,plain,
( hAPP(hAPP(X5,X7),X6) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X7),X4),X6)
| ~ c_Finite__Set_Ofolding__image(X1,X2,X3,X4,X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_7192]),
[final] ).
cnf(i_0_12613,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X4) = hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7193]),
[final] ).
cnf(i_0_12614,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk337_4(X2,X3,X1,X4)),X3))
| c_Hoare__Mirabelle_Otriple__valid(X1,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X5),X2))
| ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7194]),
[final] ).
cnf(i_0_12615,plain,
hAPP(c_Sum__Type_Osum_Osum__case(X1,X2,X3,X4,X5),hAPP(c_Sum__Type_OInl(X1,X3),X6)) = hAPP(X4,X6),
inference(split_conjunct,[status(thm)],[i_0_7195]),
[final] ).
cnf(i_0_12616,plain,
hAPP(c_Sum__Type_Osum_Osum__case(X1,X2,X3,X4,X5),hAPP(c_Sum__Type_OInr(X3,X1),X6)) = hAPP(X5,X6),
inference(split_conjunct,[status(thm)],[i_0_7196]),
[final] ).
cnf(i_0_12617,plain,
( hAPP(hAPP(c_List_Otake(X1),X4),X2) = hAPP(hAPP(c_List_Otake(X1),X4),X3)
| hAPP(hAPP(c_List_Onth(X1),X2),esk478_4(X3,X2,X1,X4)) != hAPP(hAPP(c_List_Onth(X1),X3),esk478_4(X3,X2,X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7084]),
[final] ).
cnf(i_0_12618,plain,
( X4 = X5
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X3))
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6756]),
[final] ).
cnf(i_0_12619,plain,
hAPP(c_Set_Ovimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6) = hAPP(c_Set_Ovimage(X1,X3,X5),hAPP(c_Set_Ovimage(X3,X2,X4),X6)),
inference(split_conjunct,[status(thm)],[i_0_7197]),
[final] ).
cnf(i_0_12620,plain,
hAPP(c_Set_Oimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6) = hAPP(c_Set_Oimage(X3,X2,X4),hAPP(c_Set_Oimage(X1,X3,X5),X6)),
inference(split_conjunct,[status(thm)],[i_0_7198]),
[final] ).
cnf(i_0_12621,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk367_3(X3,X2,X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7199]),
[final] ).
cnf(i_0_12622,plain,
hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),X6),X7) = hAPP(hAPP(X6,hAPP(c_Product__Type_Ofst(X2,X3),hAPP(X5,X7))),hAPP(c_Product__Type_Osnd(X2,X3),hAPP(X5,X7))),
inference(split_conjunct,[status(thm)],[i_0_7200]),
[final] ).
cnf(i_0_12623,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7201]),
[final] ).
cnf(i_0_12624,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7138]),
[final] ).
cnf(i_0_12625,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk277_4(X2,X3,X4,X1)),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Wellfounded_Omax__extp(X1,X4,X3,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6558]),
[final] ).
cnf(i_0_12626,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7202]),
[final] ).
cnf(i_0_12627,plain,
c_Transitive__Closure_Ortrancl(X1,X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_7203]),
[final] ).
cnf(i_0_12628,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_12629,plain,
( c_Fun_Oinj__on(X3,X2,X4,hAPP(c_Set_Oimage(X1,X3,X5),X6))
| ~ c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6) ),
inference(split_conjunct,[status(thm)],[i_0_7204]),
[final] ).
cnf(i_0_12630,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk158_4(X2,X3,X1,X4)),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| hAPP(X2,X4) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7205]),
[final] ).
cnf(i_0_12631,plain,
( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X3,X2))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7206]),
[final] ).
cnf(i_0_12632,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk185_4(X1,X2,X3,X4)),X1))
| X4 = X2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3) != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7146]),
[final] ).
cnf(i_0_12633,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk183_4(X1,X2,X3,X4)),X1))
| X4 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3) != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7147]),
[final] ).
cnf(i_0_12634,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7207]),
[final] ).
cnf(i_0_12635,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_12636,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6931]),
[final] ).
cnf(i_0_12637,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6932]),
[final] ).
cnf(i_0_12638,plain,
( esk91_3(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(X1,esk91_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk90_3(X1,X2,X3),esk91_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7176]),
[final] ).
cnf(i_0_12639,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),X4)) = hAPP(hAPP(X3,X6),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7208]),
[final] ).
cnf(i_0_12640,plain,
c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),c_List_OtakeWhile(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7209]),
[final] ).
cnf(i_0_12641,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk181_4(X2,X3,X4,X1)),esk180_4(X2,X3,X4,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7008]),
[final] ).
cnf(i_0_12642,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6954]),
[final] ).
cnf(i_0_12643,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk160_4(X2,X3,X1,X4)),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| hAPP(X2,X4) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7210]),
[final] ).
cnf(i_0_12644,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X3)),X3)))
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7211]),
[final] ).
cnf(i_0_12645,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7100]),
[final] ).
cnf(i_0_12646,plain,
( c_Fun_Oinj__on(X1,X5,hAPP(c_Fun_Ocomp(X2,X5,X1,X6),X3),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X2,X5,X6,hAPP(c_Set_Oimage(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7212]),
[final] ).
cnf(i_0_12647,plain,
( c_Fun_Oinj__on(X4,X2,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5),X6)
| ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(c_Set_Oimage(X4,X1,X5),X6))
| ~ c_Fun_Oinj__on(X4,X1,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_7087]),
[final] ).
cnf(i_0_12648,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_12649,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X4))) ),
inference(rw,[status(thm)],[i_0_7213,c_0_7214]),
[final] ).
cnf(i_0_12650,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7215]),
[final] ).
cnf(i_0_12651,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6928]),
[final] ).
cnf(i_0_12652,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6929]),
[final] ).
cnf(i_0_12653,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(c_Relation_OImage(X1,X4,X6),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_6303]),
[final] ).
cnf(i_0_12654,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(c_Relation_OImage(X1,X4,X6),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_7216]),
[final] ).
cnf(i_0_12655,plain,
hAPP(hAPP(c_Option_Omap(X1,X2),X3),hAPP(hAPP(c_Option_Omap(X4,X1),X5),X6)) = hAPP(hAPP(c_Option_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6),
inference(split_conjunct,[status(thm)],[i_0_7217]),
[final] ).
cnf(i_0_12656,plain,
hAPP(hAPP(c_Option_Omap(X1,X2),X3),hAPP(hAPP(c_Option_Omap(X4,X1),X5),X6)) = hAPP(hAPP(c_Option_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6),
inference(split_conjunct,[status(thm)],[i_0_7218]),
[final] ).
cnf(i_0_12657,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Omap(X4,X1),X5),X6)) = hAPP(hAPP(c_List_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6),
inference(split_conjunct,[status(thm)],[i_0_7219]),
[final] ).
cnf(i_0_12658,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Omap(X4,X1),X5),X6)) = hAPP(hAPP(c_List_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6),
inference(split_conjunct,[status(thm)],[i_0_7220]),
[final] ).
cnf(i_0_12659,plain,
hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = c_Nat_Onat_Onat__case(tc_List_Olist(X1),c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_List_Olist(X1),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X1),X3)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otake(X1)),X4)),X2),
inference(split_conjunct,[status(thm)],[i_0_7221]),
[final] ).
cnf(i_0_12660,plain,
hAPP(c_Relation_OImage(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,X3),X5)),hAPP(c_Relation_OImage(X1,X2,X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7222]),
[final] ).
cnf(i_0_12661,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Random_Oiterate(X2,X3,X1,X4),X5) = hAPP(hAPP(c_Product__Type_Oscomp(X3,X2,X3,tc_prod(X2,X3)),hAPP(X4,X5)),c_Random_Oiterate(X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7223]),
[final] ).
cnf(i_0_12662,plain,
( hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7201]),
[final] ).
cnf(i_0_12663,plain,
( hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7224]),
[final] ).
cnf(i_0_12664,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X6),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7225]),
[final] ).
cnf(i_0_12665,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X6),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7226]),
[final] ).
cnf(i_0_12666,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(X6,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_7227]),
[final] ).
cnf(i_0_12667,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,X2)),c_List_Olistrel1(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7228]),
[final] ).
cnf(i_0_12668,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_List_Olistrel(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7229]),
[final] ).
cnf(i_0_12669,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X4)) = hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X2)),hAPP(c_List_Omap(X1,X2),X3)),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7230,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_12670,plain,
hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),X6),X7) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X4),X6),hAPP(X5,X7)),
inference(split_conjunct,[status(thm)],[i_0_7231]),
[final] ).
cnf(i_0_12671,plain,
hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),X6),X7) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X4),X6),hAPP(X5,X7)),
inference(split_conjunct,[status(thm)],[i_0_7232]),
[final] ).
cnf(i_0_12672,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7233]),
[final] ).
cnf(i_0_12673,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[i_0_6965]),
[final] ).
cnf(i_0_12674,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(X2,hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5))) = hAPP(hAPP(X2,hAPP(X3,X4)),hAPP(X3,X5))
| ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7234]),
[final] ).
cnf(i_0_12675,plain,
( hAPP(X3,hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7235]),
[final] ).
cnf(i_0_12676,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7236,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12677,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7237,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12678,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool))),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4),
inference(split_conjunct,[status(thm)],[i_0_7238]),
[final] ).
cnf(i_0_12679,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4),
inference(split_conjunct,[status(thm)],[i_0_7239]),
[final] ).
cnf(i_0_12680,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool))),X4)),
inference(split_conjunct,[status(thm)],[i_0_7240]),
[final] ).
cnf(i_0_12681,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X4)),
inference(split_conjunct,[status(thm)],[i_0_7241]),
[final] ).
cnf(i_0_12682,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk264_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7242]),
[final] ).
cnf(i_0_12683,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk263_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7242]),
[final] ).
cnf(i_0_12684,plain,
( c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7243]),
[final] ).
cnf(i_0_12685,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7244]),
[final] ).
cnf(i_0_12686,plain,
( X1 = X2
| hAPP(c_Map_Omap__of(X3,X4,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5)),X6)),X2) = hAPP(c_Map_Omap__of(X3,X4,X6),X2) ),
inference(split_conjunct,[status(thm)],[i_0_7245]),
[final] ).
cnf(i_0_12687,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),X4) = hAPP(hAPP(c_List_Oappend(X1),X3),X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
| X2 != hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)
| X4 != hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X5) ),
inference(split_conjunct,[status(thm)],[i_0_7032]),
[final] ).
cnf(i_0_12688,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_7225]),
[final] ).
cnf(i_0_12689,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_7226]),
[final] ).
cnf(i_0_12690,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_7246]),
[final] ).
cnf(i_0_12691,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk210_4(X2,X3,X1,X4)),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X2),X3) != c_Groups_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Rings_Ocomm__semiring__1(X4)
| ~ class_Rings_Ono__zero__divisors(X4) ),
inference(split_conjunct,[status(thm)],[i_0_7247]),
[final] ).
cnf(i_0_12692,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk427_4(X4,X1,X3,X2)),esk426_4(X4,X1,X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),hAPP(c_Relation_Oconverse(X3,X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6477]),
[final] ).
cnf(i_0_12693,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2))),hAPP(c_Finite__Set_Ocard(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7248]),
[final] ).
cnf(i_0_12694,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(c_List_Oset(X4),X5))))
| c_List_Olinorder__class_Oinsort__insert__key(X4,X1,X2,X3,X5) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X1,X2),X3),X5)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7249]),
[final] ).
cnf(i_0_12695,plain,
( hBOOL(hAPP(X1,esk111_2(X1,X2)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk109_2(X1,X2)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X1,X2)),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7106]),
[final] ).
cnf(i_0_12696,plain,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) ),
inference(rw,[status(thm)],[i_0_7250,c_0_6053]),
[final] ).
cnf(i_0_12697,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk114_4(X2,X3,X4,X1)),esk113_4(X2,X3,X4,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7031]),
[final] ).
cnf(i_0_12698,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk108_4(X2,X3,X4,X1)),esk107_4(X2,X3,X4,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7030]),
[final] ).
cnf(i_0_12699,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk394_4(X2,X3,X4,X1)),X3))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7251]),
[final] ).
cnf(i_0_12700,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk164_4(X2,X3,X4,X1)),X3))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7252]),
[final] ).
cnf(i_0_12701,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk163_4(X2,X3,X1,X4)),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_7253]),
[final] ).
cnf(i_0_12702,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk395_4(X2,X3,X1,X4)),X3))
| c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_7254]),
[final] ).
cnf(i_0_12703,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk128_4(X2,X3,X1,X4))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7255]),
[final] ).
cnf(i_0_12704,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7256]),
[final] ).
cnf(i_0_12705,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7257]),
[final] ).
cnf(i_0_12706,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7258]),
[final] ).
cnf(i_0_12707,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7259]),
[final] ).
cnf(i_0_12708,plain,
( hAPP(X1,esk77_4(X2,X1,X3,X4)) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk76_4(X2,X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6122]),
[final] ).
cnf(i_0_12709,plain,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),X5))
| ~ c_Typedef_Otype__definition(X6,X4,X7,X1,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7260]),
[final] ).
cnf(i_0_12710,plain,
hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OField(X1),X4)),
inference(split_conjunct,[status(thm)],[i_0_7261]),
[final] ).
cnf(i_0_12711,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7262]),
[final] ).
cnf(i_0_12712,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk187_4(X2,X3,X4,X1)),esk186_4(X2,X3,X4,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7043]),
[final] ).
cnf(i_0_12713,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7263,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12714,plain,
c_Nitpick_Opair__box_Opair__box__size(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X3,X5)),hAPP(X4,X6))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_7264]),
[final] ).
cnf(i_0_12715,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk404_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk405_3(X2,X3,X1)),esk406_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7265]),
[final] ).
cnf(i_0_12716,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6971]),
[final] ).
cnf(i_0_12717,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),hAPP(X2,X3))),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7266]),
[final] ).
cnf(i_0_12718,plain,
( c_Fun_Oinj__on(X4,X2,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X4,X1,X5,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_7267]),
[final] ).
cnf(i_0_12719,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X2)))),
inference(split_conjunct,[status(thm)],[i_0_7268]),
[final] ).
cnf(i_0_12720,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7269,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12721,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7270]),
[final] ).
cnf(i_0_12722,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7271]),
[final] ).
cnf(i_0_12723,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3)),
inference(split_conjunct,[status(thm)],[i_0_7272]),
[final] ).
cnf(i_0_12724,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3)),
inference(split_conjunct,[status(thm)],[i_0_7273]),
[final] ).
cnf(i_0_12725,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk128_4(X2,X3,X4,X1)),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7255]),
[final] ).
cnf(i_0_12726,plain,
( hAPP(X4,X2) = X5
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Ovimage(X1,X3,X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_7274]),
[final] ).
cnf(i_0_12727,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7275,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12728,plain,
( c_Fun_Oinj__on(X1,X3,X5,X6)
| ~ c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6) ),
inference(split_conjunct,[status(thm)],[i_0_7276]),
[final] ).
cnf(i_0_12729,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7062]),
[final] ).
cnf(i_0_12730,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7063]),
[final] ).
cnf(i_0_12731,plain,
( X1 = hAPP(X2,esk265_4(X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_Set_Oimage(X4,X3,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_6921]),
[final] ).
cnf(i_0_12732,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7277,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12733,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7278]),
[final] ).
cnf(i_0_12734,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X3),
inference(split_conjunct,[status(thm)],[i_0_7279]),
[final] ).
cnf(i_0_12735,plain,
( hAPP(c_Map_Omap__of(X3,X4,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5)),X6)),X2) = hAPP(c_Option_Ooption_OSome(X4),X5)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_7245]),
[final] ).
cnf(i_0_12736,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7280,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12737,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7281,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12738,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7282,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12739,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7283,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12740,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7284,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12741,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7285,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12742,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7286,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12743,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7287,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12744,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5) != X6
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7288]),
[final] ).
cnf(i_0_12745,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5)),X6)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X3),X4)),X5)),X6)
| ~ class_Rings_Oring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7289]),
[final] ).
cnf(i_0_12746,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk406_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk404_3(X2,X3,X1)),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7265]),
[final] ).
cnf(i_0_12747,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk405_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk404_3(X2,X3,X1)),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7265]),
[final] ).
cnf(i_0_12748,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
| hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X2,tc_HOL_Obool)),X4),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X5),c_Relation_OImage(X2,X1,X3)),X6))
| ~ c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7290]),
[final] ).
cnf(i_0_12749,plain,
hAPP(c_Product__Type_Osnd(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Opartition(X1,X2,X3)) = hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot),X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_7291]),
[final] ).
cnf(i_0_12750,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X1,X5),X2)),hAPP(c_Set_Ovimage(X4,X1,X5),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7292]),
[final] ).
cnf(i_0_12751,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X5),X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7293]),
[final] ).
cnf(i_0_12752,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X5) = hAPP(X5,X6)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X4,tc_HOL_Obool),X3,X5)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7294]),
[final] ).
cnf(i_0_12753,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7295]),
[final] ).
cnf(i_0_12754,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7296]),
[final] ).
cnf(i_0_12755,plain,
( hAPP(hAPP(c_Fun_Ocomp(X7,X8,X9,X1),X2),X3) = hAPP(hAPP(c_Fun_Ocomp(X10,X8,X11,X4),X5),X6)
| hAPP(X1,hAPP(X2,X3)) != hAPP(X4,hAPP(X5,X6)) ),
inference(split_conjunct,[status(thm)],[i_0_7297]),
[final] ).
cnf(i_0_12756,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X4,X2) = hAPP(hAPP(X5,X3),hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ c_Finite__Set_Ofolding__one(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7298]),
[final] ).
cnf(i_0_12757,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7299]),
[final] ).
cnf(i_0_12758,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7300]),
[final] ).
cnf(i_0_12759,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
| c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6975]),
[final] ).
cnf(i_0_12760,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
| c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6976]),
[final] ).
cnf(i_0_12761,plain,
( c_Wellfounded_Owf(tc_prod(X3,X1),c_Recdef_Osame__fst(X3,X1,X4,X2))
| ~ c_Wellfounded_Owf(X1,hAPP(X2,esk322_4(X3,X2,X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7301]),
[final] ).
cnf(i_0_12762,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X5),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7302]),
[final] ).
cnf(i_0_12763,plain,
( c_Map_Oran(X1,X2,c_Map_Omap__of(X1,X2,X3)) = hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7303]),
[final] ).
cnf(i_0_12764,plain,
c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_7304]),
[final] ).
cnf(i_0_12765,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7305,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12766,plain,
( hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,X2)),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X2),X3)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7306]),
[final] ).
cnf(i_0_12767,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))) ),
inference(rw,[status(thm)],[i_0_7307,c_0_6062]),
[final] ).
cnf(i_0_12768,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7308]),
[final] ).
cnf(i_0_12769,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7309]),
[final] ).
cnf(i_0_12770,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7053]),
[final] ).
cnf(i_0_12771,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7054]),
[final] ).
cnf(i_0_12772,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X4))
| hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7310]),
[final] ).
cnf(i_0_12773,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk116_4(X2,X3,X4,X1)),esk115_4(X2,X3,X4,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7082]),
[final] ).
cnf(i_0_12774,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk106_4(X2,X3,X4,X1)),esk105_4(X2,X3,X4,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7081]),
[final] ).
cnf(i_0_12775,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)) = hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Orev(X1)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7311,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_12776,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6441]),
[final] ).
cnf(i_0_12777,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7312]),
[final] ).
cnf(i_0_12778,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7313]),
[final] ).
cnf(i_0_12779,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7314]),
[final] ).
cnf(i_0_12780,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7315]),
[final] ).
cnf(i_0_12781,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7316]),
[final] ).
cnf(i_0_12782,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7317]),
[final] ).
cnf(i_0_12783,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(X5,X3),hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ c_Finite__Set_Ofolding__one(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7318]),
[final] ).
cnf(i_0_12784,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X1,X2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7319]),
[final] ).
cnf(i_0_12785,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X1,X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7320]),
[final] ).
cnf(i_0_12786,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X1,X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7321]),
[final] ).
cnf(i_0_12787,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X1,X2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7322]),
[final] ).
cnf(i_0_12788,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),X5))
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7323]),
[final] ).
cnf(i_0_12789,plain,
( hAPP(X3,hAPP(X4,X6)) = X6
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7324]),
[final] ).
cnf(i_0_12790,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7325]),
[final] ).
cnf(i_0_12791,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7062]),
[final] ).
cnf(i_0_12792,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6999]),
[final] ).
cnf(i_0_12793,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7063]),
[final] ).
cnf(i_0_12794,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7000]),
[final] ).
cnf(i_0_12795,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk71_3(X2,X1,X3)),X3)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7326]),
[final] ).
cnf(i_0_12796,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X3)),
inference(split_conjunct,[status(thm)],[i_0_7327]),
[final] ).
cnf(i_0_12797,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X3)),
inference(split_conjunct,[status(thm)],[i_0_7328]),
[final] ).
cnf(i_0_12798,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4) != X5
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7329]),
[final] ).
cnf(i_0_12799,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7330]),
[final] ).
cnf(i_0_12800,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),X6),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),X6),X3))
| ~ class_Groups_Oab__semigroup__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7331]),
[final] ).
cnf(i_0_12801,plain,
hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)) = hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Ofilter(X1,X2)),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7332,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_12802,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X2))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7333]),
[final] ).
cnf(i_0_12803,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_7334]),
[final] ).
cnf(i_0_12804,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_7335]),
[final] ).
cnf(i_0_12805,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4)),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_7336]),
[final] ).
cnf(i_0_12806,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2)),X5)),
inference(split_conjunct,[status(thm)],[i_0_7337]),
[final] ).
cnf(i_0_12807,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2)),X5)),
inference(split_conjunct,[status(thm)],[i_0_7338]),
[final] ).
cnf(i_0_12808,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2)),X5)),
inference(split_conjunct,[status(thm)],[i_0_7339]),
[final] ).
cnf(i_0_12809,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2)),X5)),
inference(split_conjunct,[status(thm)],[i_0_7340]),
[final] ).
cnf(i_0_12810,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2)),X5)),
inference(split_conjunct,[status(thm)],[i_0_7341]),
[final] ).
cnf(i_0_12811,plain,
( hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7342]),
[final] ).
cnf(i_0_12812,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7343,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12813,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7344,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12814,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6931]),
[final] ).
cnf(i_0_12815,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6932]),
[final] ).
cnf(i_0_12816,plain,
( hBOOL(hAPP(X3,esk112_2(X3,X2)))
| hBOOL(hAPP(X3,esk109_2(X3,X2)))
| hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X3,X2)),X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7106]),
[final] ).
cnf(i_0_12817,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = X5
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7345]),
[final] ).
cnf(i_0_12818,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_7346]),
[final] ).
cnf(i_0_12819,plain,
( hAPP(X4,X5) = hAPP(X4,X6)
| ~ c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7347]),
[final] ).
cnf(i_0_12820,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7348]),
[final] ).
cnf(i_0_12821,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7349,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12822,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[i_0_7350,c_0_6062]),
[final] ).
cnf(i_0_12823,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| hAPP(hAPP(c_List_Oappend(X1),X3),X4) = hAPP(hAPP(c_List_Oappend(X1),X2),X5)
| hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3) != X2
| hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_7032]),
[final] ).
cnf(i_0_12824,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7351]),
[final] ).
cnf(i_0_12825,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7199]),
[final] ).
cnf(i_0_12826,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7077]),
[final] ).
cnf(i_0_12827,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7352]),
[final] ).
cnf(i_0_12828,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6999]),
[final] ).
cnf(i_0_12829,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7000]),
[final] ).
cnf(i_0_12830,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7353]),
[final] ).
cnf(i_0_12831,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7354]),
[final] ).
cnf(i_0_12832,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7355]),
[final] ).
cnf(i_0_12833,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7356]),
[final] ).
cnf(i_0_12834,plain,
( hAPP(c_Set_Oimage(X2,X1,X4),X5) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7357]),
[final] ).
cnf(i_0_12835,plain,
( c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),c_List_Oset(X1)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7358]),
[final] ).
cnf(i_0_12836,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7359]),
[final] ).
cnf(i_0_12837,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7360]),
[final] ).
cnf(i_0_12838,plain,
hAPP(hAPP(c_List_Olist__update(tc_prod(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5),X6) = hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X5),hAPP(c_Product__Type_Ofst(X1,X2),X6))),hAPP(hAPP(c_List_Olist__update(X2,X4),X5),hAPP(c_Product__Type_Osnd(X1,X2),X6))),
inference(split_conjunct,[status(thm)],[i_0_7361]),
[final] ).
cnf(i_0_12839,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
| ~ c_Nat__Transfer_Onat__set(X2)
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7113]),
[final] ).
cnf(i_0_12840,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
| ~ c_Nat__Transfer_Onat__set(X2)
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7114]),
[final] ).
cnf(i_0_12841,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7362,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12842,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7363,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12843,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7364,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12844,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7365,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12845,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7366,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12846,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),X3))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))) ),
inference(rw,[status(thm)],[i_0_7367,c_0_6670]),
[final] ).
cnf(i_0_12847,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X1)))),
inference(split_conjunct,[status(thm)],[i_0_7368]),
[final] ).
cnf(i_0_12848,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X1)))),
inference(split_conjunct,[status(thm)],[i_0_7369]),
[final] ).
cnf(i_0_12849,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X4,X2),X5),X6)),X7) = hAPP(hAPP(c_Relation_Orel__comp(X1,X4,X3),X5),hAPP(hAPP(c_Relation_Orel__comp(X4,X2,X3),X6),X7)),
inference(split_conjunct,[status(thm)],[i_0_7370]),
[final] ).
cnf(i_0_12850,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6928]),
[final] ).
cnf(i_0_12851,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6929]),
[final] ).
cnf(i_0_12852,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7371]),
[final] ).
cnf(i_0_12853,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7372]),
[final] ).
cnf(i_0_12854,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7373]),
[final] ).
cnf(i_0_12855,plain,
hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X2),c_Set_OPow(X1)),X4)),
inference(split_conjunct,[status(thm)],[i_0_7374]),
[final] ).
cnf(i_0_12856,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7359]),
[final] ).
cnf(i_0_12857,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7360]),
[final] ).
cnf(i_0_12858,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7375]),
[final] ).
cnf(i_0_12859,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6931]),
[final] ).
cnf(i_0_12860,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6932]),
[final] ).
cnf(i_0_12861,plain,
( c_Natural_Oevaln(c_Com_Ocom_OLocal(X2,X6,X5),X3,X7,hAPP(hAPP(hAPP(c_Natural_Oupdate,X1),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2)))
| hAPP(hAPP(hAPP(c_Natural_Oupdate,X1),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,X4),c_Com_Ovname_OLoc(X2)),hAPP(hAPP(c_Natural_Ogetlocs,X3),X2))
| ~ c_Natural_Oevaln(X5,hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),c_Com_Ovname_OLoc(X2)),hAPP(X6,X3)),X7,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6248]),
[final] ).
cnf(i_0_12862,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X2)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X3)),hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_7376]),
[final] ).
cnf(i_0_12863,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7377]),
[final] ).
cnf(i_0_12864,plain,
c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Transitive__Closure_Ortrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)))),
inference(rw,[status(thm)],[i_0_7378,c_0_6053]),
[final] ).
cnf(i_0_12865,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7379]),
[final] ).
cnf(i_0_12866,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7380]),
[final] ).
cnf(i_0_12867,plain,
( X3 = esk265_4(X1,X2,X4,X5)
| X1 != hAPP(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_Set_Oimage(X5,X4,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_6921]),
[final] ).
cnf(i_0_12868,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7278]),
[final] ).
cnf(i_0_12869,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7381]),
[final] ).
cnf(i_0_12870,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7382,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_12871,plain,
( X3 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X4),hAPP(c_Option_Ooption_OSome(X2),esk273_4(X4,X3,X2,X1)))
| c_Map_Odom(X1,X2,X3) != hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_7383]),
[final] ).
cnf(i_0_12872,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(hAPP(X3,X4),X2) = X5
| ~ c_Big__Operators_Ocomm__monoid__big(X6,X1,X7,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7191]),
[final] ).
cnf(i_0_12873,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6))
| hAPP(hAPP(X5,X7),X6) = X4
| ~ c_Big__Operators_Ocomm__monoid__big(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7384]),
[final] ).
cnf(i_0_12874,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7385]),
[final] ).
cnf(i_0_12875,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)),hAPP(X5,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7386]),
[final] ).
cnf(i_0_12876,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7387]),
[final] ).
cnf(i_0_12877,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Set_Ovimage(X1,X2,X3)),X6)),
inference(split_conjunct,[status(thm)],[i_0_7388]),
[final] ).
cnf(i_0_12878,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Set_Ovimage(X1,X2,X3)),X6)),
inference(split_conjunct,[status(thm)],[i_0_7389]),
[final] ).
cnf(i_0_12879,plain,
hAPP(c_Relation_OImage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Relation_OImage(X1,X2,X3)),X6)),
inference(split_conjunct,[status(thm)],[i_0_7390]),
[final] ).
cnf(i_0_12880,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Set_Oimage(X1,X2,X3)),X6)),
inference(split_conjunct,[status(thm)],[i_0_7391]),
[final] ).
cnf(i_0_12881,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X5),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7392]),
[final] ).
cnf(i_0_12882,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X5),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7393]),
[final] ).
cnf(i_0_12883,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),
inference(split_conjunct,[status(thm)],[i_0_7394]),
[final] ).
cnf(i_0_12884,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7395,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12885,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,esk147_3(X1,X2,X3)),esk148_3(X1,X2,X3)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6874]),
[final] ).
cnf(i_0_12886,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,esk90_3(X1,X2,X3)),esk91_3(X1,X2,X3)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7176]),
[final] ).
cnf(i_0_12887,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,esk88_3(X1,X2,X3)),esk89_3(X1,X2,X3)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7007]),
[final] ).
cnf(i_0_12888,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,esk83_3(X1,X2,X3)),esk84_3(X1,X2,X3)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5289]),
[final] ).
cnf(i_0_12889,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,esk81_3(X1,X2,X3)),esk82_3(X1,X2,X3)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5286]),
[final] ).
cnf(i_0_12890,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7396]),
[final] ).
cnf(i_0_12891,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7397]),
[final] ).
cnf(i_0_12892,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(hAPP(X1,esk55_3(X2,X1,X3)),esk56_3(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7398]),
[final] ).
cnf(i_0_12893,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X4,X5),X2),X3)))
| ~ class_Orderings_Olinorder(X4) ),
inference(split_conjunct,[status(thm)],[i_0_7399]),
[final] ).
cnf(i_0_12894,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Fun_Ocomp(X4,tc_fun(X2,tc_HOL_Obool),X1,X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5),
inference(split_conjunct,[status(thm)],[i_0_7400]),
[final] ).
cnf(i_0_12895,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),hAPP(hAPP(c_Set_Oinsert(X2),X5),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X4,X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7401]),
[final] ).
cnf(i_0_12896,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(hAPP(c_Set_Oinsert(X2),X5),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7402]),
[final] ).
cnf(i_0_12897,plain,
hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)),X4),X6) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X6),
inference(split_conjunct,[status(thm)],[i_0_7403]),
[final] ).
cnf(i_0_12898,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X5)),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7398]),
[final] ).
cnf(i_0_12899,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(hAPP(X1,esk57_3(X2,X1,X3)),esk58_3(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7404]),
[final] ).
cnf(i_0_12900,plain,
hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2) = hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X1)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))),X2),
inference(split_conjunct,[status(thm)],[i_0_7405]),
[final] ).
cnf(i_0_12901,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))),
inference(split_conjunct,[status(thm)],[i_0_7406]),
[final] ).
cnf(i_0_12902,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))),
inference(split_conjunct,[status(thm)],[i_0_7407]),
[final] ).
cnf(i_0_12903,plain,
c_Sum__Type_OPlus(X1,X2,X3,X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,tc_sum(X1,X2),c_Sum__Type_OInl(X1,X2)),X3)),hAPP(c_Set_Oimage(X2,tc_sum(X1,X2),c_Sum__Type_OInr(X2,X1)),X4)),
inference(split_conjunct,[status(thm)],[i_0_7408]),
[final] ).
cnf(i_0_12904,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7409]),
[final] ).
cnf(i_0_12905,plain,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ c_Typedef_Otype__definition(X4,X5,X1,X6,X7) ),
inference(split_conjunct,[status(thm)],[i_0_7410]),
[final] ).
cnf(i_0_12906,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7411]),
[final] ).
cnf(i_0_12907,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7412]),
[final] ).
cnf(i_0_12908,plain,
( hAPP(X4,hAPP(X3,X6)) = X6
| ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7413]),
[final] ).
cnf(i_0_12909,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X5)),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7404]),
[final] ).
cnf(i_0_12910,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7414,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12911,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7415]),
[final] ).
cnf(i_0_12912,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7416]),
[final] ).
cnf(i_0_12913,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)) ),
inference(rw,[status(thm)],[i_0_7417,c_0_6062]),
[final] ).
cnf(i_0_12914,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk183_4(X2,X3,X4,X1)),esk182_4(X2,X3,X4,X1))
| X1 = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4) != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7147]),
[final] ).
cnf(i_0_12915,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk185_4(X2,X3,X4,X1)),esk184_4(X2,X3,X4,X1))
| X1 = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4) != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7146]),
[final] ).
cnf(i_0_12916,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6999]),
[final] ).
cnf(i_0_12917,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7000]),
[final] ).
cnf(i_0_12918,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_7418]),
[final] ).
cnf(i_0_12919,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk111_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
| hBOOL(hAPP(X1,esk109_2(X1,X2)))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X1,X2)),X2))))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7106]),
[final] ).
cnf(i_0_12920,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6776]),
[final] ).
cnf(i_0_12921,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7419]),
[final] ).
cnf(i_0_12922,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6587]),
[final] ).
cnf(i_0_12923,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7420]),
[final] ).
cnf(i_0_12924,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Odrop(X3),X2),X4))),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Odrop(X3),X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7421]),
[final] ).
cnf(i_0_12925,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Otake(X3),X1),X4))),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Otake(X3),X2),X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7422]),
[final] ).
cnf(i_0_12926,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6999]),
[final] ).
cnf(i_0_12927,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7062]),
[final] ).
cnf(i_0_12928,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7000]),
[final] ).
cnf(i_0_12929,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7063]),
[final] ).
cnf(i_0_12930,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4) = X6
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7288]),
[final] ).
cnf(i_0_12931,plain,
( X4 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7289]),
[final] ).
cnf(i_0_12932,plain,
( c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7423]),
[final] ).
cnf(i_0_12933,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),hAPP(c_Nat_OSuc,X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7424]),
[final] ).
cnf(i_0_12934,plain,
hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7425,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_12935,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X4),X2)))
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7426]),
[final] ).
cnf(i_0_12936,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X4),X2)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7427]),
[final] ).
cnf(i_0_12937,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7428]),
[final] ).
cnf(i_0_12938,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7429,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_12939,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olist_ONil(X2)),X1)),c_List_Olexord(X2,X5)))
| X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_7011]),
[final] ).
cnf(i_0_12940,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7430]),
[final] ).
cnf(i_0_12941,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk440_3(X1,X2,X3)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X2))))
| X3 = X2
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_7175]),
[final] ).
cnf(i_0_12942,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
| ~ c_Nat__Transfer_Onat__set(X1)
| ~ c_Nat__Transfer_Onat__set(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7431]),
[final] ).
cnf(i_0_12943,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
| ~ c_Nat__Transfer_Onat__set(X1)
| ~ c_Nat__Transfer_Onat__set(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7432]),
[final] ).
cnf(i_0_12944,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7433]),
[final] ).
cnf(i_0_12945,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7434]),
[final] ).
cnf(i_0_12946,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Relation_OId__on(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))),
inference(split_conjunct,[status(thm)],[i_0_7435]),
[final] ).
cnf(i_0_12947,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X1))
| ~ c_Com_OWT__bodies
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X1),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) ),
inference(split_conjunct,[status(thm)],[i_0_7436]),
[final] ).
cnf(i_0_12948,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7062]),
[final] ).
cnf(i_0_12949,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7062]),
[final] ).
cnf(i_0_12950,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7063]),
[final] ).
cnf(i_0_12951,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7063]),
[final] ).
cnf(i_0_12952,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7302]),
[final] ).
cnf(i_0_12953,plain,
hAPP(c_Relation_ORange(X1,X2),hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))) = hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3))),
inference(split_conjunct,[status(thm)],[i_0_7437]),
[final] ).
cnf(i_0_12954,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))
| ~ c_Relation_Orefl__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6625]),
[final] ).
cnf(i_0_12955,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7438]),
[final] ).
cnf(i_0_12956,plain,
hAPP(c_Fun_Ocomp(tc_List_Olist(X1),tc_List_Olist(X2),tc_List_Olist(X3),hAPP(c_List_Omap(X1,X2),X4)),hAPP(c_List_Omap(X3,X1),X5)) = hAPP(c_List_Omap(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7439]),
[final] ).
cnf(i_0_12957,plain,
hAPP(c_Fun_Ocomp(tc_List_Olist(X1),tc_List_Olist(X2),tc_List_Olist(X3),hAPP(c_List_Omap(X1,X2),X4)),hAPP(c_List_Omap(X3,X1),X5)) = hAPP(c_List_Omap(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7440]),
[final] ).
cnf(i_0_12958,plain,
hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),tc_Option_Ooption(X3),hAPP(c_Option_Omap(X1,X2),X4)),hAPP(c_Option_Omap(X3,X1),X5)) = hAPP(c_Option_Omap(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7441]),
[final] ).
cnf(i_0_12959,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X3,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7201]),
[final] ).
cnf(i_0_12960,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X3,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7201]),
[final] ).
cnf(i_0_12961,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7442]),
[final] ).
cnf(i_0_12962,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X5),X2))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7443]),
[final] ).
cnf(i_0_12963,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7444,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_12964,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_7445]),
[final] ).
cnf(i_0_12965,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X3)),
inference(split_conjunct,[status(thm)],[i_0_7446]),
[final] ).
cnf(i_0_12966,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Relation_OId__on(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7447]),
[final] ).
cnf(i_0_12967,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7448]),
[final] ).
cnf(i_0_12968,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7448]),
[final] ).
cnf(i_0_12969,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7449]),
[final] ).
cnf(i_0_12970,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7450]),
[final] ).
cnf(i_0_12971,plain,
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5295]),
[final] ).
cnf(i_0_12972,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7226]),
[final] ).
cnf(i_0_12973,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7451]),
[final] ).
cnf(i_0_12974,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk409_3(X2,X3,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7452]),
[final] ).
cnf(i_0_12975,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk408_3(X2,X3,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7452]),
[final] ).
cnf(i_0_12976,plain,
( hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Groups_Osemigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7453]),
[final] ).
cnf(i_0_12977,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))),
inference(split_conjunct,[status(thm)],[i_0_7454]),
[final] ).
cnf(i_0_12978,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7455,c_0_6053]),c_0_6062]),
[final] ).
cnf(i_0_12979,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
| hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1),X5) = hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist__update(X2,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7456]),
[final] ).
cnf(i_0_12980,plain,
( X4 = X5
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7457]),
[final] ).
cnf(i_0_12981,plain,
( hAPP(c_Random_Opick(X2,hAPP(hAPP(c_List_Omap(X2,tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X3)),hAPP(c_Code__Numeral_Oof__nat,X1)) = hAPP(hAPP(c_List_Onth(X2),X3),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7458]),
[final] ).
cnf(i_0_12982,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3) = X5
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7329]),
[final] ).
cnf(i_0_12983,plain,
( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7330]),
[final] ).
cnf(i_0_12984,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7459]),
[final] ).
cnf(i_0_12985,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7459]),
[final] ).
cnf(i_0_12986,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7460]),
[final] ).
cnf(i_0_12987,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7460]),
[final] ).
cnf(i_0_12988,plain,
( X1 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1))))) ),
inference(split_conjunct,[status(thm)],[i_0_7461]),
[final] ).
cnf(i_0_12989,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X5,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7462]),
[final] ).
cnf(i_0_12990,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X5,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7463]),
[final] ).
cnf(i_0_12991,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X2,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7462]),
[final] ).
cnf(i_0_12992,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X2,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7463]),
[final] ).
cnf(i_0_12993,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X4,esk132_4(X4,X3,X5,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6786]),
[final] ).
cnf(i_0_12994,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X4,esk132_4(X4,X5,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6786]),
[final] ).
cnf(i_0_12995,plain,
c_List_Oset__Cons(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X1,tc_List_Olist(X1),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))),X2),
inference(split_conjunct,[status(thm)],[i_0_7464]),
[final] ).
cnf(i_0_12996,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk234_4(X2,X3,X4,X1)))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6550]),
[final] ).
cnf(i_0_12997,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X4),X5)),X6)) = hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7465]),
[final] ).
cnf(i_0_12998,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X4),X5)),X6)) = hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7466]),
[final] ).
cnf(i_0_12999,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| X1 != hAPP(c_Set_Oimage(tc_Nat_Onat,X2,X3),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7467]),
[final] ).
cnf(i_0_13000,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| X1 != hAPP(c_Set_Oimage(tc_Nat_Onat,X2,X3),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7468]),
[final] ).
cnf(i_0_13001,plain,
( hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Odrop(X2),X1),X3))),c_List_Olist_ONil(X2))) = hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_OSuc,X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7469]),
[final] ).
cnf(i_0_13002,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4),
inference(split_conjunct,[status(thm)],[i_0_7470]),
[final] ).
cnf(i_0_13003,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X3)))),
inference(split_conjunct,[status(thm)],[i_0_7471]),
[final] ).
cnf(i_0_13004,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6928]),
[final] ).
cnf(i_0_13005,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6929]),
[final] ).
cnf(i_0_13006,plain,
( hBOOL(hAPP(X1,esk234_4(X1,X2,X3,X4)))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6550]),
[final] ).
cnf(i_0_13007,plain,
( hBOOL(hAPP(hAPP(c_member(tc_sum(X1,X4)),hAPP(c_Sum__Type_OInl(X1,X4),X2)),c_Sum__Type_OPlus(X1,X4,X3,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7472]),
[final] ).
cnf(i_0_13008,plain,
( hBOOL(hAPP(hAPP(c_member(tc_sum(X4,X1)),hAPP(c_Sum__Type_OInr(X1,X4),X2)),c_Sum__Type_OPlus(X4,X1,X5,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7473]),
[final] ).
cnf(i_0_13009,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),X2) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7474,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13010,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk411_3(X2,X3,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7475]),
[final] ).
cnf(i_0_13011,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3),X1))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7476]),
[final] ).
cnf(i_0_13012,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7477]),
[final] ).
cnf(i_0_13013,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6928]),
[final] ).
cnf(i_0_13014,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6929]),
[final] ).
cnf(i_0_13015,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6931]),
[final] ).
cnf(i_0_13016,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6932]),
[final] ).
cnf(i_0_13017,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),X2)),X1),
inference(split_conjunct,[status(thm)],[i_0_7478]),
[final] ).
cnf(i_0_13018,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X4),c_Wellfounded_Oless__than),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3))) ),
inference(rw,[status(thm)],[i_0_7479,c_0_7214]),
[final] ).
cnf(i_0_13019,plain,
( c_Wellfounded_OwfP(X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),X1))
| hAPP(X1,esk343_3(X2,X1,X3)) != hAPP(X1,esk344_3(X2,X1,X3))
| ~ c_Wellfounded_OwfP(X3,hAPP(X1,esk342_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6872]),
[final] ).
cnf(i_0_13020,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_7480]),
[final] ).
cnf(i_0_13021,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7481]),
[final] ).
cnf(i_0_13022,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7482]),
[final] ).
cnf(i_0_13023,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7483]),
[final] ).
cnf(i_0_13024,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7484]),
[final] ).
cnf(i_0_13025,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk405_3(X2,X3,X1)),esk406_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(X1),esk404_3(X2,X3,X1)) != X2
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7265]),
[final] ).
cnf(i_0_13026,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),c_List_Orotate1(X1)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1),hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1))),hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7485,c_0_6670]),c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_13027,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7486]),
[final] ).
cnf(i_0_13028,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7433]),
[final] ).
cnf(i_0_13029,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7486]),
[final] ).
cnf(i_0_13030,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7433]),
[final] ).
cnf(i_0_13031,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),X2)),X1),
inference(split_conjunct,[status(thm)],[i_0_7487]),
[final] ).
cnf(i_0_13032,plain,
( hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7488]),
[final] ).
cnf(i_0_13033,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X5)),hAPP(hAPP(c_List_Olist__update(X2,X6),X4),X7)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X6)),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X7)),
inference(split_conjunct,[status(thm)],[i_0_7489]),
[final] ).
cnf(i_0_13034,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_7490]),
[final] ).
cnf(i_0_13035,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_7491]),
[final] ).
cnf(i_0_13036,plain,
( hAPP(c_Set_Oimage(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3)),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = X4
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7492]),
[final] ).
cnf(i_0_13037,plain,
c_Nitpick_Opair__box_Opair__box__rec(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_7493]),
[final] ).
cnf(i_0_13038,plain,
c_Nitpick_Opair__box_Opair__box__case(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_7494]),
[final] ).
cnf(i_0_13039,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ class_Rings_Odvd(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7495]),
[final] ).
cnf(i_0_13040,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))
| ~ class_Rings_Olinordered__idom(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7496,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13041,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))
| ~ class_Rings_Olinordered__idom(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7497,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13042,plain,
( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk388_2(X2,X1)),esk388_2(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) ),
inference(rw,[status(thm)],[i_0_7498,c_0_6053]),
[final] ).
cnf(i_0_13043,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X5,X4,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7499]),
[final] ).
cnf(i_0_13044,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X5,X4,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7500]),
[final] ).
cnf(i_0_13045,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X5,X4,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7501]),
[final] ).
cnf(i_0_13046,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7502,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_13047,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7503]),
[final] ).
cnf(i_0_13048,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7447]),
[final] ).
cnf(i_0_13049,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)))))
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_7504,c_0_6053]),
[final] ).
cnf(i_0_13050,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),
inference(rw,[status(thm)],[i_0_7505,c_0_6053]),
[final] ).
cnf(i_0_13051,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4),
inference(split_conjunct,[status(thm)],[i_0_7506]),
[final] ).
cnf(i_0_13052,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_7507]),
[final] ).
cnf(i_0_13053,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_7508]),
[final] ).
cnf(i_0_13054,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_7509]),
[final] ).
cnf(i_0_13055,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_7510]),
[final] ).
cnf(i_0_13056,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk176_3(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7511]),
[final] ).
cnf(i_0_13057,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk178_3(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7512]),
[final] ).
cnf(i_0_13058,plain,
( hAPP(hAPP(c_List_Otake(X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X4) = hAPP(hAPP(c_List_Oappend(X3),hAPP(hAPP(c_List_Otake(X3),X1),X4)),hAPP(hAPP(c_List_Otake(X3),X2),hAPP(hAPP(c_List_Odrop(X3),X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7513]),
[final] ).
cnf(i_0_13059,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk250_3(X2,X3,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
| hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7514]),
[final] ).
cnf(i_0_13060,plain,
hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),X2),X3) = hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)),
inference(rw,[status(thm)],[i_0_7515,c_0_6100]),
[final] ).
cnf(i_0_13061,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X3,X4),X5),X2)))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_7399]),
[final] ).
cnf(i_0_13062,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7516,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_13063,plain,
( c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X4,c_Map_Odom(X1,X2,X4))
| ~ c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X3,X4),c_Map_Odom(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7517]),
[final] ).
cnf(i_0_13064,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X1),X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7518]),
[final] ).
cnf(i_0_13065,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X4,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6336]),
[final] ).
cnf(i_0_13066,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Oimage(tc_prod(X1,X3),X1,c_Product__Type_Ofst(X1,X3)),hAPP(c_List_Oset(tc_prod(X1,X3)),X4))))
| hAPP(c_Map_Omap__of(X1,X3,X4),X2) = c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[i_0_7150]),
[final] ).
cnf(i_0_13067,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X6)),hAPP(X4,X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_7519]),
[final] ).
cnf(i_0_13068,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool))),X4)),
inference(split_conjunct,[status(thm)],[i_0_7520]),
[final] ).
cnf(i_0_13069,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool))),X4)),
inference(split_conjunct,[status(thm)],[i_0_7521]),
[final] ).
cnf(i_0_13070,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk406_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
| hAPP(c_Finite__Set_Ocard(X1),esk404_3(X2,X3,X1)) != X2
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7265]),
[final] ).
cnf(i_0_13071,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk405_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))
| hAPP(c_Finite__Set_Ocard(X1),esk404_3(X2,X3,X1)) != X2
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7265]),
[final] ).
cnf(i_0_13072,plain,
( X3 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7522]),
[final] ).
cnf(i_0_13073,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6931]),
[final] ).
cnf(i_0_13074,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6932]),
[final] ).
cnf(i_0_13075,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7523]),
[final] ).
cnf(i_0_13076,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk223_2(X2,X1)),esk223_2(X2,X1))),X2))
| c_Relation_Oirrefl(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7524]),
[final] ).
cnf(i_0_13077,plain,
( hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7525]),
[final] ).
cnf(i_0_13078,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk59_3(X1,X2,X3))),X2))
| hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7526]),
[final] ).
cnf(i_0_13079,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7527]),
[final] ).
cnf(i_0_13080,plain,
( hAPP(X4,hAPP(X5,X9)) = hAPP(X7,hAPP(X8,X9))
| hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5) != hAPP(c_Fun_Ocomp(X6,X2,X3,X7),X8) ),
inference(split_conjunct,[status(thm)],[i_0_7528]),
[final] ).
cnf(i_0_13081,plain,
( hAPP(X4,hAPP(X5,X9)) = hAPP(X7,hAPP(X8,X9))
| hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5) != hAPP(c_Fun_Ocomp(X6,X2,X3,X7),X8) ),
inference(split_conjunct,[status(thm)],[i_0_7529]),
[final] ).
cnf(i_0_13082,plain,
( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),X4)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7530]),
[final] ).
cnf(i_0_13083,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7359]),
[final] ).
cnf(i_0_13084,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7360]),
[final] ).
cnf(i_0_13085,plain,
( c_Com_OWT__bodies
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),esk438_0)) ),
inference(split_conjunct,[status(thm)],[i_0_7436]),
[final] ).
cnf(i_0_13086,plain,
( hAPP(X4,hAPP(X5,X7)) = hAPP(X6,X7)
| hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5) != hAPP(c_Fun_Ocomp(X2,X2,X3,c_Fun_Oid(X2)),X6) ),
inference(split_conjunct,[status(thm)],[i_0_7531]),
[final] ).
cnf(i_0_13087,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7499]),
[final] ).
cnf(i_0_13088,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7500]),
[final] ).
cnf(i_0_13089,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7501]),
[final] ).
cnf(i_0_13090,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6975]),
[final] ).
cnf(i_0_13091,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6976]),
[final] ).
cnf(i_0_13092,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7532]),
[final] ).
cnf(i_0_13093,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),X5)))
| ~ c_Fun_Oinj__on(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_7533]),
[final] ).
cnf(i_0_13094,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)),X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)))
| hAPP(hAPP(c_List_Oappend(X2),X3),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_7032]),
[final] ).
cnf(i_0_13095,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X3,tc_HOL_Obool)),X2)) = hAPP(c_Finite__Set_Ocard(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),esk404_3(X1,X2,X3)),X2))
| esk405_3(X1,X2,X3) != esk406_3(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7265]),
[final] ).
cnf(i_0_13096,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X4),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X5)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7534]),
[final] ).
cnf(i_0_13097,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),X5)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7535]),
[final] ).
cnf(i_0_13098,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7536]),
[final] ).
cnf(i_0_13099,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7537]),
[final] ).
cnf(i_0_13100,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7524]),
[final] ).
cnf(i_0_13101,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),c_Map_Omap__of(X2,X1,X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_7538]),
[final] ).
cnf(i_0_13102,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Set_Oinsert(X3),X4)),X5)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7539]),
[final] ).
cnf(i_0_13103,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Set_Oinsert(X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Set_Oinsert(X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7540]),
[final] ).
cnf(i_0_13104,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7359]),
[final] ).
cnf(i_0_13105,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7359]),
[final] ).
cnf(i_0_13106,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7360]),
[final] ).
cnf(i_0_13107,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7360]),
[final] ).
cnf(i_0_13108,plain,
c_Transitive__Closure_Ortrancl(X1,X2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)),
inference(rw,[status(thm)],[i_0_7541,c_0_6053]),
[final] ).
cnf(i_0_13109,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X4),X5)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),hAPP(hAPP(c_COMBB(X1,X1,X3),hAPP(c_Groups_Otimes__class_Otimes(X1),X2)),X4)),X5)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7542]),
[final] ).
cnf(i_0_13110,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X4,X5,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7499]),
[final] ).
cnf(i_0_13111,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X4,X5,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7500]),
[final] ).
cnf(i_0_13112,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X4,X5,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7501]),
[final] ).
cnf(i_0_13113,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7543]),
[final] ).
cnf(i_0_13114,plain,
hAPP(c_Set_Oimage(X1,X2,hAPP(hAPP(c_COMBB(X3,X2,X1),X4),X5)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X3,X2,X4),hAPP(c_Set_Oimage(X1,X3,X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_7544]),
[final] ).
cnf(i_0_13115,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7312]),
[final] ).
cnf(i_0_13116,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7313]),
[final] ).
cnf(i_0_13117,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4)),X5)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7314]),
[final] ).
cnf(i_0_13118,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk59_3(X1,X2,X3))),X2))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7526]),
[final] ).
cnf(i_0_13119,plain,
( c_List_Olinorder__class_Osorted(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),esk487_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk486_2(X2,X1))))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7545]),
[final] ).
cnf(i_0_13120,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6444]),
[final] ).
cnf(i_0_13121,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7546]),
[final] ).
cnf(i_0_13122,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7547]),
[final] ).
cnf(i_0_13123,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) = hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3)
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7548]),
[final] ).
cnf(i_0_13124,plain,
( X1 = X2
| hAPP(hAPP(c_List_Olist__update(X3,hAPP(hAPP(c_List_Olist__update(X3,X4),X1),X5)),X2),X6) = hAPP(hAPP(c_List_Olist__update(X3,hAPP(hAPP(c_List_Olist__update(X3,X4),X2),X6)),X1),X5) ),
inference(split_conjunct,[status(thm)],[i_0_7549]),
[final] ).
cnf(i_0_13125,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)),X2),
inference(split_conjunct,[status(thm)],[i_0_7550]),
[final] ).
cnf(i_0_13126,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk502_3(X2,X1,X3))),esk503_3(X2,X1,X3))
| X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk500_3(X2,X1,X3))),esk501_3(X2,X1,X3))
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13127,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_13128,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk25_4(X3,X2,X1,X4)))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7096]),
[final] ).
cnf(i_0_13129,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk12_4(X3,X2,X1,X4)))
| ~ hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7097]),
[final] ).
cnf(i_0_13130,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7553,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13131,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7554,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13132,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7555,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13133,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7556,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13134,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7557]),
[final] ).
cnf(i_0_13135,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7558]),
[final] ).
cnf(i_0_13136,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7559]),
[final] ).
cnf(i_0_13137,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X6)),hAPP(X4,X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7560]),
[final] ).
cnf(i_0_13138,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk498_3(X2,X1,X3))),esk499_3(X2,X1,X3))
| X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk496_3(X2,X1,X3))),esk497_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13139,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X4)),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13140,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Set_Oinsert(X1),X2)),X5)),
inference(split_conjunct,[status(thm)],[i_0_7563]),
[final] ).
cnf(i_0_13141,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk75_3(X1,X2,X3)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk74_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6221]),
[final] ).
cnf(i_0_13142,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk73_3(X1,X2,X3)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk72_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6222]),
[final] ).
cnf(i_0_13143,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)),X4),
inference(split_conjunct,[status(thm)],[i_0_7564]),
[final] ).
cnf(i_0_13144,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X3))) = hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_7565,c_0_6015]),
[final] ).
cnf(i_0_13145,plain,
hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),X3,hAPP(c_Option_Omap(X1,X2),X4)),hAPP(c_COMBK(tc_Option_Ooption(X1),X3),c_Option_Ooption_ONone(X1))),X5) = c_Option_Ooption_ONone(X2),
inference(split_conjunct,[status(thm)],[i_0_7566]),
[final] ).
cnf(i_0_13146,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5),X1) = c_Lazy__Sequence_Ohb__bind(X2,X3,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3))),X5),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7567]),
[final] ).
cnf(i_0_13147,plain,
( c_Fun_Oinj__on(X1,tc_fun(X4,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X4,X2),X1),c_COMBK(X2,X4)),X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_7568]),
[final] ).
cnf(i_0_13148,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4)))
| c_Fun_Oinj__on(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X6),X5),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7569]),
[final] ).
cnf(i_0_13149,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_7570]),
[final] ).
cnf(i_0_13150,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_7571]),
[final] ).
cnf(i_0_13151,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7572]),
[final] ).
cnf(i_0_13152,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7573]),
[final] ).
cnf(i_0_13153,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7433]),
[final] ).
cnf(i_0_13154,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7433]),
[final] ).
cnf(i_0_13155,plain,
( hAPP(hAPP(c_List_Onth(tc_prod(X2,X4)),hAPP(hAPP(c_List_Ozip(X2,X4),X3),X5)),X1) = hAPP(hAPP(c_Product__Type_OPair(X2,X4),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Onth(X4),X5),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7574]),
[final] ).
cnf(i_0_13156,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2),X3))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_7575]),
[final] ).
cnf(i_0_13157,plain,
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7576]),
[final] ).
cnf(i_0_13158,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7062]),
[final] ).
cnf(i_0_13159,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7063]),
[final] ).
cnf(i_0_13160,plain,
( hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_List_Orev(X1),X2))
| ~ class_Groups_Omonoid__add(X1) ),
inference(rw,[status(thm)],[i_0_7577,c_0_6070]),
[final] ).
cnf(i_0_13161,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7333]),
[final] ).
cnf(i_0_13162,plain,
hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X5) = hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)),
inference(split_conjunct,[status(thm)],[i_0_7578]),
[final] ).
cnf(i_0_13163,plain,
( hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),X5),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X2)))),X1) = hAPP(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))) ),
inference(rw,[status(thm)],[i_0_7579,c_0_6135]),
[final] ).
cnf(i_0_13164,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk25_4(X3,X2,X1,X4)))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7096]),
[final] ).
cnf(i_0_13165,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk12_4(X3,X2,X1,X4)))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7097]),
[final] ).
cnf(i_0_13166,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,esk59_3(X2,X1,X3)))))
| hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7526]),
[final] ).
cnf(i_0_13167,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))),
inference(split_conjunct,[status(thm)],[i_0_7580]),
[final] ).
cnf(i_0_13168,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk5_4(X3,X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7178]),
[final] ).
cnf(i_0_13169,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk2_4(X3,X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7179]),
[final] ).
cnf(i_0_13170,plain,
c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3))) = c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_7581]),
[final] ).
cnf(i_0_13171,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk502_3(X2,X1,X3))),esk503_3(X2,X1,X3))
| X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk500_3(X2,X1,X3))),esk501_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13172,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk498_3(X2,X1,X3))),esk499_3(X2,X1,X3))
| X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk496_3(X2,X1,X3))),esk497_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13173,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7582]),
[final] ).
cnf(i_0_13174,plain,
hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X4)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),c_List_Orotate1(X1)),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7583,c_0_6670]),c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_13175,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk55_3(X1,X3,X2))),esk56_3(X1,X3,X2))
| hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7398]),
[final] ).
cnf(i_0_13176,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7433]),
[final] ).
cnf(i_0_13177,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7202]),
[final] ).
cnf(i_0_13178,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1))))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7202]),
[final] ).
cnf(i_0_13179,plain,
( hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),X3),hAPP(c_List_Orev(X1),X2)) = hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Groups_Oab__semigroup__add(X1) ),
inference(rw,[status(thm)],[i_0_7584,c_0_6070]),
[final] ).
cnf(i_0_13180,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),esk94_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(X1))))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7585]),
[final] ).
cnf(i_0_13181,plain,
( hBOOL(hAPP(X1,esk111_2(X1,X2)))
| hBOOL(hAPP(X1,esk109_2(X1,X2)))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk109_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk110_2(X1,X2)),X2))))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7106]),
[final] ).
cnf(i_0_13182,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_7586]),
[final] ).
cnf(i_0_13183,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X1),X8),X6) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X7),X5)
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ c_Fun_Oinj__on(X2,X3,X4,X5)
| X6 != hAPP(c_Set_Oimage(X2,X3,X4),X5)
| X7 != hAPP(c_Fun_Ocomp(X3,X1,X2,X8),X4) ),
inference(split_conjunct,[status(thm)],[i_0_7587]),
[final] ).
cnf(i_0_13184,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk57_3(X1,X3,X2))),esk58_3(X1,X3,X2))
| hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7404]),
[final] ).
cnf(i_0_13185,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7588]),
[final] ).
cnf(i_0_13186,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
inference(split_conjunct,[status(thm)],[i_0_7589]),
[final] ).
cnf(i_0_13187,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X5)),hAPP(X3,X6)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X6)),hAPP(X3,X5))
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7590]),
[final] ).
cnf(i_0_13188,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7591]),
[final] ).
cnf(i_0_13189,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7592]),
[final] ).
cnf(i_0_13190,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7593]),
[final] ).
cnf(i_0_13191,plain,
( c_Fun_Oinj__on(X1,X2,X3,c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))
| ~ c_Fun_Oinj__on(X1,X2,X3,esk410_4(X3,X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7153]),
[final] ).
cnf(i_0_13192,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_7594]),
[final] ).
cnf(i_0_13193,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X4),X3)))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_7594]),
[final] ).
cnf(i_0_13194,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,esk59_3(X2,X1,X3)))))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7526]),
[final] ).
cnf(i_0_13195,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Oacc(X1,X3)),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7595]),
[final] ).
cnf(i_0_13196,plain,
( hAPP(X2,X3) = hAPP(X2,X4)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),X6)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X4),X6))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7596]),
[final] ).
cnf(i_0_13197,plain,
( hBOOL(hAPP(X1,esk322_4(X2,X3,X4,X1)))
| c_Wellfounded_Owf(tc_prod(X2,X4),c_Recdef_Osame__fst(X2,X4,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7301]),
[final] ).
cnf(i_0_13198,plain,
( hBOOL(hAPP(X4,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7526]),
[final] ).
cnf(i_0_13199,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))
| hAPP(c_Map_Omap__of(X1,X2,X3),X4) != hAPP(c_Option_Ooption_OSome(X2),X5) ),
inference(split_conjunct,[status(thm)],[i_0_7597]),
[final] ).
cnf(i_0_13200,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))
| hAPP(c_Map_Omap__of(X1,X2,X3),X4) != hAPP(c_Option_Ooption_OSome(X2),X5) ),
inference(split_conjunct,[status(thm)],[i_0_7598]),
[final] ).
cnf(i_0_13201,plain,
( hAPP(c_Map_Omap__of(X1,X4,hAPP(hAPP(c_List_Ozip(X1,X4),X3),hAPP(hAPP(c_List_Omap(X1,X4),X5),X3))),X2) = hAPP(c_Option_Ooption_OSome(X4),hAPP(X5,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7599]),
[final] ).
cnf(i_0_13202,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X4,X5)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6887]),
[final] ).
cnf(i_0_13203,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_7600]),
[final] ).
cnf(i_0_13204,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,tc_HOL_Obool),X1),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5),
inference(split_conjunct,[status(thm)],[i_0_7601]),
[final] ).
cnf(i_0_13205,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,tc_HOL_Obool),X1),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5),
inference(split_conjunct,[status(thm)],[i_0_7602]),
[final] ).
cnf(i_0_13206,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X4),X5)),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X3),X6),X4)),
inference(split_conjunct,[status(thm)],[i_0_7603]),
[final] ).
cnf(i_0_13207,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X4),X5)),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X3),X6),X4)),
inference(split_conjunct,[status(thm)],[i_0_7604]),
[final] ).
cnf(i_0_13208,plain,
hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)))),
inference(split_conjunct,[status(thm)],[i_0_7605]),
[final] ).
cnf(i_0_13209,plain,
hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3) = hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),c_List_Orotate1(X1)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7606,c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_13210,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7607]),
[final] ).
cnf(i_0_13211,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7385]),
[final] ).
cnf(i_0_13212,plain,
( c_Fun_Oinj__on(X1,X1,X3,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X1,X1,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7608]),
[final] ).
cnf(i_0_13213,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3))) = hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X3))),
inference(split_conjunct,[status(thm)],[i_0_7609]),
[final] ).
cnf(i_0_13214,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_7610]),
[final] ).
cnf(i_0_13215,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_7611]),
[final] ).
cnf(i_0_13216,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X5),X4)))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7325]),
[final] ).
cnf(i_0_13217,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6999]),
[final] ).
cnf(i_0_13218,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7000]),
[final] ).
cnf(i_0_13219,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7612]),
[final] ).
cnf(i_0_13220,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7612]),
[final] ).
cnf(i_0_13221,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7613]),
[final] ).
cnf(i_0_13222,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7613]),
[final] ).
cnf(i_0_13223,plain,
( c_Natural_Oevaln(X1,esk201_4(X2,X1,X3,X4),X4,esk202_4(X2,X1,X3,X4))
| c_Hoare__Mirabelle_Otriple__valid(X5,X4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X3),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6809]),
[final] ).
cnf(i_0_13224,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_New__DSequence_Opos__decr__bind(X2,X3,X4,X5),X1) = c_Lazy__Sequence_Obind(X2,X3,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X3)),X5),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7614]),
[final] ).
cnf(i_0_13225,plain,
( c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
inference(rw,[status(thm)],[i_0_7615,c_0_6053]),
[final] ).
cnf(i_0_13226,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Oaccp(X1,X3)),c_Wellfounded_Oaccp(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7616]),
[final] ).
cnf(i_0_13227,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6716]),
[final] ).
cnf(i_0_13228,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6)) = hAPP(X4,X5)
| ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7617]),
[final] ).
cnf(i_0_13229,plain,
( c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7618]),
[final] ).
cnf(i_0_13230,plain,
( X2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7619]),
[final] ).
cnf(i_0_13231,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))
| ~ class_Groups_Oab__group__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7620]),
[final] ).
cnf(i_0_13232,plain,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7621,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13233,plain,
( X3 = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_OSuc,X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7622]),
[final] ).
cnf(i_0_13234,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Set_Oimage(X1,tc_Option_Ooption(X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),hAPP(c_Option_Ooption_OSome(X4),X6))),X3) = hAPP(c_Set_Oimage(X1,tc_Option_Ooption(X4),X5),X3) ),
inference(split_conjunct,[status(thm)],[i_0_7623]),
[final] ).
cnf(i_0_13235,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7624,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13236,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7625,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13237,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7626,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13238,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7627,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13239,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Wellfounded_Oless__than)) ),
inference(split_conjunct,[status(thm)],[i_0_7628]),
[final] ).
cnf(i_0_13240,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7629,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6169]),c_0_6169]),c_0_6169]),c_0_6016]),
[final] ).
cnf(i_0_13241,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X1,X5),X6)) = hAPP(c_Set_Oimage(X4,X2,hAPP(hAPP(c_COMBB(X1,X2,X4),X3),X5)),X6),
inference(split_conjunct,[status(thm)],[i_0_7630]),
[final] ).
cnf(i_0_13242,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),X3)),hAPP(X5,X2))
| hAPP(X5,X2) = c_Groups_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Fields_Ofield(X4) ),
inference(split_conjunct,[status(thm)],[i_0_7631]),
[final] ).
cnf(i_0_13243,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)) ),
inference(rw,[status(thm)],[i_0_7632,c_0_6062]),
[final] ).
cnf(i_0_13244,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk177_3(X1,X2,X3)),X1))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7511]),
[final] ).
cnf(i_0_13245,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk179_3(X1,X2,X3)),X1))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7512]),
[final] ).
cnf(i_0_13246,plain,
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7576]),
[final] ).
cnf(i_0_13247,plain,
( X4 = X5
| hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X4)),hAPP(c_List_Oset(X1),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7633]),
[final] ).
cnf(i_0_13248,plain,
( X4 = X5
| hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X4)),hAPP(c_List_Oset(X1),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7634]),
[final] ).
cnf(i_0_13249,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_7635]),
[final] ).
cnf(i_0_13250,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X5)),X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7636]),
[final] ).
cnf(i_0_13251,plain,
c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),
inference(rw,[status(thm)],[i_0_7637,c_0_6053]),
[final] ).
cnf(i_0_13252,plain,
c_Map_Omap__add(X1,X2,X3,c_Map_Omap__add(X1,X2,X4,X5)) = c_Map_Omap__add(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5),
inference(split_conjunct,[status(thm)],[i_0_7638]),
[final] ).
cnf(i_0_13253,plain,
( hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5))
| ~ c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7639]),
[final] ).
cnf(i_0_13254,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7640]),
[final] ).
cnf(i_0_13255,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Rings_Oordered__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7641]),
[final] ).
cnf(i_0_13256,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Rings_Oordered__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7642]),
[final] ).
cnf(i_0_13257,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7643]),
[final] ).
cnf(i_0_13258,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7644]),
[final] ).
cnf(i_0_13259,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7645]),
[final] ).
cnf(i_0_13260,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7646]),
[final] ).
cnf(i_0_13261,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7647]),
[final] ).
cnf(i_0_13262,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7648]),
[final] ).
cnf(i_0_13263,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),X3)),hAPP(X5,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[i_0_7649]),
[final] ).
cnf(i_0_13264,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(X5,X4))
| ~ class_Rings_Oring(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7650]),
[final] ).
cnf(i_0_13265,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_Power_Opower__class_Opower(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Oone__class_Oone(X1)))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7651]),
[final] ).
cnf(i_0_13266,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X1,X1),c_Groups_Oabs__class_Oabs(X1)),X2))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7652]),
[final] ).
cnf(i_0_13267,plain,
hAPP(c_List_Oset(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)),c_List_Oset(X1)),
inference(rw,[status(thm)],[i_0_7653,c_0_6100]),
[final] ).
cnf(i_0_13268,plain,
( c_Natural_Oevaln(c_Com_Ocom_OLocal(X3,X4,X1),X2,X5,hAPP(hAPP(hAPP(c_Natural_Oupdate,X6),c_Com_Ovname_OLoc(X3)),hAPP(hAPP(c_Natural_Ogetlocs,X2),X3)))
| ~ c_Natural_Oevaln(X1,hAPP(hAPP(hAPP(c_Natural_Oupdate,X2),c_Com_Ovname_OLoc(X3)),hAPP(X4,X2)),X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_7654]),
[final] ).
cnf(i_0_13269,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X3,c_Groups_Otimes__class_Otimes(X4)),X1),c_Groups_Oone__class_Oone(X4)),X2) = c_Groups_Oone__class_Oone(X4)
| hAPP(X1,esk355_4(X1,X2,X3,X4)) != c_Groups_Oone__class_Oone(X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))
| ~ class_Groups_Ocomm__monoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[i_0_7128]),
[final] ).
cnf(i_0_13270,plain,
( hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_7635]),
[final] ).
cnf(i_0_13271,plain,
hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),
inference(split_conjunct,[status(thm)],[i_0_7655]),
[final] ).
cnf(i_0_13272,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))
| ~ class_Groups_Oab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7656]),
[final] ).
cnf(i_0_13273,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X4))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7657]),
[final] ).
cnf(i_0_13274,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7658]),
[final] ).
cnf(i_0_13275,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7659]),
[final] ).
cnf(i_0_13276,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7660]),
[final] ).
cnf(i_0_13277,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ class_Rings_Olinordered__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7661]),
[final] ).
cnf(i_0_13278,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7662]),
[final] ).
cnf(i_0_13279,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7663]),
[final] ).
cnf(i_0_13280,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ class_Rings_Olinordered__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7664]),
[final] ).
cnf(i_0_13281,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7665]),
[final] ).
cnf(i_0_13282,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7666]),
[final] ).
cnf(i_0_13283,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)),
inference(rw,[status(thm)],[i_0_7667,c_0_6100]),
[final] ).
cnf(i_0_13284,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7668]),
[final] ).
cnf(i_0_13285,plain,
( hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_7635]),
[final] ).
cnf(i_0_13286,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk298_3(X2,X3,X1)),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7669]),
[final] ).
cnf(i_0_13287,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk297_3(X2,X3,X1)),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7670]),
[final] ).
cnf(i_0_13288,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk297_3(X2,X3,X1)),X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7670]),
[final] ).
cnf(i_0_13289,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk298_3(X2,X3,X1)),X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7669]),
[final] ).
cnf(i_0_13290,plain,
( hBOOL(hAPP(hAPP(X4,X6),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6447]),
[final] ).
cnf(i_0_13291,plain,
( hBOOL(hAPP(hAPP(X4,X6),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7671]),
[final] ).
cnf(i_0_13292,plain,
( hBOOL(hAPP(hAPP(X4,X6),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7672]),
[final] ).
cnf(i_0_13293,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_String_Ochar,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_prod(tc_String_Onibble,tc_String_Onibble),tc_String_Ochar,hAPP(c_Product__Type_Oprod_Oprod__case(tc_String_Onibble,tc_String_Onibble,tc_String_Ochar),c_String_Ochar_OChar)),hAPP(hAPP(c_Product__Type_OSigma(tc_String_Onibble,tc_String_Onibble),c_Orderings_Otop__class_Otop(tc_fun(tc_String_Onibble,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(tc_String_Onibble,tc_HOL_Obool),tc_String_Onibble),c_Orderings_Otop__class_Otop(tc_fun(tc_String_Onibble,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[fact_UNIV__char]),
[final] ).
cnf(i_0_13294,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7673]),
[final] ).
cnf(i_0_13295,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7674]),
[final] ).
cnf(i_0_13296,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7675]),
[final] ).
cnf(i_0_13297,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7676]),
[final] ).
cnf(i_0_13298,plain,
( X1 = c_List_Olist_ONil(X2)
| hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_Product__Type_Ofst(X2,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X2,X1),X3))),hAPP(c_List_Oset(X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7677]),
[final] ).
cnf(i_0_13299,plain,
hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))) = hAPP(c_Finite__Set_Ocard(X2),X4),
inference(split_conjunct,[status(thm)],[i_0_7678]),
[final] ).
cnf(i_0_13300,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7679]),
[final] ).
cnf(i_0_13301,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7680]),
[final] ).
cnf(i_0_13302,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7459]),
[final] ).
cnf(i_0_13303,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7460]),
[final] ).
cnf(i_0_13304,plain,
( hBOOL(hAPP(hAPP(X3,X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7681]),
[final] ).
cnf(i_0_13305,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_Set_Ovimage(X4,X5,X1),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
| hAPP(X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_7274]),
[final] ).
cnf(i_0_13306,plain,
c_Fun_Oinj__on(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1))),X3),
inference(split_conjunct,[status(thm)],[i_0_7682]),
[final] ).
cnf(i_0_13307,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk304_3(X1,X2,X3))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7683]),
[final] ).
cnf(i_0_13308,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk212_3(X1,X2,X3))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7684]),
[final] ).
cnf(i_0_13309,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),hAPP(c_Nat_OSuc,X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7685]),
[final] ).
cnf(i_0_13310,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7686]),
[final] ).
cnf(i_0_13311,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7687]),
[final] ).
cnf(i_0_13312,plain,
hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),c_Option_Ooption_ONone(X2)),X4) = c_Option_Ooption_ONone(X2),
inference(split_conjunct,[status(thm)],[i_0_7688]),
[final] ).
cnf(i_0_13313,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X2)),
inference(split_conjunct,[status(thm)],[i_0_7689]),
[final] ).
cnf(i_0_13314,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3)),
inference(split_conjunct,[status(thm)],[i_0_7690]),
[final] ).
cnf(i_0_13315,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X2)),
inference(split_conjunct,[status(thm)],[i_0_7691]),
[final] ).
cnf(i_0_13316,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_13317,plain,
( c_Divides_OnegDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5296]),
[final] ).
cnf(i_0_13318,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X5),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X3)),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X5),c_List_Oremove1(X2,X3,X4))))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7692]),
[final] ).
cnf(i_0_13319,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_7693]),
[final] ).
cnf(i_0_13320,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_7694]),
[final] ).
cnf(i_0_13321,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_7695]),
[final] ).
cnf(i_0_13322,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_7696]),
[final] ).
cnf(i_0_13323,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_7697]),
[final] ).
cnf(i_0_13324,plain,
( X1 = hAPP(X2,esk167_4(X3,X2,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(c_Set_Oimage(X4,X5,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7048]),
[final] ).
cnf(i_0_13325,plain,
c_Product__Type_Oprod_Oprod__rec(X1,X2,X3,X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_7698]),
[final] ).
cnf(i_0_13326,plain,
( c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X4,X3),c_Map_Odom(X1,X2,X3))
| ~ c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X3,c_Map_Odom(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7517]),
[final] ).
cnf(i_0_13327,plain,
hAPP(c_New__DSequence_Oneg__bind(X1,X2,X3,X4),X5) = c_Lazy__Sequence_Ohb__bind(X1,X2,hAPP(X3,X5),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7699]),
[final] ).
cnf(i_0_13328,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X5,X6),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| X4 != hAPP(c_Set_Oimage(X1,X5,X6),X2) ),
inference(split_conjunct,[status(thm)],[i_0_6527]),
[final] ).
cnf(i_0_13329,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3)),hAPP(c_Nat_OSuc,X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7700]),
[final] ).
cnf(i_0_13330,plain,
hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),
inference(split_conjunct,[status(thm)],[i_0_7701]),
[final] ).
cnf(i_0_13331,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(c_List_Ofoldl(X2,X2,hAPP(c_COMBC(X2,X2,X2),c_Orderings_Oord__class_Omax(X2)),X3),hAPP(c_List_Orev(X2),X1)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(hAPP(c_List_Onth(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)
| ~ class_Orderings_Olinorder(X2)
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1)) ),
inference(rw,[status(thm)],[i_0_7702,c_0_6070]),
[final] ).
cnf(i_0_13332,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X1),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7703]),
[final] ).
cnf(i_0_13333,plain,
( hBOOL(hAPP(X4,X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X4),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7704]),
[final] ).
cnf(i_0_13334,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X5),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7705]),
[final] ).
cnf(i_0_13335,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X5)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7705]),
[final] ).
cnf(i_0_13336,plain,
c_Sum__Type_Osum_Osum__size(X1,X2,X3,X4,hAPP(c_Sum__Type_OInl(X1,X2),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X3,X5)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_7706]),
[final] ).
cnf(i_0_13337,plain,
c_Sum__Type_Osum_Osum__size(X1,X2,X3,X4,hAPP(c_Sum__Type_OInr(X2,X1),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X4,X5)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_7707]),
[final] ).
cnf(i_0_13338,plain,
( hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))
| ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_7708]),
[final] ).
cnf(i_0_13339,plain,
c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_7709,c_0_6053]),
[final] ).
cnf(i_0_13340,plain,
c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_7710,c_0_6053]),
[final] ).
cnf(i_0_13341,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6928]),
[final] ).
cnf(i_0_13342,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6929]),
[final] ).
cnf(i_0_13343,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk500_3(X1,X2,X3))),esk501_3(X1,X2,X3))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13344,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| hAPP(c_Map_Omap__of(X1,X4,hAPP(hAPP(c_List_Ozip(X1,X4),X3),hAPP(hAPP(c_List_Omap(X1,X4),X5),X3))),X2) = c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[i_0_7599]),
[final] ).
cnf(i_0_13345,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X1,X3)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X1),X2)),hAPP(c_Relation_ORange(X1,X1),X3)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7711]),
[final] ).
cnf(i_0_13346,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk502_3(X2,X1,X3))),esk503_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X2,X1,X3)),X2))
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13347,plain,
( hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4) = X5
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| hAPP(hAPP(c_List_Oappend(X1),X3),X4) != hAPP(hAPP(c_List_Oappend(X1),X2),X5) ),
inference(split_conjunct,[status(thm)],[i_0_7032]),
[final] ).
cnf(i_0_13348,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk496_3(X1,X2,X3))),esk497_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13349,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7712]),
[final] ).
cnf(i_0_13350,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7713]),
[final] ).
cnf(i_0_13351,plain,
c_Relation_Oirrefl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),
inference(rw,[status(thm)],[i_0_7714,c_0_6053]),
[final] ).
cnf(i_0_13352,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7715]),
[final] ).
cnf(i_0_13353,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7716]),
[final] ).
cnf(i_0_13354,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7717]),
[final] ).
cnf(i_0_13355,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X3),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,tc_Nat_Onat),X3),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ c_Nat__Transfer_Onat__set(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7718]),
[final] ).
cnf(i_0_13356,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X3),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,tc_Nat_Onat),X3),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ c_Nat__Transfer_Onat__set(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7719]),
[final] ).
cnf(i_0_13357,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk498_3(X2,X1,X3))),esk499_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X2,X1,X3)),X2))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13358,plain,
c_Map_Omap__of(X1,X2,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),X3),X4)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__of(X1,X2,X4)),hAPP(c_Product__Type_Ofst(X1,X2),X3)),hAPP(c_Option_Ooption_OSome(X2),hAPP(c_Product__Type_Osnd(X1,X2),X3))),
inference(split_conjunct,[status(thm)],[i_0_7720]),
[final] ).
cnf(i_0_13359,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7721]),
[final] ).
cnf(i_0_13360,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7722]),
[final] ).
cnf(i_0_13361,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7723]),
[final] ).
cnf(i_0_13362,plain,
( c_Fun_Oinj__on(X1,X2,esk269_4(X3,X2,X4,X1),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X4)),hAPP(c_Finite__Set_Ocard(X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6575]),
[final] ).
cnf(i_0_13363,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X1),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7724]),
[final] ).
cnf(i_0_13364,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),X3) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7725]),
[final] ).
cnf(i_0_13365,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7726,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13366,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))),
inference(split_conjunct,[status(thm)],[i_0_7727]),
[final] ).
cnf(i_0_13367,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_7728]),
[final] ).
cnf(i_0_13368,plain,
hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_7729]),
[final] ).
cnf(i_0_13369,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7716]),
[final] ).
cnf(i_0_13370,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7715]),
[final] ).
cnf(i_0_13371,plain,
hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X4)),
inference(split_conjunct,[status(thm)],[i_0_7730]),
[final] ).
cnf(i_0_13372,plain,
hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X4)),
inference(split_conjunct,[status(thm)],[i_0_7731]),
[final] ).
cnf(i_0_13373,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3))),hAPP(c_List_Oset(X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_7732]),
[final] ).
cnf(i_0_13374,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X2,X3))),hAPP(c_List_Oset(X1),X3))),
inference(split_conjunct,[status(thm)],[i_0_7733]),
[final] ).
cnf(i_0_13375,plain,
( c_Fun_Oinj__on(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(c_Set_Oimage(X1,X2,X3),X4))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7734]),
[final] ).
cnf(i_0_13376,plain,
hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),X3)),
inference(split_conjunct,[status(thm)],[i_0_7735]),
[final] ).
cnf(i_0_13377,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk411_3(X2,X3,X1)),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7475]),
[final] ).
cnf(i_0_13378,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7736,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13379,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7715]),
[final] ).
cnf(i_0_13380,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7716]),
[final] ).
cnf(i_0_13381,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(c_List_Oset(X1),X5)) = hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X4),X5)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7737]),
[final] ).
cnf(i_0_13382,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)),hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7738]),
[final] ).
cnf(i_0_13383,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7576]),
[final] ).
cnf(i_0_13384,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Ouminus__class_Ouminus(X1)),X3)),X4) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7739]),
[final] ).
cnf(i_0_13385,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7740]),
[final] ).
cnf(i_0_13386,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk449_3(X1,X3,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7741]),
[final] ).
cnf(i_0_13387,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7742]),
[final] ).
cnf(i_0_13388,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4)))
| hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_Relation_ODomain(X3,X3),X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_7381]),
[final] ).
cnf(i_0_13389,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7743,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13390,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))
| ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7744,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13391,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7716]),
[final] ).
cnf(i_0_13392,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7715]),
[final] ).
cnf(i_0_13393,plain,
( hBOOL(hAPP(hAPP(c_member(X5),X3),c_SetInterval_Oord_OgreaterThanLessThan(X5,X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7462]),
[final] ).
cnf(i_0_13394,plain,
( hBOOL(hAPP(hAPP(c_member(X5),X3),c_SetInterval_Oord_OatLeastAtMost(X5,X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7463]),
[final] ).
cnf(i_0_13395,plain,
( c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))
| ~ c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
inference(rw,[status(thm)],[i_0_7745,c_0_6062]),
[final] ).
cnf(i_0_13396,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk500_3(X1,X2,X3))),esk501_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13397,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk496_3(X1,X2,X3))),esk497_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13398,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4),X3),X5)),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(X5,X2)),X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6407]),
[final] ).
cnf(i_0_13399,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk483_3(X2,X3,X1)),esk484_3(X2,X3,X1)))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7746]),
[final] ).
cnf(i_0_13400,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7747]),
[final] ).
cnf(i_0_13401,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk502_3(X2,X1,X3))),esk503_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X2,X1,X3)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13402,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk498_3(X2,X1,X3))),esk499_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X2,X1,X3)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13403,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7062]),
[final] ).
cnf(i_0_13404,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7063]),
[final] ).
cnf(i_0_13405,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X2)) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7748]),
[final] ).
cnf(i_0_13406,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7749]),
[final] ).
cnf(i_0_13407,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk56_3(X1,X2,X3)),X3))
| hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7398]),
[final] ).
cnf(i_0_13408,plain,
hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,hAPP(c_COMBK(X2,X1),X4)),X5),X6) = X4,
inference(split_conjunct,[status(thm)],[i_0_7750]),
[final] ).
cnf(i_0_13409,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7359]),
[final] ).
cnf(i_0_13410,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7360]),
[final] ).
cnf(i_0_13411,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))),hAPP(c_List_Oset(X1),X3))),
inference(split_conjunct,[status(thm)],[i_0_7751]),
[final] ).
cnf(i_0_13412,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3))),hAPP(c_List_Oset(X1),X3))),
inference(split_conjunct,[status(thm)],[i_0_7752]),
[final] ).
cnf(i_0_13413,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk58_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7404]),
[final] ).
cnf(i_0_13414,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk177_3(X2,X1,X3)),esk176_3(X2,X1,X3))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3) = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7511]),
[final] ).
cnf(i_0_13415,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk179_3(X2,X1,X3)),esk178_3(X2,X1,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3) = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7512]),
[final] ).
cnf(i_0_13416,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7753]),
[final] ).
cnf(i_0_13417,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7754]),
[final] ).
cnf(i_0_13418,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7755]),
[final] ).
cnf(i_0_13419,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7459]),
[final] ).
cnf(i_0_13420,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7359]),
[final] ).
cnf(i_0_13421,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7756]),
[final] ).
cnf(i_0_13422,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7757]),
[final] ).
cnf(i_0_13423,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7758]),
[final] ).
cnf(i_0_13424,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7460]),
[final] ).
cnf(i_0_13425,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7360]),
[final] ).
cnf(i_0_13426,plain,
( X2 = hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk316_2(X2,X1)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk315_2(X2,X1))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7467]),
[final] ).
cnf(i_0_13427,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| c_Smallcheck_Osmall_H(X3,X1,X2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X3,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7759]),
[final] ).
cnf(i_0_13428,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X3),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_7703]),
[final] ).
cnf(i_0_13429,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7396]),
[final] ).
cnf(i_0_13430,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7397]),
[final] ).
cnf(i_0_13431,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk332_3(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk331_3(X2,X3,X1)),X2))
| c_Relation_Orefl__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6138]),
[final] ).
cnf(i_0_13432,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,tc_Int_Oint),X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,X2),c_Int_Oring__1__class_Oof__int(X1)),X3)),X4)
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7760]),
[final] ).
cnf(i_0_13433,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X1)),X3)),X4)
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7761]),
[final] ).
cnf(i_0_13434,plain,
( hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_7533]),
[final] ).
cnf(i_0_13435,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(rw,[status(thm)],[i_0_7762,c_0_6670]),
[final] ).
cnf(i_0_13436,plain,
( X3 = c_List_Olist_ONil(X1)
| hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) != c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
inference(rw,[status(thm)],[i_0_7763,c_0_6100]),
[final] ).
cnf(i_0_13437,plain,
( X3 = c_List_Olist_ONil(X1)
| c_List_Olist_ONil(X1) != hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
inference(rw,[status(thm)],[i_0_7764,c_0_6100]),
[final] ).
cnf(i_0_13438,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X2),X3)),hAPP(c_Relation_Oconverse(X1,X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_7765]),
[final] ).
cnf(i_0_13439,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X2),X3)),hAPP(c_Relation_Oconverse(X1,X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_7766]),
[final] ).
cnf(i_0_13440,plain,
( c_Map_Odom(X2,X3,X1) = hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))
| X1 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,tc_Option_Ooption(X3)),hAPP(c_COMBK(tc_Option_Ooption(X3),X2),c_Option_Ooption_ONone(X3))),X4),hAPP(c_Option_Ooption_OSome(X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7383]),
[final] ).
cnf(i_0_13441,plain,
hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4) = hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X4)),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_7767]),
[final] ).
cnf(i_0_13442,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Int_Oint),X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,X2),c_Int_Oring__1__class_Oof__int(X1)),X3)),X4)
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7768]),
[final] ).
cnf(i_0_13443,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X1)),X3)),X4)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7769]),
[final] ).
cnf(i_0_13444,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7717]),
[final] ).
cnf(i_0_13445,plain,
c_Fun_Oinj__on(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_7770]),
[final] ).
cnf(i_0_13446,plain,
hAPP(c_New__DSequence_Opos__bind(X1,X2,X3,X4),X5) = c_Lazy__Sequence_Obind(X1,X2,hAPP(X3,X5),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7771]),
[final] ).
cnf(i_0_13447,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X4))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7772]),
[final] ).
cnf(i_0_13448,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7773]),
[final] ).
cnf(i_0_13449,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X3,X5),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7774]),
[final] ).
cnf(i_0_13450,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7775,c_0_6135]),c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_13451,plain,
( c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7776]),
[final] ).
cnf(i_0_13452,plain,
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5297]),
[final] ).
cnf(i_0_13453,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X4,X5),X2),X3)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X3))
| ~ class_Orderings_Olinorder(X4) ),
inference(split_conjunct,[status(thm)],[i_0_7399]),
[final] ).
cnf(i_0_13454,plain,
( hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Odrop(X3),X1),X4)),X2) = hAPP(hAPP(c_List_Onth(X3),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7777]),
[final] ).
cnf(i_0_13455,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X1))),hAPP(X4,hAPP(c_Nat_OSuc,X1)))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_7778]),
[final] ).
cnf(i_0_13456,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk408_3(X2,X3,X1)),esk409_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7452]),
[final] ).
cnf(i_0_13457,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X4)),hAPP(hAPP(c_List_Onth(X1),X2),X3)))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7779]),
[final] ).
cnf(i_0_13458,plain,
( hAPP(hAPP(c_List_Ozip(X1,X3),hAPP(hAPP(c_List_Oappend(X1),X2),X5)),hAPP(hAPP(c_List_Oappend(X3),X4),X6)) = hAPP(hAPP(c_List_Oappend(tc_prod(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)),hAPP(hAPP(c_List_Ozip(X1,X3),X5),X6))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X6) ),
inference(split_conjunct,[status(thm)],[i_0_7780]),
[final] ).
cnf(i_0_13459,plain,
c_List_Olist_Olist__size(X1,X2,hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = c_List_Olist_Olist__size(X3,hAPP(c_Fun_Ocomp(X1,tc_Nat_Onat,X3,X2),X4),X5),
inference(split_conjunct,[status(thm)],[i_0_7781]),
[final] ).
cnf(i_0_13460,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Relation_Orefl__on(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6138]),
[final] ).
cnf(i_0_13461,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Relation_Orefl__on(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6625]),
[final] ).
cnf(i_0_13462,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X3))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7782]),
[final] ).
cnf(i_0_13463,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(X5,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7783]),
[final] ).
cnf(i_0_13464,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7784]),
[final] ).
cnf(i_0_13465,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk13_3(X3,X2,X1)),X3))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X3),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7785]),
[final] ).
cnf(i_0_13466,plain,
( hBOOL(hAPP(hAPP(X4,X5),X6))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4))
| ~ hBOOL(hAPP(hAPP(X3,X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_7786]),
[final] ).
cnf(i_0_13467,plain,
( hBOOL(hAPP(hAPP(X6,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_7787]),
[final] ).
cnf(i_0_13468,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6716]),
[final] ).
cnf(i_0_13469,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Set_Oinsert(X3),X4)),X5)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7539]),
[final] ).
cnf(i_0_13470,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7788]),
[final] ).
cnf(i_0_13471,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7789]),
[final] ).
cnf(i_0_13472,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7790]),
[final] ).
cnf(i_0_13473,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),esk78_3(X3,X2,X1))))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7791]),
[final] ).
cnf(i_0_13474,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7486]),
[final] ).
cnf(i_0_13475,plain,
c_Map_Orestrict__map(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4),X5) = c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7792]),
[final] ).
cnf(i_0_13476,plain,
hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6)) = hAPP(c_List_Ofoldl(X1,X2,X3,hAPP(hAPP(X3,X4),X5)),X6),
inference(split_conjunct,[status(thm)],[i_0_7793]),
[final] ).
cnf(i_0_13477,plain,
( X1 = c_List_Olist_ONil(tc_List_Olist(X2))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),c_List_Otranspose(X2,X1)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X2)),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X2))),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7794]),
[final] ).
cnf(i_0_13478,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7795]),
[final] ).
cnf(i_0_13479,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Oone__class_Oone(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7796]),
[final] ).
cnf(i_0_13480,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Oone__class_Oone(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7797]),
[final] ).
cnf(i_0_13481,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_7798]),
[final] ).
cnf(i_0_13482,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_7799]),
[final] ).
cnf(i_0_13483,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_7800]),
[final] ).
cnf(i_0_13484,plain,
hAPP(c_Relation_OImage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,X3),X4)),hAPP(c_Relation_OImage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_7801]),
[final] ).
cnf(i_0_13485,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_7802]),
[final] ).
cnf(i_0_13486,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X4)),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7803]),
[final] ).
cnf(i_0_13487,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X1,X2)),c_Predicate_OPowp(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7804]),
[final] ).
cnf(i_0_13488,plain,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X1,X2,X4,X3)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),c_Map_Odom(X1,X2,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7805]),
[final] ).
cnf(i_0_13489,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7806]),
[final] ).
cnf(i_0_13490,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7448]),
[final] ).
cnf(i_0_13491,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6931]),
[final] ).
cnf(i_0_13492,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6932]),
[final] ).
cnf(i_0_13493,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X6),X5))
| hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X6),X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7807]),
[final] ).
cnf(i_0_13494,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7447]),
[final] ).
cnf(i_0_13495,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7808]),
[final] ).
cnf(i_0_13496,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg))
| ~ hBOOL(hAPP(X2,hAPP(c_Int_ORep__Integ,esk308_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_7809]),
[final] ).
cnf(i_0_13497,plain,
( hAPP(X1,esk263_4(X2,X1,X3,X4)) = hAPP(X1,esk264_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7242]),
[final] ).
cnf(i_0_13498,plain,
( hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1),X5) = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X5)),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7456]),
[final] ).
cnf(i_0_13499,plain,
( hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1),X5) = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X5)),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7810]),
[final] ).
cnf(i_0_13500,plain,
c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
inference(split_conjunct,[status(thm)],[fact_type__definition__Integ]),
[final] ).
cnf(i_0_13501,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7811]),
[final] ).
cnf(i_0_13502,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7812]),
[final] ).
cnf(i_0_13503,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7813]),
[final] ).
cnf(i_0_13504,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7814]),
[final] ).
cnf(i_0_13505,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7815]),
[final] ).
cnf(i_0_13506,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7816]),
[final] ).
cnf(i_0_13507,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7817]),
[final] ).
cnf(i_0_13508,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7818]),
[final] ).
cnf(i_0_13509,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Relation_OImage(X1,X1,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7819]),
[final] ).
cnf(i_0_13510,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_7820]),
[final] ).
cnf(i_0_13511,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_7821]),
[final] ).
cnf(i_0_13512,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk502_3(X2,X1,X3))),esk503_3(X2,X1,X3))
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk500_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13513,plain,
( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk500_3(X2,X3,X1))),esk501_3(X2,X3,X1))
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk502_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13514,plain,
c_Fun_Ooverride__on(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X3,
inference(split_conjunct,[status(thm)],[i_0_7822]),
[final] ).
cnf(i_0_13515,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X4)),hAPP(X3,X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X5)),hAPP(X3,X4))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7823]),
[final] ).
cnf(i_0_13516,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSKIP),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_7824]),
[final] ).
cnf(i_0_13517,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSKIP),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_7825]),
[final] ).
cnf(i_0_13518,plain,
c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,hAPP(c_Option_Ooption_OSome(X2),X5)) = hAPP(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_7826]),
[final] ).
cnf(i_0_13519,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7827]),
[final] ).
cnf(i_0_13520,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6528]),
[final] ).
cnf(i_0_13521,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7828]),
[final] ).
cnf(i_0_13522,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X3 = X5
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_7829]),
[final] ).
cnf(i_0_13523,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X4 = X6
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_7830]),
[final] ).
cnf(i_0_13524,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4)))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7831]),
[final] ).
cnf(i_0_13525,plain,
( hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),esk95_3(X2,X4,X1))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Ozero__class_Ozero(X1))))
| ~ hBOOL(hAPP(X4,X3))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7585]),
[final] ).
cnf(i_0_13526,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7832]),
[final] ).
cnf(i_0_13527,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7833]),
[final] ).
cnf(i_0_13528,plain,
( c_Relation_Osingle__valued(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))
| ~ c_Relation_Osingle__valued(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7834]),
[final] ).
cnf(i_0_13529,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk498_3(X2,X1,X3))),esk499_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk497_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13530,plain,
( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk496_3(X2,X3,X1))),esk497_3(X2,X3,X1))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk499_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13531,plain,
( c_Hoare__Mirabelle_Otriple__valid(X1,X2,X5)
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,X2,esk337_4(X3,X4,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X5),X3))
| ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7194]),
[final] ).
cnf(i_0_13532,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7835,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_13533,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7836]),
[final] ).
cnf(i_0_13534,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7837]),
[final] ).
cnf(i_0_13535,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7838]),
[final] ).
cnf(i_0_13536,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7839]),
[final] ).
cnf(i_0_13537,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7840]),
[final] ).
cnf(i_0_13538,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7841]),
[final] ).
cnf(i_0_13539,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7842]),
[final] ).
cnf(i_0_13540,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7843]),
[final] ).
cnf(i_0_13541,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk11_4(X3,X4,X2,X1),X3,X4)
| ~ hBOOL(hAPP(X1,X4))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X4,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7844]),
[final] ).
cnf(i_0_13542,plain,
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,esk21_4(X3,X4,X2,X1),X3)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7845]),
[final] ).
cnf(i_0_13543,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(hAPP(c_List_Onth(X1),X2),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7846]),
[final] ).
cnf(i_0_13544,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X4)),hAPP(hAPP(c_List_Onth(X1),X2),X3)))
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7545]),
[final] ).
cnf(i_0_13545,plain,
c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_type__definition__code__numeral]),
[final] ).
cnf(i_0_13546,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X2)),X3) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)),X3),
inference(split_conjunct,[status(thm)],[i_0_7847]),
[final] ).
cnf(i_0_13547,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7848]),
[final] ).
cnf(i_0_13548,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7849]),
[final] ).
cnf(i_0_13549,plain,
( hAPP(c_List_Ofilter(X2,X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X6),X4)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X6),hAPP(c_List_Ofilter(X2,X5),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))
| ~ hBOOL(hAPP(X5,X6)) ),
inference(split_conjunct,[status(thm)],[i_0_7850]),
[final] ).
cnf(i_0_13550,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_7728]),
[final] ).
cnf(i_0_13551,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X3))) = hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_7851,c_0_6015]),
[final] ).
cnf(i_0_13552,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = c_Groups_Oone__class_Oone(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ class_Int_Onumber__ring(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7852,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13553,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X2 = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[i_0_7853]),
[final] ).
cnf(i_0_13554,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6716]),
[final] ).
cnf(i_0_13555,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7854]),
[final] ).
cnf(i_0_13556,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7855]),
[final] ).
cnf(i_0_13557,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7856]),
[final] ).
cnf(i_0_13558,plain,
( hBOOL(hAPP(X1,esk137_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X2))
| ~ hBOOL(hAPP(X1,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6784]),
[final] ).
cnf(i_0_13559,plain,
( hBOOL(hAPP(X1,esk137_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X3))
| ~ hBOOL(hAPP(X1,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6784]),
[final] ).
cnf(i_0_13560,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7582]),
[final] ).
cnf(i_0_13561,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),esk190_3(X2,X3,X1)),esk191_3(X2,X3,X1)))
| hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7857]),
[final] ).
cnf(i_0_13562,plain,
( hAPP(X1,esk75_3(X2,X1,X3)) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk74_3(X2,X1,X3)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6221]),
[final] ).
cnf(i_0_13563,plain,
( hAPP(X1,esk73_3(X2,X1,X3)) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk72_3(X2,X1,X3)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6222]),
[final] ).
cnf(i_0_13564,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6)) = hAPP(X4,X5)
| ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7858]),
[final] ).
cnf(i_0_13565,plain,
( hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_OSuc,X1)),X3) = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),c_List_Olist_ONil(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7859]),
[final] ).
cnf(i_0_13566,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7860]),
[final] ).
cnf(i_0_13567,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7861]),
[final] ).
cnf(i_0_13568,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_fun(X1,X2),tc_fun(X1,X2)),X3),c_Fun_Ocomp(X2,X2,X1,X4)) = c_Fun_Ocomp(X2,X2,X1,hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_7862]),
[final] ).
cnf(i_0_13569,plain,
hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),
inference(split_conjunct,[status(thm)],[i_0_7863]),
[final] ).
cnf(i_0_13570,plain,
hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),
inference(split_conjunct,[status(thm)],[i_0_7864]),
[final] ).
cnf(i_0_13571,plain,
( X4 = X5
| hAPP(c_Set_Oimage(X1,X2,X3),X4) != hAPP(c_Set_Oimage(X1,X2,X3),X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7865]),
[final] ).
cnf(i_0_13572,plain,
( c_Natural_Oevaln(X1,X2,X3,esk11_4(X3,X2,X1,X4))
| ~ hBOOL(hAPP(X4,X2))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X1),X2,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7844]),
[final] ).
cnf(i_0_13573,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7754]),
[final] ).
cnf(i_0_13574,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7866]),
[final] ).
cnf(i_0_13575,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7359]),
[final] ).
cnf(i_0_13576,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7753]),
[final] ).
cnf(i_0_13577,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7459]),
[final] ).
cnf(i_0_13578,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7757]),
[final] ).
cnf(i_0_13579,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7867]),
[final] ).
cnf(i_0_13580,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7360]),
[final] ).
cnf(i_0_13581,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7756]),
[final] ).
cnf(i_0_13582,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7460]),
[final] ).
cnf(i_0_13583,plain,
( c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X5))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7868]),
[final] ).
cnf(i_0_13584,plain,
( c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X5))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_7869]),
[final] ).
cnf(i_0_13585,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7433]),
[final] ).
cnf(i_0_13586,plain,
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),esk440_3(X1,X2,X3)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_7175]),
[final] ).
cnf(i_0_13587,plain,
c_Map_Omap__upds(X1,X2,X3,c_List_Olist_ONil(X1),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_7870]),
[final] ).
cnf(i_0_13588,plain,
c_Map_Omap__upds(X1,X2,X3,X4,c_List_Olist_ONil(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_7871]),
[final] ).
cnf(i_0_13589,plain,
c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,c_Option_Ooption_ONone(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_7872]),
[final] ).
cnf(i_0_13590,plain,
hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5)),
inference(split_conjunct,[status(thm)],[i_0_7873]),
[final] ).
cnf(i_0_13591,plain,
hAPP(c_Relation_ORange(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5)),
inference(split_conjunct,[status(thm)],[i_0_7874]),
[final] ).
cnf(i_0_13592,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7717]),
[final] ).
cnf(i_0_13593,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk502_3(X2,X1,X3))),esk503_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk500_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13594,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk498_3(X2,X1,X3))),esk499_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk497_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13595,plain,
( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk500_3(X2,X3,X1))),esk501_3(X2,X3,X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk502_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13596,plain,
( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk496_3(X2,X3,X1))),esk497_3(X2,X3,X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk499_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13597,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7875]),
[final] ).
cnf(i_0_13598,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7876]),
[final] ).
cnf(i_0_13599,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7877]),
[final] ).
cnf(i_0_13600,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7878]),
[final] ).
cnf(i_0_13601,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7359]),
[final] ).
cnf(i_0_13602,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7360]),
[final] ).
cnf(i_0_13603,plain,
( hBOOL(hAPP(X1,esk69_3(X2,X1,X3)))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7157]),
[final] ).
cnf(i_0_13604,plain,
( hBOOL(hAPP(X1,esk65_3(X2,X1,X3)))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7158]),
[final] ).
cnf(i_0_13605,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7879]),
[final] ).
cnf(i_0_13606,plain,
hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X1,X3),hAPP(c_Product__Type_OPair(X2,X1),X4)),X5) = hAPP(X5,X4),
inference(split_conjunct,[status(thm)],[i_0_7880]),
[final] ).
cnf(i_0_13607,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk502_3(X2,X1,X3))),esk503_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X2,X1,X3)))
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13608,plain,
( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3))) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7881,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_13609,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk448_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
| hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7741]),
[final] ).
cnf(i_0_13610,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7882]),
[final] ).
cnf(i_0_13611,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7883]),
[final] ).
cnf(i_0_13612,plain,
hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X3),tc_List_Olist(X3)),X2),c_List_Orotate1(X3)),X5)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7884,c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_13613,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))) = hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7885,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_13614,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7679]),
[final] ).
cnf(i_0_13615,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7886]),
[final] ).
cnf(i_0_13616,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk498_3(X2,X1,X3))),esk499_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X2,X1,X3)))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13617,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(X1,esk158_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X2))
| hAPP(X1,X4) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7205]),
[final] ).
cnf(i_0_13618,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2,
inference(split_conjunct,[status(thm)],[i_0_7887]),
[final] ).
cnf(i_0_13619,plain,
( hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4) = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_OSuc,X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7888]),
[final] ).
cnf(i_0_13620,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X6)) = hAPP(hAPP(c_List_Olist_OCons(X5),X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),X6))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7889]),
[final] ).
cnf(i_0_13621,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6928]),
[final] ).
cnf(i_0_13622,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6929]),
[final] ).
cnf(i_0_13623,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk503_3(X1,X2,X3)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk500_3(X1,X2,X3))),esk501_3(X1,X2,X3))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13624,plain,
( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7890]),
[final] ).
cnf(i_0_13625,plain,
hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X3)),hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oinsert(X1),X2)),hAPP(c_Set_OPow(X1),X3))),
inference(split_conjunct,[status(thm)],[i_0_7891]),
[final] ).
cnf(i_0_13626,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7499]),
[final] ).
cnf(i_0_13627,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7500]),
[final] ).
cnf(i_0_13628,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7892]),
[final] ).
cnf(i_0_13629,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Ovimage(X1,X2,X3),X4)))
| hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7893]),
[final] ).
cnf(i_0_13630,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X4)),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7803]),
[final] ).
cnf(i_0_13631,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X4),X2)),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7803]),
[final] ).
cnf(i_0_13632,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7894]),
[final] ).
cnf(i_0_13633,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6748]),
[final] ).
cnf(i_0_13634,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))
| hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7895]),
[final] ).
cnf(i_0_13635,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk499_3(X1,X2,X3)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk496_3(X1,X2,X3))),esk497_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13636,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(X1),X2))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7896]),
[final] ).
cnf(i_0_13637,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7897]),
[final] ).
cnf(i_0_13638,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7898]),
[final] ).
cnf(i_0_13639,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7899]),
[final] ).
cnf(i_0_13640,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7897]),
[final] ).
cnf(i_0_13641,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7899]),
[final] ).
cnf(i_0_13642,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7854]),
[final] ).
cnf(i_0_13643,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7900]),
[final] ).
cnf(i_0_13644,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7855]),
[final] ).
cnf(i_0_13645,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7901]),
[final] ).
cnf(i_0_13646,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_7728]),
[final] ).
cnf(i_0_13647,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_7902]),
[final] ).
cnf(i_0_13648,plain,
( c_List_Oupto(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7903]),
[final] ).
cnf(i_0_13649,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X5)
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6594]),
[final] ).
cnf(i_0_13650,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6716]),
[final] ).
cnf(i_0_13651,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))
| ~ class_Groups_Oab__semigroup__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7904]),
[final] ).
cnf(i_0_13652,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X1,X2,X3)),X1))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13653,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X4))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7905]),
[final] ).
cnf(i_0_13654,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = c_Groups_Oone__class_Oone(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ class_Int_Onumber__ring(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7906,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13655,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7499]),
[final] ).
cnf(i_0_13656,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7500]),
[final] ).
cnf(i_0_13657,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7907]),
[final] ).
cnf(i_0_13658,plain,
( c_Partial__Function_Oflat__lub(X1,X3,X2) = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[i_0_7083]),
[final] ).
cnf(i_0_13659,plain,
( c_Orderings_Oorder_Omono(tc_Nat_Onat,X1,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk145_2(X2,X1))),hAPP(X2,esk146_2(X2,X1))))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7908]),
[final] ).
cnf(i_0_13660,plain,
( hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X6),X5)) = hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))
| ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7909]),
[final] ).
cnf(i_0_13661,plain,
( hAPP(c_Map_Omap__of(X1,X2,hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5) != c_Option_Ooption_ONone(X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_7910]),
[final] ).
cnf(i_0_13662,plain,
hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,tc_prod(X2,X3)),X4),c_Product__Type_OPair(X2,X3)) = X4,
inference(split_conjunct,[status(thm)],[i_0_7911]),
[final] ).
cnf(i_0_13663,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6931]),
[final] ).
cnf(i_0_13664,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6932]),
[final] ).
cnf(i_0_13665,plain,
hAPP(c_Set_OPow(X1),X2) = hAPP(c_Set_OCollect(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2)),
inference(split_conjunct,[status(thm)],[i_0_7912]),
[final] ).
cnf(i_0_13666,plain,
hAPP(c_List_Orev(X1),X2) = hAPP(c_List_Ofoldl(tc_List_Olist(X1),X1,hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_7913]),
[final] ).
cnf(i_0_13667,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X1,X2,X3)),X1))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13668,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(X1,esk160_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X2))
| hAPP(X1,X4) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7210]),
[final] ).
cnf(i_0_13669,plain,
( hAPP(c_List_Ofoldl(X2,X2,hAPP(c_COMBC(X2,X2,X2),c_Orderings_Oord__class_Omax(X2)),X3),hAPP(c_List_Orev(X2),X1)) = X3
| X1 != c_List_Olist_ONil(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1)) ),
inference(rw,[status(thm)],[i_0_7914,c_0_6070]),
[final] ).
cnf(i_0_13670,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),c_Nat_Osemiring__1__class_Oof__nat(X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7915]),
[final] ).
cnf(i_0_13671,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7916,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13672,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| hAPP(hAPP(c_List_Omap(X1,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X4),X5),X2),X6)),X3) = hAPP(hAPP(c_List_Omap(X1,X4),X5),X3) ),
inference(split_conjunct,[status(thm)],[i_0_7917]),
[final] ).
cnf(i_0_13673,plain,
( c_Wellfounded_Oacyclic(X1,X3)
| ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7918]),
[final] ).
cnf(i_0_13674,plain,
( c_Wellfounded_Owf(X1,X3)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7919]),
[final] ).
cnf(i_0_13675,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7920]),
[final] ).
cnf(i_0_13676,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7062]),
[final] ).
cnf(i_0_13677,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7063]),
[final] ).
cnf(i_0_13678,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X3,tc_HOL_Obool)),X2)) = hAPP(c_Finite__Set_Ocard(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))
| esk405_3(X1,X2,X3) != esk406_3(X1,X2,X3)
| hAPP(c_Finite__Set_Ocard(X3),esk404_3(X1,X2,X3)) != X1
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7265]),
[final] ).
cnf(i_0_13679,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_7921]),
[final] ).
cnf(i_0_13680,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_7922]),
[final] ).
cnf(i_0_13681,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_7923]),
[final] ).
cnf(i_0_13682,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7924]),
[final] ).
cnf(i_0_13683,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7925]),
[final] ).
cnf(i_0_13684,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7926]),
[final] ).
cnf(i_0_13685,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X4,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_7927]),
[final] ).
cnf(i_0_13686,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X6)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X5,X4,X6) ),
inference(split_conjunct,[status(thm)],[i_0_7015]),
[final] ).
cnf(i_0_13687,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X6)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X5,X4,X6) ),
inference(split_conjunct,[status(thm)],[i_0_7928]),
[final] ).
cnf(i_0_13688,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_List_Oset(X1),X3))),
inference(split_conjunct,[status(thm)],[i_0_7929]),
[final] ).
cnf(i_0_13689,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk502_3(X2,X1,X3))),esk503_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X2,X1,X3)))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13690,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk498_3(X2,X1,X3))),esk499_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X2,X1,X3)))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13691,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
inference(split_conjunct,[status(thm)],[i_0_7930]),
[final] ).
cnf(i_0_13692,plain,
( X2 = X4
| X3 = X5
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7931]),
[final] ).
cnf(i_0_13693,plain,
( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(rw,[status(thm)],[i_0_7932,c_0_6135]),
[final] ).
cnf(i_0_13694,plain,
( c_Predicate_Oreflp(X1,X2)
| ~ c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7933]),
[final] ).
cnf(i_0_13695,plain,
( c_Divides_OnegDivAlg(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5296]),
[final] ).
cnf(i_0_13696,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk56_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7398]),
[final] ).
cnf(i_0_13697,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7934]),
[final] ).
cnf(i_0_13698,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
inference(rw,[status(thm)],[i_0_7935,c_0_6015]),
[final] ).
cnf(i_0_13699,plain,
c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk283_4(X3,X4,X2,X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3)),
inference(split_conjunct,[status(thm)],[i_0_6486]),
[final] ).
cnf(i_0_13700,plain,
( hBOOL(hAPP(hAPP(c_member(X3),hAPP(X4,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Ovimage(X1,X3,X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7936]),
[final] ).
cnf(i_0_13701,plain,
( hBOOL(hAPP(hAPP(c_member(X3),hAPP(X4,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Ovimage(X1,X3,X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_7937]),
[final] ).
cnf(i_0_13702,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X4),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7938]),
[final] ).
cnf(i_0_13703,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk503_3(X1,X2,X3)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk500_3(X1,X2,X3))),esk501_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13704,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk499_3(X1,X2,X3)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk496_3(X1,X2,X3))),esk497_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13705,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Set_Oimage(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X4),X5),X2),X6)),X3) = hAPP(c_Set_Oimage(X1,X4,X5),X3) ),
inference(split_conjunct,[status(thm)],[i_0_7123]),
[final] ).
cnf(i_0_13706,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7459]),
[final] ).
cnf(i_0_13707,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7459]),
[final] ).
cnf(i_0_13708,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7460]),
[final] ).
cnf(i_0_13709,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7460]),
[final] ).
cnf(i_0_13710,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7459]),
[final] ).
cnf(i_0_13711,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7460]),
[final] ).
cnf(i_0_13712,plain,
hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = c_Nat_Onat_Onat__case(tc_List_Olist(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Odrop(X1)),X4),X2),
inference(split_conjunct,[status(thm)],[i_0_7939]),
[final] ).
cnf(i_0_13713,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Oone__class_Oone(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7940]),
[final] ).
cnf(i_0_13714,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Oone__class_Oone(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7941]),
[final] ).
cnf(i_0_13715,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2),X3)))
| hAPP(c_Random_Opick(X2,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),X3),X4)),X1) = hAPP(c_Random_Opick(X2,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7942]),
[final] ).
cnf(i_0_13716,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7943,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13717,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7944,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13718,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7945,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13719,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7946,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13720,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7947]),
[final] ).
cnf(i_0_13721,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7948]),
[final] ).
cnf(i_0_13722,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6716]),
[final] ).
cnf(i_0_13723,plain,
hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_7949]),
[final] ).
cnf(i_0_13724,plain,
hAPP(c_Relation_ORange(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_ORange(X1,X2),X3)),hAPP(c_Relation_ORange(X1,X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_7950]),
[final] ).
cnf(i_0_13725,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Olist__update(X1,X4),X5),X6)) = hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)),X5),hAPP(X3,X6)),
inference(split_conjunct,[status(thm)],[i_0_7951]),
[final] ).
cnf(i_0_13726,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk58_3(X2,X3,X1)))
| hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7404]),
[final] ).
cnf(i_0_13727,plain,
hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X2,hAPP(X3,X5),c_Option_Ooption_OSome(X2)),hAPP(X4,X5)),
inference(split_conjunct,[status(thm)],[i_0_7952]),
[final] ).
cnf(i_0_13728,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7953]),
[final] ).
cnf(i_0_13729,plain,
( X1 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7954]),
[final] ).
cnf(i_0_13730,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X3),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7955]),
[final] ).
cnf(i_0_13731,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X3),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7956]),
[final] ).
cnf(i_0_13732,plain,
( c_Map_Odom(X3,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X2)),X4),X5),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),c_Map_Odom(X3,X2,X4)),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| X1 != c_Option_Ooption_ONone(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7957]),
[final] ).
cnf(i_0_13733,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7958]),
[final] ).
cnf(i_0_13734,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7894]),
[final] ).
cnf(i_0_13735,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk425_3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7959]),
[final] ).
cnf(i_0_13736,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7960]),
[final] ).
cnf(i_0_13737,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk224_3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7961]),
[final] ).
cnf(i_0_13738,plain,
( hAPP(c_Fun_Othe__inv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(X3,X4)) = X4
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_7962]),
[final] ).
cnf(i_0_13739,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X1,X2,X3)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13740,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X1,X2,X3)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13741,plain,
( hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X4)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),X6)),X4)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7963]),
[final] ).
cnf(i_0_13742,plain,
( c_Wellfounded_OwfP(X1,X3)
| ~ c_Wellfounded_OwfP(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7964]),
[final] ).
cnf(i_0_13743,plain,
( X2 = X3
| hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) != hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_7965]),
[final] ).
cnf(i_0_13744,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7966]),
[final] ).
cnf(i_0_13745,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7967]),
[final] ).
cnf(i_0_13746,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7968]),
[final] ).
cnf(i_0_13747,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7969]),
[final] ).
cnf(i_0_13748,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ class_Rings_Oordered__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7970]),
[final] ).
cnf(i_0_13749,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Rings_Oordered__comm__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7971]),
[final] ).
cnf(i_0_13750,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Rings_Oordered__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7972]),
[final] ).
cnf(i_0_13751,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7660]),
[final] ).
cnf(i_0_13752,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7973]),
[final] ).
cnf(i_0_13753,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7715]),
[final] ).
cnf(i_0_13754,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7974]),
[final] ).
cnf(i_0_13755,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7716]),
[final] ).
cnf(i_0_13756,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7975]),
[final] ).
cnf(i_0_13757,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7976]),
[final] ).
cnf(i_0_13758,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7666]),
[final] ).
cnf(i_0_13759,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X6)),
inference(split_conjunct,[status(thm)],[i_0_7977]),
[final] ).
cnf(i_0_13760,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7978]),
[final] ).
cnf(i_0_13761,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7979]),
[final] ).
cnf(i_0_13762,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7980]),
[final] ).
cnf(i_0_13763,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
| ~ c_Nat__Transfer_Onat__set(X2)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7981]),
[final] ).
cnf(i_0_13764,plain,
( c_Big__Operators_Olinorder__class_OMax(X1,X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk362_3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7982]),
[final] ).
cnf(i_0_13765,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_5441]),
[final] ).
cnf(i_0_13766,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7983]),
[final] ).
cnf(i_0_13767,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7984]),
[final] ).
cnf(i_0_13768,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7985]),
[final] ).
cnf(i_0_13769,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X2)
| ~ c_Natural_Oevaln(X1,X2,X3,X4)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7844]),
[final] ).
cnf(i_0_13770,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7684]),
[final] ).
cnf(i_0_13771,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7986]),
[final] ).
cnf(i_0_13772,plain,
( c_Fun_Oinj__on(X1,X2,X3,X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7987]),
[final] ).
cnf(i_0_13773,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),
inference(split_conjunct,[status(thm)],[i_0_7988]),
[final] ).
cnf(i_0_13774,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Ortrancl(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_7989]),
[final] ).
cnf(i_0_13775,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7990,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_13776,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7991,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_13777,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7992]),
[final] ).
cnf(i_0_13778,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7993,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_13779,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7994,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_13780,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7967]),
[final] ).
cnf(i_0_13781,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7966]),
[final] ).
cnf(i_0_13782,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7995]),
[final] ).
cnf(i_0_13783,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_7996]),
[final] ).
cnf(i_0_13784,plain,
( hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7997]),
[final] ).
cnf(i_0_13785,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),c_List_Otranspose(X2,X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_List_Olist_ONil(tc_List_Olist(X2))
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X2))),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7794]),
[final] ).
cnf(i_0_13786,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7998]),
[final] ).
cnf(i_0_13787,plain,
( hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X6) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(X3,X5) != X6
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7999]),
[final] ).
cnf(i_0_13788,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Map_Orestrict__map(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),X6),X3) = c_Map_Orestrict__map(X1,X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6621]),
[final] ).
cnf(i_0_13789,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8000]),
[final] ).
cnf(i_0_13790,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7978]),
[final] ).
cnf(i_0_13791,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7978]),
[final] ).
cnf(i_0_13792,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7979]),
[final] ).
cnf(i_0_13793,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7979]),
[final] ).
cnf(i_0_13794,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7980]),
[final] ).
cnf(i_0_13795,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7980]),
[final] ).
cnf(i_0_13796,plain,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6773]),
[final] ).
cnf(i_0_13797,plain,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6773]),
[final] ).
cnf(i_0_13798,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7589]),
[final] ).
cnf(i_0_13799,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8001]),
[final] ).
cnf(i_0_13800,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_7673]),
[final] ).
cnf(i_0_13801,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8002]),
[final] ).
cnf(i_0_13802,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_7676]),
[final] ).
cnf(i_0_13803,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8003]),
[final] ).
cnf(i_0_13804,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8004]),
[final] ).
cnf(i_0_13805,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8005]),
[final] ).
cnf(i_0_13806,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7686]),
[final] ).
cnf(i_0_13807,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8006]),
[final] ).
cnf(i_0_13808,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7715]),
[final] ).
cnf(i_0_13809,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8007]),
[final] ).
cnf(i_0_13810,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7716]),
[final] ).
cnf(i_0_13811,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8008]),
[final] ).
cnf(i_0_13812,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7687]),
[final] ).
cnf(i_0_13813,plain,
( X1 = hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
| hAPP(hAPP(c_List_Oappend(X2),X1),X4) != hAPP(hAPP(c_List_Oappend(X2),X3),X5) ),
inference(split_conjunct,[status(thm)],[i_0_7032]),
[final] ).
cnf(i_0_13814,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7712]),
[final] ).
cnf(i_0_13815,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7713]),
[final] ).
cnf(i_0_13816,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),X3)
| hAPP(X5,X2) = c_Groups_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Fields_Ofield(X4) ),
inference(split_conjunct,[status(thm)],[i_0_7631]),
[final] ).
cnf(i_0_13817,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk354_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7075]),
[final] ).
cnf(i_0_13818,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk353_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7076]),
[final] ).
cnf(i_0_13819,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk275_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7077]),
[final] ).
cnf(i_0_13820,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8009]),
[final] ).
cnf(i_0_13821,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8010]),
[final] ).
cnf(i_0_13822,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3)))
| hAPP(c_Map_Omap__of(X1,X2,hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5) != hAPP(c_Option_Ooption_OSome(X2),X6)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_6991]),
[final] ).
cnf(i_0_13823,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7894]),
[final] ).
cnf(i_0_13824,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7978]),
[final] ).
cnf(i_0_13825,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7979]),
[final] ).
cnf(i_0_13826,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7980]),
[final] ).
cnf(i_0_13827,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8011]),
[final] ).
cnf(i_0_13828,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8012,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13829,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6450]),
[final] ).
cnf(i_0_13830,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X4,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_7522]),
[final] ).
cnf(i_0_13831,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ class_Int_Onumber(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8013]),
[final] ).
cnf(i_0_13832,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_8014]),
[final] ).
cnf(i_0_13833,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X2),X1),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X2)),X3)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8015]),
[final] ).
cnf(i_0_13834,plain,
hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_8016]),
[final] ).
cnf(i_0_13835,plain,
hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_8017]),
[final] ).
cnf(i_0_13836,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2))
| ~ c_Nitpick_Orefl_H(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7156]),
[final] ).
cnf(i_0_13837,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8018]),
[final] ).
cnf(i_0_13838,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X5)))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8019]),
[final] ).
cnf(i_0_13839,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X5)))
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8020]),
[final] ).
cnf(i_0_13840,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X5)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8021]),
[final] ).
cnf(i_0_13841,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8022]),
[final] ).
cnf(i_0_13842,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8023]),
[final] ).
cnf(i_0_13843,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8024]),
[final] ).
cnf(i_0_13844,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8025]),
[final] ).
cnf(i_0_13845,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8026]),
[final] ).
cnf(i_0_13846,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Groups_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[i_0_7649]),
[final] ).
cnf(i_0_13847,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8027]),
[final] ).
cnf(i_0_13848,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8028]),
[final] ).
cnf(i_0_13849,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X5),X4)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8029]),
[final] ).
cnf(i_0_13850,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8030]),
[final] ).
cnf(i_0_13851,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2))
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8031]),
[final] ).
cnf(i_0_13852,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8032]),
[final] ).
cnf(i_0_13853,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8033]),
[final] ).
cnf(i_0_13854,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Ovimage(X3,X1,X4),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ c_Fun_Oinj__on(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8034]),
[final] ).
cnf(i_0_13855,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X4),X5)),hAPP(X5,X3)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8035]),
[final] ).
cnf(i_0_13856,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4)))),X3)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8036]),
[final] ).
cnf(i_0_13857,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8037]),
[final] ).
cnf(i_0_13858,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool)),X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8038]),
[final] ).
cnf(i_0_13859,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool)),X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6538]),
[final] ).
cnf(i_0_13860,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk400_3(X2,X3,X1)),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8039]),
[final] ).
cnf(i_0_13861,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6748]),
[final] ).
cnf(i_0_13862,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7895]),
[final] ).
cnf(i_0_13863,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),X4)) = hAPP(hAPP(X3,X6),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),X4))
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8040]),
[final] ).
cnf(i_0_13864,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X2)))
| hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8041]),
[final] ).
cnf(i_0_13865,plain,
( c_Natural_Oevaln(X1,X2,X3,X4)
| c_Natural_Oevaln(X5,X2,X3,X4)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X6,X5,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8042]),
[final] ).
cnf(i_0_13866,plain,
( c_Natural_Oevaln(X1,X2,X3,X4)
| c_Natural_Oevaln(X5,X2,X3,X4)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X6,X5,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8043]),
[final] ).
cnf(i_0_13867,plain,
( c_Natural_Oevaln(X1,X2,X3,X4)
| c_Natural_Oevaln(X5,X2,X3,X4)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X6,X5,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8044]),
[final] ).
cnf(i_0_13868,plain,
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X6)
| ~ c_Natural_Oevaln(X1,X2,X3,X4)
| ~ c_Natural_Oevaln(X5,X4,X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_7023]),
[final] ).
cnf(i_0_13869,plain,
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X6)
| ~ c_Natural_Oevaln(X1,X2,X3,X4)
| ~ c_Natural_Oevaln(X5,X4,X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_8045]),
[final] ).
cnf(i_0_13870,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8046]),
[final] ).
cnf(i_0_13871,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8047]),
[final] ).
cnf(i_0_13872,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_8048]),
[final] ).
cnf(i_0_13873,plain,
( hBOOL(hAPP(hAPP(X5,X6),X8))
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(X3,X6),X7))
| ~ c_Natural_Oevaln(X4,X7,X2,X8) ),
inference(split_conjunct,[status(thm)],[i_0_6809]),
[final] ).
cnf(i_0_13874,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
| hAPP(X1,esk394_4(X1,X2,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7251]),
[final] ).
cnf(i_0_13875,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| hAPP(X1,esk164_4(X1,X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7252]),
[final] ).
cnf(i_0_13876,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)
| hAPP(X1,esk163_4(X1,X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7253]),
[final] ).
cnf(i_0_13877,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)
| hAPP(X1,esk395_4(X1,X2,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7254]),
[final] ).
cnf(i_0_13878,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),
inference(split_conjunct,[status(thm)],[i_0_8049]),
[final] ).
cnf(i_0_13879,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),
inference(split_conjunct,[status(thm)],[i_0_8050]),
[final] ).
cnf(i_0_13880,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk63_3(X2,X1,X3))),esk64_3(X2,X1,X3))
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8051]),
[final] ).
cnf(i_0_13881,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk304_3(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7683]),
[final] ).
cnf(i_0_13882,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk212_3(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7684]),
[final] ).
cnf(i_0_13883,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk468_3(X2,X3,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8052]),
[final] ).
cnf(i_0_13884,plain,
c_List_Olist_Olist__size(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),c_List_Olist_Olist__size(X1,X2,X4))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_8053]),
[final] ).
cnf(i_0_13885,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X1),X4))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7703]),
[final] ).
cnf(i_0_13886,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7486]),
[final] ).
cnf(i_0_13887,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X5)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8054]),
[final] ).
cnf(i_0_13888,plain,
c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2)),
inference(split_conjunct,[status(thm)],[i_0_8055]),
[final] ).
cnf(i_0_13889,plain,
c_Random_Oselect__weight(X1,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X1),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X2)),X3)) = c_Random_Oselect__weight(X1,X3),
inference(split_conjunct,[status(thm)],[i_0_8056]),
[final] ).
cnf(i_0_13890,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7628]),
[final] ).
cnf(i_0_13891,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_8057]),
[final] ).
cnf(i_0_13892,plain,
( c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)) = c_List_Otranspose(X1,X2)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X1)),c_List_Otranspose__rel(X1)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8058]),
[final] ).
cnf(i_0_13893,plain,
hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X4),hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1))) = X4,
inference(rw,[status(thm)],[i_0_8059,c_0_6070]),
[final] ).
cnf(i_0_13894,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7934]),
[final] ).
cnf(i_0_13895,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8060]),
[final] ).
cnf(i_0_13896,plain,
( X3 = X2
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8061]),
[final] ).
cnf(i_0_13897,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8062]),
[final] ).
cnf(i_0_13898,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)) = hAPP(hAPP(c_Relation_Orel__comp(X2,X3,X1),hAPP(c_Relation_Oconverse(X3,X2),X5)),hAPP(c_Relation_Oconverse(X1,X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_8063]),
[final] ).
cnf(i_0_13899,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1) = X4
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_8064]),
[final] ).
cnf(i_0_13900,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk402_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7947]),
[final] ).
cnf(i_0_13901,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8065]),
[final] ).
cnf(i_0_13902,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8066]),
[final] ).
cnf(i_0_13903,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk61_3(X2,X1,X3))),esk62_3(X2,X1,X3))
| hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8067]),
[final] ).
cnf(i_0_13904,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)) = c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8068]),
[final] ).
cnf(i_0_13905,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)) = c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8069]),
[final] ).
cnf(i_0_13906,plain,
hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_Nat_OSuc,X2)),c_List_Orotate1(X1)),X3) = hAPP(c_List_Orotate1(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8070,c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_13907,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk263_4(X1,X2,X3,X4) != esk264_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7242]),
[final] ).
cnf(i_0_13908,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),X6)),X4)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8071]),
[final] ).
cnf(i_0_13909,plain,
( hAPP(c_Map_Omap__add(X1,X3,X5,X4),X2) = hAPP(X4,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8072]),
[final] ).
cnf(i_0_13910,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X5))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7097]),
[final] ).
cnf(i_0_13911,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X5))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8073]),
[final] ).
cnf(i_0_13912,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk500_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13913,plain,
( hAPP(c_Random_Opick(X2,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),X3),X4)),X1) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X2),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7942]),
[final] ).
cnf(i_0_13914,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4)
| X1 != X3
| c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) != X4
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8074,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_13915,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))),
inference(split_conjunct,[status(thm)],[i_0_8075]),
[final] ).
cnf(i_0_13916,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X2,X3,X1)),X2))
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk502_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13917,plain,
( X2 = X5
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
| ~ hBOOL(hAPP(c_List_Odistinct(X3),X4))
| c_Map_Omap__of(X3,X1,hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2)) != c_Map_Omap__of(X3,X1,hAPP(hAPP(c_List_Ozip(X3,X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8076]),
[final] ).
cnf(i_0_13918,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk497_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13919,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7897]),
[final] ).
cnf(i_0_13920,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8077]),
[final] ).
cnf(i_0_13921,plain,
c_Map_Odom(X1,X2,c_Map_Omap__add(X1,X2,X3,X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X4)),c_Map_Odom(X1,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_8078]),
[final] ).
cnf(i_0_13922,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(c_Nat_OSuc,X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1))),hAPP(X4,X1))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8079]),
[final] ).
cnf(i_0_13923,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X2,X3,X1)),X2))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk499_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13924,plain,
( hBOOL(hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5))))
| ~ hBOOL(hAPP(X6,X5))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8080]),
[final] ).
cnf(i_0_13925,plain,
( hBOOL(hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5))))
| ~ hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X6,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8080]),
[final] ).
cnf(i_0_13926,plain,
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,X1)),X4),X5),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X4),hAPP(hAPP(c_COMBC(X2,X3,X1),X5),X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8081]),
[final] ).
cnf(i_0_13927,plain,
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,X1)),X4),X5),X6) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),hAPP(hAPP(c_COMBC(X2,X3,X1),X5),X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8082]),
[final] ).
cnf(i_0_13928,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8083]),
[final] ).
cnf(i_0_13929,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8083]),
[final] ).
cnf(i_0_13930,plain,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8084]),
[final] ).
cnf(i_0_13931,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk63_3(X2,X1,X3))),esk64_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8051]),
[final] ).
cnf(i_0_13932,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = X2,
inference(split_conjunct,[status(thm)],[i_0_8085]),
[final] ).
cnf(i_0_13933,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8086]),
[final] ).
cnf(i_0_13934,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk231_3(X2,X3,X1)),esk232_3(X2,X3,X1)))
| hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6702]),
[final] ).
cnf(i_0_13935,plain,
( c_Divides_OposDivAlg(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5298]),
[final] ).
cnf(i_0_13936,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X4),X3))
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7938]),
[final] ).
cnf(i_0_13937,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8087]),
[final] ).
cnf(i_0_13938,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8087]),
[final] ).
cnf(i_0_13939,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8088]),
[final] ).
cnf(i_0_13940,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8088]),
[final] ).
cnf(i_0_13941,plain,
( c_Wellfounded_OwfP(X1,X2)
| ~ c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8089]),
[final] ).
cnf(i_0_13942,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8090]),
[final] ).
cnf(i_0_13943,plain,
( X3 = X5
| hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)) != hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8091]),
[final] ).
cnf(i_0_13944,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8092]),
[final] ).
cnf(i_0_13945,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk351_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk351_2(X2,X1))))
| c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8093]),
[final] ).
cnf(i_0_13946,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,tc_HOL_Obool),X1),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8094]),
[final] ).
cnf(i_0_13947,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,tc_HOL_Obool),X1),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8095]),
[final] ).
cnf(i_0_13948,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8096]),
[final] ).
cnf(i_0_13949,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8097]),
[final] ).
cnf(i_0_13950,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8098]),
[final] ).
cnf(i_0_13951,plain,
( c_Nitpick_Onorm__frac(X2,X1) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6708]),
[final] ).
cnf(i_0_13952,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk224_3(X3,X1,X2)),esk224_3(X3,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X1),c_Relation_OId__on(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7961]),
[final] ).
cnf(i_0_13953,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8099]),
[final] ).
cnf(i_0_13954,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X5)),hAPP(X3,X5)) = hAPP(X3,X5)
| ~ c_Finite__Set_Ofolding__idem(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8100]),
[final] ).
cnf(i_0_13955,plain,
( c_Divides_OposDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5298]),
[final] ).
cnf(i_0_13956,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8101,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6169]),c_0_6016]),
[final] ).
cnf(i_0_13957,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))),X3)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8102]),
[final] ).
cnf(i_0_13958,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),
inference(rw,[status(thm)],[i_0_8103,c_0_6062]),
[final] ).
cnf(i_0_13959,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk502_3(X2,X1,X3))),esk503_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13960,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4)))) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8104,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_13961,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8105,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_13962,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7359]),
[final] ).
cnf(i_0_13963,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7360]),
[final] ).
cnf(i_0_13964,plain,
hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_8106]),
[final] ).
cnf(i_0_13965,plain,
( hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5) = X3
| hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3) != X4
| hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),X3) != X5
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5) ),
inference(split_conjunct,[status(thm)],[i_0_8107]),
[final] ).
cnf(i_0_13966,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1)),X2),X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7785]),
[final] ).
cnf(i_0_13967,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk61_3(X2,X1,X3))),esk62_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8067]),
[final] ).
cnf(i_0_13968,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_7738]),
[final] ).
cnf(i_0_13969,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| X2 = X5
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X3)),X1),X5),hAPP(c_Option_Ooption_OSome(X3),X7)),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8108]),
[final] ).
cnf(i_0_13970,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| X5 = X4
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X3)),X1),X7),hAPP(c_Option_Ooption_OSome(X3),X5)),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8108]),
[final] ).
cnf(i_0_13971,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8109]),
[final] ).
cnf(i_0_13972,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8109]),
[final] ).
cnf(i_0_13973,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8110]),
[final] ).
cnf(i_0_13974,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8111]),
[final] ).
cnf(i_0_13975,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk500_3(X1,X2,X3))),esk501_3(X1,X2,X3))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13976,plain,
hAPP(c_List_Orotate1(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(c_List_Orotate1(X1),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8112,c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_13977,plain,
( c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_List_Olistrelp(X4,X1,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_8113]),
[final] ).
cnf(i_0_13978,plain,
( c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_List_Olistrelp(X4,X1,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_8114]),
[final] ).
cnf(i_0_13979,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk498_3(X2,X1,X3))),esk499_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13980,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8115,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13981,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk500_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13982,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk497_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13983,plain,
( X1 = hAPP(c_Int_ORep__Integ,esk307_1(X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg)) ),
inference(split_conjunct,[status(thm)],[i_0_8116]),
[final] ).
cnf(i_0_13984,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk416_3(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8117]),
[final] ).
cnf(i_0_13985,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk476_3(X2,X3,X1)),c_List_Olists(X1,X2)))
| X3 = c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8118]),
[final] ).
cnf(i_0_13986,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk449_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)))
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7741]),
[final] ).
cnf(i_0_13987,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk496_3(X1,X2,X3))),esk497_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13988,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X2,X3,X1)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk502_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13989,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X2,X3,X1)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk499_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_13990,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))
| ~ hBOOL(hAPP(X1,esk448_3(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7741]),
[final] ).
cnf(i_0_13991,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(X2,hAPP(X3,X4)),hAPP(X3,X5))
| ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8119]),
[final] ).
cnf(i_0_13992,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8120]),
[final] ).
cnf(i_0_13993,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8121]),
[final] ).
cnf(i_0_13994,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8122]),
[final] ).
cnf(i_0_13995,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X1,X2,X3)))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_13996,plain,
( c_Fun_Oinj__on(X1,X2,esk268_4(X3,X2,X1,X4),X4)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X2,X1,X5),X3) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_6585]),
[final] ).
cnf(i_0_13997,plain,
( c_List_Olistrelp(X1,X2,X3,X4)
| ~ c_List_Olistrelp(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8113]),
[final] ).
cnf(i_0_13998,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X2))
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8123]),
[final] ).
cnf(i_0_13999,plain,
( hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)
| ~ epred1_3(X5,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14000,plain,
( hBOOL(hAPP(X5,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)
| ~ epred2_3(X5,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14001,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8124]),
[final] ).
cnf(i_0_14002,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8125]),
[final] ).
cnf(i_0_14003,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8126]),
[final] ).
cnf(i_0_14004,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8127]),
[final] ).
cnf(i_0_14005,plain,
( c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk341_2(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8128]),
[final] ).
cnf(i_0_14006,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8129]),
[final] ).
cnf(i_0_14007,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8130]),
[final] ).
cnf(i_0_14008,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X4))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7670]),
[final] ).
cnf(i_0_14009,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X4))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7669]),
[final] ).
cnf(i_0_14010,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8131]),
[final] ).
cnf(i_0_14011,plain,
( hAPP(c_Finite__Set_Ocard(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8132]),
[final] ).
cnf(i_0_14012,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8133]),
[final] ).
cnf(i_0_14013,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8134]),
[final] ).
cnf(i_0_14014,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7854]),
[final] ).
cnf(i_0_14015,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8135]),
[final] ).
cnf(i_0_14016,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7811]),
[final] ).
cnf(i_0_14017,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8136]),
[final] ).
cnf(i_0_14018,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8137]),
[final] ).
cnf(i_0_14019,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7815]),
[final] ).
cnf(i_0_14020,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8138]),
[final] ).
cnf(i_0_14021,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7966]),
[final] ).
cnf(i_0_14022,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8139]),
[final] ).
cnf(i_0_14023,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7967]),
[final] ).
cnf(i_0_14024,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7818]),
[final] ).
cnf(i_0_14025,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8140]),
[final] ).
cnf(i_0_14026,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X1,X2,X3)))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14027,plain,
( c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8141]),
[final] ).
cnf(i_0_14028,plain,
( c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8142]),
[final] ).
cnf(i_0_14029,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8143]),
[final] ).
cnf(i_0_14030,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_8144]),
[final] ).
cnf(i_0_14031,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_8145]),
[final] ).
cnf(i_0_14032,plain,
( c_Nitpick_Onorm__frac(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6708]),
[final] ).
cnf(i_0_14033,plain,
( c_Nitpick_Onorm__frac(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6708]),
[final] ).
cnf(i_0_14034,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk299_3(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8146]),
[final] ).
cnf(i_0_14035,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk296_3(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8147]),
[final] ).
cnf(i_0_14036,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk295_3(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8148]),
[final] ).
cnf(i_0_14037,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X3)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_14038,plain,
( X3 = X4
| X1 != X2
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X6)),X7),X2),hAPP(c_Option_Ooption_OSome(X6),X3)),X1) != hAPP(c_Option_Ooption_OSome(X6),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8108]),
[final] ).
cnf(i_0_14039,plain,
( hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = c_List_Olist_ONil(X1)
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk490_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
inference(rw,[status(thm)],[i_0_8149,c_0_6100]),
[final] ).
cnf(i_0_14040,plain,
( c_List_Olist_ONil(X1) = hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk489_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
inference(rw,[status(thm)],[i_0_8150,c_0_6100]),
[final] ).
cnf(i_0_14041,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8151]),
[final] ).
cnf(i_0_14042,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8152]),
[final] ).
cnf(i_0_14043,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk503_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X1,X2,X3)),X1))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14044,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8153]),
[final] ).
cnf(i_0_14045,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X4)))) = hAPP(hAPP(X3,X4),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,X4)),
inference(rw,[status(thm)],[i_0_8154,c_0_8155]),
[final] ).
cnf(i_0_14046,plain,
( hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)
| ~ epred1_3(X5,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14047,plain,
( hBOOL(hAPP(X5,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)
| ~ epred2_3(X5,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14048,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(c_List_Oset(X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8156]),
[final] ).
cnf(i_0_14049,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8157]),
[final] ).
cnf(i_0_14050,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8158]),
[final] ).
cnf(i_0_14051,plain,
( hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8159]),
[final] ).
cnf(i_0_14052,plain,
( hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8160]),
[final] ).
cnf(i_0_14053,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8161]),
[final] ).
cnf(i_0_14054,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8162]),
[final] ).
cnf(i_0_14055,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))),X2)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8163]),
[final] ).
cnf(i_0_14056,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk453_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8164]),
[final] ).
cnf(i_0_14057,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk499_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X1,X2,X3)),X1))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14058,plain,
( X1 = hAPP(c_Nat_OSuc,esk21_4(X2,X1,X3,X4))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X4),X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7845]),
[final] ).
cnf(i_0_14059,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8165]),
[final] ).
cnf(i_0_14060,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8166]),
[final] ).
cnf(i_0_14061,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8167]),
[final] ).
cnf(i_0_14062,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8168]),
[final] ).
cnf(i_0_14063,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8169]),
[final] ).
cnf(i_0_14064,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8170]),
[final] ).
cnf(i_0_14065,plain,
( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X6)) = hAPP(hAPP(c_List_Olist_OCons(X5),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X6))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7889]),
[final] ).
cnf(i_0_14066,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8171]),
[final] ).
cnf(i_0_14067,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8172]),
[final] ).
cnf(i_0_14068,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8173]),
[final] ).
cnf(i_0_14069,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8174]),
[final] ).
cnf(i_0_14070,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8175]),
[final] ).
cnf(i_0_14071,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8176]),
[final] ).
cnf(i_0_14072,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X3) = X3,
inference(rw,[status(thm)],[i_0_8177,c_0_6053]),
[final] ).
cnf(i_0_14073,plain,
( hAPP(X4,X2) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ c_Finite__Set_Ofolding__one(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7298]),
[final] ).
cnf(i_0_14074,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8178]),
[final] ).
cnf(i_0_14075,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8179]),
[final] ).
cnf(i_0_14076,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7978]),
[final] ).
cnf(i_0_14077,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7978]),
[final] ).
cnf(i_0_14078,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8180]),
[final] ).
cnf(i_0_14079,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8181]),
[final] ).
cnf(i_0_14080,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8182]),
[final] ).
cnf(i_0_14081,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8181]),
[final] ).
cnf(i_0_14082,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7979]),
[final] ).
cnf(i_0_14083,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7979]),
[final] ).
cnf(i_0_14084,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8183]),
[final] ).
cnf(i_0_14085,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8184]),
[final] ).
cnf(i_0_14086,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8185]),
[final] ).
cnf(i_0_14087,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7980]),
[final] ).
cnf(i_0_14088,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7980]),
[final] ).
cnf(i_0_14089,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8186]),
[final] ).
cnf(i_0_14090,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8187]),
[final] ).
cnf(i_0_14091,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8188]),
[final] ).
cnf(i_0_14092,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)))),
inference(split_conjunct,[status(thm)],[i_0_8189]),
[final] ).
cnf(i_0_14093,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk502_3(X2,X1,X3))),esk503_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14094,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk498_3(X2,X1,X3))),esk499_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14095,plain,
c_List_Otranspose(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),X4)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),c_List_Otranspose(X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_8190]),
[final] ).
cnf(i_0_14096,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = X2
| ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Ofield(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8191,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_14097,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = X2
| ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Ofield(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8192,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_14098,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8193]),
[final] ).
cnf(i_0_14099,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8194]),
[final] ).
cnf(i_0_14100,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8195]),
[final] ).
cnf(i_0_14101,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8196]),
[final] ).
cnf(i_0_14102,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2)),X3))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8195]),
[final] ).
cnf(i_0_14103,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2)),X3))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8196]),
[final] ).
cnf(i_0_14104,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8197]),
[final] ).
cnf(i_0_14105,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8198]),
[final] ).
cnf(i_0_14106,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8197]),
[final] ).
cnf(i_0_14107,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8198]),
[final] ).
cnf(i_0_14108,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8199]),
[final] ).
cnf(i_0_14109,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8199]),
[final] ).
cnf(i_0_14110,plain,
( X3 = X4
| hAPP(hAPP(c_List_Onth(X1),X2),X3) != hAPP(hAPP(c_List_Onth(X1),X2),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8200]),
[final] ).
cnf(i_0_14111,plain,
( X3 = X4
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| hAPP(hAPP(c_List_Onth(X1),X2),X3) != hAPP(hAPP(c_List_Onth(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8201]),
[final] ).
cnf(i_0_14112,plain,
( c_Fun_Oinj__on(X1,X2,X3,hAPP(c_List_Oset(X1),X4))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8202]),
[final] ).
cnf(i_0_14113,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk341_2(X1,X2)),X2))
| c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_8128]),
[final] ).
cnf(i_0_14114,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8203]),
[final] ).
cnf(i_0_14115,plain,
( c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8204]),
[final] ).
cnf(i_0_14116,plain,
( hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ c_Fun_Oinj__on(X1,X3,X4,hAPP(c_List_Oset(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8202]),
[final] ).
cnf(i_0_14117,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk500_3(X1,X2,X3))),esk501_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14118,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk496_3(X1,X2,X3))),esk497_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14119,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8205,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_14120,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),X4)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X6),X5)),X4)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8206]),
[final] ).
cnf(i_0_14121,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = X5
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6592]),
[final] ).
cnf(i_0_14122,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5) = X5
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_6593]),
[final] ).
cnf(i_0_14123,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk402_3(X2,X3,X1)),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7947]),
[final] ).
cnf(i_0_14124,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8207]),
[final] ).
cnf(i_0_14125,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8208]),
[final] ).
cnf(i_0_14126,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8209]),
[final] ).
cnf(i_0_14127,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3)))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8210]),
[final] ).
cnf(i_0_14128,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk295_3(X2,X3,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8148]),
[final] ).
cnf(i_0_14129,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk296_3(X2,X3,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8147]),
[final] ).
cnf(i_0_14130,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk299_3(X2,X3,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8146]),
[final] ).
cnf(i_0_14131,plain,
( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_Set_Ovimage(X5,X1,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8211]),
[final] ).
cnf(i_0_14132,plain,
( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_Set_Ovimage(X5,X1,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7937]),
[final] ).
cnf(i_0_14133,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(c_List_Ohd(X2),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X3),c_List_Orotate1(X2)),X1)) = hAPP(hAPP(c_List_Onth(X2),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
inference(rw,[status(thm)],[i_0_8212,c_0_6670]),
[final] ).
cnf(i_0_14134,plain,
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5299]),
[final] ).
cnf(i_0_14135,plain,
( c_List_Olinorder__class_Osorted(X1,X3)
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8213]),
[final] ).
cnf(i_0_14136,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X2)
| ~ hBOOL(hAPP(X5,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8051]),
[final] ).
cnf(i_0_14137,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2)),X3)))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8214]),
[final] ).
cnf(i_0_14138,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8215]),
[final] ).
cnf(i_0_14139,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8216]),
[final] ).
cnf(i_0_14140,plain,
( hAPP(hAPP(c_List_Onth(X2),hAPP(c_List_Orev(X2),X3)),X1) = hAPP(hAPP(c_List_Onth(X2),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_OSuc,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8217]),
[final] ).
cnf(i_0_14141,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X1),X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8010]),
[final] ).
cnf(i_0_14142,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(X5,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8218]),
[final] ).
cnf(i_0_14143,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(X5,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8219]),
[final] ).
cnf(i_0_14144,plain,
hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X3),X5) = hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X5),
inference(split_conjunct,[status(thm)],[i_0_8220]),
[final] ).
cnf(i_0_14145,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))),
inference(split_conjunct,[status(thm)],[i_0_8221]),
[final] ).
cnf(i_0_14146,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8222]),
[final] ).
cnf(i_0_14147,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8223]),
[final] ).
cnf(i_0_14148,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Nat_Osemiring__1__class_ONats(X1)))
| ~ class_Rings_Osemiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Nat_Osemiring__1__class_ONats(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Nat_Osemiring__1__class_ONats(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8224]),
[final] ).
cnf(i_0_14149,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8225]),
[final] ).
cnf(i_0_14150,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Nat_Osemiring__1__class_ONats(X1)))
| ~ class_Rings_Osemiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Nat_Osemiring__1__class_ONats(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Nat_Osemiring__1__class_ONats(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8226]),
[final] ).
cnf(i_0_14151,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8227]),
[final] ).
cnf(i_0_14152,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8228]),
[final] ).
cnf(i_0_14153,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8229]),
[final] ).
cnf(i_0_14154,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8230]),
[final] ).
cnf(i_0_14155,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X1,X2,X3)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14156,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X1,X2,X3)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14157,plain,
c_List_Olist_Olist__size(X1,X2,X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X1,tc_Nat_Onat),X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),
inference(split_conjunct,[status(thm)],[i_0_8231]),
[final] ).
cnf(i_0_14158,plain,
c_Map_Odom(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X4),
inference(split_conjunct,[status(thm)],[i_0_8232]),
[final] ).
cnf(i_0_14159,plain,
( hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)) = hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X4))
| c_Map_Omap__of(X1,X2,X3) != c_Map_Omap__of(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8233]),
[final] ).
cnf(i_0_14160,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),hAPP(X6,X2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(split_conjunct,[status(thm)],[i_0_6545]),
[final] ).
cnf(i_0_14161,plain,
( hAPP(c_Set_Oimage(X1,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8234]),
[final] ).
cnf(i_0_14162,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X4,X3))))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7920]),
[final] ).
cnf(i_0_14163,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_7635]),
[final] ).
cnf(i_0_14164,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_8057]),
[final] ).
cnf(i_0_14165,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_COMBK(X1,X2),X3)),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))),X3)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8235]),
[final] ).
cnf(i_0_14166,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8236]),
[final] ).
cnf(i_0_14167,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_8237]),
[final] ).
cnf(i_0_14168,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8238]),
[final] ).
cnf(i_0_14169,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8239]),
[final] ).
cnf(i_0_14170,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X6,X3,X1,X5),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8240]),
[final] ).
cnf(i_0_14171,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X6,X3,X1,X5),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8241]),
[final] ).
cnf(i_0_14172,plain,
( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7270]),
[final] ).
cnf(i_0_14173,plain,
( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7271]),
[final] ).
cnf(i_0_14174,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8242]),
[final] ).
cnf(i_0_14175,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8243]),
[final] ).
cnf(i_0_14176,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8244]),
[final] ).
cnf(i_0_14177,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8245]),
[final] ).
cnf(i_0_14178,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8246]),
[final] ).
cnf(i_0_14179,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7833]),
[final] ).
cnf(i_0_14180,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7832]),
[final] ).
cnf(i_0_14181,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8247]),
[final] ).
cnf(i_0_14182,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7836]),
[final] ).
cnf(i_0_14183,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8248]),
[final] ).
cnf(i_0_14184,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7838]),
[final] ).
cnf(i_0_14185,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8249]),
[final] ).
cnf(i_0_14186,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7841]),
[final] ).
cnf(i_0_14187,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8250]),
[final] ).
cnf(i_0_14188,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7843]),
[final] ).
cnf(i_0_14189,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8251]),
[final] ).
cnf(i_0_14190,plain,
hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)) = hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)),hAPP(c_List_Orev(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_8252]),
[final] ).
cnf(i_0_14191,plain,
hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)) = hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)),hAPP(c_List_Orev(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_8253]),
[final] ).
cnf(i_0_14192,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1) = X4
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_8064]),
[final] ).
cnf(i_0_14193,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8254]),
[final] ).
cnf(i_0_14194,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8255]),
[final] ).
cnf(i_0_14195,plain,
( X5 = X7
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X6),X4),hAPP(c_Option_Ooption_OSome(X2),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_8256]),
[final] ).
cnf(i_0_14196,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X3) ),
inference(split_conjunct,[status(thm)],[i_0_8257]),
[final] ).
cnf(i_0_14197,plain,
c_Divides_Opdivmod(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))),
inference(split_conjunct,[status(thm)],[i_0_8258]),
[final] ).
cnf(i_0_14198,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8259]),
[final] ).
cnf(i_0_14199,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk503_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X1,X2,X3)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14200,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk499_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X1,X2,X3)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14201,plain,
hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X4) = c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_8260]),
[final] ).
cnf(i_0_14202,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_8261]),
[final] ).
cnf(i_0_14203,plain,
hAPP(c_Relation_OField(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),c_Relation_OField(X1)),X2)),
inference(split_conjunct,[status(thm)],[i_0_8262]),
[final] ).
cnf(i_0_14204,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8097]),
[final] ).
cnf(i_0_14205,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8098]),
[final] ).
cnf(i_0_14206,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8263]),
[final] ).
cnf(i_0_14207,plain,
( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8264]),
[final] ).
cnf(i_0_14208,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8265]),
[final] ).
cnf(i_0_14209,plain,
( c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8141]),
[final] ).
cnf(i_0_14210,plain,
( c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8266]),
[final] ).
cnf(i_0_14211,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),
inference(split_conjunct,[status(thm)],[i_0_8267]),
[final] ).
cnf(i_0_14212,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),
inference(split_conjunct,[status(thm)],[i_0_8268]),
[final] ).
cnf(i_0_14213,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X4,X1,X5),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8269]),
[final] ).
cnf(i_0_14214,plain,
( hBOOL(hAPP(X4,hAPP(X3,X5)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8270]),
[final] ).
cnf(i_0_14215,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8240]),
[final] ).
cnf(i_0_14216,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8241]),
[final] ).
cnf(i_0_14217,plain,
( epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk502_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk500_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14218,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk398_3(X2,X3,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8271]),
[final] ).
cnf(i_0_14219,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk398_3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8271]),
[final] ).
cnf(i_0_14220,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))),X4)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8272]),
[final] ).
cnf(i_0_14221,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))),X4)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8273]),
[final] ).
cnf(i_0_14222,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))),X4)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8274]),
[final] ).
cnf(i_0_14223,plain,
hAPP(c_Option_Omap(X1,X2),X3) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X1,c_Option_Ooption_ONone(X2),hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3)),
inference(split_conjunct,[status(thm)],[i_0_8275]),
[final] ).
cnf(i_0_14224,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8276]),
[final] ).
cnf(i_0_14225,plain,
( hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Omap(X2,X4),X5),X3)),X1) = hAPP(X5,hAPP(hAPP(c_List_Onth(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8277]),
[final] ).
cnf(i_0_14226,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8278]),
[final] ).
cnf(i_0_14227,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nitpick_Onat__gcd(X2,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8279]),
[final] ).
cnf(i_0_14228,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8280]),
[final] ).
cnf(i_0_14229,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X5)))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X5))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7746]),
[final] ).
cnf(i_0_14230,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8281]),
[final] ).
cnf(i_0_14231,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8282]),
[final] ).
cnf(i_0_14232,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X2)
| ~ hBOOL(hAPP(X5,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8067]),
[final] ).
cnf(i_0_14233,plain,
( epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk499_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk497_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14234,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8283]),
[final] ).
cnf(i_0_14235,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_8284]),
[final] ).
cnf(i_0_14236,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8148]),
[final] ).
cnf(i_0_14237,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8147]),
[final] ).
cnf(i_0_14238,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8146]),
[final] ).
cnf(i_0_14239,plain,
( c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = c_List_Oremove1(X1,X3,c_List_Olinorder__class_Osorted__list__of__set(X1,X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8285]),
[final] ).
cnf(i_0_14240,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8209]),
[final] ).
cnf(i_0_14241,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2,X1),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8209]),
[final] ).
cnf(i_0_14242,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8286]),
[final] ).
cnf(i_0_14243,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7459]),
[final] ).
cnf(i_0_14244,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7460]),
[final] ).
cnf(i_0_14245,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk475_3(X2,X3,X1)),X2))
| X3 = c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8118]),
[final] ).
cnf(i_0_14246,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8287]),
[final] ).
cnf(i_0_14247,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8288]),
[final] ).
cnf(i_0_14248,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_8289]),
[final] ).
cnf(i_0_14249,plain,
( hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ c_Finite__Set_Ofolding__one(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7318]),
[final] ).
cnf(i_0_14250,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk13_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X1)),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7785]),
[final] ).
cnf(i_0_14251,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8290]),
[final] ).
cnf(i_0_14252,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8291]),
[final] ).
cnf(i_0_14253,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8292]),
[final] ).
cnf(i_0_14254,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8293]),
[final] ).
cnf(i_0_14255,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),
inference(split_conjunct,[status(thm)],[i_0_8294]),
[final] ).
cnf(i_0_14256,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))),
inference(split_conjunct,[status(thm)],[i_0_8295]),
[final] ).
cnf(i_0_14257,plain,
( c_Divides_OnegDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5306]),
[final] ).
cnf(i_0_14258,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8296]),
[final] ).
cnf(i_0_14259,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8297]),
[final] ).
cnf(i_0_14260,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8298]),
[final] ).
cnf(i_0_14261,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8195]),
[final] ).
cnf(i_0_14262,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8299]),
[final] ).
cnf(i_0_14263,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8300]),
[final] ).
cnf(i_0_14264,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8197]),
[final] ).
cnf(i_0_14265,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8301]),
[final] ).
cnf(i_0_14266,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8302]),
[final] ).
cnf(i_0_14267,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8199]),
[final] ).
cnf(i_0_14268,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_8303]),
[final] ).
cnf(i_0_14269,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_8304]),
[final] ).
cnf(i_0_14270,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_8305]),
[final] ).
cnf(i_0_14271,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_8306]),
[final] ).
cnf(i_0_14272,plain,
( hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_8307,c_0_6670]),
[final] ).
cnf(i_0_14273,plain,
( hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8308]),
[final] ).
cnf(i_0_14274,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8309]),
[final] ).
cnf(i_0_14275,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8310]),
[final] ).
cnf(i_0_14276,plain,
( c_Finite__Set_Ofun__left__comm(X4,X2,hAPP(hAPP(c_COMBB(X1,tc_fun(X2,X2),X4),X3),X5))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_8311]),
[final] ).
cnf(i_0_14277,plain,
( c_Finite__Set_Ofun__left__comm__idem(X4,X2,hAPP(hAPP(c_COMBB(X1,tc_fun(X2,X2),X4),X3),X5))
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_8312]),
[final] ).
cnf(i_0_14278,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8313]),
[final] ).
cnf(i_0_14279,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8314]),
[final] ).
cnf(i_0_14280,plain,
( X4 = X5
| hAPP(c_Set_Oimage(X1,X2,X3),X4) != hAPP(c_Set_Oimage(X1,X2,X3),X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8315]),
[final] ).
cnf(i_0_14281,plain,
( c_Natural_Oevaln(X3,X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8042]),
[final] ).
cnf(i_0_14282,plain,
( c_Natural_Oevaln(X3,X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8043]),
[final] ).
cnf(i_0_14283,plain,
( c_Natural_Oevaln(X3,X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8044]),
[final] ).
cnf(i_0_14284,plain,
( hAPP(X4,hAPP(X5,X7)) = hAPP(X6,X7)
| hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5) != X6 ),
inference(split_conjunct,[status(thm)],[i_0_8316]),
[final] ).
cnf(i_0_14285,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_8317]),
[final] ).
cnf(i_0_14286,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7879]),
[final] ).
cnf(i_0_14287,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| c_List_Oupto(X1,X2) = c_List_Olist_ONil(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7903]),
[final] ).
cnf(i_0_14288,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk422_3(X2,X1,X3)),esk420_2(X2,X1)))
| c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk420_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6982]),
[final] ).
cnf(i_0_14289,plain,
( c_Big__Operators_Olattice__class_OInf__fin(X1,X2) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7319]),
[final] ).
cnf(i_0_14290,plain,
( c_Big__Operators_Olinorder__class_OMin(X1,X2) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7320]),
[final] ).
cnf(i_0_14291,plain,
( c_Big__Operators_Olinorder__class_OMax(X1,X2) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7321]),
[final] ).
cnf(i_0_14292,plain,
( c_Big__Operators_Olattice__class_OSup__fin(X1,X2) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7322]),
[final] ).
cnf(i_0_14293,plain,
( hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_OSuc,X1)),X3)) = hAPP(hAPP(c_List_Odrop(X2),X1),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8318]),
[final] ).
cnf(i_0_14294,plain,
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8037]),
[final] ).
cnf(i_0_14295,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_8319]),
[final] ).
cnf(i_0_14296,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8320]),
[final] ).
cnf(i_0_14297,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8321]),
[final] ).
cnf(i_0_14298,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8322]),
[final] ).
cnf(i_0_14299,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8323]),
[final] ).
cnf(i_0_14300,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8324]),
[final] ).
cnf(i_0_14301,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X1)),hAPP(hAPP(c_Set_Oinsert(X4),X2),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X1)),X5)
| hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8325]),
[final] ).
cnf(i_0_14302,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8326]),
[final] ).
cnf(i_0_14303,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7789]),
[final] ).
cnf(i_0_14304,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8327]),
[final] ).
cnf(i_0_14305,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8328]),
[final] ).
cnf(i_0_14306,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7789]),
[final] ).
cnf(i_0_14307,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8327]),
[final] ).
cnf(i_0_14308,plain,
( c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| hAPP(c_Set_Oimage(X1,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8329]),
[final] ).
cnf(i_0_14309,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8330]),
[final] ).
cnf(i_0_14310,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8331]),
[final] ).
cnf(i_0_14311,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8332]),
[final] ).
cnf(i_0_14312,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))
| hAPP(c_Map_Omap__add(X1,X3,X4,X5),X2) = hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8333]),
[final] ).
cnf(i_0_14313,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))
| hAPP(c_Map_Omap__add(X1,X3,X5,X4),X2) = hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8334]),
[final] ).
cnf(i_0_14314,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_8335]),
[final] ).
cnf(i_0_14315,plain,
( ~ class_Rings_Olinordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8336]),
[final] ).
cnf(i_0_14316,plain,
( c_Natural_Oevaln(X1,X2,X3,X4)
| hBOOL(hAPP(X5,X2))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X5,X6,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8042]),
[final] ).
cnf(i_0_14317,plain,
( c_Natural_Oevaln(X1,X2,X3,X4)
| hBOOL(hAPP(X5,X2))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X5,X6,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8043]),
[final] ).
cnf(i_0_14318,plain,
( c_Natural_Oevaln(X1,X2,X3,X4)
| hBOOL(hAPP(X5,X2))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X5,X6,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8044]),
[final] ).
cnf(i_0_14319,plain,
( hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = X4
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8337]),
[final] ).
cnf(i_0_14320,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8338]),
[final] ).
cnf(i_0_14321,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8339]),
[final] ).
cnf(i_0_14322,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8340]),
[final] ).
cnf(i_0_14323,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))),X2)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8341]),
[final] ).
cnf(i_0_14324,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(X2,X1,X3),X4))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8342]),
[final] ).
cnf(i_0_14325,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(X2,X1,X3),X4))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8343]),
[final] ).
cnf(i_0_14326,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X3,X4,X1),X5),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8269]),
[final] ).
cnf(i_0_14327,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8344]),
[final] ).
cnf(i_0_14328,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),X1),X3))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8345]),
[final] ).
cnf(i_0_14329,plain,
( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7295]),
[final] ).
cnf(i_0_14330,plain,
( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7296]),
[final] ).
cnf(i_0_14331,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8346]),
[final] ).
cnf(i_0_14332,plain,
( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8347]),
[final] ).
cnf(i_0_14333,plain,
( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8348]),
[final] ).
cnf(i_0_14334,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_8057]),
[final] ).
cnf(i_0_14335,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X2,X3)))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8349]),
[final] ).
cnf(i_0_14336,plain,
hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(c_Nat_OSuc,X2)),X3) = hAPP(c_Fun_Ocomp(X1,X1,X1,X3),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_8350]),
[final] ).
cnf(i_0_14337,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),c_List_Olist_Olist__size(X1,X5,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8351]),
[final] ).
cnf(i_0_14338,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),c_List_Olist_Olist__size(X1,X5,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8352]),
[final] ).
cnf(i_0_14339,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk502_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk500_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14340,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk499_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk497_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14341,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X2),X1)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8353]),
[final] ).
cnf(i_0_14342,plain,
c_Map_Omap__of(X1,X2,hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),X3),X4)) = c_Map_Omap__add(X1,X2,c_Map_Omap__of(X1,X2,X4),c_Map_Omap__of(X1,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_8354]),
[final] ).
cnf(i_0_14343,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8355]),
[final] ).
cnf(i_0_14344,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_8356]),
[final] ).
cnf(i_0_14345,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rw,[status(thm)],[i_0_8357,c_0_6015]),
[final] ).
cnf(i_0_14346,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8358,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14347,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8046]),
[final] ).
cnf(i_0_14348,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8046]),
[final] ).
cnf(i_0_14349,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8359]),
[final] ).
cnf(i_0_14350,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8360]),
[final] ).
cnf(i_0_14351,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,hAPP(hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Oone__class_Oone(X1)),X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8361]),
[final] ).
cnf(i_0_14352,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
| X2 != hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_8362]),
[final] ).
cnf(i_0_14353,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1) = X4
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_8064]),
[final] ).
cnf(i_0_14354,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8288]),
[final] ).
cnf(i_0_14355,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8363]),
[final] ).
cnf(i_0_14356,plain,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),hAPP(c_Nat_OSuc,X5)) = hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_8364]),
[final] ).
cnf(i_0_14357,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X4,X3,X1,X5),X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8365]),
[final] ).
cnf(i_0_14358,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X4,X3,X5,X1),X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8365]),
[final] ).
cnf(i_0_14359,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olinorder__class_OMin(X1,X3)),c_Big__Operators_Olinorder__class_OMin(X1,X2)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8366]),
[final] ).
cnf(i_0_14360,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8367]),
[final] ).
cnf(i_0_14361,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8368]),
[final] ).
cnf(i_0_14362,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8060]),
[final] ).
cnf(i_0_14363,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk468_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8052]),
[final] ).
cnf(i_0_14364,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[i_0_8369]),
[final] ).
cnf(i_0_14365,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[i_0_8370]),
[final] ).
cnf(i_0_14366,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_Set_Oimage(X5,X4,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
| X1 != hAPP(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_8371]),
[final] ).
cnf(i_0_14367,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X2,X3,X1)))
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk502_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14368,plain,
( hAPP(c_Set_Oimage(tc_prod(X2,X3),X3,c_Product__Type_Osnd(X2,X3)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8372]),
[final] ).
cnf(i_0_14369,plain,
( hAPP(c_Set_Oimage(tc_prod(X3,X2),X3,c_Product__Type_Ofst(X3,X2)),hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X1))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8373]),
[final] ).
cnf(i_0_14370,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8374]),
[final] ).
cnf(i_0_14371,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8374]),
[final] ).
cnf(i_0_14372,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8374]),
[final] ).
cnf(i_0_14373,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8374]),
[final] ).
cnf(i_0_14374,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8375]),
[final] ).
cnf(i_0_14375,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7938]),
[final] ).
cnf(i_0_14376,plain,
( X1 = X2
| hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Olist__update(X3,X4),X1),X5)),X2) = hAPP(hAPP(c_List_Onth(X3),X4),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8376]),
[final] ).
cnf(i_0_14377,plain,
( hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| hAPP(hAPP(c_List_Oappend(X1),X3),X4) != hAPP(hAPP(c_List_Oappend(X1),X2),X5) ),
inference(split_conjunct,[status(thm)],[i_0_7032]),
[final] ).
cnf(i_0_14378,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,X1,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8377]),
[final] ).
cnf(i_0_14379,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8378]),
[final] ).
cnf(i_0_14380,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8378]),
[final] ).
cnf(i_0_14381,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8379]),
[final] ).
cnf(i_0_14382,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8380]),
[final] ).
cnf(i_0_14383,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8381]),
[final] ).
cnf(i_0_14384,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk64_3(X1,X2,X3)),X1))
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8051]),
[final] ).
cnf(i_0_14385,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X2,X3,X1)))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk499_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14386,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8382]),
[final] ).
cnf(i_0_14387,plain,
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,hAPP(c_Nat_OSuc,X3),X4)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8383]),
[final] ).
cnf(i_0_14388,plain,
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,hAPP(c_Nat_OSuc,X3),X4)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8384]),
[final] ).
cnf(i_0_14389,plain,
( c_Map_Oran(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X1),X2),hAPP(c_Option_Ooption_OSome(X3),X5))) = hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Map_Oran(X4,X3,X1))
| hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8385]),
[final] ).
cnf(i_0_14390,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8041]),
[final] ).
cnf(i_0_14391,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk503_3(X1,X2,X3)))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk500_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14392,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8386]),
[final] ).
cnf(i_0_14393,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8387]),
[final] ).
cnf(i_0_14394,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_8388]),
[final] ).
cnf(i_0_14395,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls)) ),
inference(rw,[status(thm)],[i_0_8389,c_0_6015]),
[final] ).
cnf(i_0_14396,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) ),
inference(rw,[status(thm)],[i_0_8390,c_0_6015]),
[final] ).
cnf(i_0_14397,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) ),
inference(rw,[status(thm)],[i_0_8391,c_0_6015]),
[final] ).
cnf(i_0_14398,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls)) ),
inference(rw,[status(thm)],[i_0_8392,c_0_6015]),
[final] ).
cnf(i_0_14399,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))) ),
inference(rw,[status(thm)],[i_0_8393,c_0_6015]),
[final] ).
cnf(i_0_14400,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[i_0_8394,c_0_6015]),
[final] ).
cnf(i_0_14401,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8395]),
[final] ).
cnf(i_0_14402,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X3),
inference(split_conjunct,[status(thm)],[i_0_8396]),
[final] ).
cnf(i_0_14403,plain,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6728]),
[final] ).
cnf(i_0_14404,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk399_3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8397]),
[final] ).
cnf(i_0_14405,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)))
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8398]),
[final] ).
cnf(i_0_14406,plain,
hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X2) = X2,
inference(rw,[status(thm)],[i_0_8399,c_0_6053]),
[final] ).
cnf(i_0_14407,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8400]),
[final] ).
cnf(i_0_14408,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8401]),
[final] ).
cnf(i_0_14409,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8402]),
[final] ).
cnf(i_0_14410,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk499_3(X1,X2,X3)))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk497_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14411,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_8113]),
[final] ).
cnf(i_0_14412,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8403]),
[final] ).
cnf(i_0_14413,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8404]),
[final] ).
cnf(i_0_14414,plain,
( c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8042]),
[final] ).
cnf(i_0_14415,plain,
( c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8043]),
[final] ).
cnf(i_0_14416,plain,
( c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8405]),
[final] ).
cnf(i_0_14417,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))
| ~ c_Nat__Transfer_Onat__set(X2)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7981]),
[final] ).
cnf(i_0_14418,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk361_3(X2,X3,X1)),X3))
| c_Big__Operators_Olinorder__class_OMin(X1,X3) = X2
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8406]),
[final] ).
cnf(i_0_14419,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk362_3(X2,X3,X1)),X3))
| c_Big__Operators_Olinorder__class_OMax(X1,X3) = X2
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7982]),
[final] ).
cnf(i_0_14420,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Oappend(X1),X4),X5)) = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_8407]),
[final] ).
cnf(i_0_14421,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk407_2(X2,X1)),X2))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8408]),
[final] ).
cnf(i_0_14422,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X4) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8409]),
[final] ).
cnf(i_0_14423,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8410]),
[final] ).
cnf(i_0_14424,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8411]),
[final] ).
cnf(i_0_14425,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8412]),
[final] ).
cnf(i_0_14426,plain,
hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X1,c_Option_Ooption_ONone(X2),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),hAPP(X4,X5)) = c_Option_Ooption_ONone(X2),
inference(rw,[status(thm)],[i_0_8413,c_0_6226]),
[final] ).
cnf(i_0_14427,plain,
hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X1,c_Option_Ooption_ONone(X2),X4),hAPP(hAPP(c_COMBK(tc_Option_Ooption(X1),X3),c_Option_Ooption_ONone(X1)),X5)) = c_Option_Ooption_ONone(X2),
inference(rw,[status(thm)],[i_0_8414,c_0_6226]),
[final] ).
cnf(i_0_14428,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_3(X1,X2,X3)),X1))
| hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8067]),
[final] ).
cnf(i_0_14429,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2)) ),
inference(rw,[status(thm)],[i_0_8415,c_0_6169]),
[final] ).
cnf(i_0_14430,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8416,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_14431,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_8417]),
[final] ).
cnf(i_0_14432,plain,
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,hAPP(c_Nat_OSuc,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8383]),
[final] ).
cnf(i_0_14433,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7984]),
[final] ).
cnf(i_0_14434,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8418]),
[final] ).
cnf(i_0_14435,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8419]),
[final] ).
cnf(i_0_14436,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8420]),
[final] ).
cnf(i_0_14437,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8090]),
[final] ).
cnf(i_0_14438,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8096]),
[final] ).
cnf(i_0_14439,plain,
( c_Natural_Oevaln(X1,X2,X5,X4)
| ~ c_Natural_Oevaln(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8421]),
[final] ).
cnf(i_0_14440,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X5)))
| X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_8118]),
[final] ).
cnf(i_0_14441,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8422]),
[final] ).
cnf(i_0_14442,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8423]),
[final] ).
cnf(i_0_14443,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8424]),
[final] ).
cnf(i_0_14444,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8425]),
[final] ).
cnf(i_0_14445,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8425]),
[final] ).
cnf(i_0_14446,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8426]),
[final] ).
cnf(i_0_14447,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8426]),
[final] ).
cnf(i_0_14448,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8425]),
[final] ).
cnf(i_0_14449,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8425]),
[final] ).
cnf(i_0_14450,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8426]),
[final] ).
cnf(i_0_14451,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8426]),
[final] ).
cnf(i_0_14452,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8427]),
[final] ).
cnf(i_0_14453,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8427]),
[final] ).
cnf(i_0_14454,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8427]),
[final] ).
cnf(i_0_14455,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8427]),
[final] ).
cnf(i_0_14456,plain,
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7353]),
[final] ).
cnf(i_0_14457,plain,
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7354]),
[final] ).
cnf(i_0_14458,plain,
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7355]),
[final] ).
cnf(i_0_14459,plain,
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7356]),
[final] ).
cnf(i_0_14460,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7985]),
[final] ).
cnf(i_0_14461,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8428,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14462,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8429,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14463,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8430]),
[final] ).
cnf(i_0_14464,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8431]),
[final] ).
cnf(i_0_14465,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8432]),
[final] ).
cnf(i_0_14466,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8433]),
[final] ).
cnf(i_0_14467,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7813]),
[final] ).
cnf(i_0_14468,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8434]),
[final] ).
cnf(i_0_14469,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7816]),
[final] ).
cnf(i_0_14470,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8435]),
[final] ).
cnf(i_0_14471,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8436]),
[final] ).
cnf(i_0_14472,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7992]),
[final] ).
cnf(i_0_14473,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8437,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14474,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8438,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14475,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8439]),
[final] ).
cnf(i_0_14476,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8440]),
[final] ).
cnf(i_0_14477,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7995]),
[final] ).
cnf(i_0_14478,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7996]),
[final] ).
cnf(i_0_14479,plain,
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8441]),
[final] ).
cnf(i_0_14480,plain,
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8442]),
[final] ).
cnf(i_0_14481,plain,
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8443]),
[final] ).
cnf(i_0_14482,plain,
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8444]),
[final] ).
cnf(i_0_14483,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8445]),
[final] ).
cnf(i_0_14484,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))),c_Divides_Odiv__class_Omod(X1,X3,X2)) = X3
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8446]),
[final] ).
cnf(i_0_14485,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))),X2)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[i_0_8447,c_0_6016]),
[final] ).
cnf(i_0_14486,plain,
hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(c_Nat_OSuc,X4)),X5) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_8448]),
[final] ).
cnf(i_0_14487,plain,
( X1 = X2
| c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) != c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X6) ),
inference(split_conjunct,[status(thm)],[i_0_8449]),
[final] ).
cnf(i_0_14488,plain,
( X1 = X2
| c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) != c_Nitpick_Opair__box_OPairBox(X3,X4,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8449]),
[final] ).
cnf(i_0_14489,plain,
( X4 = X5
| c_Sum__Type_OSumr(X1,X2,X3,X4) != c_Sum__Type_OSumr(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8450]),
[final] ).
cnf(i_0_14490,plain,
( X4 = X5
| c_Sum__Type_OSuml(X1,X2,X3,X4) != c_Sum__Type_OSuml(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8451]),
[final] ).
cnf(i_0_14491,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk484_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
| c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7746]),
[final] ).
cnf(i_0_14492,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk483_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
| c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7746]),
[final] ).
cnf(i_0_14493,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk467_2(X1,X2)),hAPP(c_List_Oset(tc_Nat_Onat),X1)))
| hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8041]),
[final] ).
cnf(i_0_14494,plain,
( hBOOL(hAPP(hAPP(c_member(X6),X2),hAPP(c_Set_Ovimage(X6,X4,X1),X5)))
| hAPP(X1,X2) != X3
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8452]),
[final] ).
cnf(i_0_14495,plain,
( hBOOL(hAPP(hAPP(c_member(X6),X1),hAPP(c_Set_Oimage(X4,X6,X2),X5)))
| X1 != hAPP(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8453]),
[final] ).
cnf(i_0_14496,plain,
( hBOOL(hAPP(hAPP(c_member(X6),X4),hAPP(c_Set_Oimage(X1,X6,X5),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| X4 != hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7048]),
[final] ).
cnf(i_0_14497,plain,
( hBOOL(hAPP(hAPP(c_member(X6),X4),hAPP(c_Set_Oimage(X1,X6,X5),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| X4 != hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8454]),
[final] ).
cnf(i_0_14498,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))
| ~ hBOOL(hAPP(X1,esk85_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7149]),
[final] ).
cnf(i_0_14499,plain,
( c_Random__Sequence_ORandom(X2,X3,X1,X4) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
inference(split_conjunct,[status(thm)],[i_0_6139]),
[final] ).
cnf(i_0_14500,plain,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X6,X3),X2,X4,X5)
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8042]),
[final] ).
cnf(i_0_14501,plain,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X6,X3),X2,X4,X5)
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8043]),
[final] ).
cnf(i_0_14502,plain,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X6,X3),X2,X4,X5)
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8455]),
[final] ).
cnf(i_0_14503,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X2,X3),X3,c_Product__Type_Osnd(X2,X3)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4))) = X4 ),
inference(split_conjunct,[status(thm)],[i_0_8372]),
[final] ).
cnf(i_0_14504,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X3,X2),X3,c_Product__Type_Ofst(X3,X2)),hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X1))) = X4 ),
inference(split_conjunct,[status(thm)],[i_0_8373]),
[final] ).
cnf(i_0_14505,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X2),X3) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != esk158_4(X2,X3,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X1),X3))
| hAPP(X2,X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7205]),
[final] ).
cnf(i_0_14506,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| hAPP(c_Map_Omap__of(X1,X4,hAPP(hAPP(c_List_Ozip(X1,X4),X3),X5)),X2) = c_Option_Ooption_ONone(X4)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5) ),
inference(split_conjunct,[status(thm)],[i_0_7910]),
[final] ).
cnf(i_0_14507,plain,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),X5))
| ~ c_Fun_Oinj__on(X4,X6,X1,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8456]),
[final] ).
cnf(i_0_14508,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
| hAPP(X3,X5) != hAPP(X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_7242]),
[final] ).
cnf(i_0_14509,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(X3,X5) != hAPP(X3,X6)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8457]),
[final] ).
cnf(i_0_14510,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
| hAPP(X3,X5) != hAPP(X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_8458]),
[final] ).
cnf(i_0_14511,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8459]),
[final] ).
cnf(i_0_14512,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8460]),
[final] ).
cnf(i_0_14513,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8461]),
[final] ).
cnf(i_0_14514,plain,
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(X2,hAPP(X3,X5)),hAPP(X3,X4)) = hAPP(X3,X4)
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8462]),
[final] ).
cnf(i_0_14515,plain,
( hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Olist__update(X3,X4),X1),X5)),X2) = X5
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8376]),
[final] ).
cnf(i_0_14516,plain,
( c_Equiv__Relations_Oequiv(X1,X3,X2)
| hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2) != X2
| hAPP(c_Relation_ODomain(X1,X1),X2) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_8463]),
[final] ).
cnf(i_0_14517,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk64_3(X1,X2,X3)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8051]),
[final] ).
cnf(i_0_14518,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_8464]),
[final] ).
cnf(i_0_14519,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X3,X5)),hAPP(X4,X5)))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8465]),
[final] ).
cnf(i_0_14520,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X3,X5)),hAPP(X4,X5)))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8466]),
[final] ).
cnf(i_0_14521,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(X3,X5)),hAPP(X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_6567]),
[final] ).
cnf(i_0_14522,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X2,X3,X1)))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk502_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14523,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X2,X3,X1)))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk499_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14524,plain,
( X4 = X5
| hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8467]),
[final] ).
cnf(i_0_14525,plain,
( X4 = X5
| hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8468]),
[final] ).
cnf(i_0_14526,plain,
( hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)),X1) = X4
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8469]),
[final] ).
cnf(i_0_14527,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X3))),hAPP(X2,hAPP(c_Nat_OSuc,X3)))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8470]),
[final] ).
cnf(i_0_14528,plain,
( c_Big__Operators_Olinorder__class_OMin(X1,X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk361_3(X2,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8406]),
[final] ).
cnf(i_0_14529,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk157_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7205]),
[final] ).
cnf(i_0_14530,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8471]),
[final] ).
cnf(i_0_14531,plain,
( c_Nitpick_Onat__gcd(X2,X1) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8279]),
[final] ).
cnf(i_0_14532,plain,
c_List_Obutlast(X1,X2) = hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),
inference(split_conjunct,[status(thm)],[i_0_8472]),
[final] ).
cnf(i_0_14533,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)),X3))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8473]),
[final] ).
cnf(i_0_14534,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8474]),
[final] ).
cnf(i_0_14535,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1))))),
inference(split_conjunct,[status(thm)],[i_0_8475]),
[final] ).
cnf(i_0_14536,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk485_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
| c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8476]),
[final] ).
cnf(i_0_14537,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk482_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
| c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8477]),
[final] ).
cnf(i_0_14538,plain,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X1,X2)),X3),hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3)))),
inference(split_conjunct,[status(thm)],[i_0_8478]),
[final] ).
cnf(i_0_14539,plain,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X1,X2)),X3),hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3)))),
inference(split_conjunct,[status(thm)],[i_0_8479]),
[final] ).
cnf(i_0_14540,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8480]),
[final] ).
cnf(i_0_14541,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7459]),
[final] ).
cnf(i_0_14542,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7460]),
[final] ).
cnf(i_0_14543,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8481]),
[final] ).
cnf(i_0_14544,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8425]),
[final] ).
cnf(i_0_14545,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8482]),
[final] ).
cnf(i_0_14546,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8483]),
[final] ).
cnf(i_0_14547,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8426]),
[final] ).
cnf(i_0_14548,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8484]),
[final] ).
cnf(i_0_14549,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8485]),
[final] ).
cnf(i_0_14550,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8486]),
[final] ).
cnf(i_0_14551,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8427]),
[final] ).
cnf(i_0_14552,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8487]),
[final] ).
cnf(i_0_14553,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8488]),
[final] ).
cnf(i_0_14554,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8489]),
[final] ).
cnf(i_0_14555,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8490]),
[final] ).
cnf(i_0_14556,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk71_3(X1,X2,X3)),X3))
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7326]),
[final] ).
cnf(i_0_14557,plain,
( c_Fun_Oinj__on(X1,X3,X4,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)) != hAPP(c_Finite__Set_Ocard(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_8491]),
[final] ).
cnf(i_0_14558,plain,
( c_Fun_Oinj__on(X2,X1,X3,X4)
| hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4)) != hAPP(c_Finite__Set_Ocard(X2),X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8492]),
[final] ).
cnf(i_0_14559,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_8493]),
[final] ).
cnf(i_0_14560,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_8494,c_0_6053]),
[final] ).
cnf(i_0_14561,plain,
( X2 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8495]),
[final] ).
cnf(i_0_14562,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),esk416_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8117]),
[final] ).
cnf(i_0_14563,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8496,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14564,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8497,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14565,plain,
hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_8498]),
[final] ).
cnf(i_0_14566,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk400_3(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X3)),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8039]),
[final] ).
cnf(i_0_14567,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8499]),
[final] ).
cnf(i_0_14568,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8500]),
[final] ).
cnf(i_0_14569,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
| X3 = X2
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_8501]),
[final] ).
cnf(i_0_14570,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk503_3(X1,X2,X3)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk500_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14571,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk499_3(X1,X2,X3)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk497_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14572,plain,
( hAPP(hAPP(X4,X5),X6) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X5)
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8502]),
[final] ).
cnf(i_0_14573,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8503]),
[final] ).
cnf(i_0_14574,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),X5)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8504]),
[final] ).
cnf(i_0_14575,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8505]),
[final] ).
cnf(i_0_14576,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8506]),
[final] ).
cnf(i_0_14577,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8507]),
[final] ).
cnf(i_0_14578,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8508]),
[final] ).
cnf(i_0_14579,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8509]),
[final] ).
cnf(i_0_14580,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8510]),
[final] ).
cnf(i_0_14581,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8511]),
[final] ).
cnf(i_0_14582,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8083]),
[final] ).
cnf(i_0_14583,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8512]),
[final] ).
cnf(i_0_14584,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8011]),
[final] ).
cnf(i_0_14585,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14586,plain,
hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_8513]),
[final] ).
cnf(i_0_14587,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X3),X4),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X1,c_Groups_Otimes__class_Otimes(X3)),X4),c_Groups_Oone__class_Oone(X3)),X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Groups_Ocomm__monoid__mult(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8514]),
[final] ).
cnf(i_0_14588,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),X3)
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8515]),
[final] ).
cnf(i_0_14589,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X1,c_Groups_Oplus__class_Oplus(X3)),X4),c_Groups_Ozero__class_Ozero(X3)),X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8516]),
[final] ).
cnf(i_0_14590,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Oplus__class_Oplus(X1)),X4),c_Groups_Ozero__class_Ozero(X1)),X3)
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8517]),
[final] ).
cnf(i_0_14591,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8518]),
[final] ).
cnf(i_0_14592,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8510]),
[final] ).
cnf(i_0_14593,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8511]),
[final] ).
cnf(i_0_14594,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8519]),
[final] ).
cnf(i_0_14595,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
| hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1) = hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8520]),
[final] ).
cnf(i_0_14596,plain,
( hAPP(X1,esk210_4(X1,X2,X3,X4)) = c_Groups_Ozero__class_Ozero(X4)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),X1),X2) != c_Groups_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X4)
| ~ class_Rings_Ono__zero__divisors(X4) ),
inference(split_conjunct,[status(thm)],[i_0_7247]),
[final] ).
cnf(i_0_14597,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8521]),
[final] ).
cnf(i_0_14598,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8522]),
[final] ).
cnf(i_0_14599,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8523]),
[final] ).
cnf(i_0_14600,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7816]),
[final] ).
cnf(i_0_14601,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7813]),
[final] ).
cnf(i_0_14602,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk503_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X1,X2,X3)))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14603,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X2),X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != esk160_4(X2,X3,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X1),X3))
| hAPP(X2,X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7210]),
[final] ).
cnf(i_0_14604,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk97_2(X1,X2)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8524]),
[final] ).
cnf(i_0_14605,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk159_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7210]),
[final] ).
cnf(i_0_14606,plain,
hAPP(c_Map_Orestrict__map(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3),X4) = c_Option_Ooption_ONone(X2),
inference(split_conjunct,[status(thm)],[i_0_8525]),
[final] ).
cnf(i_0_14607,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Odrop(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8526]),
[final] ).
cnf(i_0_14608,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk336_2(X1,X2)),c_Int_OInteg))
| hBOOL(hAPP(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8527]),
[final] ).
cnf(i_0_14609,plain,
( c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))
| ~ c_Predicate_Oreflp(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7933]),
[final] ).
cnf(i_0_14610,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8528]),
[final] ).
cnf(i_0_14611,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_8529,c_0_6015]),
[final] ).
cnf(i_0_14612,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14613,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8530]),
[final] ).
cnf(i_0_14614,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8531]),
[final] ).
cnf(i_0_14615,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8532]),
[final] ).
cnf(i_0_14616,plain,
( hAPP(c_Finite__Set_Ocard(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = hAPP(c_Finite__Set_Ocard(X1),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8492]),
[final] ).
cnf(i_0_14617,plain,
( X2 = c_List_Olist_ONil(X1)
| hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_List_Oset(X1),X2)) = hAPP(c_List_Ofoldl(X1,X1,c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Ohd(X1),X2)),hAPP(c_List_Otl(X1),X2))
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8533]),
[final] ).
cnf(i_0_14618,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_3(X1,X2,X3)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8067]),
[final] ).
cnf(i_0_14619,plain,
hAPP(hAPP(c_List_Odrop(tc_prod(X1,X2)),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)) = hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4)),hAPP(hAPP(c_List_Odrop(X2),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_8534]),
[final] ).
cnf(i_0_14620,plain,
hAPP(hAPP(c_List_Otake(tc_prod(X1,X2)),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)) = hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Otake(X1),X3),X4)),hAPP(hAPP(c_List_Otake(X2),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_8535]),
[final] ).
cnf(i_0_14621,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7832]),
[final] ).
cnf(i_0_14622,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7833]),
[final] ).
cnf(i_0_14623,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8536]),
[final] ).
cnf(i_0_14624,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X1,X2,X3)),X1))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14625,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8537]),
[final] ).
cnf(i_0_14626,plain,
( c_Relation_Osingle__valued(X1,X4,hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X4),X3),X5))
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ c_Relation_Osingle__valued(X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8538]),
[final] ).
cnf(i_0_14627,plain,
c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)))),
inference(split_conjunct,[status(thm)],[i_0_8539]),
[final] ).
cnf(i_0_14628,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk499_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X1,X2,X3)))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14629,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8540]),
[final] ).
cnf(i_0_14630,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X4,X5)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8541]),
[final] ).
cnf(i_0_14631,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X4,X5)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8542]),
[final] ).
cnf(i_0_14632,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8543]),
[final] ).
cnf(i_0_14633,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8544]),
[final] ).
cnf(i_0_14634,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8545]),
[final] ).
cnf(i_0_14635,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8546]),
[final] ).
cnf(i_0_14636,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8547]),
[final] ).
cnf(i_0_14637,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8548]),
[final] ).
cnf(i_0_14638,plain,
hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_8549]),
[final] ).
cnf(i_0_14639,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ class_Int_Onumber(X1)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8550]),
[final] ).
cnf(i_0_14640,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ class_Int_Onumber(X1)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8551]),
[final] ).
cnf(i_0_14641,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))
| X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
inference(split_conjunct,[status(thm)],[i_0_7930]),
[final] ).
cnf(i_0_14642,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))
| X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
inference(split_conjunct,[status(thm)],[i_0_7931]),
[final] ).
cnf(i_0_14643,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8552]),
[final] ).
cnf(i_0_14644,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_8553]),
[final] ).
cnf(i_0_14645,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8554]),
[final] ).
cnf(i_0_14646,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8461]),
[final] ).
cnf(i_0_14647,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X1,X2,X3)),X1))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14648,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8555]),
[final] ).
cnf(i_0_14649,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8556]),
[final] ).
cnf(i_0_14650,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8557]),
[final] ).
cnf(i_0_14651,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8558]),
[final] ).
cnf(i_0_14652,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Oremove1(X2,X5,X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8559]),
[final] ).
cnf(i_0_14653,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk419_3(X2,X1,X3)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6982]),
[final] ).
cnf(i_0_14654,plain,
hAPP(c_Relation_ODomain(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_Relation_ODomain(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_8560]),
[final] ).
cnf(i_0_14655,plain,
hAPP(c_Relation_ORange(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Relation_ORange(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_8561]),
[final] ).
cnf(i_0_14656,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk98_2(X1,X2)),X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8562]),
[final] ).
cnf(i_0_14657,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8563]),
[final] ).
cnf(i_0_14658,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8125]),
[final] ).
cnf(i_0_14659,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8126]),
[final] ).
cnf(i_0_14660,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8127]),
[final] ).
cnf(i_0_14661,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_8564]),
[final] ).
cnf(i_0_14662,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8565]),
[final] ).
cnf(i_0_14663,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8052]),
[final] ).
cnf(i_0_14664,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8566]),
[final] ).
cnf(i_0_14665,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8567]),
[final] ).
cnf(i_0_14666,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8568]),
[final] ).
cnf(i_0_14667,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8425]),
[final] ).
cnf(i_0_14668,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Rings_Oordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8569]),
[final] ).
cnf(i_0_14669,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8482]),
[final] ).
cnf(i_0_14670,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8426]),
[final] ).
cnf(i_0_14671,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Fields_Olinordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8570]),
[final] ).
cnf(i_0_14672,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8427]),
[final] ).
cnf(i_0_14673,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8571]),
[final] ).
cnf(i_0_14674,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8400]),
[final] ).
cnf(i_0_14675,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8401]),
[final] ).
cnf(i_0_14676,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8402]),
[final] ).
cnf(i_0_14677,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3))),hAPP(X2,X3))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8572]),
[final] ).
cnf(i_0_14678,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_8573]),
[final] ).
cnf(i_0_14679,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
inference(split_conjunct,[status(thm)],[i_0_8574]),
[final] ).
cnf(i_0_14680,plain,
( c_Map_Odom(X1,X3,c_Map_Omap__of(X1,X3,hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))) = hAPP(c_List_Oset(X1),X2)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8575]),
[final] ).
cnf(i_0_14681,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),esk425_3(X3,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7959]),
[final] ).
cnf(i_0_14682,plain,
( c_Divides_OposDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8576]),
[final] ).
cnf(i_0_14683,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8461]),
[final] ).
cnf(i_0_14684,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8577]),
[final] ).
cnf(i_0_14685,plain,
( c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))
| ~ c_FunDef_Oreduction__pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6327]),
[final] ).
cnf(i_0_14686,plain,
c_List_Olex(X1,X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_8578]),
[final] ).
cnf(i_0_14687,plain,
( c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),c_List_Oremove1(X1,X2,X3)),X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8579]),
[final] ).
cnf(i_0_14688,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))) ),
inference(rw,[status(thm)],[i_0_8580,c_0_6169]),
[final] ).
cnf(i_0_14689,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8581]),
[final] ).
cnf(i_0_14690,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8582]),
[final] ).
cnf(i_0_14691,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)),
inference(split_conjunct,[status(thm)],[i_0_8583]),
[final] ).
cnf(i_0_14692,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8584]),
[final] ).
cnf(i_0_14693,plain,
( X1 = c_List_Olist_ONil(X2)
| c_Random_Oselect__weight(X2,hAPP(hAPP(c_List_Omap(X2,tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X1)) = c_Random_Oselect(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_8585]),
[final] ).
cnf(i_0_14694,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8586]),
[final] ).
cnf(i_0_14695,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Oordered__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8587]),
[final] ).
cnf(i_0_14696,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8588,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_14697,plain,
( c_List_Obutlast(X2,hAPP(hAPP(c_List_Otake(X2),X1),X3)) = hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8589]),
[final] ).
cnf(i_0_14698,plain,
( X1 = c_Option_Ooption_ONone(X2)
| c_Map_Odom(X3,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X2)),X4),X5),X1)) = hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Map_Odom(X3,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7957]),
[final] ).
cnf(i_0_14699,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk475_3(X3,X1,X2)),esk476_3(X3,X1,X2))
| X1 = c_List_Olist_ONil(X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8118]),
[final] ).
cnf(i_0_14700,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8590]),
[final] ).
cnf(i_0_14701,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk244_3(X2,X3,X1)),X2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8591]),
[final] ).
cnf(i_0_14702,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk243_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8591]),
[final] ).
cnf(i_0_14703,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),X1))
| esk408_3(X1,X2,X3) != esk409_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7452]),
[final] ).
cnf(i_0_14704,plain,
( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),c_List_Oremove1(X1,X2,X3)) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ c_List_Olinorder__class_Osorted(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_8592]),
[final] ).
cnf(i_0_14705,plain,
( c_Divides_OnegDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8593]),
[final] ).
cnf(i_0_14706,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8151]),
[final] ).
cnf(i_0_14707,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8152]),
[final] ).
cnf(i_0_14708,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X3)),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)) = c_Big__Operators_Olattice__class_OInf__fin(X1,X2)
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8594]),
[final] ).
cnf(i_0_14709,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X3)),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)) = c_Big__Operators_Olattice__class_OSup__fin(X1,X2)
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8595]),
[final] ).
cnf(i_0_14710,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X3)),c_Big__Operators_Olinorder__class_OMax(X1,X2)) = c_Big__Operators_Olinorder__class_OMax(X1,X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8596]),
[final] ).
cnf(i_0_14711,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X3)),c_Big__Operators_Olinorder__class_OMin(X1,X2)) = c_Big__Operators_Olinorder__class_OMin(X1,X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8597]),
[final] ).
cnf(i_0_14712,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_8598]),
[final] ).
cnf(i_0_14713,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_8599]),
[final] ).
cnf(i_0_14714,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk401_3(X2,X3,X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8600]),
[final] ).
cnf(i_0_14715,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8601]),
[final] ).
cnf(i_0_14716,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8602]),
[final] ).
cnf(i_0_14717,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))
| X2 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7619]),
[final] ).
cnf(i_0_14718,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),c_Int_OInteg)),
inference(split_conjunct,[status(thm)],[i_0_8603]),
[final] ).
cnf(i_0_14719,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)) = hAPP(hAPP(X2,hAPP(X3,X4)),hAPP(X3,X5))
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8604]),
[final] ).
cnf(i_0_14720,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8175]),
[final] ).
cnf(i_0_14721,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8173]),
[final] ).
cnf(i_0_14722,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8174]),
[final] ).
cnf(i_0_14723,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8172]),
[final] ).
cnf(i_0_14724,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8176]),
[final] ).
cnf(i_0_14725,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk503_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14726,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk499_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14727,plain,
( c_Divides_OnegDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_5307]),
[final] ).
cnf(i_0_14728,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8605]),
[final] ).
cnf(i_0_14729,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8606]),
[final] ).
cnf(i_0_14730,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8607]),
[final] ).
cnf(i_0_14731,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8608]),
[final] ).
cnf(i_0_14732,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8609]),
[final] ).
cnf(i_0_14733,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8310]),
[final] ).
cnf(i_0_14734,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_8610]),
[final] ).
cnf(i_0_14735,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),X3))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8611]),
[final] ).
cnf(i_0_14736,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X2)),X3))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8612]),
[final] ).
cnf(i_0_14737,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8613]),
[final] ).
cnf(i_0_14738,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8065]),
[final] ).
cnf(i_0_14739,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8614]),
[final] ).
cnf(i_0_14740,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8065]),
[final] ).
cnf(i_0_14741,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),X3))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8615]),
[final] ).
cnf(i_0_14742,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X2)),X3))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8616]),
[final] ).
cnf(i_0_14743,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8066]),
[final] ).
cnf(i_0_14744,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8617]),
[final] ).
cnf(i_0_14745,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8066]),
[final] ).
cnf(i_0_14746,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8618]),
[final] ).
cnf(i_0_14747,plain,
hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_8619]),
[final] ).
cnf(i_0_14748,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk211_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8620]),
[final] ).
cnf(i_0_14749,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk156_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8621]),
[final] ).
cnf(i_0_14750,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ class_Rings_Oordered__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8587]),
[final] ).
cnf(i_0_14751,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8587]),
[final] ).
cnf(i_0_14752,plain,
( hAPP(c_Map_Orestrict__map(X1,X4,X5,X3),X2) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8622]),
[final] ).
cnf(i_0_14753,plain,
( hAPP(c_Map_Orestrict__map(X1,X4,X5,X3),X2) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8623]),
[final] ).
cnf(i_0_14754,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk68_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8624]),
[final] ).
cnf(i_0_14755,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk67_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8625]),
[final] ).
cnf(i_0_14756,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X4) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X2)
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8626]),
[final] ).
cnf(i_0_14757,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8627]),
[final] ).
cnf(i_0_14758,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8628]),
[final] ).
cnf(i_0_14759,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk503_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X1,X2,X3)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14760,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk499_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X1,X2,X3)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14761,plain,
( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X5,X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8269]),
[final] ).
cnf(i_0_14762,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_8629]),
[final] ).
cnf(i_0_14763,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ class_Int_Onumber(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8013]),
[final] ).
cnf(i_0_14764,plain,
( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X3,c_Option_Ooption_ONone(X6),X5),hAPP(X1,X2)) = hAPP(c_Option_Ooption_OSome(X6),X7)
| hAPP(X5,X4) != hAPP(c_Option_Ooption_OSome(X6),X7)
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(rw,[status(thm)],[i_0_8630,c_0_6226]),
[final] ).
cnf(i_0_14765,plain,
( hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X4)),hAPP(X3,X4)) = hAPP(X3,X4)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_8631]),
[final] ).
cnf(i_0_14766,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Map_Odom(X1,X2,c_Map_Omap__of(X1,X2,X3)))),
inference(split_conjunct,[status(thm)],[i_0_8632]),
[final] ).
cnf(i_0_14767,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_8633]),
[final] ).
cnf(i_0_14768,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8634]),
[final] ).
cnf(i_0_14769,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk501_3(X1,X2,X3)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_14770,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X1,X2,X3)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_14771,plain,
hAPP(c_Product__Type_Osnd(X1,X2),X3) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X2),hAPP(c_COMBK(tc_fun(X2,X2),X1),c_COMBI(X2))),X3),
inference(split_conjunct,[status(thm)],[i_0_8635]),
[final] ).
cnf(i_0_14772,plain,
( ~ class_Int_Oring__char__0(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8636]),
[final] ).
cnf(i_0_14773,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8637]),
[final] ).
cnf(i_0_14774,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8637]),
[final] ).
cnf(i_0_14775,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8638]),
[final] ).
cnf(i_0_14776,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8202]),
[final] ).
cnf(i_0_14777,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8639]),
[final] ).
cnf(i_0_14778,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8640]),
[final] ).
cnf(i_0_14779,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X4
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8641]),
[final] ).
cnf(i_0_14780,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8642]),
[final] ).
cnf(i_0_14781,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8643]),
[final] ).
cnf(i_0_14782,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8644]),
[final] ).
cnf(i_0_14783,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8645]),
[final] ).
cnf(i_0_14784,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8646]),
[final] ).
cnf(i_0_14785,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),
inference(split_conjunct,[status(thm)],[i_0_8647]),
[final] ).
cnf(i_0_14786,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ class_Divides_Osemiring__div(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8648]),
[final] ).
cnf(i_0_14787,plain,
( hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3)),hAPP(c_Set_OPow(X1),X4)) = hAPP(c_Set_OPow(X2),X5)
| hAPP(c_Set_Oimage(X1,X2,X3),X4) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_8649]),
[final] ).
cnf(i_0_14788,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8650]),
[final] ).
cnf(i_0_14789,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4)) = X4
| hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8651]),
[final] ).
cnf(i_0_14790,plain,
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5304]),
[final] ).
cnf(i_0_14791,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) = X3
| c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8652,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14792,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8653]),
[final] ).
cnf(i_0_14793,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = X3
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8654]),
[final] ).
cnf(i_0_14794,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| hAPP(X3,esk345_3(X3,X2,X1)) = c_Option_Ooption_ONone(X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Map_Odom(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8655]),
[final] ).
cnf(i_0_14795,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8330]),
[final] ).
cnf(i_0_14796,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8656]),
[final] ).
cnf(i_0_14797,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8657]),
[final] ).
cnf(i_0_14798,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8657]),
[final] ).
cnf(i_0_14799,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8332]),
[final] ).
cnf(i_0_14800,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8658]),
[final] ).
cnf(i_0_14801,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8658]),
[final] ).
cnf(i_0_14802,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8102]),
[final] ).
cnf(i_0_14803,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8659]),
[final] ).
cnf(i_0_14804,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8660]),
[final] ).
cnf(i_0_14805,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8346]),
[final] ).
cnf(i_0_14806,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3),
inference(rw,[status(thm)],[i_0_8661,c_0_6670]),
[final] ).
cnf(i_0_14807,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_OCollect(X2),X4)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)),
inference(split_conjunct,[status(thm)],[i_0_8662]),
[final] ).
cnf(i_0_14808,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = X3
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8663]),
[final] ).
cnf(i_0_14809,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Oordered__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8587]),
[final] ).
cnf(i_0_14810,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk64_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8051]),
[final] ).
cnf(i_0_14811,plain,
( hAPP(c_Finite__Set_Ocard(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = hAPP(c_Finite__Set_Ocard(X1),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8664]),
[final] ).
cnf(i_0_14812,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk401_3(X3,X2,X1)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8600]),
[final] ).
cnf(i_0_14813,plain,
hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4)) = hAPP(hAPP(c_List_Odrop(X1),X3),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4)),
inference(split_conjunct,[status(thm)],[i_0_8665]),
[final] ).
cnf(i_0_14814,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,X5),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8666]),
[final] ).
cnf(i_0_14815,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk70_3(X3,X2,X1)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8667]),
[final] ).
cnf(i_0_14816,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8668]),
[final] ).
cnf(i_0_14817,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8669]),
[final] ).
cnf(i_0_14818,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8670]),
[final] ).
cnf(i_0_14819,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8671]),
[final] ).
cnf(i_0_14820,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X6),X3)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_8672]),
[final] ).
cnf(i_0_14821,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X6),X3)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_8673]),
[final] ).
cnf(i_0_14822,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X5),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X6),X3)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_8674]),
[final] ).
cnf(i_0_14823,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8675]),
[final] ).
cnf(i_0_14824,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8423]),
[final] ).
cnf(i_0_14825,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Fields_Ofield(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8676]),
[final] ).
cnf(i_0_14826,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X3 ),
inference(split_conjunct,[status(thm)],[i_0_8677]),
[final] ).
cnf(i_0_14827,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8678]),
[final] ).
cnf(i_0_14828,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8679]),
[final] ).
cnf(i_0_14829,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8680]),
[final] ).
cnf(i_0_14830,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8681]),
[final] ).
cnf(i_0_14831,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(c_Divides_OnegateSnd,X3)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8682]),
[final] ).
cnf(i_0_14832,plain,
( c_Natural_Oevaln(X1,X2,hAPP(c_Nat_OSuc,X3),X4)
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8683]),
[final] ).
cnf(i_0_14833,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk66_3(X2,X3,X1)),c_Groups_Oone__class_Oone(X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6939]),
[final] ).
cnf(i_0_14834,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8684]),
[final] ).
cnf(i_0_14835,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8404]),
[final] ).
cnf(i_0_14836,plain,
c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_8685]),
[final] ).
cnf(i_0_14837,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8686]),
[final] ).
cnf(i_0_14838,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk102_2(X1,X2)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8687]),
[final] ).
cnf(i_0_14839,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_8688]),
[final] ).
cnf(i_0_14840,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_14841,plain,
( X2 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),hAPP(c_Nat_OSuc,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8689]),
[final] ).
cnf(i_0_14842,plain,
hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8690,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14843,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_8691]),
[final] ).
cnf(i_0_14844,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_8691]),
[final] ).
cnf(i_0_14845,plain,
( c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X1))))
| ~ class_Orderings_Owellorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8692]),
[final] ).
cnf(i_0_14846,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk480_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
| hAPP(c_List_Ofilter(X1,X3),X2) = c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8693]),
[final] ).
cnf(i_0_14847,plain,
( hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1) = hAPP(hAPP(c_List_Onth(X2),X3),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8520]),
[final] ).
cnf(i_0_14848,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)))
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8694]),
[final] ).
cnf(i_0_14849,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8695]),
[final] ).
cnf(i_0_14850,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8696]),
[final] ).
cnf(i_0_14851,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8697]),
[final] ).
cnf(i_0_14852,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8698]),
[final] ).
cnf(i_0_14853,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8699]),
[final] ).
cnf(i_0_14854,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8700]),
[final] ).
cnf(i_0_14855,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8701]),
[final] ).
cnf(i_0_14856,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8702]),
[final] ).
cnf(i_0_14857,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk98_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8562]),
[final] ).
cnf(i_0_14858,plain,
( X1 = X2
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X4)),X3),X2),hAPP(c_Option_Ooption_OSome(X4),X7)),X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
| hAPP(X3,X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_8108]),
[final] ).
cnf(i_0_14859,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))),
inference(split_conjunct,[status(thm)],[i_0_8703]),
[final] ).
cnf(i_0_14860,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8704]),
[final] ).
cnf(i_0_14861,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk68_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8624]),
[final] ).
cnf(i_0_14862,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk67_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8625]),
[final] ).
cnf(i_0_14863,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk61_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8067]),
[final] ).
cnf(i_0_14864,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk479_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
| hAPP(c_List_Ofilter(X1,X3),X2) = X2 ),
inference(split_conjunct,[status(thm)],[i_0_8705]),
[final] ).
cnf(i_0_14865,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk485_3(X3,X2,X1)))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8476]),
[final] ).
cnf(i_0_14866,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk482_3(X3,X2,X1)))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8477]),
[final] ).
cnf(i_0_14867,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8706]),
[final] ).
cnf(i_0_14868,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_7179]),
[final] ).
cnf(i_0_14869,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_8707]),
[final] ).
cnf(i_0_14870,plain,
hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X4)) = hAPP(hAPP(c_List_Onth(X1),X3),X4),
inference(split_conjunct,[status(thm)],[i_0_8708]),
[final] ).
cnf(i_0_14871,plain,
hAPP(c_List_Oset(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)) = hAPP(c_List_Oset(X1),X3),
inference(rw,[status(thm)],[i_0_8709,c_0_6670]),
[final] ).
cnf(i_0_14872,plain,
hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_8710]),
[final] ).
cnf(i_0_14873,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8711]),
[final] ).
cnf(i_0_14874,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8712]),
[final] ).
cnf(i_0_14875,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8713]),
[final] ).
cnf(i_0_14876,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8712]),
[final] ).
cnf(i_0_14877,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8714]),
[final] ).
cnf(i_0_14878,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(c_Nat_OSuc,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8715]),
[final] ).
cnf(i_0_14879,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8716]),
[final] ).
cnf(i_0_14880,plain,
( c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))
| ~ c_Wellfounded_OwfP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8717]),
[final] ).
cnf(i_0_14881,plain,
( c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))
| ~ c_Wellfounded_OwfP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8089]),
[final] ).
cnf(i_0_14882,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_8718]),
[final] ).
cnf(i_0_14883,plain,
( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X3,c_Option_Ooption_ONone(X6),X5),hAPP(X1,X2)) = c_Option_Ooption_ONone(X6)
| hAPP(X5,X4) != c_Option_Ooption_ONone(X6)
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(rw,[status(thm)],[i_0_8719,c_0_6226]),
[final] ).
cnf(i_0_14884,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
| hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_7635]),
[final] ).
cnf(i_0_14885,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_8720]),
[final] ).
cnf(i_0_14886,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_8721]),
[final] ).
cnf(i_0_14887,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(X4,X2))
| c_List_Opartition(X1,X4,X5) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X6),X3) ),
inference(split_conjunct,[status(thm)],[i_0_8722]),
[final] ).
cnf(i_0_14888,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8723]),
[final] ).
cnf(i_0_14889,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8724]),
[final] ).
cnf(i_0_14890,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8725]),
[final] ).
cnf(i_0_14891,plain,
( hAPP(c_Lazy__Sequence_Oanamorph(X2,X3,X4,X1),X5) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),X2),c_List_Olist_ONil(X3)),X5)
| X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(split_conjunct,[status(thm)],[i_0_6084]),
[final] ).
cnf(i_0_14892,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk103_2(X1,X2)),X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8726]),
[final] ).
cnf(i_0_14893,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_7985]),
[final] ).
cnf(i_0_14894,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8727]),
[final] ).
cnf(i_0_14895,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8728]),
[final] ).
cnf(i_0_14896,plain,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(X4,X5,X2),X1),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8270]),
[final] ).
cnf(i_0_14897,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk339_3(X2,X3,X1)),X2))
| c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7194]),
[final] ).
cnf(i_0_14898,plain,
hAPP(c_Relation_ODomain(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))) = hAPP(c_Relation_ODomain(X1,X1),X2),
inference(rw,[status(thm)],[i_0_8729,c_0_6062]),
[final] ).
cnf(i_0_14899,plain,
hAPP(c_Relation_ORange(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))) = hAPP(c_Relation_ORange(X1,X1),X2),
inference(rw,[status(thm)],[i_0_8730,c_0_6062]),
[final] ).
cnf(i_0_14900,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8731]),
[final] ).
cnf(i_0_14901,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8732]),
[final] ).
cnf(i_0_14902,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8733]),
[final] ).
cnf(i_0_14903,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8734]),
[final] ).
cnf(i_0_14904,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8735]),
[final] ).
cnf(i_0_14905,plain,
( hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8736]),
[final] ).
cnf(i_0_14906,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)))),
inference(split_conjunct,[status(thm)],[i_0_8737]),
[final] ).
cnf(i_0_14907,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_8738]),
[final] ).
cnf(i_0_14908,plain,
( hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)) = hAPP(c_Set_Oimage(X1,X4,X5),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8739]),
[final] ).
cnf(i_0_14909,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8740,c_0_6015]),c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14910,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8741,c_0_6015]),c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14911,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8742]),
[final] ).
cnf(i_0_14912,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8743]),
[final] ).
cnf(i_0_14913,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,X2),X5),X4)
| ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8744]),
[final] ).
cnf(i_0_14914,plain,
( c_Wellfounded_Owf(X1,X3)
| ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8745]),
[final] ).
cnf(i_0_14915,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8746]),
[final] ).
cnf(i_0_14916,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8747]),
[final] ).
cnf(i_0_14917,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8748]),
[final] ).
cnf(i_0_14918,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8749]),
[final] ).
cnf(i_0_14919,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8750]),
[final] ).
cnf(i_0_14920,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8639]),
[final] ).
cnf(i_0_14921,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk335_1(X1)),c_Int_OInteg)),
inference(split_conjunct,[status(thm)],[i_0_8751]),
[final] ).
cnf(i_0_14922,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X2))
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8263]),
[final] ).
cnf(i_0_14923,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),X2))
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8264]),
[final] ).
cnf(i_0_14924,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8752,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14925,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8753,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14926,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8754]),
[final] ).
cnf(i_0_14927,plain,
( hBOOL(hAPP(X1,esk94_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4)))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Osemiring__0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_7585]),
[final] ).
cnf(i_0_14928,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8755]),
[final] ).
cnf(i_0_14929,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8320]),
[final] ).
cnf(i_0_14930,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8756]),
[final] ).
cnf(i_0_14931,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8757]),
[final] ).
cnf(i_0_14932,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8758]),
[final] ).
cnf(i_0_14933,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8759]),
[final] ).
cnf(i_0_14934,plain,
( X1 = X2
| hAPP(c_Code__Numeral_Oof__nat,X1) != hAPP(c_Code__Numeral_Oof__nat,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8760]),
[final] ).
cnf(i_0_14935,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8761]),
[final] ).
cnf(i_0_14936,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8761]),
[final] ).
cnf(i_0_14937,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8762]),
[final] ).
cnf(i_0_14938,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8763]),
[final] ).
cnf(i_0_14939,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk64_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8051]),
[final] ).
cnf(i_0_14940,plain,
( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5),X3,c_Option_Ooption_ONone(X5),X7),hAPP(X1,X2)) = hAPP(X7,X4)
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(rw,[status(thm)],[i_0_8764,c_0_6226]),
[final] ).
cnf(i_0_14941,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| c_List_Opartition(X1,X4,X5) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X6) ),
inference(split_conjunct,[status(thm)],[i_0_8722]),
[final] ).
cnf(i_0_14942,plain,
hAPP(X1,hAPP(hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X1),X4)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X1),hAPP(X1,X4)),
inference(split_conjunct,[status(thm)],[i_0_8765]),
[final] ).
cnf(i_0_14943,plain,
( hBOOL(hAPP(X1,esk97_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8524]),
[final] ).
cnf(i_0_14944,plain,
( hBOOL(hAPP(X2,X3))
| hAPP(c_List_Ofilter(X4,X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X1,X5),X3),X6)) = hAPP(c_List_Ofilter(X4,X2),X6)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8766]),
[final] ).
cnf(i_0_14945,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8767]),
[final] ).
cnf(i_0_14946,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8768]),
[final] ).
cnf(i_0_14947,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8769]),
[final] ).
cnf(i_0_14948,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8770]),
[final] ).
cnf(i_0_14949,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8771]),
[final] ).
cnf(i_0_14950,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8772]),
[final] ).
cnf(i_0_14951,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8773]),
[final] ).
cnf(i_0_14952,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8774]),
[final] ).
cnf(i_0_14953,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8775]),
[final] ).
cnf(i_0_14954,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8776]),
[final] ).
cnf(i_0_14955,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8777]),
[final] ).
cnf(i_0_14956,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8778]),
[final] ).
cnf(i_0_14957,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8779]),
[final] ).
cnf(i_0_14958,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8780]),
[final] ).
cnf(i_0_14959,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8781]),
[final] ).
cnf(i_0_14960,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8782]),
[final] ).
cnf(i_0_14961,plain,
( hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(c_List_Oset(X2),X5))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8783]),
[final] ).
cnf(i_0_14962,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8784]),
[final] ).
cnf(i_0_14963,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8554]),
[final] ).
cnf(i_0_14964,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8785]),
[final] ).
cnf(i_0_14965,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8786]),
[final] ).
cnf(i_0_14966,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8787]),
[final] ).
cnf(i_0_14967,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X5),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8788]),
[final] ).
cnf(i_0_14968,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)
| X5 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8788]),
[final] ).
cnf(i_0_14969,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8789]),
[final] ).
cnf(i_0_14970,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8790]),
[final] ).
cnf(i_0_14971,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8791]),
[final] ).
cnf(i_0_14972,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(c_Relation_Oconverse(X2,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8792]),
[final] ).
cnf(i_0_14973,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_8793]),
[final] ).
cnf(i_0_14974,plain,
( hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X3,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8794]),
[final] ).
cnf(i_0_14975,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_8795]),
[final] ).
cnf(i_0_14976,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_8796]),
[final] ).
cnf(i_0_14977,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8797]),
[final] ).
cnf(i_0_14978,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8798]),
[final] ).
cnf(i_0_14979,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8799]),
[final] ).
cnf(i_0_14980,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rw,[status(thm)],[i_0_8800,c_0_6015]),
[final] ).
cnf(i_0_14981,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8639]),
[final] ).
cnf(i_0_14982,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_8801]),
[final] ).
cnf(i_0_14983,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8718]),
[final] ).
cnf(i_0_14984,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Map_Orestrict__map(X1,X4,X5,X3),X2) = c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[i_0_8622]),
[final] ).
cnf(i_0_14985,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Map_Orestrict__map(X1,X4,X5,X3),X2) = c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[i_0_8802]),
[final] ).
cnf(i_0_14986,plain,
( c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3)) = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8803]),
[final] ).
cnf(i_0_14987,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk333_3(X2,X3,X1)),X2))
| hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8804]),
[final] ).
cnf(i_0_14988,plain,
hAPP(c_Map_Orestrict__map(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4) = c_Option_Ooption_ONone(X2),
inference(split_conjunct,[status(thm)],[i_0_8805]),
[final] ).
cnf(i_0_14989,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),c_Product__Type_Ocurry(X1,X2,X3,X4)) = X4,
inference(split_conjunct,[status(thm)],[i_0_8806]),
[final] ).
cnf(i_0_14990,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk96_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8524]),
[final] ).
cnf(i_0_14991,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3))))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8807]),
[final] ).
cnf(i_0_14992,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X4) = X3
| X1 != hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)
| X4 != hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_8808]),
[final] ).
cnf(i_0_14993,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Groups_Otimes__class_Otimes(X1)),X3),X2)
| ~ class_Groups_Oab__semigroup__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8809]),
[final] ).
cnf(i_0_14994,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_8810,c_0_6015]),
[final] ).
cnf(i_0_14995,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8039]),
[final] ).
cnf(i_0_14996,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
| hAPP(hAPP(c_List_Onth(X2),X3),X1) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_8164]),
[final] ).
cnf(i_0_14997,plain,
( hBOOL(hAPP(X1,esk59_3(X2,X3,X1)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7526]),
[final] ).
cnf(i_0_14998,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_8811]),
[final] ).
cnf(i_0_14999,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_8812]),
[final] ).
cnf(i_0_15000,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8813,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15001,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(c_Finite__Set_Ocard(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8298]),
[final] ).
cnf(i_0_15002,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(c_Finite__Set_Ocard(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8298]),
[final] ).
cnf(i_0_15003,plain,
( hAPP(c_Map_Omap__add(X6,X3,X4,X1),X2) = hAPP(c_Option_Ooption_OSome(X3),X5)
| hAPP(X1,X2) != c_Option_Ooption_ONone(X3)
| hAPP(X4,X2) != hAPP(c_Option_Ooption_OSome(X3),X5) ),
inference(split_conjunct,[status(thm)],[i_0_8241]),
[final] ).
cnf(i_0_15004,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8368]),
[final] ).
cnf(i_0_15005,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7514]),
[final] ).
cnf(i_0_15006,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3))))
| X3 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7619]),
[final] ).
cnf(i_0_15007,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3),
inference(split_conjunct,[status(thm)],[i_0_8814]),
[final] ).
cnf(i_0_15008,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3))
| X4 != X5 ),
inference(split_conjunct,[status(thm)],[i_0_8591]),
[final] ).
cnf(i_0_15009,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7635]),
[final] ).
cnf(i_0_15010,plain,
( X4 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X1,X2)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8815]),
[final] ).
cnf(i_0_15011,plain,
( hAPP(X3,X6) = hAPP(X5,X6)
| hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X1,X2),X5),X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6570]),
[final] ).
cnf(i_0_15012,plain,
( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X6)),X7),X2),hAPP(c_Option_Ooption_OSome(X6),X3)),X1) = hAPP(c_Option_Ooption_OSome(X6),X4)
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[i_0_8108]),
[final] ).
cnf(i_0_15013,plain,
hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))) = X2,
inference(rw,[status(thm)],[i_0_8816,c_0_6135]),
[final] ).
cnf(i_0_15014,plain,
( X2 = X3
| hAPP(hAPP(c_List_Onth(X1),X2),esk452_3(X1,X3,X2)) != hAPP(hAPP(c_List_Onth(X1),X3),esk452_3(X1,X3,X2))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_8501]),
[final] ).
cnf(i_0_15015,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8584]),
[final] ).
cnf(i_0_15016,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8577]),
[final] ).
cnf(i_0_15017,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8798]),
[final] ).
cnf(i_0_15018,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8799]),
[final] ).
cnf(i_0_15019,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8817]),
[final] ).
cnf(i_0_15020,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_15021,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8818]),
[final] ).
cnf(i_0_15022,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8698]),
[final] ).
cnf(i_0_15023,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3)))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8818]),
[final] ).
cnf(i_0_15024,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3)))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8698]),
[final] ).
cnf(i_0_15025,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8699]),
[final] ).
cnf(i_0_15026,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8819]),
[final] ).
cnf(i_0_15027,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8699]),
[final] ).
cnf(i_0_15028,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8819]),
[final] ).
cnf(i_0_15029,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8702]),
[final] ).
cnf(i_0_15030,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8702]),
[final] ).
cnf(i_0_15031,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk502_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_15032,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8820]),
[final] ).
cnf(i_0_15033,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8821]),
[final] ).
cnf(i_0_15034,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8822]),
[final] ).
cnf(i_0_15035,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8823]),
[final] ).
cnf(i_0_15036,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8824]),
[final] ).
cnf(i_0_15037,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8825]),
[final] ).
cnf(i_0_15038,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8826]),
[final] ).
cnf(i_0_15039,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8827]),
[final] ).
cnf(i_0_15040,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8828]),
[final] ).
cnf(i_0_15041,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8627]),
[final] ).
cnf(i_0_15042,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_8829]),
[final] ).
cnf(i_0_15043,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_8314]),
[final] ).
cnf(i_0_15044,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_8830]),
[final] ).
cnf(i_0_15045,plain,
hAPP(c_Sum__Type_OSumr(X1,X2,X3,X4),hAPP(c_Sum__Type_OInr(X1,X3),X5)) = hAPP(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_8831]),
[final] ).
cnf(i_0_15046,plain,
hAPP(c_Sum__Type_OSuml(X1,X2,X3,X4),hAPP(c_Sum__Type_OInl(X1,X3),X5)) = hAPP(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_8832]),
[final] ).
cnf(i_0_15047,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),X2))
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8213]),
[final] ).
cnf(i_0_15048,plain,
( hAPP(hAPP(c_List_Odrop(X1),X3),X2) = c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8833]),
[final] ).
cnf(i_0_15049,plain,
( hAPP(hAPP(c_List_Odrop(X1),X3),X2) = c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8834]),
[final] ).
cnf(i_0_15050,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8835]),
[final] ).
cnf(i_0_15051,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8836]),
[final] ).
cnf(i_0_15052,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk61_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8067]),
[final] ).
cnf(i_0_15053,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk99_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8562]),
[final] ).
cnf(i_0_15054,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X2,X3,X1)
| ~ hBOOL(hAPP(X2,esk500_3(X1,X3,X2)))
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_15055,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(rw,[status(thm)],[i_0_8837,c_0_6015]),
[final] ).
cnf(i_0_15056,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
inference(rw,[status(thm)],[i_0_8838,c_0_6015]),
[final] ).
cnf(i_0_15057,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(rw,[status(thm)],[i_0_8839,c_0_6015]),
[final] ).
cnf(i_0_15058,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
inference(rw,[status(thm)],[i_0_8840,c_0_6015]),
[final] ).
cnf(i_0_15059,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[i_0_8841,c_0_6015]),
[final] ).
cnf(i_0_15060,plain,
( hAPP(hAPP(c_List_Otake(X1),X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8842]),
[final] ).
cnf(i_0_15061,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(c_Nat_OSuc,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8843,c_0_8844]),c_0_8844]),
[final] ).
cnf(i_0_15062,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(rw,[status(thm)],[i_0_8845,c_0_6062]),
[final] ).
cnf(i_0_15063,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X1)))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8255]),
[final] ).
cnf(i_0_15064,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk499_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_15065,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8846]),
[final] ).
cnf(i_0_15066,plain,
( hBOOL(hAPP(hAPP(X1,esk80_3(X2,X1,X3)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8847]),
[final] ).
cnf(i_0_15067,plain,
( hBOOL(hAPP(hAPP(X1,esk79_3(X2,X1,X3)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8848]),
[final] ).
cnf(i_0_15068,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Transitive__Closure_Ortrancl(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))) = X3,
inference(rw,[status(thm)],[i_0_8849,c_0_6053]),
[final] ).
cnf(i_0_15069,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8850]),
[final] ).
cnf(i_0_15070,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(rw,[status(thm)],[i_0_8851,c_0_6169]),
[final] ).
cnf(i_0_15071,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8852]),
[final] ).
cnf(i_0_15072,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8853]),
[final] ).
cnf(i_0_15073,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8854]),
[final] ).
cnf(i_0_15074,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_List_Oset(X1),X2)) = hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8855]),
[final] ).
cnf(i_0_15075,plain,
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_List_Oset(X1),X2)) = hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8856]),
[final] ).
cnf(i_0_15076,plain,
( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X4),X3,c_Option_Ooption_ONone(X4),X6),hAPP(X1,X2)) = c_Option_Ooption_ONone(X4)
| hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
inference(rw,[status(thm)],[i_0_8857,c_0_6226]),
[final] ).
cnf(i_0_15077,plain,
( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X4),X3,c_Option_Ooption_ONone(X4),X6),hAPP(X1,X2)) = c_Option_Ooption_ONone(X4)
| hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
inference(rw,[status(thm)],[i_0_8858,c_0_6226]),
[final] ).
cnf(i_0_15078,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_8859]),
[final] ).
cnf(i_0_15079,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8860]),
[final] ).
cnf(i_0_15080,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk370_3(X2,X3,X1)),X3))
| c_Relation_Ototal__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6756]),
[final] ).
cnf(i_0_15081,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk369_3(X2,X3,X1)),X3))
| c_Relation_Ototal__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6756]),
[final] ).
cnf(i_0_15082,plain,
( hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1) = c_List_Olist_ONil(X2)
| esk490_2(X1,X2) != c_List_Olist_ONil(X2) ),
inference(rw,[status(thm)],[i_0_8861,c_0_6100]),
[final] ).
cnf(i_0_15083,plain,
( c_List_Olist_ONil(X2) = hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1)
| esk489_2(X1,X2) != c_List_Olist_ONil(X2) ),
inference(rw,[status(thm)],[i_0_8862,c_0_6100]),
[final] ).
cnf(i_0_15084,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8863]),
[final] ).
cnf(i_0_15085,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8864]),
[final] ).
cnf(i_0_15086,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8865]),
[final] ).
cnf(i_0_15087,plain,
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8866]),
[final] ).
cnf(i_0_15088,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X2,X3,X1)
| ~ hBOOL(hAPP(X2,esk497_3(X1,X3,X2)))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_15089,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2)
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8867]),
[final] ).
cnf(i_0_15090,plain,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatMost(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8868]),
[final] ).
cnf(i_0_15091,plain,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OlessThan(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8869]),
[final] ).
cnf(i_0_15092,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeast(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8870]),
[final] ).
cnf(i_0_15093,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThan(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_8871]),
[final] ).
cnf(i_0_15094,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X4)),hAPP(c_List_Oset(X1),X5)) = hAPP(c_List_Oset(X1),X3)
| c_List_Opartition(X1,X2,X3) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_8872]),
[final] ).
cnf(i_0_15095,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8476]),
[final] ).
cnf(i_0_15096,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8477]),
[final] ).
cnf(i_0_15097,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8873]),
[final] ).
cnf(i_0_15098,plain,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
inference(split_conjunct,[status(thm)],[fact_wf__less]),
[final] ).
cnf(i_0_15099,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2),
inference(split_conjunct,[status(thm)],[i_0_8874]),
[final] ).
cnf(i_0_15100,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2),
inference(rw,[status(thm)],[i_0_8875,c_0_6062]),
[final] ).
cnf(i_0_15101,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_8876]),
[final] ).
cnf(i_0_15102,plain,
c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_8877,c_0_6062]),
[final] ).
cnf(i_0_15103,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk399_3(X3,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8397]),
[final] ).
cnf(i_0_15104,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8878]),
[final] ).
cnf(i_0_15105,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_8879]),
[final] ).
cnf(i_0_15106,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_8880]),
[final] ).
cnf(i_0_15107,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_8880]),
[final] ).
cnf(i_0_15108,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8102]),
[final] ).
cnf(i_0_15109,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8735]),
[final] ).
cnf(i_0_15110,plain,
( hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8881]),
[final] ).
cnf(i_0_15111,plain,
( hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8241]),
[final] ).
cnf(i_0_15112,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Finite__Set_Ofold(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1)),X3),X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8882]),
[final] ).
cnf(i_0_15113,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8883]),
[final] ).
cnf(i_0_15114,plain,
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8884]),
[final] ).
cnf(i_0_15115,plain,
( c_Wellfounded_Owf(tc_prod(X1,X3),c_Wellfounded_Olex__prod(X1,X3,X2,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_8885]),
[final] ).
cnf(i_0_15116,plain,
( hBOOL(hAPP(X1,esk59_3(X2,X3,X1)))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7526]),
[final] ).
cnf(i_0_15117,plain,
hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1))) = c_List_Olist_ONil(X1),
inference(rw,[status(thm)],[i_0_8886,c_0_6100]),
[final] ).
cnf(i_0_15118,plain,
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8887]),
[final] ).
cnf(i_0_15119,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8888]),
[final] ).
cnf(i_0_15120,plain,
( hBOOL(hAPP(c_List_Odistinct(tc_prod(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8889]),
[final] ).
cnf(i_0_15121,plain,
( hBOOL(hAPP(c_List_Odistinct(tc_prod(X3,X1)),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8890]),
[final] ).
cnf(i_0_15122,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2)
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8891]),
[final] ).
cnf(i_0_15123,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8892]),
[final] ).
cnf(i_0_15124,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8893]),
[final] ).
cnf(i_0_15125,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2)
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8894]),
[final] ).
cnf(i_0_15126,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8628]),
[final] ).
cnf(i_0_15127,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),c_Set_Ovimage(X1,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_8895]),
[final] ).
cnf(i_0_15128,plain,
hAPP(c_Set_Oimage(X1,X2,X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X4),c_Set_Oimage(X1,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_8896]),
[final] ).
cnf(i_0_15129,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Set_OPow(X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_8897]),
[final] ).
cnf(i_0_15130,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8322]),
[final] ).
cnf(i_0_15131,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Ozero__class_Ozero(X1))),X3)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8898]),
[final] ).
cnf(i_0_15132,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_8899]),
[final] ).
cnf(i_0_15133,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_8900]),
[final] ).
cnf(i_0_15134,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_8901]),
[final] ).
cnf(i_0_15135,plain,
( hAPP(c_List_Orotate1(X1),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8902]),
[final] ).
cnf(i_0_15136,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk103_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8726]),
[final] ).
cnf(i_0_15137,plain,
hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = X5,
inference(split_conjunct,[status(thm)],[i_0_8903]),
[final] ).
cnf(i_0_15138,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8904]),
[final] ).
cnf(i_0_15139,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8905]),
[final] ).
cnf(i_0_15140,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8906]),
[final] ).
cnf(i_0_15141,plain,
c_Hoare__Mirabelle_Otriple_Otriple__case(X1,X2,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X4),X5),X6)) = hAPP(hAPP(hAPP(X3,X4),X5),X6),
inference(split_conjunct,[status(thm)],[i_0_8907]),
[final] ).
cnf(i_0_15142,plain,
c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,X2,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X4),X5),X6)) = hAPP(hAPP(hAPP(X3,X4),X5),X6),
inference(split_conjunct,[status(thm)],[i_0_8908]),
[final] ).
cnf(i_0_15143,plain,
( hBOOL(hAPP(hAPP(X3,esk325_2(X4,X3)),X4))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8909]),
[final] ).
cnf(i_0_15144,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8910]),
[final] ).
cnf(i_0_15145,plain,
( hAPP(c_Map_Omap__add(X5,X3,X4,X1),X2) = c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) != c_Option_Ooption_ONone(X3)
| hAPP(X4,X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8365]),
[final] ).
cnf(i_0_15146,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8911]),
[final] ).
cnf(i_0_15147,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X1,X2)),c_Nitpick_Opair__box_OPairBox(X1,X2,X3,X4)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_8912]),
[final] ).
cnf(i_0_15148,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)) = hAPP(hAPP(c_List_Olist__update(X2,c_List_Obutlast(X2,X3)),X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8913]),
[final] ).
cnf(i_0_15149,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_8914]),
[final] ).
cnf(i_0_15150,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) = c_List_Olist_ONil(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
inference(rw,[status(thm)],[i_0_8915,c_0_6135]),
[final] ).
cnf(i_0_15151,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8916]),
[final] ).
cnf(i_0_15152,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8917]),
[final] ).
cnf(i_0_15153,plain,
( hAPP(hAPP(c_Set_Oinsert(X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7540]),
[final] ).
cnf(i_0_15154,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8918]),
[final] ).
cnf(i_0_15155,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8919]),
[final] ).
cnf(i_0_15156,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk101_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8687]),
[final] ).
cnf(i_0_15157,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| c_Divides_Odiv__class_Omod(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8648]),
[final] ).
cnf(i_0_15158,plain,
( hAPP(hAPP(c_List_Ozip(X1,X3),hAPP(c_List_Orev(X1),X2)),hAPP(c_List_Orev(X3),X4)) = hAPP(c_List_Orev(tc_prod(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8920]),
[final] ).
cnf(i_0_15159,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8921]),
[final] ).
cnf(i_0_15160,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8271]),
[final] ).
cnf(i_0_15161,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8922]),
[final] ).
cnf(i_0_15162,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8923]),
[final] ).
cnf(i_0_15163,plain,
hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4) = hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3),
inference(split_conjunct,[status(thm)],[i_0_8924]),
[final] ).
cnf(i_0_15164,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_8925]),
[final] ).
cnf(i_0_15165,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_8926]),
[final] ).
cnf(i_0_15166,plain,
hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),hAPP(c_Option_Ooption_OSome(X2),X5)) = hAPP(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_8927]),
[final] ).
cnf(i_0_15167,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8928]),
[final] ).
cnf(i_0_15168,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8787]),
[final] ).
cnf(i_0_15169,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8787]),
[final] ).
cnf(i_0_15170,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_8929]),
[final] ).
cnf(i_0_15171,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2),
inference(split_conjunct,[status(thm)],[i_0_8930]),
[final] ).
cnf(i_0_15172,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = X4
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7315]),
[final] ).
cnf(i_0_15173,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = X4
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7316]),
[final] ).
cnf(i_0_15174,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = X4
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7317]),
[final] ).
cnf(i_0_15175,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8931]),
[final] ).
cnf(i_0_15176,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8932]),
[final] ).
cnf(i_0_15177,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8933]),
[final] ).
cnf(i_0_15178,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8934]),
[final] ).
cnf(i_0_15179,plain,
( hAPP(c_Random_Oiterate(X2,X3,X1,X4),X5) = hAPP(c_Product__Type_OPair(X2,X3),X5)
| X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(split_conjunct,[status(thm)],[i_0_7223]),
[final] ).
cnf(i_0_15180,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X1,X2))),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),
inference(split_conjunct,[status(thm)],[i_0_8935]),
[final] ).
cnf(i_0_15181,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(X2,tc_fun(X1,tc_HOL_Obool),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3),
inference(split_conjunct,[status(thm)],[i_0_8936]),
[final] ).
cnf(i_0_15182,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(X2,tc_fun(X1,tc_HOL_Obool),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3),
inference(split_conjunct,[status(thm)],[i_0_8937]),
[final] ).
cnf(i_0_15183,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3)),
inference(split_conjunct,[status(thm)],[i_0_8938]),
[final] ).
cnf(i_0_15184,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3)),
inference(split_conjunct,[status(thm)],[i_0_8939]),
[final] ).
cnf(i_0_15185,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(c_Nat_OSuc,X3),X4) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,X3,hAPP(X2,X4))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8940]),
[final] ).
cnf(i_0_15186,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8941]),
[final] ).
cnf(i_0_15187,plain,
( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8942]),
[final] ).
cnf(i_0_15188,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X2)),
inference(split_conjunct,[status(thm)],[i_0_8943]),
[final] ).
cnf(i_0_15189,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X2)),
inference(split_conjunct,[status(thm)],[i_0_8944]),
[final] ).
cnf(i_0_15190,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk502_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_15191,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk499_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_15192,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)),X1)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8289]),
[final] ).
cnf(i_0_15193,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8945]),
[final] ).
cnf(i_0_15194,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8946]),
[final] ).
cnf(i_0_15195,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8668]),
[final] ).
cnf(i_0_15196,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8947]),
[final] ).
cnf(i_0_15197,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8669]),
[final] ).
cnf(i_0_15198,plain,
( hAPP(c_Set_Oimage(X1,X4,hAPP(c_COMBK(X4,X1),X5)),X3) = hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8948]),
[final] ).
cnf(i_0_15199,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8761]),
[final] ).
cnf(i_0_15200,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8761]),
[final] ).
cnf(i_0_15201,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8762]),
[final] ).
cnf(i_0_15202,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8763]),
[final] ).
cnf(i_0_15203,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8949]),
[final] ).
cnf(i_0_15204,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_8950]),
[final] ).
cnf(i_0_15205,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(split_conjunct,[status(thm)],[i_0_8951]),
[final] ).
cnf(i_0_15206,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk80_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8847]),
[final] ).
cnf(i_0_15207,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk79_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8848]),
[final] ).
cnf(i_0_15208,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8289]),
[final] ).
cnf(i_0_15209,plain,
hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8952,c_0_6053]),c_0_6053]),
[final] ).
cnf(i_0_15210,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8953]),
[final] ).
cnf(i_0_15211,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8954]),
[final] ).
cnf(i_0_15212,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk407_2(X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8408]),
[final] ).
cnf(i_0_15213,plain,
hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),X4)) = hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4),
inference(split_conjunct,[status(thm)],[i_0_8955]),
[final] ).
cnf(i_0_15214,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk104_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8726]),
[final] ).
cnf(i_0_15215,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8956]),
[final] ).
cnf(i_0_15216,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8957]),
[final] ).
cnf(i_0_15217,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8958]),
[final] ).
cnf(i_0_15218,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8959]),
[final] ).
cnf(i_0_15219,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8960]),
[final] ).
cnf(i_0_15220,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8961]),
[final] ).
cnf(i_0_15221,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8628]),
[final] ).
cnf(i_0_15222,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8962]),
[final] ).
cnf(i_0_15223,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8963]),
[final] ).
cnf(i_0_15224,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8964]),
[final] ).
cnf(i_0_15225,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(split_conjunct,[status(thm)],[i_0_8965]),
[final] ).
cnf(i_0_15226,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(split_conjunct,[status(thm)],[i_0_8966]),
[final] ).
cnf(i_0_15227,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))),X3)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8967]),
[final] ).
cnf(i_0_15228,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8968]),
[final] ).
cnf(i_0_15229,plain,
( hAPP(hAPP(c_List_Onth(X1),X2),X3) = X4
| hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8969]),
[final] ).
cnf(i_0_15230,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8970]),
[final] ).
cnf(i_0_15231,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X1))
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8398]),
[final] ).
cnf(i_0_15232,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8971]),
[final] ).
cnf(i_0_15233,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8972]),
[final] ).
cnf(i_0_15234,plain,
( X5 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3))
| ~ c_Natural_Oevaln(c_Com_Ocom_OAss(X1,X2),X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_8973]),
[final] ).
cnf(i_0_15235,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))),
inference(split_conjunct,[status(thm)],[i_0_8974]),
[final] ).
cnf(i_0_15236,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2))),
inference(split_conjunct,[status(thm)],[i_0_8975]),
[final] ).
cnf(i_0_15237,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X2,X3,X1)
| ~ hBOOL(hAPP(X2,esk500_3(X1,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_15238,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X2,X3,X1)
| ~ hBOOL(hAPP(X2,esk497_3(X1,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_15239,plain,
( hBOOL(hAPP(X1,esk102_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8687]),
[final] ).
cnf(i_0_15240,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),X3)),X2),
inference(split_conjunct,[status(thm)],[i_0_8976]),
[final] ).
cnf(i_0_15241,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_8977]),
[final] ).
cnf(i_0_15242,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8978,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_15243,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_8979]),
[final] ).
cnf(i_0_15244,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_8980]),
[final] ).
cnf(i_0_15245,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_8981]),
[final] ).
cnf(i_0_15246,plain,
hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4) = c_Nat_Onat_Onat__case(X1,X2,hAPP(c_List_Onth(X1),X3),X4),
inference(split_conjunct,[status(thm)],[i_0_8982]),
[final] ).
cnf(i_0_15247,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8344]),
[final] ).
cnf(i_0_15248,plain,
( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| esk467_2(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8041]),
[final] ).
cnf(i_0_15249,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Sum__Type_OPlus(X2,X3,X1,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2,X3),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8983]),
[final] ).
cnf(i_0_15250,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Sum__Type_OPlus(X3,X2,X4,X1) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X3,X2),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8983]),
[final] ).
cnf(i_0_15251,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8984]),
[final] ).
cnf(i_0_15252,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8985]),
[final] ).
cnf(i_0_15253,plain,
( hAPP(X4,X5) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7252]),
[final] ).
cnf(i_0_15254,plain,
( hAPP(X4,X5) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7251]),
[final] ).
cnf(i_0_15255,plain,
( hAPP(X4,X5) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7253]),
[final] ).
cnf(i_0_15256,plain,
( hAPP(X4,X5) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7254]),
[final] ).
cnf(i_0_15257,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))) = c_Groups_Ozero__class_Ozero(X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_7778]),
[final] ).
cnf(i_0_15258,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_15259,plain,
( X1 = X2
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8986]),
[final] ).
cnf(i_0_15260,plain,
( X1 = X2
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_8986]),
[final] ).
cnf(i_0_15261,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8910]),
[final] ).
cnf(i_0_15262,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),
inference(split_conjunct,[status(thm)],[i_0_8987]),
[final] ).
cnf(i_0_15263,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),
inference(split_conjunct,[status(thm)],[i_0_8988]),
[final] ).
cnf(i_0_15264,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8989]),
[final] ).
cnf(i_0_15265,plain,
( c_Wellfounded_Owf(X1,X2)
| hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8990]),
[final] ).
cnf(i_0_15266,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8991]),
[final] ).
cnf(i_0_15267,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| ~ class_Int_Onumber(X1)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8550]),
[final] ).
cnf(i_0_15268,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
| ~ class_Int_Onumber(X1)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8551]),
[final] ).
cnf(i_0_15269,plain,
hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)) != hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),
inference(split_conjunct,[status(thm)],[i_0_8992]),
[final] ).
cnf(i_0_15270,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_COMBK(X1,X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Finite__Set_Ocard(X2),X4))),X3)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8993]),
[final] ).
cnf(i_0_15271,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8994]),
[final] ).
cnf(i_0_15272,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8995]),
[final] ).
cnf(i_0_15273,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8996]),
[final] ).
cnf(i_0_15274,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8997]),
[final] ).
cnf(i_0_15275,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8998]),
[final] ).
cnf(i_0_15276,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8999]),
[final] ).
cnf(i_0_15277,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9000]),
[final] ).
cnf(i_0_15278,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9001]),
[final] ).
cnf(i_0_15279,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9002]),
[final] ).
cnf(i_0_15280,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X1,X2,X3)))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_15281,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9003]),
[final] ).
cnf(i_0_15282,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9004]),
[final] ).
cnf(i_0_15283,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9005]),
[final] ).
cnf(i_0_15284,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))
| hAPP(X4,X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[i_0_9006]),
[final] ).
cnf(i_0_15285,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),hAPP(c_Relation_Oconverse(X1,X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8792]),
[final] ).
cnf(i_0_15286,plain,
( hAPP(hAPP(c_List_Omap(tc_prod(X1,X3),X1),c_Product__Type_Ofst(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)) = X2
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9007]),
[final] ).
cnf(i_0_15287,plain,
( hAPP(hAPP(c_List_Omap(tc_prod(X1,X3),X3),c_Product__Type_Osnd(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)) = X4
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9008]),
[final] ).
cnf(i_0_15288,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9009]),
[final] ).
cnf(i_0_15289,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9010]),
[final] ).
cnf(i_0_15290,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9011]),
[final] ).
cnf(i_0_15291,plain,
hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))),
inference(split_conjunct,[status(thm)],[i_0_9012]),
[final] ).
cnf(i_0_15292,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8600]),
[final] ).
cnf(i_0_15293,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9013]),
[final] ).
cnf(i_0_15294,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9014]),
[final] ).
cnf(i_0_15295,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9015]),
[final] ).
cnf(i_0_15296,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9016]),
[final] ).
cnf(i_0_15297,plain,
c_Map_Odom(X1,X2,c_Map_Omap__of(X1,X2,X3)) = hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)),
inference(split_conjunct,[status(thm)],[i_0_9017]),
[final] ).
cnf(i_0_15298,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk503_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_15299,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),X5) = hAPP(hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X2),X5)),hAPP(c_Product__Type_Osnd(X1,X2),X5)),
inference(split_conjunct,[status(thm)],[i_0_9018]),
[final] ).
cnf(i_0_15300,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),X5) = hAPP(hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X2),X5)),hAPP(c_Product__Type_Osnd(X1,X2),X5)),
inference(split_conjunct,[status(thm)],[i_0_9019]),
[final] ).
cnf(i_0_15301,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),X5) = hAPP(hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X2),X5)),hAPP(c_Product__Type_Osnd(X1,X2),X5)),
inference(split_conjunct,[status(thm)],[i_0_9020]),
[final] ).
cnf(i_0_15302,plain,
( hBOOL(hAPP(X1,X2))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X4)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7096]),
[final] ).
cnf(i_0_15303,plain,
( hBOOL(hAPP(X1,X2))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X4)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7097]),
[final] ).
cnf(i_0_15304,plain,
( X1 = X2
| hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X4),c_List_Olist_ONil(X3))) != hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9021]),
[final] ).
cnf(i_0_15305,plain,
( X1 = X2
| hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))) != hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9021]),
[final] ).
cnf(i_0_15306,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9022]),
[final] ).
cnf(i_0_15307,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Odrop(X2),X3),X1)) = hAPP(hAPP(c_List_Onth(X2),X1),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9023]),
[final] ).
cnf(i_0_15308,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9024]),
[final] ).
cnf(i_0_15309,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X1,X2,X3)))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_15310,plain,
( hAPP(hAPP(c_Set_Oinsert(X5),X1),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X5),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[i_0_8374]),
[final] ).
cnf(i_0_15311,plain,
( hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,X2),X5),X4)
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9025]),
[final] ).
cnf(i_0_15312,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9026]),
[final] ).
cnf(i_0_15313,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9027]),
[final] ).
cnf(i_0_15314,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9028]),
[final] ).
cnf(i_0_15315,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9029]),
[final] ).
cnf(i_0_15316,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9030]),
[final] ).
cnf(i_0_15317,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9031]),
[final] ).
cnf(i_0_15318,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9032]),
[final] ).
cnf(i_0_15319,plain,
( c_Natural_Oevaln(X1,X2,esk7_3(X3,X2,X1),X3)
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9033]),
[final] ).
cnf(i_0_15320,plain,
( c_Natural_Oevaln(X1,X2,esk3_3(X3,X2,X1),X3)
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9034]),
[final] ).
cnf(i_0_15321,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_8370]),
[final] ).
cnf(i_0_15322,plain,
( hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) = X2
| hAPP(hAPP(c_List_Onth(X1),X2),X3) != X4
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8969]),
[final] ).
cnf(i_0_15323,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9035]),
[final] ).
cnf(i_0_15324,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9036]),
[final] ).
cnf(i_0_15325,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9037]),
[final] ).
cnf(i_0_15326,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9038]),
[final] ).
cnf(i_0_15327,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9039]),
[final] ).
cnf(i_0_15328,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8330]),
[final] ).
cnf(i_0_15329,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9040]),
[final] ).
cnf(i_0_15330,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8332]),
[final] ).
cnf(i_0_15331,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9041]),
[final] ).
cnf(i_0_15332,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9042]),
[final] ).
cnf(i_0_15333,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9043]),
[final] ).
cnf(i_0_15334,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9044]),
[final] ).
cnf(i_0_15335,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9045]),
[final] ).
cnf(i_0_15336,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9046]),
[final] ).
cnf(i_0_15337,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9047]),
[final] ).
cnf(i_0_15338,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)),hAPP(c_Set_Oimage(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_9048]),
[final] ).
cnf(i_0_15339,plain,
hAPP(c_Fun_Ocomp(X1,X1,X2,c_Fun_Oid(X1)),X3) = X3,
inference(split_conjunct,[status(thm)],[i_0_9049]),
[final] ).
cnf(i_0_15340,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9050]),
[final] ).
cnf(i_0_15341,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2))
| ~ class_Groups_Oab__semigroup__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9051]),
[final] ).
cnf(i_0_15342,plain,
( c_Relation_Osingle__valued(X1,X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))
| ~ c_Relation_Osingle__valued(X1,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9052]),
[final] ).
cnf(i_0_15343,plain,
hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X1),X2),X3),X4) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9053]),
[final] ).
cnf(i_0_15344,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk499_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_15345,plain,
( hBOOL(hAPP(hAPP(X3,X4),esk329_2(X4,X3)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9054]),
[final] ).
cnf(i_0_15346,plain,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ c_Fun_Oinj__on(X4,X5,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_9055]),
[final] ).
cnf(i_0_15347,plain,
( X4 = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| hAPP(X3,X4) != hAPP(X3,X5) ),
inference(split_conjunct,[status(thm)],[i_0_9056]),
[final] ).
cnf(i_0_15348,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_8826]),
[final] ).
cnf(i_0_15349,plain,
( hAPP(c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5),X1) = c_Lazy__Sequence_Ohit__bound(X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(split_conjunct,[status(thm)],[i_0_7567]),
[final] ).
cnf(i_0_15350,plain,
( hAPP(c_New__DSequence_Opos__decr__bind(X2,X3,X4,X5),X1) = c_Lazy__Sequence_Oempty(X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(split_conjunct,[status(thm)],[i_0_7614]),
[final] ).
cnf(i_0_15351,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9057]),
[final] ).
cnf(i_0_15352,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8624]),
[final] ).
cnf(i_0_15353,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8625]),
[final] ).
cnf(i_0_15354,plain,
( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9058]),
[final] ).
cnf(i_0_15355,plain,
( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9059]),
[final] ).
cnf(i_0_15356,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(rw,[status(thm)],[i_0_9060,c_0_6169]),
[final] ).
cnf(i_0_15357,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk53_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9061]),
[final] ).
cnf(i_0_15358,plain,
hAPP(c_List_Ofoldl(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X4,
inference(split_conjunct,[status(thm)],[i_0_9062]),
[final] ).
cnf(i_0_15359,plain,
hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_9063]),
[final] ).
cnf(i_0_15360,plain,
hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1)) = X3,
inference(split_conjunct,[status(thm)],[i_0_9064]),
[final] ).
cnf(i_0_15361,plain,
hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),c_Option_Ooption_ONone(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_9065]),
[final] ).
cnf(i_0_15362,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9066]),
[final] ).
cnf(i_0_15363,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X3))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9066]),
[final] ).
cnf(i_0_15364,plain,
c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))),
inference(rw,[status(thm)],[i_0_9067,c_0_6135]),
[final] ).
cnf(i_0_15365,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9068]),
[final] ).
cnf(i_0_15366,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9069]),
[final] ).
cnf(i_0_15367,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9070]),
[final] ).
cnf(i_0_15368,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8723]),
[final] ).
cnf(i_0_15369,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ class_Lattices_Oboolean__algebra(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9071]),
[final] ).
cnf(i_0_15370,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8724]),
[final] ).
cnf(i_0_15371,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9072]),
[final] ).
cnf(i_0_15372,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8725]),
[final] ).
cnf(i_0_15373,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) ),
inference(rw,[status(thm)],[i_0_9073,c_0_6015]),
[final] ).
cnf(i_0_15374,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) ),
inference(rw,[status(thm)],[i_0_9074,c_0_6015]),
[final] ).
cnf(i_0_15375,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) ),
inference(rw,[status(thm)],[i_0_9075,c_0_6015]),
[final] ).
cnf(i_0_15376,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) ),
inference(rw,[status(thm)],[i_0_9076,c_0_6015]),
[final] ).
cnf(i_0_15377,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9077]),
[final] ).
cnf(i_0_15378,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_9078]),
[final] ).
cnf(i_0_15379,plain,
hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_9079]),
[final] ).
cnf(i_0_15380,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Complete__Lattice_OSup__class_OSup(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8397]),
[final] ).
cnf(i_0_15381,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9080]),
[final] ).
cnf(i_0_15382,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9081]),
[final] ).
cnf(i_0_15383,plain,
( hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Groups_Otimes__class_Otimes(X1)),X3),X2)
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9082]),
[final] ).
cnf(i_0_15384,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),esk145_2(X1,X2)),esk146_2(X1,X2)))
| c_Orderings_Oorder_Omono(tc_Nat_Onat,X2,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7908]),
[final] ).
cnf(i_0_15385,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk232_3(X2,X3,X1)))
| hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6702]),
[final] ).
cnf(i_0_15386,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X5 = X6
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != X4
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_9083]),
[final] ).
cnf(i_0_15387,plain,
c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
inference(split_conjunct,[status(thm)],[fact_int__of__def]),
[final] ).
cnf(i_0_15388,plain,
c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_9084]),
[final] ).
cnf(i_0_15389,plain,
c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_9085]),
[final] ).
cnf(i_0_15390,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_OSuc,X1))),
inference(split_conjunct,[status(thm)],[i_0_9086]),
[final] ).
cnf(i_0_15391,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
inference(split_conjunct,[status(thm)],[i_0_9087]),
[final] ).
cnf(i_0_15392,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))),
inference(split_conjunct,[status(thm)],[i_0_9088]),
[final] ).
cnf(i_0_15393,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),X3),c_List_Oremove1(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8579]),
[final] ).
cnf(i_0_15394,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ class_Int_Onumber__ring(X3)
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8732]),
[final] ).
cnf(i_0_15395,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ class_Int_Onumber__ring(X3)
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8733]),
[final] ).
cnf(i_0_15396,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9089]),
[final] ).
cnf(i_0_15397,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9090]),
[final] ).
cnf(i_0_15398,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9091]),
[final] ).
cnf(i_0_15399,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9092]),
[final] ).
cnf(i_0_15400,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9093]),
[final] ).
cnf(i_0_15401,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8650]),
[final] ).
cnf(i_0_15402,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)),
inference(split_conjunct,[status(thm)],[i_0_9094]),
[final] ).
cnf(i_0_15403,plain,
( hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3) = X4
| hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5) != X3
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5) ),
inference(split_conjunct,[status(thm)],[i_0_8107]),
[final] ).
cnf(i_0_15404,plain,
( hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),X3) = X4
| hAPP(hAPP(c_List_Ozip(X1,X2),X5),X4) != X3
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8107]),
[final] ).
cnf(i_0_15405,plain,
( hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X3)),X3) = X3
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9095]),
[final] ).
cnf(i_0_15406,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9096]),
[final] ).
cnf(i_0_15407,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_8500]),
[final] ).
cnf(i_0_15408,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_9097]),
[final] ).
cnf(i_0_15409,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_9034]),
[final] ).
cnf(i_0_15410,plain,
c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
inference(split_conjunct,[status(thm)],[fact_number__of__code__numeral__def]),
[final] ).
cnf(i_0_15411,plain,
c_Natural_Oevaln(c_Com_Ocom_OAss(X1,X2),X3,X4,hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_9098]),
[final] ).
cnf(i_0_15412,plain,
c_Natural_Oevaln(c_Com_Ocom_OAss(X1,X2),X3,X4,hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_9099]),
[final] ).
cnf(i_0_15413,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9100]),
[final] ).
cnf(i_0_15414,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))),
inference(split_conjunct,[status(thm)],[i_0_9101]),
[final] ).
cnf(i_0_15415,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_9102]),
[final] ).
cnf(i_0_15416,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_9103]),
[final] ).
cnf(i_0_15417,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3),
inference(split_conjunct,[status(thm)],[i_0_9104]),
[final] ).
cnf(i_0_15418,plain,
( hBOOL(hAPP(X1,esk232_3(X1,X2,X3)))
| hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6702]),
[final] ).
cnf(i_0_15419,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)) = hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9105]),
[final] ).
cnf(i_0_15420,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9066]),
[final] ).
cnf(i_0_15421,plain,
( hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X1),c_List_Orotate1(X2)),X3) = X3
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_9106,c_0_6670]),
[final] ).
cnf(i_0_15422,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9107]),
[final] ).
cnf(i_0_15423,plain,
( X3 = c_List_Olist_ONil(X1)
| hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3) != c_List_Olist_ONil(X1) ),
inference(rw,[status(thm)],[i_0_9108,c_0_6670]),
[final] ).
cnf(i_0_15424,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_9109]),
[final] ).
cnf(i_0_15425,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8746]),
[final] ).
cnf(i_0_15426,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8747]),
[final] ).
cnf(i_0_15427,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9110]),
[final] ).
cnf(i_0_15428,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8748]),
[final] ).
cnf(i_0_15429,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8750]),
[final] ).
cnf(i_0_15430,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),X4)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9111]),
[final] ).
cnf(i_0_15431,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9112]),
[final] ).
cnf(i_0_15432,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9113]),
[final] ).
cnf(i_0_15433,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9114]),
[final] ).
cnf(i_0_15434,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_8528]),
[final] ).
cnf(i_0_15435,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9115]),
[final] ).
cnf(i_0_15436,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),esk438_0),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
| c_Com_OWT__bodies ),
inference(split_conjunct,[status(thm)],[i_0_7436]),
[final] ).
cnf(i_0_15437,plain,
hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Otake(X1),X3),X4)) = hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_List_Odrop(X1),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_9116]),
[final] ).
cnf(i_0_15438,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9117]),
[final] ).
cnf(i_0_15439,plain,
c_Product__Type_Ocurry(X1,X2,X3,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4)) = X4,
inference(split_conjunct,[status(thm)],[i_0_9118]),
[final] ).
cnf(i_0_15440,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9119]),
[final] ).
cnf(i_0_15441,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X3) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_9120]),
[final] ).
cnf(i_0_15442,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8984]),
[final] ).
cnf(i_0_15443,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8985]),
[final] ).
cnf(i_0_15444,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9121]),
[final] ).
cnf(i_0_15445,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9122]),
[final] ).
cnf(i_0_15446,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9123]),
[final] ).
cnf(i_0_15447,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9124]),
[final] ).
cnf(i_0_15448,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X3)))
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9125]),
[final] ).
cnf(i_0_15449,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9126]),
[final] ).
cnf(i_0_15450,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8581]),
[final] ).
cnf(i_0_15451,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9127]),
[final] ).
cnf(i_0_15452,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8581]),
[final] ).
cnf(i_0_15453,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9128]),
[final] ).
cnf(i_0_15454,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X3)))
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9129]),
[final] ).
cnf(i_0_15455,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9130]),
[final] ).
cnf(i_0_15456,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8582]),
[final] ).
cnf(i_0_15457,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9131]),
[final] ).
cnf(i_0_15458,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8582]),
[final] ).
cnf(i_0_15459,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_9132,c_0_6015]),
[final] ).
cnf(i_0_15460,plain,
( c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)) = c_List_Obutlast(X2,X3)
| X1 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_8913]),
[final] ).
cnf(i_0_15461,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_9133]),
[final] ).
cnf(i_0_15462,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8918]),
[final] ).
cnf(i_0_15463,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8919]),
[final] ).
cnf(i_0_15464,plain,
( X3 = c_List_Olist_ONil(X1)
| c_List_Otranspose(X1,X2) != c_List_Olist_ONil(tc_List_Olist(X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9134]),
[final] ).
cnf(i_0_15465,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9135]),
[final] ).
cnf(i_0_15466,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9136]),
[final] ).
cnf(i_0_15467,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9137]),
[final] ).
cnf(i_0_15468,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9138]),
[final] ).
cnf(i_0_15469,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8644]),
[final] ).
cnf(i_0_15470,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9139]),
[final] ).
cnf(i_0_15471,plain,
c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(split_conjunct,[status(thm)],[i_0_9140]),
[final] ).
cnf(i_0_15472,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk501_3(X1,X2,X3)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_15473,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_3(X1,X2,X3)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_15474,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)) = hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(X3,X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_9141]),
[final] ).
cnf(i_0_15475,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)),X3)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9142]),
[final] ).
cnf(i_0_15476,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9143]),
[final] ).
cnf(i_0_15477,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8835]),
[final] ).
cnf(i_0_15478,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9144]),
[final] ).
cnf(i_0_15479,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9145]),
[final] ).
cnf(i_0_15480,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9146]),
[final] ).
cnf(i_0_15481,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9146]),
[final] ).
cnf(i_0_15482,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9147]),
[final] ).
cnf(i_0_15483,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9147]),
[final] ).
cnf(i_0_15484,plain,
( c_List_Olast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)) = X4
| X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_9148]),
[final] ).
cnf(i_0_15485,plain,
( hBOOL(hAPP(X1,esk71_3(X2,X1,X3)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7326]),
[final] ).
cnf(i_0_15486,plain,
( c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,esk338_3(X2,X3,X1),esk339_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7194]),
[final] ).
cnf(i_0_15487,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9149]),
[final] ).
cnf(i_0_15488,plain,
( hAPP(hAPP(c_List_Otake(X2),X1),c_List_Obutlast(X2,X3)) = hAPP(hAPP(c_List_Otake(X2),X1),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9150]),
[final] ).
cnf(i_0_15489,plain,
( c_List_Olast(X2,hAPP(hAPP(c_List_Odrop(X2),X1),X3)) = c_List_Olast(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9151]),
[final] ).
cnf(i_0_15490,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9152,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15491,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(rw,[status(thm)],[i_0_9153,c_0_9154]),
[final] ).
cnf(i_0_15492,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_9155]),
[final] ).
cnf(i_0_15493,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_9156]),
[final] ).
cnf(i_0_15494,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_8906]),
[final] ).
cnf(i_0_15495,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_8257]),
[final] ).
cnf(i_0_15496,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)) = c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9157]),
[final] ).
cnf(i_0_15497,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)) = c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9158]),
[final] ).
cnf(i_0_15498,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk503_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_15499,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk499_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_15500,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8523]),
[final] ).
cnf(i_0_15501,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9159]),
[final] ).
cnf(i_0_15502,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8953]),
[final] ).
cnf(i_0_15503,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8954]),
[final] ).
cnf(i_0_15504,plain,
( hAPP(c_Set_Ovimage(X4,X1,hAPP(c_COMBK(X1,X4),X2)),X3) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9160]),
[final] ).
cnf(i_0_15505,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8949]),
[final] ).
cnf(i_0_15506,plain,
( X1 = X2
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X1),X4) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X2),X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X4))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_9161]),
[final] ).
cnf(i_0_15507,plain,
( X1 = X2
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X4),X1) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X5),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X4),X1))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_9161]),
[final] ).
cnf(i_0_15508,plain,
( X2 = X4
| ~ class_Orderings_Olinorder(X1)
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_9162]),
[final] ).
cnf(i_0_15509,plain,
( X3 = X5
| ~ class_Orderings_Olinorder(X1)
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_9163]),
[final] ).
cnf(i_0_15510,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(X2,X5),hAPP(X3,X4))
| ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9164]),
[final] ).
cnf(i_0_15511,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_9165,c_0_6169]),
[final] ).
cnf(i_0_15512,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),c_Divides_OposDivAlg(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9166]),
[final] ).
cnf(i_0_15513,plain,
( X1 = X2
| hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Olist__update(X3,X4),X1),X5)),X2) = hAPP(hAPP(c_List_Onth(X3),X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_9167]),
[final] ).
cnf(i_0_15514,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9168]),
[final] ).
cnf(i_0_15515,plain,
hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X3),X4)) = hAPP(hAPP(c_Relation_Oinv__image(X2,X1),hAPP(c_Relation_Oconverse(X2,X2),X3)),X4),
inference(split_conjunct,[status(thm)],[i_0_9169]),
[final] ).
cnf(i_0_15516,plain,
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2)
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9170]),
[final] ).
cnf(i_0_15517,plain,
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9171]),
[final] ).
cnf(i_0_15518,plain,
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9172]),
[final] ).
cnf(i_0_15519,plain,
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2)
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9173]),
[final] ).
cnf(i_0_15520,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2),X1))
| c_Random_Olog(X1,X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9174]),
[final] ).
cnf(i_0_15521,plain,
( esk157_3(X4,X3,X1) = X2
| hAPP(X4,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7205]),
[final] ).
cnf(i_0_15522,plain,
( hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X2))
| ~ hBOOL(hAPP(X1,esk333_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8804]),
[final] ).
cnf(i_0_15523,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_15524,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9175]),
[final] ).
cnf(i_0_15525,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9176]),
[final] ).
cnf(i_0_15526,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9177]),
[final] ).
cnf(i_0_15527,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_9178]),
[final] ).
cnf(i_0_15528,plain,
hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9179,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_15529,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),X2) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9180]),
[final] ).
cnf(i_0_15530,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),X2) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9181]),
[final] ).
cnf(i_0_15531,plain,
( hBOOL(hAPP(X1,X2))
| X3 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X4),X2,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7014]),
[final] ).
cnf(i_0_15532,plain,
( hBOOL(hAPP(X1,X2))
| X3 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X4),X2,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7015]),
[final] ).
cnf(i_0_15533,plain,
hAPP(c_Set_OPow(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_9182]),
[final] ).
cnf(i_0_15534,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8863]),
[final] ).
cnf(i_0_15535,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8864]),
[final] ).
cnf(i_0_15536,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))
| hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_9183]),
[final] ).
cnf(i_0_15537,plain,
( c_Hoare__Mirabelle_Otriple__valid(X1,esk338_3(X4,X3,X1),X2)
| c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7194]),
[final] ).
cnf(i_0_15538,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9184]),
[final] ).
cnf(i_0_15539,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9185]),
[final] ).
cnf(i_0_15540,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9186]),
[final] ).
cnf(i_0_15541,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9187]),
[final] ).
cnf(i_0_15542,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9188]),
[final] ).
cnf(i_0_15543,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9189]),
[final] ).
cnf(i_0_15544,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),c_Divides_OnegDivAlg(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9190]),
[final] ).
cnf(i_0_15545,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_8659]),
[final] ).
cnf(i_0_15546,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_9191]),
[final] ).
cnf(i_0_15547,plain,
( hAPP(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Fun_Oid(X2)
| ~ c_Finite__Set_Ofolding(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_9192]),
[final] ).
cnf(i_0_15548,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X1,X2) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9193]),
[final] ).
cnf(i_0_15549,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk68_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8624]),
[final] ).
cnf(i_0_15550,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk67_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8625]),
[final] ).
cnf(i_0_15551,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8511]),
[final] ).
cnf(i_0_15552,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9194]),
[final] ).
cnf(i_0_15553,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9195]),
[final] ).
cnf(i_0_15554,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9196]),
[final] ).
cnf(i_0_15555,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9197]),
[final] ).
cnf(i_0_15556,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8949]),
[final] ).
cnf(i_0_15557,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9198]),
[final] ).
cnf(i_0_15558,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9199]),
[final] ).
cnf(i_0_15559,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9200]),
[final] ).
cnf(i_0_15560,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk78_3(X2,X3,X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7791]),
[final] ).
cnf(i_0_15561,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk66_3(X2,X3,X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6939]),
[final] ).
cnf(i_0_15562,plain,
( hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Otake(X3),X2),X4)),X1) = hAPP(hAPP(c_List_Onth(X3),X4),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9201]),
[final] ).
cnf(i_0_15563,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9202]),
[final] ).
cnf(i_0_15564,plain,
( hAPP(c_List_Orev(X2),X1) = hAPP(hAPP(c_List_Olist_OCons(X2),X4),X3)
| X1 != hAPP(hAPP(c_List_Oappend(X2),hAPP(c_List_Orev(X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9203]),
[final] ).
cnf(i_0_15565,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9204]),
[final] ).
cnf(i_0_15566,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8921]),
[final] ).
cnf(i_0_15567,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8670]),
[final] ).
cnf(i_0_15568,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8670]),
[final] ).
cnf(i_0_15569,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_9205]),
[final] ).
cnf(i_0_15570,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_9206]),
[final] ).
cnf(i_0_15571,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9207]),
[final] ).
cnf(i_0_15572,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9208]),
[final] ).
cnf(i_0_15573,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_9209]),
[final] ).
cnf(i_0_15574,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_9210]),
[final] ).
cnf(i_0_15575,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_9211]),
[final] ).
cnf(i_0_15576,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_9212]),
[final] ).
cnf(i_0_15577,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_9213]),
[final] ).
cnf(i_0_15578,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2),
inference(split_conjunct,[status(thm)],[i_0_9214]),
[final] ).
cnf(i_0_15579,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9215]),
[final] ).
cnf(i_0_15580,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9216]),
[final] ).
cnf(i_0_15581,plain,
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X2)))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9217]),
[final] ).
cnf(i_0_15582,plain,
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X2)))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9218]),
[final] ).
cnf(i_0_15583,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_9109]),
[final] ).
cnf(i_0_15584,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatMost(X4,X1,X3)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8868]),
[final] ).
cnf(i_0_15585,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OlessThan(X4,X1,X3)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8869]),
[final] ).
cnf(i_0_15586,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeast(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8870]),
[final] ).
cnf(i_0_15587,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThan(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8871]),
[final] ).
cnf(i_0_15588,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9219]),
[final] ).
cnf(i_0_15589,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9220]),
[final] ).
cnf(i_0_15590,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9221]),
[final] ).
cnf(i_0_15591,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9222]),
[final] ).
cnf(i_0_15592,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9223]),
[final] ).
cnf(i_0_15593,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9224]),
[final] ).
cnf(i_0_15594,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9225]),
[final] ).
cnf(i_0_15595,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9226]),
[final] ).
cnf(i_0_15596,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9227]),
[final] ).
cnf(i_0_15597,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ),
inference(split_conjunct,[status(thm)],[i_0_9228]),
[final] ).
cnf(i_0_15598,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9229]),
[final] ).
cnf(i_0_15599,plain,
( hAPP(hAPP(c_List_Onth(X1),X2),esk453_3(X2,X3,X1)) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8164]),
[final] ).
cnf(i_0_15600,plain,
( esk159_3(X4,X3,X1) = X2
| hAPP(X4,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7210]),
[final] ).
cnf(i_0_15601,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9230]),
[final] ).
cnf(i_0_15602,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9230]),
[final] ).
cnf(i_0_15603,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9231]),
[final] ).
cnf(i_0_15604,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9231]),
[final] ).
cnf(i_0_15605,plain,
( X1 = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9232]),
[final] ).
cnf(i_0_15606,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9233]),
[final] ).
cnf(i_0_15607,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9234]),
[final] ).
cnf(i_0_15608,plain,
c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
inference(rw,[status(thm)],[i_0_9235,c_0_6053]),
[final] ).
cnf(i_0_15609,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onat,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9113]),
[final] ).
cnf(i_0_15610,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9236,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15611,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9237]),
[final] ).
cnf(i_0_15612,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9238,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15613,plain,
( c_Groups_Oone__class_Oone(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9239,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15614,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9240]),
[final] ).
cnf(i_0_15615,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8798]),
[final] ).
cnf(i_0_15616,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8989]),
[final] ).
cnf(i_0_15617,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9241]),
[final] ).
cnf(i_0_15618,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9242]),
[final] ).
cnf(i_0_15619,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9243]),
[final] ).
cnf(i_0_15620,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9244]),
[final] ).
cnf(i_0_15621,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9245]),
[final] ).
cnf(i_0_15622,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X2)),c_Com_Ocom_Ocom__size(X3))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_9246]),
[final] ).
cnf(i_0_15623,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9247]),
[final] ).
cnf(i_0_15624,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9248]),
[final] ).
cnf(i_0_15625,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9249]),
[final] ).
cnf(i_0_15626,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8716]),
[final] ).
cnf(i_0_15627,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_8994]),
[final] ).
cnf(i_0_15628,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_8995]),
[final] ).
cnf(i_0_15629,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9250]),
[final] ).
cnf(i_0_15630,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9251]),
[final] ).
cnf(i_0_15631,plain,
( hBOOL(hAPP(X4,X3))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)
| ~ hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8624]),
[final] ).
cnf(i_0_15632,plain,
( hBOOL(hAPP(X4,X3))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)
| ~ hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8625]),
[final] ).
cnf(i_0_15633,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8956]),
[final] ).
cnf(i_0_15634,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8957]),
[final] ).
cnf(i_0_15635,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8958]),
[final] ).
cnf(i_0_15636,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8959]),
[final] ).
cnf(i_0_15637,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8960]),
[final] ).
cnf(i_0_15638,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8731]),
[final] ).
cnf(i_0_15639,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8961]),
[final] ).
cnf(i_0_15640,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8962]),
[final] ).
cnf(i_0_15641,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8963]),
[final] ).
cnf(i_0_15642,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8964]),
[final] ).
cnf(i_0_15643,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8966]),
[final] ).
cnf(i_0_15644,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8965]),
[final] ).
cnf(i_0_15645,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8951]),
[final] ).
cnf(i_0_15646,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9039]),
[final] ).
cnf(i_0_15647,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9038]),
[final] ).
cnf(i_0_15648,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9252]),
[final] ).
cnf(i_0_15649,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9253]),
[final] ).
cnf(i_0_15650,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Wellfounded_Omax__extp(X2,X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_6558]),
[final] ).
cnf(i_0_15651,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2))
| hAPP(hAPP(c_List_Odrop(X1),X2),X3) != c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8834]),
[final] ).
cnf(i_0_15652,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X2) = X3
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9254]),
[final] ).
cnf(i_0_15653,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))
| ~ class_Rings_Oring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9255]),
[final] ).
cnf(i_0_15654,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))) ),
inference(rw,[status(thm)],[i_0_9256,c_0_6015]),
[final] ).
cnf(i_0_15655,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_9257]),
[final] ).
cnf(i_0_15656,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9258]),
[final] ).
cnf(i_0_15657,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ c_Wellfounded_Omax__extp(X1,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6558]),
[final] ).
cnf(i_0_15658,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ c_Wellfounded_Omax__extp(X1,X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6558]),
[final] ).
cnf(i_0_15659,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9259]),
[final] ).
cnf(i_0_15660,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3))))
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8807]),
[final] ).
cnf(i_0_15661,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8346]),
[final] ).
cnf(i_0_15662,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8346]),
[final] ).
cnf(i_0_15663,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8650]),
[final] ).
cnf(i_0_15664,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9260]),
[final] ).
cnf(i_0_15665,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9261,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_15666,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_8731]),
[final] ).
cnf(i_0_15667,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9262]),
[final] ).
cnf(i_0_15668,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9263]),
[final] ).
cnf(i_0_15669,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9264,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15670,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9265,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15671,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9266,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15672,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9267,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15673,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9268]),
[final] ).
cnf(i_0_15674,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X2) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9269]),
[final] ).
cnf(i_0_15675,plain,
c_Sum__Type_OPlus(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9270]),
[final] ).
cnf(i_0_15676,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9004]),
[final] ).
cnf(i_0_15677,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9005]),
[final] ).
cnf(i_0_15678,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9271]),
[final] ).
cnf(i_0_15679,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9272]),
[final] ).
cnf(i_0_15680,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9273]),
[final] ).
cnf(i_0_15681,plain,
( c_Random_Ominus__shift(X3,X1,X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X3),X1)),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9274]),
[final] ).
cnf(i_0_15682,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9275]),
[final] ).
cnf(i_0_15683,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9276]),
[final] ).
cnf(i_0_15684,plain,
( epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9277]),
[final] ).
cnf(i_0_15685,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_ODomain(X1,X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9278]),
[final] ).
cnf(i_0_15686,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(c_Relation_ORange(X1,X2),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9279]),
[final] ).
cnf(i_0_15687,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,X3),X4))
| X3 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9280]),
[final] ).
cnf(i_0_15688,plain,
hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))),
inference(split_conjunct,[status(thm)],[i_0_9281]),
[final] ).
cnf(i_0_15689,plain,
hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(c_List_Odrop(X3),X2),X5)),
inference(split_conjunct,[status(thm)],[i_0_9282]),
[final] ).
cnf(i_0_15690,plain,
hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)) = hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(c_List_Otake(X3),X2),X5)),
inference(split_conjunct,[status(thm)],[i_0_9283]),
[final] ).
cnf(i_0_15691,plain,
hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_9284]),
[final] ).
cnf(i_0_15692,plain,
( c_List_Oupto(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9285]),
[final] ).
cnf(i_0_15693,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8691]),
[final] ).
cnf(i_0_15694,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5709]),
[final] ).
cnf(i_0_15695,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk317_2(X2,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9286]),
[final] ).
cnf(i_0_15696,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)) = c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9287]),
[final] ).
cnf(i_0_15697,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)) = c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9288]),
[final] ).
cnf(i_0_15698,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9289]),
[final] ).
cnf(i_0_15699,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_8910]),
[final] ).
cnf(i_0_15700,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9290]),
[final] ).
cnf(i_0_15701,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9291]),
[final] ).
cnf(i_0_15702,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))
| ~ class_Divides_Oring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9292]),
[final] ).
cnf(i_0_15703,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9293,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15704,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9294,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15705,plain,
( X1 = hAPP(hAPP(c_Set_Oinsert(X2),esk190_3(X3,X1,X2)),esk191_3(X3,X1,X2))
| hAPP(c_Finite__Set_Ocard(X2),X1) != hAPP(c_Nat_OSuc,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7857]),
[final] ).
cnf(i_0_15706,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9295]),
[final] ).
cnf(i_0_15707,plain,
( hAPP(c_List_Ofilter(X3,X1),X2) = X2
| ~ hBOOL(hAPP(X1,esk479_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8705]),
[final] ).
cnf(i_0_15708,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9296]),
[final] ).
cnf(i_0_15709,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9297]),
[final] ).
cnf(i_0_15710,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9077]),
[final] ).
cnf(i_0_15711,plain,
c_Random__Sequence_Oempty(X1,X2,X3) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X1)),
inference(split_conjunct,[status(thm)],[i_0_9298]),
[final] ).
cnf(i_0_15712,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),X3),X4)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9299]),
[final] ).
cnf(i_0_15713,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9300]),
[final] ).
cnf(i_0_15714,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9301]),
[final] ).
cnf(i_0_15715,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9302]),
[final] ).
cnf(i_0_15716,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9303]),
[final] ).
cnf(i_0_15717,plain,
c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
inference(rw,[status(thm)],[i_0_9304,c_0_7027]),
[final] ).
cnf(i_0_15718,plain,
hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(c_Nat_OSuc,X4)) = hAPP(hAPP(X3,X4),hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_9305]),
[final] ).
cnf(i_0_15719,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9022]),
[final] ).
cnf(i_0_15720,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9306]),
[final] ).
cnf(i_0_15721,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9307]),
[final] ).
cnf(i_0_15722,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9308]),
[final] ).
cnf(i_0_15723,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9309]),
[final] ).
cnf(i_0_15724,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9310]),
[final] ).
cnf(i_0_15725,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9311]),
[final] ).
cnf(i_0_15726,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9312]),
[final] ).
cnf(i_0_15727,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9313]),
[final] ).
cnf(i_0_15728,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9314]),
[final] ).
cnf(i_0_15729,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9315]),
[final] ).
cnf(i_0_15730,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk31_2(X1,X2)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9316]),
[final] ).
cnf(i_0_15731,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk68_3(X2,X1,X3))
| hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8624]),
[final] ).
cnf(i_0_15732,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk67_3(X2,X1,X3))
| hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8625]),
[final] ).
cnf(i_0_15733,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X4)))) = hAPP(X3,X4),
inference(rw,[status(thm)],[i_0_9317,c_0_8155]),
[final] ).
cnf(i_0_15734,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9178]),
[final] ).
cnf(i_0_15735,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(c_List_Orotate1(X2),X1) = hAPP(hAPP(c_List_Oappend(X2),hAPP(c_List_Otl(X2),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(c_List_Ohd(X2),X1)),c_List_Olist_ONil(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9318]),
[final] ).
cnf(i_0_15736,plain,
( X1 = X2
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_9319]),
[final] ).
cnf(i_0_15737,plain,
( X1 = X2
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_9320]),
[final] ).
cnf(i_0_15738,plain,
( X1 = X2
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_9321]),
[final] ).
cnf(i_0_15739,plain,
c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))),
inference(rw,[status(thm)],[i_0_9322,c_0_6135]),
[final] ).
cnf(i_0_15740,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X3,X4))) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X1),X2),c_List_Oupto(X3,X4)))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9323]),
[final] ).
cnf(i_0_15741,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X1),X2),c_List_Oupto(X3,X4))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X3,X4)))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9324]),
[final] ).
cnf(i_0_15742,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9325]),
[final] ).
cnf(i_0_15743,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9326]),
[final] ).
cnf(i_0_15744,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9327]),
[final] ).
cnf(i_0_15745,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9328]),
[final] ).
cnf(i_0_15746,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9329]),
[final] ).
cnf(i_0_15747,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9330]),
[final] ).
cnf(i_0_15748,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9331]),
[final] ).
cnf(i_0_15749,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9332]),
[final] ).
cnf(i_0_15750,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9333]),
[final] ).
cnf(i_0_15751,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9334]),
[final] ).
cnf(i_0_15752,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9335]),
[final] ).
cnf(i_0_15753,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Groups_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9336]),
[final] ).
cnf(i_0_15754,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9337]),
[final] ).
cnf(i_0_15755,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9338]),
[final] ).
cnf(i_0_15756,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Groups_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9339]),
[final] ).
cnf(i_0_15757,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9340]),
[final] ).
cnf(i_0_15758,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9341]),
[final] ).
cnf(i_0_15759,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9342]),
[final] ).
cnf(i_0_15760,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X2,X1) = hAPP(hAPP(c_List_Onth(X2),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_9343]),
[final] ).
cnf(i_0_15761,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Oring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9344]),
[final] ).
cnf(i_0_15762,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Nat_Osemiring__1__class_ONats(X1)))
| ~ class_Int_Onumber__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9345]),
[final] ).
cnf(i_0_15763,plain,
( hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9346]),
[final] ).
cnf(i_0_15764,plain,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X1)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_9347]),
[final] ).
cnf(i_0_15765,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_9348]),
[final] ).
cnf(i_0_15766,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),
inference(split_conjunct,[status(thm)],[i_0_9349]),
[final] ).
cnf(i_0_15767,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9149]),
[final] ).
cnf(i_0_15768,plain,
( c_Divides_OposDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5308]),
[final] ).
cnf(i_0_15769,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9350]),
[final] ).
cnf(i_0_15770,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(split_conjunct,[status(thm)],[i_0_9351]),
[final] ).
cnf(i_0_15771,plain,
( c_Sum__Type_OPlus(X2,X4,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2,X4),tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X3 != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8983]),
[final] ).
cnf(i_0_15772,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9352]),
[final] ).
cnf(i_0_15773,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9353]),
[final] ).
cnf(i_0_15774,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9354]),
[final] ).
cnf(i_0_15775,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9355]),
[final] ).
cnf(i_0_15776,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X2
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9356]),
[final] ).
cnf(i_0_15777,plain,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9357]),
[final] ).
cnf(i_0_15778,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_COMBK(X1,X2),X4)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),hAPP(c_Finite__Set_Ocard(X2),X3))
| ~ class_Groups_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9358]),
[final] ).
cnf(i_0_15779,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2))
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9359]),
[final] ).
cnf(i_0_15780,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9360]),
[final] ).
cnf(i_0_15781,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9361]),
[final] ).
cnf(i_0_15782,plain,
hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),X4) = hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_9362]),
[final] ).
cnf(i_0_15783,plain,
hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_9363]),
[final] ).
cnf(i_0_15784,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9364]),
[final] ).
cnf(i_0_15785,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9365]),
[final] ).
cnf(i_0_15786,plain,
( hBOOL(hAPP(X2,X3))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8051]),
[final] ).
cnf(i_0_15787,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_OSuc,X3)),X1) = hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(c_List_Ohd(X2),X1)),hAPP(hAPP(c_List_Otake(X2),X3),hAPP(c_List_Otl(X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9366]),
[final] ).
cnf(i_0_15788,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Set_Ovimage(X4,X1,hAPP(c_COMBK(X1,X4),X2)),X3) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9160]),
[final] ).
cnf(i_0_15789,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9367]),
[final] ).
cnf(i_0_15790,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)),X1) = hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_9368]),
[final] ).
cnf(i_0_15791,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X2,X3,hAPP(c_COMBK(X3,X2),X4)),X1) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_9369]),
[final] ).
cnf(i_0_15792,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk481_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
| c_List_Otranspose(X1,X2) = c_List_Olist_ONil(tc_List_Olist(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9134]),
[final] ).
cnf(i_0_15793,plain,
( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6),X1) = X6
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9319]),
[final] ).
cnf(i_0_15794,plain,
( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6),X1) = X6
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9321]),
[final] ).
cnf(i_0_15795,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(rw,[status(thm)],[i_0_9370,c_0_6015]),
[final] ).
cnf(i_0_15796,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
inference(rw,[status(thm)],[i_0_9371,c_0_6015]),
[final] ).
cnf(i_0_15797,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(rw,[status(thm)],[i_0_9372,c_0_6015]),
[final] ).
cnf(i_0_15798,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)) ),
inference(rw,[status(thm)],[i_0_9373,c_0_6015]),
[final] ).
cnf(i_0_15799,plain,
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9374]),
[final] ).
cnf(i_0_15800,plain,
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9375]),
[final] ).
cnf(i_0_15801,plain,
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9374]),
[final] ).
cnf(i_0_15802,plain,
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9375]),
[final] ).
cnf(i_0_15803,plain,
( hBOOL(hAPP(c_Com_OWT,X3))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9376]),
[final] ).
cnf(i_0_15804,plain,
( hBOOL(hAPP(c_Com_OWT,X3))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9377]),
[final] ).
cnf(i_0_15805,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X3)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(c_List_Oset(X2),X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9378]),
[final] ).
cnf(i_0_15806,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9379]),
[final] ).
cnf(i_0_15807,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9380]),
[final] ).
cnf(i_0_15808,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9381]),
[final] ).
cnf(i_0_15809,plain,
( hAPP(c_List_Ofilter(X1,X2),X3) != c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8693]),
[final] ).
cnf(i_0_15810,plain,
hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)) = hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_9382]),
[final] ).
cnf(i_0_15811,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9383]),
[final] ).
cnf(i_0_15812,plain,
hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[i_0_9384,c_0_6053]),
[final] ).
cnf(i_0_15813,plain,
hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[i_0_9385,c_0_6053]),
[final] ).
cnf(i_0_15814,plain,
hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X4) = X5,
inference(split_conjunct,[status(thm)],[i_0_9386]),
[final] ).
cnf(i_0_15815,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9387]),
[final] ).
cnf(i_0_15816,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9388]),
[final] ).
cnf(i_0_15817,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9389]),
[final] ).
cnf(i_0_15818,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9390]),
[final] ).
cnf(i_0_15819,plain,
( X2 = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(X1),X2) != hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_9391]),
[final] ).
cnf(i_0_15820,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8798]),
[final] ).
cnf(i_0_15821,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Odrop(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Odrop(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9392]),
[final] ).
cnf(i_0_15822,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1))))),
inference(split_conjunct,[status(thm)],[i_0_9393]),
[final] ).
cnf(i_0_15823,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9394]),
[final] ).
cnf(i_0_15824,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9215]),
[final] ).
cnf(i_0_15825,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9216]),
[final] ).
cnf(i_0_15826,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9395]),
[final] ).
cnf(i_0_15827,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9396]),
[final] ).
cnf(i_0_15828,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9397]),
[final] ).
cnf(i_0_15829,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9398]),
[final] ).
cnf(i_0_15830,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9399]),
[final] ).
cnf(i_0_15831,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9400]),
[final] ).
cnf(i_0_15832,plain,
( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9401]),
[final] ).
cnf(i_0_15833,plain,
( hAPP(hAPP(X2,X5),hAPP(X3,X4)) = hAPP(X3,X4)
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9402]),
[final] ).
cnf(i_0_15834,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9403]),
[final] ).
cnf(i_0_15835,plain,
( c_Divides_OnegDivAlg(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_5307]),
[final] ).
cnf(i_0_15836,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9404]),
[final] ).
cnf(i_0_15837,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9405]),
[final] ).
cnf(i_0_15838,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9406]),
[final] ).
cnf(i_0_15839,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_9407]),
[final] ).
cnf(i_0_15840,plain,
hAPP(c_Relation_OField(X1),X2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X1),X2)),hAPP(c_Relation_ORange(X1,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9408]),
[final] ).
cnf(i_0_15841,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2))) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_9409,c_0_6062]),
[final] ).
cnf(i_0_15842,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))),
inference(split_conjunct,[status(thm)],[i_0_9410]),
[final] ).
cnf(i_0_15843,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9291]),
[final] ).
cnf(i_0_15844,plain,
( c_List_Osublist(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)),X1) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9411]),
[final] ).
cnf(i_0_15845,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9412]),
[final] ).
cnf(i_0_15846,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),X1) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9413]),
[final] ).
cnf(i_0_15847,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_9257]),
[final] ).
cnf(i_0_15848,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| c_Divides_Odivmod__int(X2,X1) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9193]),
[final] ).
cnf(i_0_15849,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_9414]),
[final] ).
cnf(i_0_15850,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8884]),
[final] ).
cnf(i_0_15851,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8883]),
[final] ).
cnf(i_0_15852,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_9415]),
[final] ).
cnf(i_0_15853,plain,
c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
inference(split_conjunct,[status(thm)],[fact_Integ__def]),
[final] ).
cnf(i_0_15854,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9416]),
[final] ).
cnf(i_0_15855,plain,
c_Relation_Osingle__valued(X1,X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
inference(rw,[status(thm)],[i_0_9417,c_0_6053]),
[final] ).
cnf(i_0_15856,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9418]),
[final] ).
cnf(i_0_15857,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9419]),
[final] ).
cnf(i_0_15858,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9420]),
[final] ).
cnf(i_0_15859,plain,
( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X4,X3),X2) = c_Divides_Odiv__class_Omod(X1,X4,X2)
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9421]),
[final] ).
cnf(i_0_15860,plain,
( hAPP(X2,X4) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8620]),
[final] ).
cnf(i_0_15861,plain,
( hAPP(X2,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8621]),
[final] ).
cnf(i_0_15862,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_List_Olast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)) = c_List_Olast(X2,X3)
| X3 = c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9148]),
[final] ).
cnf(i_0_15863,plain,
( X3 = X1
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9422]),
[final] ).
cnf(i_0_15864,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9423]),
[final] ).
cnf(i_0_15865,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9424]),
[final] ).
cnf(i_0_15866,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9425]),
[final] ).
cnf(i_0_15867,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))
| ~ class_Divides_Oring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9426]),
[final] ).
cnf(i_0_15868,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_8880]),
[final] ).
cnf(i_0_15869,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9427]),
[final] ).
cnf(i_0_15870,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9428]),
[final] ).
cnf(i_0_15871,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9429]),
[final] ).
cnf(i_0_15872,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9430]),
[final] ).
cnf(i_0_15873,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9431]),
[final] ).
cnf(i_0_15874,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9432]),
[final] ).
cnf(i_0_15875,plain,
hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4)) = hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4),
inference(split_conjunct,[status(thm)],[i_0_9433]),
[final] ).
cnf(i_0_15876,plain,
hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Otake(X1),X3),X4)) = hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2),X3)),X4),
inference(split_conjunct,[status(thm)],[i_0_9434]),
[final] ).
cnf(i_0_15877,plain,
( epred2_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9435]),
[final] ).
cnf(i_0_15878,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9436]),
[final] ).
cnf(i_0_15879,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk47_1(X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9437]),
[final] ).
cnf(i_0_15880,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9438]),
[final] ).
cnf(i_0_15881,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9439]),
[final] ).
cnf(i_0_15882,plain,
( hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8850]),
[final] ).
cnf(i_0_15883,plain,
( hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X1)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8850]),
[final] ).
cnf(i_0_15884,plain,
( c_Divides_Odivmod__int(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9193]),
[final] ).
cnf(i_0_15885,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X2)))
| ~ c_Nat__Transfer_Ois__nat(X1)
| ~ c_Nat__Transfer_Ois__nat(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9440]),
[final] ).
cnf(i_0_15886,plain,
( c_List_Otranspose(X1,c_List_Olist_ONil(tc_List_Olist(X1))) = c_List_Olist_ONil(tc_List_Olist(X1))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X1)),c_List_Otranspose__rel(X1)),c_List_Olist_ONil(tc_List_Olist(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_9441]),
[final] ).
cnf(i_0_15887,plain,
( hBOOL(hAPP(X2,X4))
| hAPP(c_List_Ofilter(X1,X2),X3) != X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8705]),
[final] ).
cnf(i_0_15888,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_9442]),
[final] ).
cnf(i_0_15889,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9243]),
[final] ).
cnf(i_0_15890,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9244]),
[final] ).
cnf(i_0_15891,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9245]),
[final] ).
cnf(i_0_15892,plain,
( X1 = X2
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_9443]),
[final] ).
cnf(i_0_15893,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)) = X4 ),
inference(split_conjunct,[status(thm)],[i_0_9296]),
[final] ).
cnf(i_0_15894,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)) = X4 ),
inference(split_conjunct,[status(thm)],[i_0_9297]),
[final] ).
cnf(i_0_15895,plain,
hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_9444]),
[final] ).
cnf(i_0_15896,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9195]),
[final] ).
cnf(i_0_15897,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9194]),
[final] ).
cnf(i_0_15898,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9196]),
[final] ).
cnf(i_0_15899,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9198]),
[final] ).
cnf(i_0_15900,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9197]),
[final] ).
cnf(i_0_15901,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9199]),
[final] ).
cnf(i_0_15902,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9445]),
[final] ).
cnf(i_0_15903,plain,
( X3 = X4
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9446]),
[final] ).
cnf(i_0_15904,plain,
( X3 = X4
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9447]),
[final] ).
cnf(i_0_15905,plain,
c_List_Olistset(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = c_List_Oset__Cons(X1,X2,c_List_Olistset(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_9448]),
[final] ).
cnf(i_0_15906,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9299]),
[final] ).
cnf(i_0_15907,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,X2) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),c_Orderings_Obot__class_Obot(X1)),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9449]),
[final] ).
cnf(i_0_15908,plain,
( c_Complete__Lattice_OInf__class_OInf(X1,X2) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),c_Orderings_Otop__class_Otop(X1)),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9450]),
[final] ).
cnf(i_0_15909,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_9451]),
[final] ).
cnf(i_0_15910,plain,
( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9452]),
[final] ).
cnf(i_0_15911,plain,
( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9453]),
[final] ).
cnf(i_0_15912,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(c_Finite__Set_Ocard(X1),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9454]),
[final] ).
cnf(i_0_15913,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1))),
inference(split_conjunct,[status(thm)],[i_0_9455]),
[final] ).
cnf(i_0_15914,plain,
c_Code__Numeral_Odiv__mod__code__numeral(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_9456]),
[final] ).
cnf(i_0_15915,plain,
c_Divides_Odivmod__int(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_9457]),
[final] ).
cnf(i_0_15916,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_9458]),
[final] ).
cnf(i_0_15917,plain,
( X1 = X2
| hAPP(c_Int_Onat,X1) != hAPP(c_Int_Onat,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9459]),
[final] ).
cnf(i_0_15918,plain,
( X1 = X2
| hAPP(c_Int_Onat,X1) != hAPP(c_Int_Onat,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9460]),
[final] ).
cnf(i_0_15919,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk36_2(X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9461]),
[final] ).
cnf(i_0_15920,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9354]),
[final] ).
cnf(i_0_15921,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9355]),
[final] ).
cnf(i_0_15922,plain,
( c_List_Olast(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[i_0_9462,c_0_6135]),
[final] ).
cnf(i_0_15923,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_9463]),
[final] ).
cnf(i_0_15924,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9464]),
[final] ).
cnf(i_0_15925,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9465]),
[final] ).
cnf(i_0_15926,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)
| X1 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9466]),
[final] ).
cnf(i_0_15927,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X4),c_Map_Oran(X5,X3,X1)))
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9467]),
[final] ).
cnf(i_0_15928,plain,
( hBOOL(hAPP(hAPP(c_member(X5),X2),c_Map_Odom(X5,X3,X1)))
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9468]),
[final] ).
cnf(i_0_15929,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X4),X3) = c_Groups_Ozero__class_Ozero(X5)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(X4,X2) != c_Groups_Ozero__class_Ozero(X5)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Rings_Ocomm__semiring__1(X5)
| ~ class_Rings_Ono__zero__divisors(X5) ),
inference(split_conjunct,[status(thm)],[i_0_7247]),
[final] ).
cnf(i_0_15930,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9469]),
[final] ).
cnf(i_0_15931,plain,
( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9054]),
[final] ).
cnf(i_0_15932,plain,
( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9470]),
[final] ).
cnf(i_0_15933,plain,
( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8909]),
[final] ).
cnf(i_0_15934,plain,
( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9471]),
[final] ).
cnf(i_0_15935,plain,
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8067]),
[final] ).
cnf(i_0_15936,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| X2 != c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9472]),
[final] ).
cnf(i_0_15937,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9473]),
[final] ).
cnf(i_0_15938,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9474]),
[final] ).
cnf(i_0_15939,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9233]),
[final] ).
cnf(i_0_15940,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X1,
inference(rw,[status(thm)],[i_0_9475,c_0_8155]),
[final] ).
cnf(i_0_15941,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9476]),
[final] ).
cnf(i_0_15942,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9015]),
[final] ).
cnf(i_0_15943,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8970]),
[final] ).
cnf(i_0_15944,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9477]),
[final] ).
cnf(i_0_15945,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9478]),
[final] ).
cnf(i_0_15946,plain,
hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))),
inference(rw,[status(thm)],[i_0_9479,c_0_6135]),
[final] ).
cnf(i_0_15947,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),
inference(split_conjunct,[status(thm)],[i_0_9480]),
[final] ).
cnf(i_0_15948,plain,
( X1 = X2
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)
| ~ c_Nat__Transfer_Onat__set(X2)
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9481]),
[final] ).
cnf(i_0_15949,plain,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X1),X4),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X2),X6),X7) ),
inference(split_conjunct,[status(thm)],[i_0_9482]),
[final] ).
cnf(i_0_15950,plain,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X1),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X2),X7) ),
inference(split_conjunct,[status(thm)],[i_0_9482]),
[final] ).
cnf(i_0_15951,plain,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X5),X1) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X7),X2) ),
inference(split_conjunct,[status(thm)],[i_0_9482]),
[final] ).
cnf(i_0_15952,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = c_List_Olist_ONil(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_7890]),
[final] ).
cnf(i_0_15953,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8887]),
[final] ).
cnf(i_0_15954,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8888]),
[final] ).
cnf(i_0_15955,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
| hAPP(X5,X4) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9483]),
[final] ).
cnf(i_0_15956,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_9484]),
[final] ).
cnf(i_0_15957,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk451_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))
| hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8201]),
[final] ).
cnf(i_0_15958,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk450_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))
| hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8201]),
[final] ).
cnf(i_0_15959,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_9485]),
[final] ).
cnf(i_0_15960,plain,
hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))),
inference(split_conjunct,[status(thm)],[i_0_9486]),
[final] ).
cnf(i_0_15961,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
inference(rw,[status(thm)],[i_0_9487,c_0_6053]),
[final] ).
cnf(i_0_15962,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9488]),
[final] ).
cnf(i_0_15963,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9489]),
[final] ).
cnf(i_0_15964,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8459]),
[final] ).
cnf(i_0_15965,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9490]),
[final] ).
cnf(i_0_15966,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
| hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8928]),
[final] ).
cnf(i_0_15967,plain,
( hBOOL(hAPP(hAPP(X2,X3),X5))
| ~ c_Equiv__Relations_Oequivp(X1,X2)
| ~ hBOOL(hAPP(hAPP(X2,X3),X4))
| ~ hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_9491]),
[final] ).
cnf(i_0_15968,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(X2,X5),hAPP(X3,X4))
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9492]),
[final] ).
cnf(i_0_15969,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X4),X3)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9493]),
[final] ).
cnf(i_0_15970,plain,
( c_Divides_Odivmod__int(X2,X1) = c_Divides_OposDivAlg(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9193]),
[final] ).
cnf(i_0_15971,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_9494]),
[final] ).
cnf(i_0_15972,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_9495]),
[final] ).
cnf(i_0_15973,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_9496]),
[final] ).
cnf(i_0_15974,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_9497]),
[final] ).
cnf(i_0_15975,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(c_Nat_OSuc,X1))) = c_Groups_Ozero__class_Ozero(X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8079]),
[final] ).
cnf(i_0_15976,plain,
( hAPP(X1,esk157_3(X1,X2,X3)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7205]),
[final] ).
cnf(i_0_15977,plain,
c_Map_Omap__add(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3) = X3,
inference(split_conjunct,[status(thm)],[i_0_9498]),
[final] ).
cnf(i_0_15978,plain,
c_Map_Omap__add(X1,X2,X3,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))) = X3,
inference(split_conjunct,[status(thm)],[i_0_9499]),
[final] ).
cnf(i_0_15979,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk53_2(X2,X3)))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9061]),
[final] ).
cnf(i_0_15980,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9500]),
[final] ).
cnf(i_0_15981,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9501]),
[final] ).
cnf(i_0_15982,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_9502]),
[final] ).
cnf(i_0_15983,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3),
inference(split_conjunct,[status(thm)],[i_0_9503]),
[final] ).
cnf(i_0_15984,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_9504]),
[final] ).
cnf(i_0_15985,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_9505]),
[final] ).
cnf(i_0_15986,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_9506]),
[final] ).
cnf(i_0_15987,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_9507]),
[final] ).
cnf(i_0_15988,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_9508]),
[final] ).
cnf(i_0_15989,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_9509]),
[final] ).
cnf(i_0_15990,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_9510]),
[final] ).
cnf(i_0_15991,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_9511]),
[final] ).
cnf(i_0_15992,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9512]),
[final] ).
cnf(i_0_15993,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9513]),
[final] ).
cnf(i_0_15994,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9514]),
[final] ).
cnf(i_0_15995,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9515]),
[final] ).
cnf(i_0_15996,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9275]),
[final] ).
cnf(i_0_15997,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9276]),
[final] ).
cnf(i_0_15998,plain,
hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) = hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_List_Oset(X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_9516]),
[final] ).
cnf(i_0_15999,plain,
hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),X2),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_9517]),
[final] ).
cnf(i_0_16000,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_9518]),
[final] ).
cnf(i_0_16001,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2),
inference(split_conjunct,[status(thm)],[i_0_9519]),
[final] ).
cnf(i_0_16002,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_9520]),
[final] ).
cnf(i_0_16003,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9397]),
[final] ).
cnf(i_0_16004,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9399]),
[final] ).
cnf(i_0_16005,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9398]),
[final] ).
cnf(i_0_16006,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9400]),
[final] ).
cnf(i_0_16007,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9396]),
[final] ).
cnf(i_0_16008,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9395]),
[final] ).
cnf(i_0_16009,plain,
( X2 = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))
| hAPP(c_List_Orev(X1),X2) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9203]),
[final] ).
cnf(i_0_16010,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9521]),
[final] ).
cnf(i_0_16011,plain,
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X2,X1,X3)))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9217]),
[final] ).
cnf(i_0_16012,plain,
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X2,X1,X3)))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9522]),
[final] ).
cnf(i_0_16013,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9523]),
[final] ).
cnf(i_0_16014,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9489]),
[final] ).
cnf(i_0_16015,plain,
( c_Int_OMin = X1
| c_Int_OMin != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9524,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16016,plain,
( X1 = c_Int_OMin
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) != c_Int_OMin ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9525,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16017,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_8820]),
[final] ).
cnf(i_0_16018,plain,
hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(hAPP(c_List_Otake(X1),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_9526]),
[final] ).
cnf(i_0_16019,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X7)
| hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X5,X2),X6),X7) ),
inference(split_conjunct,[status(thm)],[i_0_9527]),
[final] ).
cnf(i_0_16020,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) != c_Int_OPls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9528,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16021,plain,
c_Int_OPls != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9529,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16022,plain,
hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_9530]),
[final] ).
cnf(i_0_16023,plain,
( X3 = X5
| hAPP(c_Product__Type_Ofst(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_9531]),
[final] ).
cnf(i_0_16024,plain,
( X4 = X5
| hAPP(c_Product__Type_Osnd(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_9532]),
[final] ).
cnf(i_0_16025,plain,
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)) = X1
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9533]),
[final] ).
cnf(i_0_16026,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(X1,esk211_3(X1,X2,X3)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8620]),
[final] ).
cnf(i_0_16027,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(X1,esk156_3(X1,X2,X3)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8621]),
[final] ).
cnf(i_0_16028,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_OField(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9534]),
[final] ).
cnf(i_0_16029,plain,
( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9535]),
[final] ).
cnf(i_0_16030,plain,
( hAPP(c_Nat_OSuc,X1) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9536]),
[final] ).
cnf(i_0_16031,plain,
( hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X4)),X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_7097]),
[final] ).
cnf(i_0_16032,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk153_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9537]),
[final] ).
cnf(i_0_16033,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk155_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9538]),
[final] ).
cnf(i_0_16034,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9539]),
[final] ).
cnf(i_0_16035,plain,
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| X1 != X2
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_8986]),
[final] ).
cnf(i_0_16036,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3)))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9540]),
[final] ).
cnf(i_0_16037,plain,
( hAPP(c_Set_Oimage(X2,X3,hAPP(c_COMBK(X3,X2),X4)),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9369]),
[final] ).
cnf(i_0_16038,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9454]),
[final] ).
cnf(i_0_16039,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9541]),
[final] ).
cnf(i_0_16040,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9542]),
[final] ).
cnf(i_0_16041,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),X2))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_9543]),
[final] ).
cnf(i_0_16042,plain,
c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = X2,
inference(split_conjunct,[status(thm)],[i_0_9544]),
[final] ).
cnf(i_0_16043,plain,
c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = X3,
inference(split_conjunct,[status(thm)],[i_0_9545]),
[final] ).
cnf(i_0_16044,plain,
hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_9546]),
[final] ).
cnf(i_0_16045,plain,
hAPP(c_Product__Type_Ofst(X1,X2),X3) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X1),c_COMBK(X1,X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_9547]),
[final] ).
cnf(i_0_16046,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_9548]),
[final] ).
cnf(i_0_16047,plain,
( c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9549]),
[final] ).
cnf(i_0_16048,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9550]),
[final] ).
cnf(i_0_16049,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9551]),
[final] ).
cnf(i_0_16050,plain,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9552]),
[final] ).
cnf(i_0_16051,plain,
( X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9553]),
[final] ).
cnf(i_0_16052,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk486_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))
| c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7545]),
[final] ).
cnf(i_0_16053,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7785]),
[final] ).
cnf(i_0_16054,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9554]),
[final] ).
cnf(i_0_16055,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9555]),
[final] ).
cnf(i_0_16056,plain,
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9556]),
[final] ).
cnf(i_0_16057,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9557]),
[final] ).
cnf(i_0_16058,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9558]),
[final] ).
cnf(i_0_16059,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9424]),
[final] ).
cnf(i_0_16060,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9559]),
[final] ).
cnf(i_0_16061,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9560]),
[final] ).
cnf(i_0_16062,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9561]),
[final] ).
cnf(i_0_16063,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9562]),
[final] ).
cnf(i_0_16064,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9563]),
[final] ).
cnf(i_0_16065,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9564]),
[final] ).
cnf(i_0_16066,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9565]),
[final] ).
cnf(i_0_16067,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9566]),
[final] ).
cnf(i_0_16068,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9567]),
[final] ).
cnf(i_0_16069,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9568]),
[final] ).
cnf(i_0_16070,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9569]),
[final] ).
cnf(i_0_16071,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9570]),
[final] ).
cnf(i_0_16072,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9571]),
[final] ).
cnf(i_0_16073,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X2,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9572]),
[final] ).
cnf(i_0_16074,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X2,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8847]),
[final] ).
cnf(i_0_16075,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X2,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8848]),
[final] ).
cnf(i_0_16076,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9573]),
[final] ).
cnf(i_0_16077,plain,
( X1 = c_List_Olist_ONil(X2)
| hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_List_Ohd(X2),X1)),hAPP(c_List_Oset(X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9574]),
[final] ).
cnf(i_0_16078,plain,
c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X1) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_9575]),
[final] ).
cnf(i_0_16079,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9576]),
[final] ).
cnf(i_0_16080,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9577]),
[final] ).
cnf(i_0_16081,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9465]),
[final] ).
cnf(i_0_16082,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hBOOL(hAPP(hAPP(c_member(X4),X2),c_Map_Odom(X4,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9006]),
[final] ).
cnf(i_0_16083,plain,
( X4 = X3
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9578]),
[final] ).
cnf(i_0_16084,plain,
( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X3)),X1),X2),hAPP(c_Option_Ooption_OSome(X3),X4)) = X1
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9579]),
[final] ).
cnf(i_0_16085,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X3),X4)),X5) = hAPP(hAPP(X2,X3),hAPP(hAPP(X2,X4),X5))
| ~ c_Groups_Osemigroup(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9580]),
[final] ).
cnf(i_0_16086,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_9581]),
[final] ).
cnf(i_0_16087,plain,
( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk44_1(X2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9582]),
[final] ).
cnf(i_0_16088,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9428]),
[final] ).
cnf(i_0_16089,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9429]),
[final] ).
cnf(i_0_16090,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9583]),
[final] ).
cnf(i_0_16091,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)) = c_Big__Operators_Olattice__class_OInf__fin(X1,X2)
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9584]),
[final] ).
cnf(i_0_16092,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)) = c_Big__Operators_Olattice__class_OSup__fin(X1,X2)
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9585]),
[final] ).
cnf(i_0_16093,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2)) = c_Big__Operators_Olinorder__class_OMax(X1,X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9586]),
[final] ).
cnf(i_0_16094,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2)) = c_Big__Operators_Olinorder__class_OMin(X1,X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9587]),
[final] ).
cnf(i_0_16095,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9588]),
[final] ).
cnf(i_0_16096,plain,
( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[i_0_9589,c_0_6135]),
[final] ).
cnf(i_0_16097,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9590]),
[final] ).
cnf(i_0_16098,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9591]),
[final] ).
cnf(i_0_16099,plain,
hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(c_Nat_OSuc,X4)) = hAPP(hAPP(c_List_Onth(X1),X3),X4),
inference(split_conjunct,[status(thm)],[i_0_9592]),
[final] ).
cnf(i_0_16100,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Otl(X1),X4)) = hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_9593]),
[final] ).
cnf(i_0_16101,plain,
hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) = hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Orev(X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_9594]),
[final] ).
cnf(i_0_16102,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9595]),
[final] ).
cnf(i_0_16103,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_9596]),
[final] ).
cnf(i_0_16104,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_9597]),
[final] ).
cnf(i_0_16105,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)) = X3
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9598]),
[final] ).
cnf(i_0_16106,plain,
( hBOOL(hAPP(X2,esk49_1(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9599]),
[final] ).
cnf(i_0_16107,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9591]),
[final] ).
cnf(i_0_16108,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9600]),
[final] ).
cnf(i_0_16109,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) ),
inference(rw,[status(thm)],[i_0_9601,c_0_6015]),
[final] ).
cnf(i_0_16110,plain,
( hAPP(X1,esk159_3(X1,X2,X3)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7210]),
[final] ).
cnf(i_0_16111,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9602]),
[final] ).
cnf(i_0_16112,plain,
( X2 = X3
| hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_9603]),
[final] ).
cnf(i_0_16113,plain,
( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1)) = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_9604]),
[final] ).
cnf(i_0_16114,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4)
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9605]),
[final] ).
cnf(i_0_16115,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3) != X4
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9606]),
[final] ).
cnf(i_0_16116,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| X1 = hAPP(c_Nat_OSuc,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9607]),
[final] ).
cnf(i_0_16117,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| X1 = hAPP(c_Nat_OSuc,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9608]),
[final] ).
cnf(i_0_16118,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),c_List_Obutlast(X2,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),c_List_Olast(X2,X1)),c_List_Olist_ONil(X2))) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_9609]),
[final] ).
cnf(i_0_16119,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)))),
inference(rw,[status(thm)],[i_0_9610,c_0_6135]),
[final] ).
cnf(i_0_16120,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Predicate_OPowp(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8804]),
[final] ).
cnf(i_0_16121,plain,
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X3,X1,X2)))
| ~ hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9611]),
[final] ).
cnf(i_0_16122,plain,
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X3,X1,X2)))
| ~ hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9374]),
[final] ).
cnf(i_0_16123,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3)))
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9121]),
[final] ).
cnf(i_0_16124,plain,
hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(c_Product__Type_Ofst(X1,X2),X3)),hAPP(c_Product__Type_Osnd(X1,X2),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_9612]),
[final] ).
cnf(i_0_16125,plain,
X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(c_Product__Type_Ofst(X2,X3),X1)),hAPP(c_Product__Type_Osnd(X2,X3),X1)),
inference(split_conjunct,[status(thm)],[i_0_9613]),
[final] ).
cnf(i_0_16126,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9614]),
[final] ).
cnf(i_0_16127,plain,
( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),c_List_Olist_ONil(X2)) = hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9615]),
[final] ).
cnf(i_0_16128,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_9484]),
[final] ).
cnf(i_0_16129,plain,
( hAPP(X3,X4) = X5
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_9616]),
[final] ).
cnf(i_0_16130,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9277]),
[final] ).
cnf(i_0_16131,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Osublist(X1,X2,X3)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9617]),
[final] ).
cnf(i_0_16132,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremove1(X1,X3,X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9618]),
[final] ).
cnf(i_0_16133,plain,
c_List_Oremove1(X1,X2,c_List_Oremove1(X1,X3,X4)) = c_List_Oremove1(X1,X3,c_List_Oremove1(X1,X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_9619]),
[final] ).
cnf(i_0_16134,plain,
( hAPP(hAPP(X3,X4),hAPP(hAPP(X3,X5),X6)) = hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X4),X6))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9620]),
[final] ).
cnf(i_0_16135,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)) = X3
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9621]),
[final] ).
cnf(i_0_16136,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)) = X3
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9622]),
[final] ).
cnf(i_0_16137,plain,
c_Wellfounded_OwfP(X1,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse))),
inference(split_conjunct,[status(thm)],[i_0_9623]),
[final] ).
cnf(i_0_16138,plain,
( hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = X3
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8873]),
[final] ).
cnf(i_0_16139,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9542]),
[final] ).
cnf(i_0_16140,plain,
( hAPP(c_List_Ofilter(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Olist_OCons(X3),X2),hAPP(c_List_Ofilter(X3,X1),X4))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9624]),
[final] ).
cnf(i_0_16141,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| epred2_3(X2,X3,X1)
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_16142,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9625]),
[final] ).
cnf(i_0_16143,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9626]),
[final] ).
cnf(i_0_16144,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9627]),
[final] ).
cnf(i_0_16145,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9628]),
[final] ).
cnf(i_0_16146,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9629]),
[final] ).
cnf(i_0_16147,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9630]),
[final] ).
cnf(i_0_16148,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9631]),
[final] ).
cnf(i_0_16149,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9632]),
[final] ).
cnf(i_0_16150,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_OCollect(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9633]),
[final] ).
cnf(i_0_16151,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_OCollect(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9634]),
[final] ).
cnf(i_0_16152,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_OCollect(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9635]),
[final] ).
cnf(i_0_16153,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X1)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9636]),
[final] ).
cnf(i_0_16154,plain,
( hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X3),c_List_Orotate1(X2)),X1) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2) ),
inference(rw,[status(thm)],[i_0_9637,c_0_6670]),
[final] ).
cnf(i_0_16155,plain,
( X1 = X2
| c_List_Oremove1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Oremove1(X3,X1,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9638]),
[final] ).
cnf(i_0_16156,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),X1),X4) = X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X4),X1))
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9639]),
[final] ).
cnf(i_0_16157,plain,
( X2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3) != X4
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9639]),
[final] ).
cnf(i_0_16158,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9640]),
[final] ).
cnf(i_0_16159,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9641]),
[final] ).
cnf(i_0_16160,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9642]),
[final] ).
cnf(i_0_16161,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9643]),
[final] ).
cnf(i_0_16162,plain,
hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))),
inference(rw,[status(thm)],[i_0_9644,c_0_7027]),
[final] ).
cnf(i_0_16163,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_9645,c_0_8155]),
[final] ).
cnf(i_0_16164,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1)))),
inference(rw,[status(thm)],[i_0_9646,c_0_6135]),
[final] ).
cnf(i_0_16165,plain,
hAPP(c_Relation_OImage(X1,X1,c_Relation_OId__on(X1,X2)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_9647]),
[final] ).
cnf(i_0_16166,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9648]),
[final] ).
cnf(i_0_16167,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9649]),
[final] ).
cnf(i_0_16168,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9650]),
[final] ).
cnf(i_0_16169,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9651]),
[final] ).
cnf(i_0_16170,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9652]),
[final] ).
cnf(i_0_16171,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9653]),
[final] ).
cnf(i_0_16172,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9654]),
[final] ).
cnf(i_0_16173,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9655]),
[final] ).
cnf(i_0_16174,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9656]),
[final] ).
cnf(i_0_16175,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9657]),
[final] ).
cnf(i_0_16176,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9658]),
[final] ).
cnf(i_0_16177,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9659]),
[final] ).
cnf(i_0_16178,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9660]),
[final] ).
cnf(i_0_16179,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9661]),
[final] ).
cnf(i_0_16180,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9662]),
[final] ).
cnf(i_0_16181,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))),
inference(split_conjunct,[status(thm)],[i_0_9663]),
[final] ).
cnf(i_0_16182,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_8835]),
[final] ).
cnf(i_0_16183,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9145]),
[final] ).
cnf(i_0_16184,plain,
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9664]),
[final] ).
cnf(i_0_16185,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Odrop(X1),X3),X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9665]),
[final] ).
cnf(i_0_16186,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Otake(X1),X3),X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9666]),
[final] ).
cnf(i_0_16187,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9260]),
[final] ).
cnf(i_0_16188,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9667]),
[final] ).
cnf(i_0_16189,plain,
hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2)),
inference(split_conjunct,[status(thm)],[i_0_9668]),
[final] ).
cnf(i_0_16190,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9669]),
[final] ).
cnf(i_0_16191,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))),
inference(split_conjunct,[status(thm)],[i_0_9670]),
[final] ).
cnf(i_0_16192,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2),
inference(split_conjunct,[status(thm)],[i_0_9671]),
[final] ).
cnf(i_0_16193,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Obutlast(X1,X4)) = c_List_Obutlast(X2,hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_9672]),
[final] ).
cnf(i_0_16194,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk336_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_8527]),
[final] ).
cnf(i_0_16195,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9673]),
[final] ).
cnf(i_0_16196,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9674]),
[final] ).
cnf(i_0_16197,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk152_1(X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9537]),
[final] ).
cnf(i_0_16198,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk154_1(X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9538]),
[final] ).
cnf(i_0_16199,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Oring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5210]),
[final] ).
cnf(i_0_16200,plain,
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(X1,esk50_1(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9675]),
[final] ).
cnf(i_0_16201,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
inference(split_conjunct,[status(thm)],[i_0_9676]),
[final] ).
cnf(i_0_16202,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X3)))
| X1 != hAPP(c_Nat_OSuc,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9316]),
[final] ).
cnf(i_0_16203,plain,
c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
inference(split_conjunct,[status(thm)],[fact_transfer__morphism__int__nat]),
[final] ).
cnf(i_0_16204,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| epred1_3(X2,X3,X1)
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_16205,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9521]),
[final] ).
cnf(i_0_16206,plain,
( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = X2
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9677]),
[final] ).
cnf(i_0_16207,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_8910]),
[final] ).
cnf(i_0_16208,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(rw,[status(thm)],[i_0_9678,c_0_6169]),
[final] ).
cnf(i_0_16209,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(rw,[status(thm)],[i_0_9679,c_0_6016]),
[final] ).
cnf(i_0_16210,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_9680]),
[final] ).
cnf(i_0_16211,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_8721]),
[final] ).
cnf(i_0_16212,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk104_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8726]),
[final] ).
cnf(i_0_16213,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk99_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8562]),
[final] ).
cnf(i_0_16214,plain,
( hBOOL(hAPP(X3,X2))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X4),X2,X5,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_7015]),
[final] ).
cnf(i_0_16215,plain,
( hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X4
| ~ c_Finite__Set_Ofolding__one(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9681]),
[final] ).
cnf(i_0_16216,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),
inference(split_conjunct,[status(thm)],[i_0_9682]),
[final] ).
cnf(i_0_16217,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9683]),
[final] ).
cnf(i_0_16218,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9557]),
[final] ).
cnf(i_0_16219,plain,
hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X4,
inference(split_conjunct,[status(thm)],[i_0_9684]),
[final] ).
cnf(i_0_16220,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1)))
| ~ hBOOL(hAPP(X2,esk40_2(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9664]),
[final] ).
cnf(i_0_16221,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9258]),
[final] ).
cnf(i_0_16222,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Odrop(X1),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2),
inference(split_conjunct,[status(thm)],[i_0_9685]),
[final] ).
cnf(i_0_16223,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Otake(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2),
inference(split_conjunct,[status(thm)],[i_0_9686]),
[final] ).
cnf(i_0_16224,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_9687,c_0_6169]),
[final] ).
cnf(i_0_16225,plain,
( c_Fun_Oinj__on(tc_Nat_Onat,X1,c_Nat_Osemiring__1__class_Oof__nat(X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9688]),
[final] ).
cnf(i_0_16226,plain,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7844]),
[final] ).
cnf(i_0_16227,plain,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9689]),
[final] ).
cnf(i_0_16228,plain,
hAPP(hAPP(c_List_Otake(X1),X2),hAPP(c_List_Otl(X1),X3)) = hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),X3)),
inference(split_conjunct,[status(thm)],[i_0_9690]),
[final] ).
cnf(i_0_16229,plain,
( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk33_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9691]),
[final] ).
cnf(i_0_16230,plain,
( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk32_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9692]),
[final] ).
cnf(i_0_16231,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9693]),
[final] ).
cnf(i_0_16232,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9694]),
[final] ).
cnf(i_0_16233,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9695]),
[final] ).
cnf(i_0_16234,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9696]),
[final] ).
cnf(i_0_16235,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_6414]),
[final] ).
cnf(i_0_16236,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_9257]),
[final] ).
cnf(i_0_16237,plain,
( c_Divides_Odivmod__int(X2,X1) = c_Divides_OnegDivAlg(X2,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9193]),
[final] ).
cnf(i_0_16238,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
inference(split_conjunct,[status(thm)],[i_0_9697]),
[final] ).
cnf(i_0_16239,plain,
( hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8526]),
[final] ).
cnf(i_0_16240,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9698]),
[final] ).
cnf(i_0_16241,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| c_Nitpick_Osetsum_H(X1,X3,X4,X2) = c_Groups_Ozero__class_Ozero(X3)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_6131]),
[final] ).
cnf(i_0_16242,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
| hAPP(c_Finite__Set_Ocard(X2),X3) = hAPP(c_Nat_OSuc,X5)
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X3 != hAPP(hAPP(c_Set_Oinsert(X2),X4),X1)
| hAPP(c_Finite__Set_Ocard(X2),X1) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_7857]),
[final] ).
cnf(i_0_16243,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_8910]),
[final] ).
cnf(i_0_16244,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk356_2(X2,X1)),X2))
| hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9699]),
[final] ).
cnf(i_0_16245,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9700]),
[final] ).
cnf(i_0_16246,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9701]),
[final] ).
cnf(i_0_16247,plain,
c_Fun_Oinj__on(X1,tc_sum(X1,X2),c_Sum__Type_OInl(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_9702]),
[final] ).
cnf(i_0_16248,plain,
c_Fun_Oinj__on(X1,tc_sum(X2,X1),c_Sum__Type_OInr(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_9703]),
[final] ).
cnf(i_0_16249,plain,
c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_9704]),
[final] ).
cnf(i_0_16250,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9705]),
[final] ).
cnf(i_0_16251,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9706]),
[final] ).
cnf(i_0_16252,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9707]),
[final] ).
cnf(i_0_16253,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9708]),
[final] ).
cnf(i_0_16254,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9709]),
[final] ).
cnf(i_0_16255,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9710]),
[final] ).
cnf(i_0_16256,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9711]),
[final] ).
cnf(i_0_16257,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9712]),
[final] ).
cnf(i_0_16258,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9713]),
[final] ).
cnf(i_0_16259,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9714]),
[final] ).
cnf(i_0_16260,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9715]),
[final] ).
cnf(i_0_16261,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4) ),
inference(rw,[status(thm)],[i_0_9716,c_0_6135]),
[final] ).
cnf(i_0_16262,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9717]),
[final] ).
cnf(i_0_16263,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8798]),
[final] ).
cnf(i_0_16264,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9718]),
[final] ).
cnf(i_0_16265,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9719]),
[final] ).
cnf(i_0_16266,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9720]),
[final] ).
cnf(i_0_16267,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2))
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9721]),
[final] ).
cnf(i_0_16268,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))
| ~ epred2_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9435]),
[final] ).
cnf(i_0_16269,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9722]),
[final] ).
cnf(i_0_16270,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9722]),
[final] ).
cnf(i_0_16271,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X3))
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9723]),
[final] ).
cnf(i_0_16272,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9724]),
[final] ).
cnf(i_0_16273,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9725]),
[final] ).
cnf(i_0_16274,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9726]),
[final] ).
cnf(i_0_16275,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9727]),
[final] ).
cnf(i_0_16276,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9728]),
[final] ).
cnf(i_0_16277,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9729]),
[final] ).
cnf(i_0_16278,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9730]),
[final] ).
cnf(i_0_16279,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9731]),
[final] ).
cnf(i_0_16280,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1) = hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)),X1)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9605]),
[final] ).
cnf(i_0_16281,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),X1) != X4
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9606]),
[final] ).
cnf(i_0_16282,plain,
( c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[i_0_9732,c_0_7027]),
[final] ).
cnf(i_0_16283,plain,
( c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[i_0_9733,c_0_7027]),
[final] ).
cnf(i_0_16284,plain,
hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X2),X3) != hAPP(c_Set_OPow(X1),X3),
inference(split_conjunct,[status(thm)],[i_0_9734]),
[final] ).
cnf(i_0_16285,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_inj__int]),
[final] ).
cnf(i_0_16286,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_9735]),
[final] ).
cnf(i_0_16287,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9735]),
[final] ).
cnf(i_0_16288,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_8215]),
[final] ).
cnf(i_0_16289,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_8215]),
[final] ).
cnf(i_0_16290,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_8510]),
[final] ).
cnf(i_0_16291,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9736]),
[final] ).
cnf(i_0_16292,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9737]),
[final] ).
cnf(i_0_16293,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8921]),
[final] ).
cnf(i_0_16294,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9474]),
[final] ).
cnf(i_0_16295,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(split_conjunct,[status(thm)],[i_0_9738]),
[final] ).
cnf(i_0_16296,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| c_SMT_Oz3div(X2,X1) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9739]),
[final] ).
cnf(i_0_16297,plain,
( X1 = c_List_Olist_ONil(X2)
| hBOOL(hAPP(hAPP(c_member(X2),c_List_Olast(X2,X1)),hAPP(c_List_Oset(X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9740]),
[final] ).
cnf(i_0_16298,plain,
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8051]),
[final] ).
cnf(i_0_16299,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9461]),
[final] ).
cnf(i_0_16300,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_9741]),
[final] ).
cnf(i_0_16301,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X6) ),
inference(split_conjunct,[status(thm)],[i_0_9742]),
[final] ).
cnf(i_0_16302,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X6) ),
inference(split_conjunct,[status(thm)],[i_0_9743]),
[final] ).
cnf(i_0_16303,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X1) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2) ),
inference(split_conjunct,[status(thm)],[i_0_9742]),
[final] ).
cnf(i_0_16304,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X1) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2) ),
inference(split_conjunct,[status(thm)],[i_0_9743]),
[final] ).
cnf(i_0_16305,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9744]),
[final] ).
cnf(i_0_16306,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_9745]),
[final] ).
cnf(i_0_16307,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_9746]),
[final] ).
cnf(i_0_16308,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_8951]),
[final] ).
cnf(i_0_16309,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(split_conjunct,[status(thm)],[i_0_9747]),
[final] ).
cnf(i_0_16310,plain,
hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)),
inference(split_conjunct,[status(thm)],[i_0_9748]),
[final] ).
cnf(i_0_16311,plain,
hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X3)),hAPP(c_List_Orev(X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9749]),
[final] ).
cnf(i_0_16312,plain,
hAPP(c_List_Orotate1(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))),
inference(split_conjunct,[status(thm)],[i_0_9750]),
[final] ).
cnf(i_0_16313,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9751]),
[final] ).
cnf(i_0_16314,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9608]),
[final] ).
cnf(i_0_16315,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9662]),
[final] ).
cnf(i_0_16316,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9752]),
[final] ).
cnf(i_0_16317,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9640]),
[final] ).
cnf(i_0_16318,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9753]),
[final] ).
cnf(i_0_16319,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_9573]),
[final] ).
cnf(i_0_16320,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9016]),
[final] ).
cnf(i_0_16321,plain,
( hBOOL(hAPP(X1,esk480_3(X2,X1,X3)))
| hAPP(c_List_Ofilter(X3,X1),X2) = c_List_Olist_ONil(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8693]),
[final] ).
cnf(i_0_16322,plain,
c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),
inference(split_conjunct,[status(thm)],[i_0_9754]),
[final] ).
cnf(i_0_16323,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9755]),
[final] ).
cnf(i_0_16324,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_9489]),
[final] ).
cnf(i_0_16325,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9756]),
[final] ).
cnf(i_0_16326,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_9757]),
[final] ).
cnf(i_0_16327,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_9758]),
[final] ).
cnf(i_0_16328,plain,
c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_9759]),
[final] ).
cnf(i_0_16329,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Groups_Oabs__class_Oabs(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9247]),
[final] ).
cnf(i_0_16330,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk39_1(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9760]),
[final] ).
cnf(i_0_16331,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X5 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9761]),
[final] ).
cnf(i_0_16332,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| X5 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9761]),
[final] ).
cnf(i_0_16333,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_9762]),
[final] ).
cnf(i_0_16334,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_9763]),
[final] ).
cnf(i_0_16335,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))),
inference(split_conjunct,[status(thm)],[i_0_9764]),
[final] ).
cnf(i_0_16336,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))),
inference(split_conjunct,[status(thm)],[i_0_9765]),
[final] ).
cnf(i_0_16337,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X1),X2) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))),
inference(split_conjunct,[status(thm)],[i_0_9766]),
[final] ).
cnf(i_0_16338,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),X2) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))),
inference(split_conjunct,[status(thm)],[i_0_9767]),
[final] ).
cnf(i_0_16339,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9768]),
[final] ).
cnf(i_0_16340,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9769]),
[final] ).
cnf(i_0_16341,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9770]),
[final] ).
cnf(i_0_16342,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_9771]),
[final] ).
cnf(i_0_16343,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),hAPP(c_List_Oset(tc_Nat_Onat),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9772]),
[final] ).
cnf(i_0_16344,plain,
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X2,X3,X1)))
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9773]),
[final] ).
cnf(i_0_16345,plain,
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X2,X3,X1)))
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9376]),
[final] ).
cnf(i_0_16346,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9543]),
[final] ).
cnf(i_0_16347,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9774]),
[final] ).
cnf(i_0_16348,plain,
( X3 = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9775]),
[final] ).
cnf(i_0_16349,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9776]),
[final] ).
cnf(i_0_16350,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9777]),
[final] ).
cnf(i_0_16351,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9778]),
[final] ).
cnf(i_0_16352,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9779]),
[final] ).
cnf(i_0_16353,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9780]),
[final] ).
cnf(i_0_16354,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9781]),
[final] ).
cnf(i_0_16355,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9782]),
[final] ).
cnf(i_0_16356,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9783]),
[final] ).
cnf(i_0_16357,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9784]),
[final] ).
cnf(i_0_16358,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9785]),
[final] ).
cnf(i_0_16359,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9786]),
[final] ).
cnf(i_0_16360,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9787]),
[final] ).
cnf(i_0_16361,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9788]),
[final] ).
cnf(i_0_16362,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9789]),
[final] ).
cnf(i_0_16363,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9790]),
[final] ).
cnf(i_0_16364,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9791]),
[final] ).
cnf(i_0_16365,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[fact_INT__greaterThan__UNIV]),
[final] ).
cnf(i_0_16366,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[fact_UN__atLeast__UNIV]),
[final] ).
cnf(i_0_16367,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[fact_UN__atMost__UNIV]),
[final] ).
cnf(i_0_16368,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[fact_UN__lessThan__UNIV]),
[final] ).
cnf(i_0_16369,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9792]),
[final] ).
cnf(i_0_16370,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Oone__class_Oone(X1))),X3) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9793]),
[final] ).
cnf(i_0_16371,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Ozero__class_Ozero(X1))),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9794]),
[final] ).
cnf(i_0_16372,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk53_2(X1,X2)),X1))
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9061]),
[final] ).
cnf(i_0_16373,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9394]),
[final] ).
cnf(i_0_16374,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_9795]),
[final] ).
cnf(i_0_16375,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_9489]),
[final] ).
cnf(i_0_16376,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9796]),
[final] ).
cnf(i_0_16377,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9424]),
[final] ).
cnf(i_0_16378,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9779]),
[final] ).
cnf(i_0_16379,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9780]),
[final] ).
cnf(i_0_16380,plain,
hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[i_0_9797]),
[final] ).
cnf(i_0_16381,plain,
c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[fact_transfer__morphism__nat__int]),
[final] ).
cnf(i_0_16382,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9798]),
[final] ).
cnf(i_0_16383,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9241]),
[final] ).
cnf(i_0_16384,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9799]),
[final] ).
cnf(i_0_16385,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9800]),
[final] ).
cnf(i_0_16386,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(rw,[status(thm)],[i_0_9801,c_0_6016]),
[final] ).
cnf(i_0_16387,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| c_List_Osublist(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)),X1) = c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9411]),
[final] ).
cnf(i_0_16388,plain,
( esk243_3(X1,X2,X3) = esk244_3(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8591]),
[final] ).
cnf(i_0_16389,plain,
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
| ~ c_Nat__Transfer_Onat__set(X1)
| ~ c_Nat__Transfer_Onat__set(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9802]),
[final] ).
cnf(i_0_16390,plain,
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))
| ~ c_Nat__Transfer_Onat__set(X1)
| ~ c_Nat__Transfer_Onat__set(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9803]),
[final] ).
cnf(i_0_16391,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk52_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9804]),
[final] ).
cnf(i_0_16392,plain,
hAPP(c_List_Ofilter(X1,X2),c_List_Oremove1(X1,X3,X4)) = c_List_Oremove1(X1,X3,hAPP(c_List_Ofilter(X1,X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_9805]),
[final] ).
cnf(i_0_16393,plain,
( hBOOL(hAPP(X1,esk101_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8687]),
[final] ).
cnf(i_0_16394,plain,
( hBOOL(hAPP(X1,esk96_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8524]),
[final] ).
cnf(i_0_16395,plain,
( c_List_Obutlast(X1,X2) = X3
| hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Olist_ONil(X1))) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9806]),
[final] ).
cnf(i_0_16396,plain,
( c_List_Olast(X1,X2) = X3
| hAPP(hAPP(c_List_Oappend(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9806]),
[final] ).
cnf(i_0_16397,plain,
( X1 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk41_1(X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_9807]),
[final] ).
cnf(i_0_16398,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9808]),
[final] ).
cnf(i_0_16399,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9809]),
[final] ).
cnf(i_0_16400,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9810]),
[final] ).
cnf(i_0_16401,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Nat_Osemiring__1__class_ONats(X1)))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9811]),
[final] ).
cnf(i_0_16402,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X2),X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9591]),
[final] ).
cnf(i_0_16403,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9812]),
[final] ).
cnf(i_0_16404,plain,
( X1 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9813]),
[final] ).
cnf(i_0_16405,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9469]),
[final] ).
cnf(i_0_16406,plain,
hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_9814]),
[final] ).
cnf(i_0_16407,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9815]),
[final] ).
cnf(i_0_16408,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk421_2(X2,X1)),esk420_2(X2,X1)))
| c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6982]),
[final] ).
cnf(i_0_16409,plain,
c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_9816]),
[final] ).
cnf(i_0_16410,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_8811]),
[final] ).
cnf(i_0_16411,plain,
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9817]),
[final] ).
cnf(i_0_16412,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_9489]),
[final] ).
cnf(i_0_16413,plain,
( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9818]),
[final] ).
cnf(i_0_16414,plain,
( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9819]),
[final] ).
cnf(i_0_16415,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9820]),
[final] ).
cnf(i_0_16416,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9820]),
[final] ).
cnf(i_0_16417,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9821]),
[final] ).
cnf(i_0_16418,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9822]),
[final] ).
cnf(i_0_16419,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9823]),
[final] ).
cnf(i_0_16420,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_9824]),
[final] ).
cnf(i_0_16421,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))),
inference(split_conjunct,[status(thm)],[i_0_9825]),
[final] ).
cnf(i_0_16422,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_9826]),
[final] ).
cnf(i_0_16423,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))),
inference(split_conjunct,[status(thm)],[i_0_9827]),
[final] ).
cnf(i_0_16424,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = X4
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9828]),
[final] ).
cnf(i_0_16425,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = X4
| X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9829]),
[final] ).
cnf(i_0_16426,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) != X4
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9829]),
[final] ).
cnf(i_0_16427,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) != X4
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9828]),
[final] ).
cnf(i_0_16428,plain,
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8067]),
[final] ).
cnf(i_0_16429,plain,
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_7526]),
[final] ).
cnf(i_0_16430,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(X3,X1),X2))
| X2 = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9830]),
[final] ).
cnf(i_0_16431,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),
inference(split_conjunct,[status(thm)],[i_0_9831]),
[final] ).
cnf(i_0_16432,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9416]),
[final] ).
cnf(i_0_16433,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X4
| X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
inference(split_conjunct,[status(thm)],[i_0_9832]),
[final] ).
cnf(i_0_16434,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X4
| X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
inference(split_conjunct,[status(thm)],[i_0_6573]),
[final] ).
cnf(i_0_16435,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
| hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X4
| X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
inference(split_conjunct,[status(thm)],[i_0_9833]),
[final] ).
cnf(i_0_16436,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
| hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X4
| X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
inference(split_conjunct,[status(thm)],[i_0_6805]),
[final] ).
cnf(i_0_16437,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X5) = hAPP(hAPP(c_List_Oappend(X2),X3),X6)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X4)
| hAPP(hAPP(c_List_Oappend(X2),X4),X5) != X6 ),
inference(split_conjunct,[status(thm)],[i_0_6573]),
[final] ).
cnf(i_0_16438,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X5) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),X6)
| X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
| hAPP(hAPP(c_List_Oappend(X2),X4),X5) != X6 ),
inference(split_conjunct,[status(thm)],[i_0_6806]),
[final] ).
cnf(i_0_16439,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_9834]),
[final] ).
cnf(i_0_16440,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_9835]),
[final] ).
cnf(i_0_16441,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(split_conjunct,[status(thm)],[i_0_9836]),
[final] ).
cnf(i_0_16442,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_9837]),
[final] ).
cnf(i_0_16443,plain,
( X1 != c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2))) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_9806]),
[final] ).
cnf(i_0_16444,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk487_2(X1,X2)),esk486_2(X1,X2)))
| c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7545]),
[final] ).
cnf(i_0_16445,plain,
( c_Orderings_Oord_Omax(X1,hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1))) = c_Orderings_Oord__class_Omin(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9838]),
[final] ).
cnf(i_0_16446,plain,
( c_Orderings_Oord_Omin(X1,hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1))) = c_Orderings_Oord__class_Omax(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9839]),
[final] ).
cnf(i_0_16447,plain,
( c_List_Omonoid__add__class_Olistsum(X1) = c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9840]),
[final] ).
cnf(i_0_16448,plain,
( X3 = hAPP(c_Option_Ooption_OSome(X1),X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Option_Oset(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9841]),
[final] ).
cnf(i_0_16449,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2) = X3
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9842]),
[final] ).
cnf(i_0_16450,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) = X3
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9843]),
[final] ).
cnf(i_0_16451,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3) = X2
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9844]),
[final] ).
cnf(i_0_16452,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) != X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9844]),
[final] ).
cnf(i_0_16453,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9845]),
[final] ).
cnf(i_0_16454,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_9489]),
[final] ).
cnf(i_0_16455,negated_conjecture,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),esk494_0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),esk495_0),
inference(split_conjunct,[status(thm)],[i_0_9846]),
[final] ).
cnf(i_0_16456,plain,
c_Com_Ovname_Ovname__rec(X1,X2,X3,c_Com_Ovname_OGlb(X4)) = hAPP(X2,X4),
inference(split_conjunct,[status(thm)],[i_0_9847]),
[final] ).
cnf(i_0_16457,plain,
c_Com_Ovname_Ovname__rec(X1,X2,X3,c_Com_Ovname_OLoc(X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_9848]),
[final] ).
cnf(i_0_16458,plain,
c_Com_Ovname_Ovname__case(X1,X2,X3,c_Com_Ovname_OGlb(X4)) = hAPP(X2,X4),
inference(split_conjunct,[status(thm)],[i_0_9849]),
[final] ).
cnf(i_0_16459,plain,
c_Com_Ovname_Ovname__case(X1,X2,X3,c_Com_Ovname_OLoc(X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_9850]),
[final] ).
cnf(i_0_16460,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk45_1(X1)))
| ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9582]),
[final] ).
cnf(i_0_16461,plain,
( hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Map_Odom(X5,X3,X1)) = c_Map_Odom(X5,X3,X1)
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9851]),
[final] ).
cnf(i_0_16462,plain,
( c_Nitpick_Owf_H(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9852]),
[final] ).
cnf(i_0_16463,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9853]),
[final] ).
cnf(i_0_16464,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9853]),
[final] ).
cnf(i_0_16465,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9854]),
[final] ).
cnf(i_0_16466,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_16467,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_16468,plain,
c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_9855]),
[final] ).
cnf(i_0_16469,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofilter(X1,X3),X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9856]),
[final] ).
cnf(i_0_16470,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),X3),X4)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_9857]),
[final] ).
cnf(i_0_16471,plain,
( c_Equiv__Relations_Oequivp(X2,X1)
| ~ hBOOL(hAPP(hAPP(X1,esk259_1(X1)),esk260_1(X1)))
| hAPP(X1,esk259_1(X1)) != hAPP(X1,esk260_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9858]),
[final] ).
cnf(i_0_16472,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9859]),
[final] ).
cnf(i_0_16473,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9860]),
[final] ).
cnf(i_0_16474,plain,
hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),X3) = hAPP(c_Relation_ODomain(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_9861]),
[final] ).
cnf(i_0_16475,plain,
hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),X3) = hAPP(c_Relation_ORange(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_9862]),
[final] ).
cnf(i_0_16476,plain,
( hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk29_2(X2,X1))))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9863]),
[final] ).
cnf(i_0_16477,plain,
( X1 = hAPP(c_Nat_OSuc,esk31_2(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9316]),
[final] ).
cnf(i_0_16478,plain,
( hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)),X1) = X3
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_9368]),
[final] ).
cnf(i_0_16479,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8970]),
[final] ).
cnf(i_0_16480,plain,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9864]),
[final] ).
cnf(i_0_16481,plain,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9865]),
[final] ).
cnf(i_0_16482,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),X1) = X4
| hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9606]),
[final] ).
cnf(i_0_16483,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)),X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1) != hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9605]),
[final] ).
cnf(i_0_16484,plain,
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,esk40_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9664]),
[final] ).
cnf(i_0_16485,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9677]),
[final] ).
cnf(i_0_16486,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_9866]),
[final] ).
cnf(i_0_16487,plain,
( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X1) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1))
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9867]),
[final] ).
cnf(i_0_16488,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ c_Nat__Transfer_Onat__set(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9868]),
[final] ).
cnf(i_0_16489,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ c_Nat__Transfer_Onat__set(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9869]),
[final] ).
cnf(i_0_16490,plain,
( X1 = hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)
| hAPP(hAPP(c_List_Oappend(X2),X3),X1) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_8808]),
[final] ).
cnf(i_0_16491,plain,
( X1 = hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)
| hAPP(hAPP(c_List_Oappend(X2),X1),X4) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_8808]),
[final] ).
cnf(i_0_16492,plain,
c_Relation_Orefl__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_9870]),
[final] ).
cnf(i_0_16493,plain,
hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),
inference(split_conjunct,[status(thm)],[i_0_9871]),
[final] ).
cnf(i_0_16494,plain,
( X3 = X4
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X3))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9872]),
[final] ).
cnf(i_0_16495,plain,
( c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9873]),
[final] ).
cnf(i_0_16496,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_member(X3),X4),X5))
| hAPP(c_Finite__Set_Ocard(X3),X2) = hAPP(c_Nat_OSuc,X1)
| X2 != hAPP(hAPP(c_Set_Oinsert(X3),X4),X5)
| hAPP(c_Finite__Set_Ocard(X3),X5) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_7857]),
[final] ).
cnf(i_0_16497,plain,
c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,X2) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X1),hAPP(c_Code__Numeral_Onat__of,X2))),
inference(split_conjunct,[status(thm)],[i_0_9874]),
[final] ).
cnf(i_0_16498,plain,
hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(split_conjunct,[status(thm)],[i_0_9875]),
[final] ).
cnf(i_0_16499,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X1,X2,X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9876]),
[final] ).
cnf(i_0_16500,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_Set_Oimage(X2,X1,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9877]),
[final] ).
cnf(i_0_16501,plain,
c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_9878]),
[final] ).
cnf(i_0_16502,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_9879]),
[final] ).
cnf(i_0_16503,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_9880]),
[final] ).
cnf(i_0_16504,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_5896]),
[final] ).
cnf(i_0_16505,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_5897]),
[final] ).
cnf(i_0_16506,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X3) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X3 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9722]),
[final] ).
cnf(i_0_16507,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(c_List_Ohd(X3),hAPP(hAPP(c_List_Omap(X2,X3),X4),X1)) = hAPP(X4,hAPP(c_List_Ohd(X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9881]),
[final] ).
cnf(i_0_16508,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),c_Int_Oring__1__class_OInts(X2)))
| ~ class_Int_Oring__char__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9755]),
[final] ).
cnf(i_0_16509,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) = X3
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9882]),
[final] ).
cnf(i_0_16510,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X2) != hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_9883]),
[final] ).
cnf(i_0_16511,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) != hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_9883]),
[final] ).
cnf(i_0_16512,plain,
hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X1),X2),X3),X4),X5) = c_New__DSequence_Oneg__single(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_9884]),
[final] ).
cnf(i_0_16513,plain,
hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X1),X2),X3),X4),X5) = c_New__DSequence_Opos__single(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_9885]),
[final] ).
cnf(i_0_16514,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(X2),X4))
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9828]),
[final] ).
cnf(i_0_16515,plain,
( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)) != X4
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9829]),
[final] ).
cnf(i_0_16516,plain,
( c_Divides_OposDivAlg(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_5309]),
[final] ).
cnf(i_0_16517,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9886]),
[final] ).
cnf(i_0_16518,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9887]),
[final] ).
cnf(i_0_16519,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9888]),
[final] ).
cnf(i_0_16520,plain,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(split_conjunct,[status(thm)],[i_0_9889]),
[final] ).
cnf(i_0_16521,plain,
c_List_Omap__filter(X1,X2,X3,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
inference(split_conjunct,[status(thm)],[i_0_9890]),
[final] ).
cnf(i_0_16522,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9692]),
[final] ).
cnf(i_0_16523,plain,
( X1 = X2
| hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))) != hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9891,c_0_8155]),c_0_8155]),
[final] ).
cnf(i_0_16524,plain,
( c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9892]),
[final] ).
cnf(i_0_16525,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9893]),
[final] ).
cnf(i_0_16526,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9894]),
[final] ).
cnf(i_0_16527,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_9895]),
[final] ).
cnf(i_0_16528,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Oappend(X2),X1),X3)) = hAPP(hAPP(c_List_Oappend(X2),hAPP(c_List_Otl(X2),X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_9896]),
[final] ).
cnf(i_0_16529,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_9897]),
[final] ).
cnf(i_0_16530,plain,
( X3 = X4
| hAPP(c_Product__Type_Ofst(X1,X2),X3) != hAPP(c_Product__Type_Ofst(X1,X2),X4)
| hAPP(c_Product__Type_Osnd(X1,X2),X3) != hAPP(c_Product__Type_Osnd(X1,X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9898]),
[final] ).
cnf(i_0_16531,plain,
( X3 = X4
| hAPP(c_Product__Type_Ofst(X1,X2),X3) != hAPP(c_Product__Type_Ofst(X1,X2),X4)
| hAPP(c_Product__Type_Osnd(X1,X2),X3) != hAPP(c_Product__Type_Osnd(X1,X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9899]),
[final] ).
cnf(i_0_16532,plain,
c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_9900]),
[final] ).
cnf(i_0_16533,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_9901]),
[final] ).
cnf(i_0_16534,plain,
( hAPP(hAPP(c_List_Otake(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = c_List_Olist_ONil(X2)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_7784]),
[final] ).
cnf(i_0_16535,plain,
( c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9902]),
[final] ).
cnf(i_0_16536,plain,
( X2 = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X3))
| hAPP(c_List_Oset(X1),X2) != hAPP(c_List_Oset(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_9903]),
[final] ).
cnf(i_0_16537,plain,
hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = hAPP(hAPP(c_List_Odrop(X1),X2),X4),
inference(split_conjunct,[status(thm)],[i_0_9904]),
[final] ).
cnf(i_0_16538,plain,
c_Wellfounded_Oless__than = hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)),
inference(rw,[status(thm)],[i_0_9905,c_0_6062]),
[final] ).
cnf(i_0_16539,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9906]),
[final] ).
cnf(i_0_16540,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_9907,c_0_8155]),
[final] ).
cnf(i_0_16541,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(split_conjunct,[status(thm)],[i_0_9908]),
[final] ).
cnf(i_0_16542,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X2,
inference(split_conjunct,[status(thm)],[i_0_9909]),
[final] ).
cnf(i_0_16543,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X2,
inference(split_conjunct,[status(thm)],[i_0_9910]),
[final] ).
cnf(i_0_16544,plain,
( c_Nitpick_Onorm__frac(X2,X1) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6763]),
[final] ).
cnf(i_0_16545,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9911]),
[final] ).
cnf(i_0_16546,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9912]),
[final] ).
cnf(i_0_16547,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9913]),
[final] ).
cnf(i_0_16548,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9914]),
[final] ).
cnf(i_0_16549,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9915]),
[final] ).
cnf(i_0_16550,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9916]),
[final] ).
cnf(i_0_16551,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_9917]),
[final] ).
cnf(i_0_16552,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9918,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_16553,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[i_0_9919]),
[final] ).
cnf(i_0_16554,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[i_0_9920]),
[final] ).
cnf(i_0_16555,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[i_0_9921]),
[final] ).
cnf(i_0_16556,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_9922]),
[final] ).
cnf(i_0_16557,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_9923]),
[final] ).
cnf(i_0_16558,plain,
( c_Divides_OposDivAlg(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_5309]),
[final] ).
cnf(i_0_16559,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9924]),
[final] ).
cnf(i_0_16560,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9924]),
[final] ).
cnf(i_0_16561,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9925,c_0_6014]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_16562,plain,
hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X3,
inference(split_conjunct,[status(thm)],[i_0_9926]),
[final] ).
cnf(i_0_16563,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_9927]),
[final] ).
cnf(i_0_16564,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4),
inference(split_conjunct,[status(thm)],[i_0_9928]),
[final] ).
cnf(i_0_16565,plain,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_9929]),
[final] ).
cnf(i_0_16566,plain,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_9930]),
[final] ).
cnf(i_0_16567,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),X3)
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9931]),
[final] ).
cnf(i_0_16568,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),X3)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9932]),
[final] ).
cnf(i_0_16569,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9933]),
[final] ).
cnf(i_0_16570,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9934]),
[final] ).
cnf(i_0_16571,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9935]),
[final] ).
cnf(i_0_16572,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9936]),
[final] ).
cnf(i_0_16573,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X4
| X1 != c_Finite__Set_Ofold1(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9937]),
[final] ).
cnf(i_0_16574,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Otl(X1),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_9938]),
[final] ).
cnf(i_0_16575,plain,
( hAPP(hAPP(X3,X4),hAPP(hAPP(X3,X4),X5)) = hAPP(hAPP(X3,X4),X5)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9939]),
[final] ).
cnf(i_0_16576,plain,
c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),
inference(split_conjunct,[status(thm)],[i_0_9940]),
[final] ).
cnf(i_0_16577,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_9941]),
[final] ).
cnf(i_0_16578,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_9942]),
[final] ).
cnf(i_0_16579,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_9943]),
[final] ).
cnf(i_0_16580,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_9944]),
[final] ).
cnf(i_0_16581,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_9945]),
[final] ).
cnf(i_0_16582,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_9946]),
[final] ).
cnf(i_0_16583,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_9947]),
[final] ).
cnf(i_0_16584,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_9948]),
[final] ).
cnf(i_0_16585,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9933]),
[final] ).
cnf(i_0_16586,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9934]),
[final] ).
cnf(i_0_16587,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9935]),
[final] ).
cnf(i_0_16588,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9949]),
[final] ).
cnf(i_0_16589,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9950]),
[final] ).
cnf(i_0_16590,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9951]),
[final] ).
cnf(i_0_16591,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9952]),
[final] ).
cnf(i_0_16592,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9953]),
[final] ).
cnf(i_0_16593,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(split_conjunct,[status(thm)],[fact_pair__less__def]),
[final] ).
cnf(i_0_16594,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X3,hAPP(hAPP(c_List_Omap(X2,X3),X4),X1)) = hAPP(X4,c_List_Olast(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9954]),
[final] ).
cnf(i_0_16595,plain,
hAPP(c_Map_Omap__of(X1,X2,c_List_Olist_ONil(tc_prod(X1,X2))),X3) = c_Option_Ooption_ONone(X2),
inference(split_conjunct,[status(thm)],[i_0_9955]),
[final] ).
cnf(i_0_16596,plain,
hAPP(c_Map_Omap__of(X1,X2,c_List_Olist_ONil(tc_prod(X1,X2))),X3) = c_Option_Ooption_ONone(X2),
inference(split_conjunct,[status(thm)],[i_0_9956]),
[final] ).
cnf(i_0_16597,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(rw,[status(thm)],[i_0_9957,c_0_6016]),
[final] ).
cnf(i_0_16598,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| X2 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_8910]),
[final] ).
cnf(i_0_16599,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9958]),
[final] ).
cnf(i_0_16600,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X2),esk166_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9959]),
[final] ).
cnf(i_0_16601,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk165_2(X2,X1)),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9960]),
[final] ).
cnf(i_0_16602,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| c_List_Oremove1(X1,X2,X3) = X3 ),
inference(split_conjunct,[status(thm)],[i_0_9961]),
[final] ).
cnf(i_0_16603,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),
inference(rw,[status(thm)],[i_0_9962,c_0_6135]),
[final] ).
cnf(i_0_16604,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9641]),
[final] ).
cnf(i_0_16605,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9394]),
[final] ).
cnf(i_0_16606,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)
| ~ class_Rings_Oring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9963]),
[final] ).
cnf(i_0_16607,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_9964]),
[final] ).
cnf(i_0_16608,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_9965]),
[final] ).
cnf(i_0_16609,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[i_0_9966]),
[final] ).
cnf(i_0_16610,plain,
( X1 = c_List_Olist_ONil(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9472]),
[final] ).
cnf(i_0_16611,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Groups_Osgn__if(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9967]),
[final] ).
cnf(i_0_16612,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_COMBI(X1)),hAPP(c_List_Oset(X1),X2))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9968]),
[final] ).
cnf(i_0_16613,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9969]),
[final] ).
cnf(i_0_16614,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9970]),
[final] ).
cnf(i_0_16615,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9971]),
[final] ).
cnf(i_0_16616,plain,
( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)) = hAPP(c_SetInterval_Oord__class_OatMost(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9972]),
[final] ).
cnf(i_0_16617,plain,
( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9973]),
[final] ).
cnf(i_0_16618,plain,
( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)) = hAPP(c_SetInterval_Oord__class_OlessThan(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9974]),
[final] ).
cnf(i_0_16619,plain,
( hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9975]),
[final] ).
cnf(i_0_16620,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1)) = c_List_Olist_ONil(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[i_0_9976,c_0_6135]),
[final] ).
cnf(i_0_16621,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1)) = c_List_Olist_ONil(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[i_0_9977,c_0_6135]),
[final] ).
cnf(i_0_16622,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
| c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) != c_List_Olist_ONil(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_9978,c_0_6135]),
[final] ).
cnf(i_0_16623,plain,
( c_SMT_Oz3mod(X2,X1) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9979]),
[final] ).
cnf(i_0_16624,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9478]),
[final] ).
cnf(i_0_16625,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk155_2(X1,X2)),X1))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9538]),
[final] ).
cnf(i_0_16626,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk153_2(X1,X2)),X1))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9537]),
[final] ).
cnf(i_0_16627,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_9497]),
[final] ).
cnf(i_0_16628,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_9496]),
[final] ).
cnf(i_0_16629,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9980]),
[final] ).
cnf(i_0_16630,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9981]),
[final] ).
cnf(i_0_16631,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oabs__if(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9982]),
[final] ).
cnf(i_0_16632,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9983]),
[final] ).
cnf(i_0_16633,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9984]),
[final] ).
cnf(i_0_16634,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9985]),
[final] ).
cnf(i_0_16635,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9986]),
[final] ).
cnf(i_0_16636,plain,
( hBOOL(hAPP(hAPP(X2,X4),X3))
| ~ c_Equiv__Relations_Oequivp(X1,X2)
| ~ hBOOL(hAPP(hAPP(X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9987]),
[final] ).
cnf(i_0_16637,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9539]),
[final] ).
cnf(i_0_16638,plain,
( c_Divides_Odiv__class_Omod(X1,X3,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9988]),
[final] ).
cnf(i_0_16639,plain,
( c_Divides_Odiv__class_Omod(X1,X3,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9989]),
[final] ).
cnf(i_0_16640,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Obutlast(X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_9990]),
[final] ).
cnf(i_0_16641,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9991]),
[final] ).
cnf(i_0_16642,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9992]),
[final] ).
cnf(i_0_16643,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_9993]),
[final] ).
cnf(i_0_16644,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_9994]),
[final] ).
cnf(i_0_16645,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),
inference(split_conjunct,[status(thm)],[fact_finite__dom__body]),
[final] ).
cnf(i_0_16646,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9995]),
[final] ).
cnf(i_0_16647,plain,
( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9996]),
[final] ).
cnf(i_0_16648,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9997]),
[final] ).
cnf(i_0_16649,plain,
c_List_Olists(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_9998]),
[final] ).
cnf(i_0_16650,plain,
c_List_Olistset(X1,c_List_Olist_ONil(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_9999]),
[final] ).
cnf(i_0_16651,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_Set_OCollect(X3),X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9633]),
[final] ).
cnf(i_0_16652,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_Set_OCollect(X3),X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10000]),
[final] ).
cnf(i_0_16653,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_5918]),
[final] ).
cnf(i_0_16654,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_10001]),
[final] ).
cnf(i_0_16655,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_10002]),
[final] ).
cnf(i_0_16656,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10003]),
[final] ).
cnf(i_0_16657,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)) = c_Fun_Oid(tc_prod(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10004]),
[final] ).
cnf(i_0_16658,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9924]),
[final] ).
cnf(i_0_16659,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = X2
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10005]),
[final] ).
cnf(i_0_16660,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10006]),
[final] ).
cnf(i_0_16661,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10007]),
[final] ).
cnf(i_0_16662,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10008]),
[final] ).
cnf(i_0_16663,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = X3
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10009]),
[final] ).
cnf(i_0_16664,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2) = X3
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10010]),
[final] ).
cnf(i_0_16665,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10011]),
[final] ).
cnf(i_0_16666,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10012]),
[final] ).
cnf(i_0_16667,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10013]),
[final] ).
cnf(i_0_16668,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10014]),
[final] ).
cnf(i_0_16669,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10015]),
[final] ).
cnf(i_0_16670,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10016]),
[final] ).
cnf(i_0_16671,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10017]),
[final] ).
cnf(i_0_16672,plain,
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10018]),
[final] ).
cnf(i_0_16673,plain,
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10019]),
[final] ).
cnf(i_0_16674,plain,
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10020]),
[final] ).
cnf(i_0_16675,plain,
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10021]),
[final] ).
cnf(i_0_16676,plain,
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10022]),
[final] ).
cnf(i_0_16677,plain,
( c_SMT_Oz3div(X2,X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9739]),
[final] ).
cnf(i_0_16678,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10023]),
[final] ).
cnf(i_0_16679,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10024]),
[final] ).
cnf(i_0_16680,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) = c_Int_OMin
| X1 != c_Int_OMin ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10025,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16681,plain,
( c_Int_OMin = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)
| c_Int_OMin != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10026,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16682,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))) = c_List_Olist_ONil(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[i_0_10027,c_0_6135]),
[final] ).
cnf(i_0_16683,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1) = X2,
inference(split_conjunct,[status(thm)],[i_0_10028]),
[final] ).
cnf(i_0_16684,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_10029]),
[final] ).
cnf(i_0_16685,plain,
( c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)) = X2
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_10030]),
[final] ).
cnf(i_0_16686,plain,
( c_Relation_Osingle__valued(X3,X2,X1)
| esk379_3(X1,X2,X3) != esk380_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6930]),
[final] ).
cnf(i_0_16687,plain,
( c_Relation_Ototal__on(X3,X2,X1)
| esk369_3(X1,X2,X3) != esk370_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6756]),
[final] ).
cnf(i_0_16688,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10031]),
[final] ).
cnf(i_0_16689,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10032]),
[final] ).
cnf(i_0_16690,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10033]),
[final] ).
cnf(i_0_16691,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10034]),
[final] ).
cnf(i_0_16692,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9114]),
[final] ).
cnf(i_0_16693,plain,
( c_Wellfounded_OwfP(X1,X2)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk326_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10035]),
[final] ).
cnf(i_0_16694,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10036]),
[final] ).
cnf(i_0_16695,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))),
inference(rw,[status(thm)],[i_0_10037,c_0_6135]),
[final] ).
cnf(i_0_16696,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_9466]),
[final] ).
cnf(i_0_16697,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10038]),
[final] ).
cnf(i_0_16698,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10039]),
[final] ).
cnf(i_0_16699,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
| X1 != X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_9774]),
[final] ).
cnf(i_0_16700,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),
inference(split_conjunct,[status(thm)],[i_0_10040]),
[final] ).
cnf(i_0_16701,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X1))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_10041]),
[final] ).
cnf(i_0_16702,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10042]),
[final] ).
cnf(i_0_16703,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10043]),
[final] ).
cnf(i_0_16704,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10044]),
[final] ).
cnf(i_0_16705,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9566]),
[final] ).
cnf(i_0_16706,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10045]),
[final] ).
cnf(i_0_16707,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10046]),
[final] ).
cnf(i_0_16708,plain,
( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10047]),
[final] ).
cnf(i_0_16709,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10048]),
[final] ).
cnf(i_0_16710,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10049]),
[final] ).
cnf(i_0_16711,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10050]),
[final] ).
cnf(i_0_16712,plain,
hAPP(c_Relation_ODomain(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10051]),
[final] ).
cnf(i_0_16713,plain,
hAPP(c_Relation_ORange(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10052]),
[final] ).
cnf(i_0_16714,plain,
hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),hAPP(X3,X4)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10053]),
[final] ).
cnf(i_0_16715,plain,
hAPP(c_Product__Type_Ofst(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10054]),
[final] ).
cnf(i_0_16716,plain,
hAPP(c_Product__Type_Osnd(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)) = X4,
inference(split_conjunct,[status(thm)],[i_0_10055]),
[final] ).
cnf(i_0_16717,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10056,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16718,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk34_2(X2,X1)) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9683]),
[final] ).
cnf(i_0_16719,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk43_2(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10057]),
[final] ).
cnf(i_0_16720,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10058]),
[final] ).
cnf(i_0_16721,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk40_2(X1,X2))
| hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9664]),
[final] ).
cnf(i_0_16722,plain,
c_Set_Othe__elem(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2,
inference(split_conjunct,[status(thm)],[i_0_10059]),
[final] ).
cnf(i_0_16723,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2))) = X1
| c_List_Obutlast(X2,X1) != X3
| c_List_Olast(X2,X1) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_9806]),
[final] ).
cnf(i_0_16724,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10060]),
[final] ).
cnf(i_0_16725,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10061]),
[final] ).
cnf(i_0_16726,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10062]),
[final] ).
cnf(i_0_16727,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9565]),
[final] ).
cnf(i_0_16728,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10063]),
[final] ).
cnf(i_0_16729,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10064]),
[final] ).
cnf(i_0_16730,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9563]),
[final] ).
cnf(i_0_16731,plain,
( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X5),X1),X2),X3) = X1
| hAPP(X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_10065]),
[final] ).
cnf(i_0_16732,plain,
( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X5),X1),X2),X3) = X1
| hAPP(X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_9616]),
[final] ).
cnf(i_0_16733,plain,
hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2),
inference(rw,[status(thm)],[i_0_10066,c_0_6135]),
[final] ).
cnf(i_0_16734,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),
inference(rw,[status(thm)],[i_0_10067,c_0_6135]),
[final] ).
cnf(i_0_16735,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Groups_Oabs__class_Oabs(X2),X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9571]),
[final] ).
cnf(i_0_16736,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X3))
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10068]),
[final] ).
cnf(i_0_16737,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10069]),
[final] ).
cnf(i_0_16738,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10070]),
[final] ).
cnf(i_0_16739,plain,
c_Option_Ooption_Ooption__size(X1,X2,hAPP(c_Option_Ooption_OSome(X1),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_10071]),
[final] ).
cnf(i_0_16740,plain,
c_List_Opartition(X1,X2,c_List_Olist_ONil(X1)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_10072]),
[final] ).
cnf(i_0_16741,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),c_Int_OMin) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10073,c_0_6169]),c_0_6016]),
[final] ).
cnf(i_0_16742,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9804]),
[final] ).
cnf(i_0_16743,plain,
( c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9864]),
[final] ).
cnf(i_0_16744,plain,
( c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9865]),
[final] ).
cnf(i_0_16745,plain,
hAPP(hAPP(c_List_Otake(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_10074]),
[final] ).
cnf(i_0_16746,plain,
( c_Wellfounded_Owf(X3,hAPP(hAPP(c_Relation_Oinv__image(X1,X3),X2),X4))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10075]),
[final] ).
cnf(i_0_16747,plain,
( c_FunDef_Oreduction__pair(X3,hAPP(hAPP(c_FunDef_Orp__inv__image(X1,X3),X2),X4))
| ~ c_FunDef_Oreduction__pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10076]),
[final] ).
cnf(i_0_16748,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10077]),
[final] ).
cnf(i_0_16749,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X2) = c_Divides_Odiv__class_Omod(X1,X3,X2)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10078]),
[final] ).
cnf(i_0_16750,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10079]),
[final] ).
cnf(i_0_16751,plain,
( hAPP(hAPP(c_List_Onth(X1),X3),X2) = X4
| hAPP(hAPP(c_List_Odrop(X1),X2),X3) != hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_10080]),
[final] ).
cnf(i_0_16752,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10081]),
[final] ).
cnf(i_0_16753,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10082]),
[final] ).
cnf(i_0_16754,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10083]),
[final] ).
cnf(i_0_16755,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10084]),
[final] ).
cnf(i_0_16756,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10085]),
[final] ).
cnf(i_0_16757,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10086]),
[final] ).
cnf(i_0_16758,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10087]),
[final] ).
cnf(i_0_16759,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_10088]),
[final] ).
cnf(i_0_16760,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_10089,c_0_6016]),
[final] ).
cnf(i_0_16761,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X3)))
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_8118]),
[final] ).
cnf(i_0_16762,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10090]),
[final] ).
cnf(i_0_16763,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10091]),
[final] ).
cnf(i_0_16764,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10092]),
[final] ).
cnf(i_0_16765,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,esk29_2(X2,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9863]),
[final] ).
cnf(i_0_16766,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10093]),
[final] ).
cnf(i_0_16767,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10094]),
[final] ).
cnf(i_0_16768,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10095]),
[final] ).
cnf(i_0_16769,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10096]),
[final] ).
cnf(i_0_16770,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10097]),
[final] ).
cnf(i_0_16771,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10098]),
[final] ).
cnf(i_0_16772,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10099]),
[final] ).
cnf(i_0_16773,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10100]),
[final] ).
cnf(i_0_16774,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10101]),
[final] ).
cnf(i_0_16775,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10102]),
[final] ).
cnf(i_0_16776,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10103]),
[final] ).
cnf(i_0_16777,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk46_1(X1)))
| hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9437]),
[final] ).
cnf(i_0_16778,plain,
( hBOOL(hAPP(X1,X2))
| hAPP(c_List_Ofilter(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(c_List_Ofilter(X3,X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_9624]),
[final] ).
cnf(i_0_16779,plain,
hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(c_List_Otl(X1),X3)) = hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_10104]),
[final] ).
cnf(i_0_16780,plain,
hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)) = hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(c_List_Otl(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_10105]),
[final] ).
cnf(i_0_16781,plain,
hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_10106]),
[final] ).
cnf(i_0_16782,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1),
inference(split_conjunct,[status(thm)],[i_0_10107]),
[final] ).
cnf(i_0_16783,plain,
( hAPP(hAPP(c_List_Odrop(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_9392]),
[final] ).
cnf(i_0_16784,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10108]),
[final] ).
cnf(i_0_16785,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9960]),
[final] ).
cnf(i_0_16786,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| X3 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9959]),
[final] ).
cnf(i_0_16787,plain,
hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10109]),
[final] ).
cnf(i_0_16788,plain,
( hBOOL(hAPP(X1,esk350_2(X2,X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10110]),
[final] ).
cnf(i_0_16789,plain,
hAPP(c_Product__Type_Ofst(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Opartition(X1,X2,X3)) = hAPP(c_List_Ofilter(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_10111]),
[final] ).
cnf(i_0_16790,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10112]),
[final] ).
cnf(i_0_16791,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)),
inference(split_conjunct,[status(thm)],[i_0_10113]),
[final] ).
cnf(i_0_16792,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_10114]),
[final] ).
cnf(i_0_16793,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_10115]),
[final] ).
cnf(i_0_16794,plain,
( c_Smallcheck_Osmall_H(X3,X1,X2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7759]),
[final] ).
cnf(i_0_16795,plain,
( hAPP(c_Int_Onat,X1) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10116]),
[final] ).
cnf(i_0_16796,plain,
( X2 = hAPP(c_Int_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X1 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10117]),
[final] ).
cnf(i_0_16797,plain,
( c_Nitpick_Onorm__frac(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_6763]),
[final] ).
cnf(i_0_16798,plain,
( c_Nitpick_Onorm__frac(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_6763]),
[final] ).
cnf(i_0_16799,plain,
( X2 = X3
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10118]),
[final] ).
cnf(i_0_16800,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X1)),X3),X4) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(X3,X4))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10119]),
[final] ).
cnf(i_0_16801,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X1)),X3),X4) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(X3,X4))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10120]),
[final] ).
cnf(i_0_16802,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1)) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10121]),
[final] ).
cnf(i_0_16803,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1)) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10122]),
[final] ).
cnf(i_0_16804,plain,
( c_Nat__Transfer_Otsub(X2,X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10123]),
[final] ).
cnf(i_0_16805,plain,
( c_Nat__Transfer_Otsub(X2,X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10124]),
[final] ).
cnf(i_0_16806,plain,
hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10125]),
[final] ).
cnf(i_0_16807,plain,
c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X1,X2) = c_Smallcheck_Ofull__small_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2))),
inference(split_conjunct,[status(thm)],[i_0_10126]),
[final] ).
cnf(i_0_16808,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X2
| X1 != hAPP(c_Int_Onat,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10127]),
[final] ).
cnf(i_0_16809,plain,
( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hAPP(c_Int_Onat,X1) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10116]),
[final] ).
cnf(i_0_16810,plain,
( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X2 != hAPP(c_Int_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10117]),
[final] ).
cnf(i_0_16811,plain,
( hAPP(X3,X4) = hAPP(c_Finite__Set_Ofold1(X1,X2),X4)
| ~ c_Big__Operators_Osemilattice__big(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_10128]),
[final] ).
cnf(i_0_16812,plain,
( hAPP(X3,X4) = hAPP(c_Finite__Set_Ofold1(X1,X2),X4)
| ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_10129]),
[final] ).
cnf(i_0_16813,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10130]),
[final] ).
cnf(i_0_16814,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10131]),
[final] ).
cnf(i_0_16815,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10132]),
[final] ).
cnf(i_0_16816,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10133]),
[final] ).
cnf(i_0_16817,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10134]),
[final] ).
cnf(i_0_16818,plain,
( X1 = X2
| c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3)) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),X4) ),
inference(rw,[status(thm)],[i_0_10135,c_0_6135]),
[final] ).
cnf(i_0_16819,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_10136]),
[final] ).
cnf(i_0_16820,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),c_Int_OMin) = c_Int_OMin,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10137,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16821,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9988]),
[final] ).
cnf(i_0_16822,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1),X2),hAPP(c_COMBK(X1,X3),X4)) = X4
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10138]),
[final] ).
cnf(i_0_16823,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1),X2),hAPP(c_COMBK(X1,X3),X4)) = X4
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10139]),
[final] ).
cnf(i_0_16824,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10140]),
[final] ).
cnf(i_0_16825,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| c_SMT_Oz3mod(X2,X1) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9979]),
[final] ).
cnf(i_0_16826,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10141]),
[final] ).
cnf(i_0_16827,plain,
( c_List_Olinorder__class_Osorted(X1,X2)
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7746]),
[final] ).
cnf(i_0_16828,plain,
( c_List_Olinorder__class_Osorted(X1,X2)
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7746]),
[final] ).
cnf(i_0_16829,plain,
( c_List_Olinorder__class_Osorted(X1,X2)
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8476]),
[final] ).
cnf(i_0_16830,plain,
( c_List_Olinorder__class_Osorted(X1,X2)
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8477]),
[final] ).
cnf(i_0_16831,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))),
inference(rw,[status(thm)],[i_0_10142,c_0_7027]),
[final] ).
cnf(i_0_16832,plain,
c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
inference(split_conjunct,[status(thm)],[fact_equiv__intrel]),
[final] ).
cnf(i_0_16833,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))),
inference(split_conjunct,[status(thm)],[i_0_10143]),
[final] ).
cnf(i_0_16834,plain,
c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)) = c_List_Otranspose(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10144]),
[final] ).
cnf(i_0_16835,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk447_1(X1)),hAPP(c_List_Oset(tc_Nat_Onat),X1)))
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_9772]),
[final] ).
cnf(i_0_16836,plain,
( hBOOL(hAPP(X1,X2))
| c_List_Oremove1(X3,X2,hAPP(c_List_Ofilter(X3,X1),X4)) = hAPP(c_List_Ofilter(X3,X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_10145]),
[final] ).
cnf(i_0_16837,plain,
hAPP(c_Relation_OField(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10146]),
[final] ).
cnf(i_0_16838,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9745]),
[final] ).
cnf(i_0_16839,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10147]),
[final] ).
cnf(i_0_16840,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10148]),
[final] ).
cnf(i_0_16841,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) != X3
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9828]),
[final] ).
cnf(i_0_16842,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9829]),
[final] ).
cnf(i_0_16843,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10149]),
[final] ).
cnf(i_0_16844,plain,
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10150]),
[final] ).
cnf(i_0_16845,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_10151]),
[final] ).
cnf(i_0_16846,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_10152]),
[final] ).
cnf(i_0_16847,plain,
hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X1),X2) = c_Smallcheck_Osmall_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2))),
inference(split_conjunct,[status(thm)],[i_0_10153]),
[final] ).
cnf(i_0_16848,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Obutlast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = hAPP(hAPP(c_List_Oappend(X2),X3),c_List_Obutlast(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10154]),
[final] ).
cnf(i_0_16849,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Obutlast(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10155]),
[final] ).
cnf(i_0_16850,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10156]),
[final] ).
cnf(i_0_16851,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10157]),
[final] ).
cnf(i_0_16852,plain,
hAPP(c_Relation_OImage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10158]),
[final] ).
cnf(i_0_16853,plain,
hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10159]),
[final] ).
cnf(i_0_16854,plain,
( c_Relation_Orefl__on(tc_List_Olist(X1),c_List_Olists(X1,X2),c_List_Olistrel(X1,X3))
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_10160]),
[final] ).
cnf(i_0_16855,plain,
( c_Equiv__Relations_Oequiv(tc_List_Olist(X1),c_List_Olists(X1,X2),c_List_Olistrel(X1,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_10161]),
[final] ).
cnf(i_0_16856,plain,
( hAPP(hAPP(c_List_Onth(X1),X2),esk450_2(X2,X1)) = hAPP(hAPP(c_List_Onth(X1),X2),esk451_2(X2,X1))
| hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8201]),
[final] ).
cnf(i_0_16857,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10162]),
[final] ).
cnf(i_0_16858,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_10163]),
[final] ).
cnf(i_0_16859,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) != X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10006]),
[final] ).
cnf(i_0_16860,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) != X3
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10008]),
[final] ).
cnf(i_0_16861,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10011]),
[final] ).
cnf(i_0_16862,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10014]),
[final] ).
cnf(i_0_16863,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
| ~ class_Rings_Odvd(X1)
| X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_10164]),
[final] ).
cnf(i_0_16864,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))),
inference(rw,[status(thm)],[i_0_10165,c_0_7027]),
[final] ).
cnf(i_0_16865,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10166]),
[final] ).
cnf(i_0_16866,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10167]),
[final] ).
cnf(i_0_16867,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10168]),
[final] ).
cnf(i_0_16868,plain,
( hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = hAPP(hAPP(c_List_Oappend(X2),X1),X5)
| X1 != c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_6805]),
[final] ).
cnf(i_0_16869,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)
| X1 != c_List_Olist_ONil(X2)
| X3 != hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_6806]),
[final] ).
cnf(i_0_16870,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = X2,
inference(split_conjunct,[status(thm)],[i_0_10169]),
[final] ).
cnf(i_0_16871,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X2,
inference(split_conjunct,[status(thm)],[i_0_10170]),
[final] ).
cnf(i_0_16872,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X2,
inference(split_conjunct,[status(thm)],[i_0_10171]),
[final] ).
cnf(i_0_16873,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10172]),
[final] ).
cnf(i_0_16874,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10173]),
[final] ).
cnf(i_0_16875,plain,
c_Map_Odom(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10174]),
[final] ).
cnf(i_0_16876,plain,
c_Map_Oran(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10175]),
[final] ).
cnf(i_0_16877,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10176]),
[final] ).
cnf(i_0_16878,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9693]),
[final] ).
cnf(i_0_16879,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9694]),
[final] ).
cnf(i_0_16880,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9695]),
[final] ).
cnf(i_0_16881,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9696]),
[final] ).
cnf(i_0_16882,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))
| c_Random_Ominus__shift(X3,X1,X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_9274]),
[final] ).
cnf(i_0_16883,plain,
hAPP(hAPP(c_List_Olist__update(X1,X2),X3),hAPP(hAPP(c_List_Onth(X1),X2),X3)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10177]),
[final] ).
cnf(i_0_16884,plain,
( X2 = X3
| X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10178]),
[final] ).
cnf(i_0_16885,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10179]),
[final] ).
cnf(i_0_16886,plain,
hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Obutlast(X1,X3)) = c_List_Obutlast(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_10180]),
[final] ).
cnf(i_0_16887,plain,
c_List_Obutlast(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3)) = hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Obutlast(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_10181]),
[final] ).
cnf(i_0_16888,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1))
| X1 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10182]),
[final] ).
cnf(i_0_16889,plain,
( hAPP(c_Relation_ODomain(X2,X3),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10183]),
[final] ).
cnf(i_0_16890,plain,
( hAPP(c_Relation_ORange(X2,X3),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10184]),
[final] ).
cnf(i_0_16891,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_10185]),
[final] ).
cnf(i_0_16892,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10186]),
[final] ).
cnf(i_0_16893,plain,
( hAPP(c_Set_Oimage(X2,X3,X4),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9876]),
[final] ).
cnf(i_0_16894,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X2,X3,X4),X1)
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9877]),
[final] ).
cnf(i_0_16895,plain,
( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk39_1(X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9760]),
[final] ).
cnf(i_0_16896,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X3),c_Option_Oset(X2,X1)))
| X1 != hAPP(c_Option_Ooption_OSome(X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_9841]),
[final] ).
cnf(i_0_16897,plain,
( c_Nat__Transfer_Onat__set(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk130_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9869]),
[final] ).
cnf(i_0_16898,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| X1 = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10187]),
[final] ).
cnf(i_0_16899,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10188]),
[final] ).
cnf(i_0_16900,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10189]),
[final] ).
cnf(i_0_16901,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),
inference(split_conjunct,[status(thm)],[i_0_10190]),
[final] ).
cnf(i_0_16902,plain,
( hBOOL(hAPP(X1,esk45_1(X1)))
| ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9582]),
[final] ).
cnf(i_0_16903,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5923]),
[final] ).
cnf(i_0_16904,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J]),
[final] ).
cnf(i_0_16905,plain,
( c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)) = X3
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X3)) ),
inference(rw,[status(thm)],[i_0_10191,c_0_7027]),
[final] ).
cnf(i_0_16906,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10192]),
[final] ).
cnf(i_0_16907,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[i_0_10193]),
[final] ).
cnf(i_0_16908,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| c_Groups_Osgn__class_Osgn(X1,X2) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9985]),
[final] ).
cnf(i_0_16909,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10194]),
[final] ).
cnf(i_0_16910,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10195]),
[final] ).
cnf(i_0_16911,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk51_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_9675]),
[final] ).
cnf(i_0_16912,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_10196]),
[final] ).
cnf(i_0_16913,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_10197]),
[final] ).
cnf(i_0_16914,plain,
hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3) = hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(c_List_Otl(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_10198]),
[final] ).
cnf(i_0_16915,plain,
( X3 = hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))
| c_Map_Odom(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10199]),
[final] ).
cnf(i_0_16916,plain,
( X1 = hAPP(c_Nat_OSuc,esk35_1(X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10200]),
[final] ).
cnf(i_0_16917,plain,
( X1 = hAPP(c_Nat_OSuc,esk30_1(X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10201]),
[final] ).
cnf(i_0_16918,plain,
( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10202]),
[final] ).
cnf(i_0_16919,plain,
( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omax(X1)),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10203]),
[final] ).
cnf(i_0_16920,plain,
( c_Finite__Set_Ofun__left__comm(X1,tc_List_Olist(X1),c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10204]),
[final] ).
cnf(i_0_16921,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10205]),
[final] ).
cnf(i_0_16922,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10001]),
[final] ).
cnf(i_0_16923,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Otl(X1),X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10206]),
[final] ).
cnf(i_0_16924,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10002]),
[final] ).
cnf(i_0_16925,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10207]),
[final] ).
cnf(i_0_16926,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_10208]),
[final] ).
cnf(i_0_16927,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))
| hAPP(c_Relation_ODomain(X1,X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10183]),
[final] ).
cnf(i_0_16928,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))
| hAPP(c_Relation_ORange(X1,X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10184]),
[final] ).
cnf(i_0_16929,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),X2))
| hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10209]),
[final] ).
cnf(i_0_16930,plain,
c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10210]),
[final] ).
cnf(i_0_16931,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| c_Groups_Osgn__class_Osgn(X1,X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Osgn__if(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9967]),
[final] ).
cnf(i_0_16932,plain,
( X3 = hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))
| hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)) != hAPP(c_List_Orev(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10211]),
[final] ).
cnf(i_0_16933,plain,
( X2 = hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))
| hAPP(c_List_Orev(X1),X2) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10212]),
[final] ).
cnf(i_0_16934,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_10213]),
[final] ).
cnf(i_0_16935,plain,
c_List_Olistrel1(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10214]),
[final] ).
cnf(i_0_16936,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10215]),
[final] ).
cnf(i_0_16937,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = c_List_Olist_ONil(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[i_0_10216,c_0_6135]),
[final] ).
cnf(i_0_16938,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J]),
[final] ).
cnf(i_0_16939,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9286]),
[final] ).
cnf(i_0_16940,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10217]),
[final] ).
cnf(i_0_16941,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9799]),
[final] ).
cnf(i_0_16942,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9800]),
[final] ).
cnf(i_0_16943,plain,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_Equiv__Relations_Oequivp(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_9858]),
[final] ).
cnf(i_0_16944,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10218]),
[final] ).
cnf(i_0_16945,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_10219]),
[final] ).
cnf(i_0_16946,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_10220]),
[final] ).
cnf(i_0_16947,plain,
( hAPP(c_Finite__Set_Ocard(X1),esk191_3(X2,X3,X1)) = X2
| hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7857]),
[final] ).
cnf(i_0_16948,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_10221]),
[final] ).
cnf(i_0_16949,plain,
c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),
inference(rw,[status(thm)],[i_0_10222,c_0_6135]),
[final] ).
cnf(i_0_16950,plain,
( hBOOL(hAPP(X3,X2))
| X1 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)
| ~ hBOOL(hAPP(X3,hAPP(c_Int_Onat,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9664]),
[final] ).
cnf(i_0_16951,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_9895]),
[final] ).
cnf(i_0_16952,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_9566]),
[final] ).
cnf(i_0_16953,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_9780]),
[final] ).
cnf(i_0_16954,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10041]),
[final] ).
cnf(i_0_16955,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10041]),
[final] ).
cnf(i_0_16956,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10223]),
[final] ).
cnf(i_0_16957,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_10224]),
[final] ).
cnf(i_0_16958,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_10225]),
[final] ).
cnf(i_0_16959,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9614]),
[final] ).
cnf(i_0_16960,plain,
( X2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk40_2(X2,X1))
| hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_9664]),
[final] ).
cnf(i_0_16961,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_10226]),
[final] ).
cnf(i_0_16962,plain,
hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_greaterThan__0]),
[final] ).
cnf(i_0_16963,plain,
c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X2)),
inference(rw,[status(thm)],[i_0_10227,c_0_7214]),
[final] ).
cnf(i_0_16964,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Rings_Olinordered__idom(X1)
| hAPP(c_Groups_Oabs__class_Oabs(X1),X2) != hAPP(c_Groups_Oabs__class_Oabs(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10228]),
[final] ).
cnf(i_0_16965,plain,
( X3 = X4
| X1 != X2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X1),X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),X4)
| ~ class_Groups_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_10229]),
[final] ).
cnf(i_0_16966,plain,
( X3 = X4
| X1 != X2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),X4) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X1),X2)
| ~ class_Groups_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_10229]),
[final] ).
cnf(i_0_16967,plain,
hAPP(hAPP(c_Option_Omap(X1,X2),X3),hAPP(c_Option_Ooption_OSome(X1),X4)) = hAPP(c_Option_Ooption_OSome(X2),hAPP(X3,X4)),
inference(split_conjunct,[status(thm)],[i_0_10230]),
[final] ).
cnf(i_0_16968,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Ofilter(X1,X2),X3)) = hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Orev(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_10231]),
[final] ).
cnf(i_0_16969,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_9744]),
[final] ).
cnf(i_0_16970,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10232]),
[final] ).
cnf(i_0_16971,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_9414]),
[final] ).
cnf(i_0_16972,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10233]),
[final] ).
cnf(i_0_16973,plain,
( c_Map_Odom(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != hAPP(c_COMBK(tc_Option_Ooption(X2),X3),c_Option_Ooption_ONone(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10199]),
[final] ).
cnf(i_0_16974,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10234]),
[final] ).
cnf(i_0_16975,plain,
( c_Random_Olog(X1,X2) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
inference(split_conjunct,[status(thm)],[i_0_9174]),
[final] ).
cnf(i_0_16976,plain,
( hBOOL(hAPP(hAPP(X1,esk259_1(X1)),esk260_1(X1)))
| hAPP(X1,esk259_1(X1)) = hAPP(X1,esk260_1(X1))
| c_Equiv__Relations_Oequivp(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_9858]),
[final] ).
cnf(i_0_16977,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10235]),
[final] ).
cnf(i_0_16978,plain,
( X2 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10236]),
[final] ).
cnf(i_0_16979,plain,
( X2 = X4
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10237]),
[final] ).
cnf(i_0_16980,plain,
( X3 = X4
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_10238]),
[final] ).
cnf(i_0_16981,plain,
( X3 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_10239]),
[final] ).
cnf(i_0_16982,plain,
( X3 = X4
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10240]),
[final] ).
cnf(i_0_16983,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X1,X3,X4) != c_Com_Ocom_OLocal(X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10241]),
[final] ).
cnf(i_0_16984,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X3,X1,X4) != c_Com_Ocom_OLocal(X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10241]),
[final] ).
cnf(i_0_16985,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X3,X4,X1) != c_Com_Ocom_OLocal(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10241]),
[final] ).
cnf(i_0_16986,plain,
( X1 = X2
| c_Com_Ocom_OCond(X1,X3,X4) != c_Com_Ocom_OCond(X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10242]),
[final] ).
cnf(i_0_16987,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X1,X4) != c_Com_Ocom_OCond(X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10242]),
[final] ).
cnf(i_0_16988,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X4,X1) != c_Com_Ocom_OCond(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10242]),
[final] ).
cnf(i_0_16989,plain,
( X1 = X2
| c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OCall(X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10243]),
[final] ).
cnf(i_0_16990,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X1,X4) != c_Com_Ocom_OCall(X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10243]),
[final] ).
cnf(i_0_16991,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X4,X1) != c_Com_Ocom_OCall(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10243]),
[final] ).
cnf(i_0_16992,plain,
( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_10244]),
[final] ).
cnf(i_0_16993,plain,
( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_10245]),
[final] ).
cnf(i_0_16994,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X4,X1,X2) = hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))
| X1 != X2
| X2 != X3
| ~ class_Orderings_Oorder(X4) ),
inference(split_conjunct,[status(thm)],[i_0_9883]),
[final] ).
cnf(i_0_16995,plain,
( c_Nat__Transfer_Ois__nat(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10246]),
[final] ).
cnf(i_0_16996,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))
| c_Nitpick_Ounknown(tc_HOL_Obool)
| ~ c_Nitpick_Owf_H(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9852]),
[final] ).
cnf(i_0_16997,plain,
( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6997]),
[final] ).
cnf(i_0_16998,plain,
( hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)) = hAPP(c_List_Orev(X2),X1)
| X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10211]),
[final] ).
cnf(i_0_16999,plain,
( hAPP(c_List_Orev(X2),X1) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))
| X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10212]),
[final] ).
cnf(i_0_17000,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10247]),
[final] ).
cnf(i_0_17001,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OCond(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10248]),
[final] ).
cnf(i_0_17002,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10249]),
[final] ).
cnf(i_0_17003,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OLocal(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10250]),
[final] ).
cnf(i_0_17004,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OLocal(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10251]),
[final] ).
cnf(i_0_17005,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10252]),
[final] ).
cnf(i_0_17006,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OCond(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10253]),
[final] ).
cnf(i_0_17007,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10166]),
[final] ).
cnf(i_0_17008,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10130]),
[final] ).
cnf(i_0_17009,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onat,X1))
| ~ class_Rings_Oring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9344]),
[final] ).
cnf(i_0_17010,plain,
hAPP(c_List_Olexn(X1,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10254]),
[final] ).
cnf(i_0_17011,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
inference(split_conjunct,[status(thm)],[i_0_10255]),
[final] ).
cnf(i_0_17012,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
inference(split_conjunct,[status(thm)],[i_0_10256]),
[final] ).
cnf(i_0_17013,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10257]),
[final] ).
cnf(i_0_17014,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1)) = hAPP(c_Int_Onat,X2)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_6416]),
[final] ).
cnf(i_0_17015,plain,
c_Wellfounded_Owf(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_10258]),
[final] ).
cnf(i_0_17016,plain,
( hAPP(hAPP(c_Option_Omap(X2,X6),X4),X1) = hAPP(c_Option_Ooption_OSome(X6),X5)
| X1 != hAPP(c_Option_Ooption_OSome(X2),X3)
| hAPP(X4,X3) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_7169]),
[final] ).
cnf(i_0_17017,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_10259]),
[final] ).
cnf(i_0_17018,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X1),X3)
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10038]),
[final] ).
cnf(i_0_17019,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X1),X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10039]),
[final] ).
cnf(i_0_17020,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10260]),
[final] ).
cnf(i_0_17021,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10057]),
[final] ).
cnf(i_0_17022,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10261]),
[final] ).
cnf(i_0_17023,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10262]),
[final] ).
cnf(i_0_17024,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9996]),
[final] ).
cnf(i_0_17025,plain,
( X1 = c_List_Olist_ONil(X2)
| hBOOL(hAPP(c_List_Odistinct(X2),c_List_Obutlast(X2,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10263]),
[final] ).
cnf(i_0_17026,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_10264]),
[final] ).
cnf(i_0_17027,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk48_1(X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9599]),
[final] ).
cnf(i_0_17028,plain,
( X1 = X2
| hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4) != hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5) ),
inference(split_conjunct,[status(thm)],[i_0_10265]),
[final] ).
cnf(i_0_17029,plain,
( X1 = X2
| hAPP(hAPP(c_List_Olist_OCons(X3),X4),X1) != hAPP(hAPP(c_List_Olist_OCons(X3),X5),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10265]),
[final] ).
cnf(i_0_17030,plain,
( X2 = X4
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10266]),
[final] ).
cnf(i_0_17031,plain,
( X3 = X4
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != hAPP(hAPP(c_List_Oappend(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_10267]),
[final] ).
cnf(i_0_17032,plain,
c_String_Ochar_Ochar__case(X1,X2,hAPP(hAPP(c_String_Ochar_OChar,X3),X4)) = hAPP(hAPP(X2,X3),X4),
inference(split_conjunct,[status(thm)],[i_0_10268]),
[final] ).
cnf(i_0_17033,plain,
c_String_Ochar_Ochar__rec(X1,X2,hAPP(hAPP(c_String_Ochar_OChar,X3),X4)) = hAPP(hAPP(X2,X3),X4),
inference(split_conjunct,[status(thm)],[i_0_10269]),
[final] ).
cnf(i_0_17034,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10270]),
[final] ).
cnf(i_0_17035,plain,
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X2)))
| ~ hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10271]),
[final] ).
cnf(i_0_17036,plain,
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X2)))
| ~ hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10272]),
[final] ).
cnf(i_0_17037,plain,
( c_List_Oupto(X2,X1) = c_List_Olist_ONil(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10273]),
[final] ).
cnf(i_0_17038,plain,
( c_Random_Olog(X2,X1) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9174]),
[final] ).
cnf(i_0_17039,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_number__of2]),
[final] ).
cnf(i_0_17040,plain,
( hAPP(hAPP(c_List_Otake(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)) = c_List_Olist_ONil(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8601]),
[final] ).
cnf(i_0_17041,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1)),
inference(split_conjunct,[status(thm)],[i_0_10274]),
[final] ).
cnf(i_0_17042,plain,
( c_Quickcheck_Obeyond(X1,X2) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10275]),
[final] ).
cnf(i_0_17043,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_10276]),
[final] ).
cnf(i_0_17044,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10277]),
[final] ).
cnf(i_0_17045,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
inference(split_conjunct,[status(thm)],[i_0_10278]),
[final] ).
cnf(i_0_17046,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_List_Orotate1(X1)) = c_Fun_Oid(tc_List_Olist(X1)),
inference(rw,[status(thm)],[i_0_10279,c_0_6670]),
[final] ).
cnf(i_0_17047,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10280]),
[final] ).
cnf(i_0_17048,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10281]),
[final] ).
cnf(i_0_17049,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10282]),
[final] ).
cnf(i_0_17050,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10283]),
[final] ).
cnf(i_0_17051,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_10284]),
[final] ).
cnf(i_0_17052,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_10285]),
[final] ).
cnf(i_0_17053,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9608]),
[final] ).
cnf(i_0_17054,plain,
( hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(X1,esk46_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9437]),
[final] ).
cnf(i_0_17055,plain,
hAPP(hAPP(c_List_Odrop(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10286]),
[final] ).
cnf(i_0_17056,plain,
( c_List_Oremove1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = X4
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9638]),
[final] ).
cnf(i_0_17057,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1) != hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9605]),
[final] ).
cnf(i_0_17058,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9606]),
[final] ).
cnf(i_0_17059,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_10287]),
[final] ).
cnf(i_0_17060,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)),
inference(split_conjunct,[status(thm)],[i_0_10288]),
[final] ).
cnf(i_0_17061,plain,
hAPP(c_Finite__Set_Ofold1(X1,X2),X3) = c_HOL_OThe(X1,c_Finite__Set_Ofold1Set(X1,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_10289]),
[final] ).
cnf(i_0_17062,plain,
( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk54_2(X2,X1))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10290]),
[final] ).
cnf(i_0_17063,plain,
( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk60_2(X2,X1))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10291]),
[final] ).
cnf(i_0_17064,plain,
( c_Nat__Transfer_Ois__nat(X2)
| ~ c_Nat__Transfer_Onat__set(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10292]),
[final] ).
cnf(i_0_17065,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10293]),
[final] ).
cnf(i_0_17066,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_9947]),
[final] ).
cnf(i_0_17067,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_10294]),
[final] ).
cnf(i_0_17068,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_10295]),
[final] ).
cnf(i_0_17069,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_10296]),
[final] ).
cnf(i_0_17070,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10297]),
[final] ).
cnf(i_0_17071,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10176]),
[final] ).
cnf(i_0_17072,plain,
hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = hAPP(c_Relation_ORange(X2,X1),X3),
inference(split_conjunct,[status(thm)],[i_0_10298]),
[final] ).
cnf(i_0_17073,plain,
hAPP(c_Relation_ORange(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = hAPP(c_Relation_ODomain(X2,X1),X3),
inference(split_conjunct,[status(thm)],[i_0_10299]),
[final] ).
cnf(i_0_17074,plain,
c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) = hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10300]),
[final] ).
cnf(i_0_17075,plain,
hAPP(c_Relation_ORange(X1,X2),X3) = hAPP(c_Relation_ODomain(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_10301]),
[final] ).
cnf(i_0_17076,plain,
( X2 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) != c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10302]),
[final] ).
cnf(i_0_17077,plain,
( X4 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10303]),
[final] ).
cnf(i_0_17078,plain,
( X4 = c_Option_Ooption_ONone(X1)
| hAPP(hAPP(c_Option_Omap(X1,X2),X3),X4) != c_Option_Ooption_ONone(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10304]),
[final] ).
cnf(i_0_17079,plain,
( X4 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Omap(X2,X1),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_10305]),
[final] ).
cnf(i_0_17080,plain,
c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_10306]),
[final] ).
cnf(i_0_17081,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9953]),
[final] ).
cnf(i_0_17082,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10307]),
[final] ).
cnf(i_0_17083,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10308]),
[final] ).
cnf(i_0_17084,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10309]),
[final] ).
cnf(i_0_17085,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10310]),
[final] ).
cnf(i_0_17086,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10311]),
[final] ).
cnf(i_0_17087,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10162]),
[final] ).
cnf(i_0_17088,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10312]),
[final] ).
cnf(i_0_17089,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10313]),
[final] ).
cnf(i_0_17090,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10314]),
[final] ).
cnf(i_0_17091,plain,
( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X3)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10315]),
[final] ).
cnf(i_0_17092,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10316]),
[final] ).
cnf(i_0_17093,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9828]),
[final] ).
cnf(i_0_17094,plain,
( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| hAPP(c_Int_Onumber__class_Onumber__of(X2),X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9829]),
[final] ).
cnf(i_0_17095,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
inference(split_conjunct,[status(thm)],[i_0_10317]),
[final] ).
cnf(i_0_17096,plain,
hAPP(c_Nat_Osize__class_Osize(tc_sum(X1,X2)),hAPP(c_Sum__Type_OInl(X1,X2),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10318]),
[final] ).
cnf(i_0_17097,plain,
hAPP(c_Nat_Osize__class_Osize(tc_sum(X1,X2)),hAPP(c_Sum__Type_OInr(X2,X1),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10319]),
[final] ).
cnf(i_0_17098,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9933]),
[final] ).
cnf(i_0_17099,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9934]),
[final] ).
cnf(i_0_17100,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10320]),
[final] ).
cnf(i_0_17101,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_10321]),
[final] ).
cnf(i_0_17102,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10189]),
[final] ).
cnf(i_0_17103,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_10189]),
[final] ).
cnf(i_0_17104,plain,
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_10272]),
[final] ).
cnf(i_0_17105,plain,
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_10322]),
[final] ).
cnf(i_0_17106,plain,
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10272]),
[final] ).
cnf(i_0_17107,plain,
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10322]),
[final] ).
cnf(i_0_17108,plain,
( hBOOL(hAPP(c_Com_OWT,X2))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_10323]),
[final] ).
cnf(i_0_17109,plain,
( hBOOL(hAPP(c_Com_OWT,X2))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_10324]),
[final] ).
cnf(i_0_17110,plain,
c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(rw,[status(thm)],[i_0_10325,c_0_7027]),
[final] ).
cnf(i_0_17111,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_10326]),
[final] ).
cnf(i_0_17112,plain,
( c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X2,X1)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_10327,c_0_7027]),
[final] ).
cnf(i_0_17113,plain,
( c_List_Olinorder__class_Osorted(X1,c_List_Oremove1(X1,X3,X2))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10328]),
[final] ).
cnf(i_0_17114,plain,
( X1 = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10329]),
[final] ).
cnf(i_0_17115,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10330]),
[final] ).
cnf(i_0_17116,plain,
( X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10331]),
[final] ).
cnf(i_0_17117,plain,
( hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Oappend(X2),X1),X3)) = hAPP(c_List_Ohd(X2),X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10332]),
[final] ).
cnf(i_0_17118,plain,
( hAPP(c_Com_Obody,X1) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk22_1(X1))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10333]),
[final] ).
cnf(i_0_17119,plain,
( hAPP(c_Com_Obody,X1) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk16_1(X1))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10334]),
[final] ).
cnf(i_0_17120,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10335]),
[final] ).
cnf(i_0_17121,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)) = X2
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10336]),
[final] ).
cnf(i_0_17122,plain,
( hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10337]),
[final] ).
cnf(i_0_17123,plain,
( hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_ONats(X1)))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10338]),
[final] ).
cnf(i_0_17124,plain,
( hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10339]),
[final] ).
cnf(i_0_17125,plain,
( hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_Osemiring__1__class_ONats(X1)))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10340]),
[final] ).
cnf(i_0_17126,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10341]),
[final] ).
cnf(i_0_17127,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10342]),
[final] ).
cnf(i_0_17128,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1) = X4
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10314]),
[final] ).
cnf(i_0_17129,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) = X4
| X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10315]),
[final] ).
cnf(i_0_17130,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = X4
| ~ class_Rings_Odivision__ring(X1)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10343]),
[final] ).
cnf(i_0_17131,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X4) = X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
| ~ class_Rings_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10344]),
[final] ).
cnf(i_0_17132,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4) = X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4)
| ~ class_Rings_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10345]),
[final] ).
cnf(i_0_17133,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10315]),
[final] ).
cnf(i_0_17134,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10314]),
[final] ).
cnf(i_0_17135,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_10346]),
[final] ).
cnf(i_0_17136,plain,
( X2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != X4
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10345]),
[final] ).
cnf(i_0_17137,plain,
( X2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) != X4
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10344]),
[final] ).
cnf(i_0_17138,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10347]),
[final] ).
cnf(i_0_17139,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10348]),
[final] ).
cnf(i_0_17140,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10349]),
[final] ).
cnf(i_0_17141,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10350]),
[final] ).
cnf(i_0_17142,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10351]),
[final] ).
cnf(i_0_17143,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10352]),
[final] ).
cnf(i_0_17144,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ c_Equiv__Relations_Oequivp(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_9858]),
[final] ).
cnf(i_0_17145,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10121]),
[final] ).
cnf(i_0_17146,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk51_1(X1)))
| hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9675]),
[final] ).
cnf(i_0_17147,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_10353]),
[final] ).
cnf(i_0_17148,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10354]),
[final] ).
cnf(i_0_17149,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10355]),
[final] ).
cnf(i_0_17150,plain,
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk48_1(X1))))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9599]),
[final] ).
cnf(i_0_17151,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Oappend(X2),X1),X3)) = hAPP(c_List_Ohd(X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10356]),
[final] ).
cnf(i_0_17152,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Oappend(X2),X1),X3)) = hAPP(c_List_Ohd(X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10332]),
[final] ).
cnf(i_0_17153,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = X2
| ~ class_Groups_Oabs__if(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9982]),
[final] ).
cnf(i_0_17154,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10357,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_17155,plain,
( X1 = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10358]),
[final] ).
cnf(i_0_17156,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10359]),
[final] ).
cnf(i_0_17157,plain,
hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_10360]),
[final] ).
cnf(i_0_17158,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Odrop(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10361]),
[final] ).
cnf(i_0_17159,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Otake(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10362]),
[final] ).
cnf(i_0_17160,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_10363]),
[final] ).
cnf(i_0_17161,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_10364]),
[final] ).
cnf(i_0_17162,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_9316]),
[final] ).
cnf(i_0_17163,plain,
hAPP(c_Set_OPow(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10365]),
[final] ).
cnf(i_0_17164,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X3),X4),X2) = c_Groups_Oone__class_Oone(X3)
| ~ class_Groups_Ocomm__monoid__mult(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8514]),
[final] ).
cnf(i_0_17165,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10366]),
[final] ).
cnf(i_0_17166,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10367]),
[final] ).
cnf(i_0_17167,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X2) = c_Groups_Ozero__class_Ozero(X3)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8516]),
[final] ).
cnf(i_0_17168,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10368]),
[final] ).
cnf(i_0_17169,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10369]),
[final] ).
cnf(i_0_17170,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10178]),
[final] ).
cnf(i_0_17171,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10370]),
[final] ).
cnf(i_0_17172,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10371]),
[final] ).
cnf(i_0_17173,plain,
hAPP(c_Set_OPow(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10372]),
[final] ).
cnf(i_0_17174,plain,
c_Relation_OId__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10373]),
[final] ).
cnf(i_0_17175,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10374]),
[final] ).
cnf(i_0_17176,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10375]),
[final] ).
cnf(i_0_17177,plain,
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10376]),
[final] ).
cnf(i_0_17178,plain,
( c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X3,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10377]),
[final] ).
cnf(i_0_17179,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9640]),
[final] ).
cnf(i_0_17180,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
inference(split_conjunct,[status(thm)],[i_0_10378]),
[final] ).
cnf(i_0_17181,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10208]),
[final] ).
cnf(i_0_17182,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10205]),
[final] ).
cnf(i_0_17183,plain,
( c_Big__Operators_Olattice__class_OInf__fin(X1,X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10379]),
[final] ).
cnf(i_0_17184,plain,
( c_Big__Operators_Olinorder__class_OMin(X1,X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10380]),
[final] ).
cnf(i_0_17185,plain,
( c_Big__Operators_Olinorder__class_OMax(X1,X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omax(X1)),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10381]),
[final] ).
cnf(i_0_17186,plain,
( c_Big__Operators_Olattice__class_OSup__fin(X1,X2) = hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2)
| ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10382]),
[final] ).
cnf(i_0_17187,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(split_conjunct,[status(thm)],[i_0_10383]),
[final] ).
cnf(i_0_17188,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10384]),
[final] ).
cnf(i_0_17189,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10385]),
[final] ).
cnf(i_0_17190,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10386]),
[final] ).
cnf(i_0_17191,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10387]),
[final] ).
cnf(i_0_17192,plain,
( esk191_3(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(X3),X2) != hAPP(c_Nat_OSuc,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7857]),
[final] ).
cnf(i_0_17193,plain,
( c_List_Obutlast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Obutlast(X2,X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10154]),
[final] ).
cnf(i_0_17194,plain,
( c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10388]),
[final] ).
cnf(i_0_17195,plain,
( c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10389]),
[final] ).
cnf(i_0_17196,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10390]),
[final] ).
cnf(i_0_17197,plain,
c_List_Osublist(X1,X2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3)) = hAPP(hAPP(c_List_Otake(X1),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_10391]),
[final] ).
cnf(i_0_17198,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10392]),
[final] ).
cnf(i_0_17199,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10393]),
[final] ).
cnf(i_0_17200,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),c_Divides_Odivmod__int(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10394]),
[final] ).
cnf(i_0_17201,plain,
( c_Divides_Opdivmod(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10395]),
[final] ).
cnf(i_0_17202,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10396]),
[final] ).
cnf(i_0_17203,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10388]),
[final] ).
cnf(i_0_17204,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10397]),
[final] ).
cnf(i_0_17205,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = c_List_Olast(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10398]),
[final] ).
cnf(i_0_17206,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = c_List_Olast(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10399]),
[final] ).
cnf(i_0_17207,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nitpick_Onat__gcd(X2,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10400]),
[final] ).
cnf(i_0_17208,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10401]),
[final] ).
cnf(i_0_17209,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_10127]),
[final] ).
cnf(i_0_17210,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_10402]),
[final] ).
cnf(i_0_17211,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(split_conjunct,[status(thm)],[i_0_10403]),
[final] ).
cnf(i_0_17212,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(split_conjunct,[status(thm)],[i_0_10404]),
[final] ).
cnf(i_0_17213,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(split_conjunct,[status(thm)],[i_0_10405]),
[final] ).
cnf(i_0_17214,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(split_conjunct,[status(thm)],[i_0_10406]),
[final] ).
cnf(i_0_17215,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(split_conjunct,[status(thm)],[i_0_10407]),
[final] ).
cnf(i_0_17216,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10112]),
[final] ).
cnf(i_0_17217,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Olist_ONil(X1)),X3) = c_List_Olist_ONil(tc_prod(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10408]),
[final] ).
cnf(i_0_17218,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_10409]),
[final] ).
cnf(i_0_17219,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10410]),
[final] ).
cnf(i_0_17220,plain,
hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10411]),
[final] ).
cnf(i_0_17221,plain,
hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10412]),
[final] ).
cnf(i_0_17222,plain,
hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10413]),
[final] ).
cnf(i_0_17223,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9605]),
[final] ).
cnf(i_0_17224,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9606]),
[final] ).
cnf(i_0_17225,plain,
c_Sum__Type_OProjr(X1,X2,hAPP(c_Sum__Type_OInr(X2,X1),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10414]),
[final] ).
cnf(i_0_17226,plain,
c_Sum__Type_OProjl(X1,X2,hAPP(c_Sum__Type_OInl(X1,X2),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10415]),
[final] ).
cnf(i_0_17227,plain,
c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10416]),
[final] ).
cnf(i_0_17228,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Int_Onat,X1) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10116]),
[final] ).
cnf(i_0_17229,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != hAPP(c_Int_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10117]),
[final] ).
cnf(i_0_17230,plain,
hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(rw,[status(thm)],[i_0_10417,c_0_8155]),
[final] ).
cnf(i_0_17231,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))),
inference(rw,[status(thm)],[i_0_10418,c_0_8155]),
[final] ).
cnf(i_0_17232,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10226]),
[final] ).
cnf(i_0_17233,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10419]),
[final] ).
cnf(i_0_17234,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)) = hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10420]),
[final] ).
cnf(i_0_17235,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10421]),
[final] ).
cnf(i_0_17236,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)) = hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10422]),
[final] ).
cnf(i_0_17237,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10423]),
[final] ).
cnf(i_0_17238,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10424]),
[final] ).
cnf(i_0_17239,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_10425]),
[final] ).
cnf(i_0_17240,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_10426]),
[final] ).
cnf(i_0_17241,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X1,X2) = c_Complete__Lattice_OSup__class_OSup(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10427]),
[final] ).
cnf(i_0_17242,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X1,X2) = c_Complete__Lattice_OInf__class_OInf(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10428]),
[final] ).
cnf(i_0_17243,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)),X2) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10429]),
[final] ).
cnf(i_0_17244,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10430]),
[final] ).
cnf(i_0_17245,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10431]),
[final] ).
cnf(i_0_17246,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10432]),
[final] ).
cnf(i_0_17247,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10110]),
[final] ).
cnf(i_0_17248,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10433]),
[final] ).
cnf(i_0_17249,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10434]),
[final] ).
cnf(i_0_17250,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10290]),
[final] ).
cnf(i_0_17251,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10291]),
[final] ).
cnf(i_0_17252,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10435]),
[final] ).
cnf(i_0_17253,plain,
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ epred2_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7551]),
[final] ).
cnf(i_0_17254,plain,
( c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10155]),
[final] ).
cnf(i_0_17255,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10436]),
[final] ).
cnf(i_0_17256,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10437]),
[final] ).
cnf(i_0_17257,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10201]),
[final] ).
cnf(i_0_17258,plain,
( X3 = X4
| hAPP(c_Sum__Type_OInl(X1,X2),X3) != hAPP(c_Sum__Type_OInl(X1,X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_10438]),
[final] ).
cnf(i_0_17259,plain,
( X3 = X4
| hAPP(c_Sum__Type_OInl(X1,X2),X3) != hAPP(c_Sum__Type_OInl(X1,X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_10439]),
[final] ).
cnf(i_0_17260,plain,
( X3 = X4
| hAPP(c_Sum__Type_OInr(X1,X2),X3) != hAPP(c_Sum__Type_OInr(X1,X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_10440]),
[final] ).
cnf(i_0_17261,plain,
( X3 = X4
| hAPP(c_Sum__Type_OInr(X1,X2),X3) != hAPP(c_Sum__Type_OInr(X1,X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_10441]),
[final] ).
cnf(i_0_17262,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10442]),
[final] ).
cnf(i_0_17263,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),X3),c_List_Olist_ONil(X2)) = c_List_Olist_ONil(tc_prod(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10443]),
[final] ).
cnf(i_0_17264,plain,
( hAPP(hAPP(X2,X4),X3) = X4
| ~ c_Groups_Ocomm__monoid(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_10444]),
[final] ).
cnf(i_0_17265,plain,
( hAPP(hAPP(X2,X4),X4) = X4
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_10445]),
[final] ).
cnf(i_0_17266,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X1,X2,X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10446]),
[final] ).
cnf(i_0_17267,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| hAPP(c_Int_Onat,X2) = X1
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10116]),
[final] ).
cnf(i_0_17268,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| X1 = hAPP(c_Int_Onat,X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10117]),
[final] ).
cnf(i_0_17269,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10447]),
[final] ).
cnf(i_0_17270,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10448]),
[final] ).
cnf(i_0_17271,plain,
hAPP(c_Sum__Type_OInl(X1,X2),X3) != hAPP(c_Sum__Type_OInr(X2,X1),X4),
inference(split_conjunct,[status(thm)],[i_0_10449]),
[final] ).
cnf(i_0_17272,plain,
hAPP(c_Sum__Type_OInl(X1,X2),X3) != hAPP(c_Sum__Type_OInr(X2,X1),X4),
inference(split_conjunct,[status(thm)],[i_0_10450]),
[final] ).
cnf(i_0_17273,plain,
hAPP(c_Sum__Type_OInr(X1,X2),X3) != hAPP(c_Sum__Type_OInl(X2,X1),X4),
inference(split_conjunct,[status(thm)],[i_0_10451]),
[final] ).
cnf(i_0_17274,plain,
hAPP(c_Sum__Type_OInr(X1,X2),X3) != hAPP(c_Sum__Type_OInl(X2,X1),X4),
inference(split_conjunct,[status(thm)],[i_0_10452]),
[final] ).
cnf(i_0_17275,plain,
( c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10398]),
[final] ).
cnf(i_0_17276,plain,
( c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10453]),
[final] ).
cnf(i_0_17277,plain,
hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10454]),
[final] ).
cnf(i_0_17278,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10455]),
[final] ).
cnf(i_0_17279,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_10456]),
[final] ).
cnf(i_0_17280,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10245]),
[final] ).
cnf(i_0_17281,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10457]),
[final] ).
cnf(i_0_17282,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10458]),
[final] ).
cnf(i_0_17283,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[i_0_10459]),
[final] ).
cnf(i_0_17284,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_10460]),
[final] ).
cnf(i_0_17285,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[i_0_10461]),
[final] ).
cnf(i_0_17286,plain,
( X1 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10182]),
[final] ).
cnf(i_0_17287,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk130_1(X1)),X1))
| c_Nat__Transfer_Onat__set(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9869]),
[final] ).
cnf(i_0_17288,plain,
hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10462]),
[final] ).
cnf(i_0_17289,plain,
hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10463]),
[final] ).
cnf(i_0_17290,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10464]),
[final] ).
cnf(i_0_17291,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10464]),
[final] ).
cnf(i_0_17292,plain,
( hBOOL(hAPP(X2,X3))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ epred1_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7561]),
[final] ).
cnf(i_0_17293,plain,
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
| ~ c_Nat__Transfer_Ois__nat(X1)
| ~ c_Nat__Transfer_Ois__nat(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10465]),
[final] ).
cnf(i_0_17294,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10276]),
[final] ).
cnf(i_0_17295,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10278]),
[final] ).
cnf(i_0_17296,plain,
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X2,X1)))
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10323]),
[final] ).
cnf(i_0_17297,plain,
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X2,X1)))
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10466]),
[final] ).
cnf(i_0_17298,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_Set_OCollect(X1),X2)
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10467]),
[final] ).
cnf(i_0_17299,plain,
( hAPP(c_Set_OCollect(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10468]),
[final] ).
cnf(i_0_17300,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10469]),
[final] ).
cnf(i_0_17301,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10470]),
[final] ).
cnf(i_0_17302,plain,
( hAPP(c_List_Oset(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X2)) = X2
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10260]),
[final] ).
cnf(i_0_17303,plain,
( c_Wellfounded_Owf(tc_List_Olist(X1),hAPP(c_List_Olexn(X1,X2),X3))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10471]),
[final] ).
cnf(i_0_17304,plain,
hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10472]),
[final] ).
cnf(i_0_17305,plain,
hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10473]),
[final] ).
cnf(i_0_17306,plain,
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1)))
| hAPP(c_Com_Obody,X1) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10334]),
[final] ).
cnf(i_0_17307,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_10474]),
[final] ).
cnf(i_0_17308,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_10185]),
[final] ).
cnf(i_0_17309,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_10475]),
[final] ).
cnf(i_0_17310,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10476]),
[final] ).
cnf(i_0_17311,plain,
( X1 = X2
| hAPP(hAPP(c_String_Ochar_OChar,X1),X3) != hAPP(hAPP(c_String_Ochar_OChar,X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_10477]),
[final] ).
cnf(i_0_17312,plain,
( X1 = X2
| hAPP(hAPP(c_String_Ochar_OChar,X3),X1) != hAPP(hAPP(c_String_Ochar_OChar,X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10477]),
[final] ).
cnf(i_0_17313,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_atMost__0]),
[final] ).
cnf(i_0_17314,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1)),
inference(split_conjunct,[status(thm)],[i_0_10478]),
[final] ).
cnf(i_0_17315,plain,
hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X2)) = hAPP(c_Relation_OField(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_10479]),
[final] ).
cnf(i_0_17316,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10480]),
[final] ).
cnf(i_0_17317,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10481]),
[final] ).
cnf(i_0_17318,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10482]),
[final] ).
cnf(i_0_17319,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10430]),
[final] ).
cnf(i_0_17320,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10430]),
[final] ).
cnf(i_0_17321,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10483]),
[final] ).
cnf(i_0_17322,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10431]),
[final] ).
cnf(i_0_17323,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10431]),
[final] ).
cnf(i_0_17324,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_10484]),
[final] ).
cnf(i_0_17325,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9550]),
[final] ).
cnf(i_0_17326,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9550]),
[final] ).
cnf(i_0_17327,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),X2))
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_9779]),
[final] ).
cnf(i_0_17328,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_10485]),
[final] ).
cnf(i_0_17329,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) = X3
| ~ class_Groups_Ogroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10486]),
[final] ).
cnf(i_0_17330,plain,
( X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10487]),
[final] ).
cnf(i_0_17331,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)),
inference(split_conjunct,[status(thm)],[i_0_10488]),
[final] ).
cnf(i_0_17332,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)),
inference(split_conjunct,[status(thm)],[i_0_10489]),
[final] ).
cnf(i_0_17333,plain,
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10490]),
[final] ).
cnf(i_0_17334,plain,
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10293]),
[final] ).
cnf(i_0_17335,plain,
( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osorted__list__of__set(X1,X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10260]),
[final] ).
cnf(i_0_17336,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10491]),
[final] ).
cnf(i_0_17337,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10492]),
[final] ).
cnf(i_0_17338,plain,
c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_10493]),
[final] ).
cnf(i_0_17339,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10246]),
[final] ).
cnf(i_0_17340,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X2))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10494]),
[final] ).
cnf(i_0_17341,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10495]),
[final] ).
cnf(i_0_17342,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10492]),
[final] ).
cnf(i_0_17343,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10492]),
[final] ).
cnf(i_0_17344,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) = hAPP(c_Int_Onat,X1),
inference(split_conjunct,[status(thm)],[i_0_10496]),
[final] ).
cnf(i_0_17345,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X1,X2,X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10497]),
[final] ).
cnf(i_0_17346,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]),
[final] ).
cnf(i_0_17347,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]),
[final] ).
cnf(i_0_17348,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[fact_int__0__less__1]),
[final] ).
cnf(i_0_17349,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_10498]),
[final] ).
cnf(i_0_17350,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10499]),
[final] ).
cnf(i_0_17351,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10500]),
[final] ).
cnf(i_0_17352,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10501]),
[final] ).
cnf(i_0_17353,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10502]),
[final] ).
cnf(i_0_17354,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10503]),
[final] ).
cnf(i_0_17355,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10504]),
[final] ).
cnf(i_0_17356,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10505]),
[final] ).
cnf(i_0_17357,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10506]),
[final] ).
cnf(i_0_17358,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10507]),
[final] ).
cnf(i_0_17359,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10508]),
[final] ).
cnf(i_0_17360,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10509]),
[final] ).
cnf(i_0_17361,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10510]),
[final] ).
cnf(i_0_17362,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10511]),
[final] ).
cnf(i_0_17363,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10512]),
[final] ).
cnf(i_0_17364,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| c_List_Oupto(X1,X2) = c_List_Olist_ONil(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_9285]),
[final] ).
cnf(i_0_17365,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))
| c_Quickcheck_Obeyond(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(split_conjunct,[status(thm)],[i_0_10275]),
[final] ).
cnf(i_0_17366,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
| c_Nat__Transfer_Otsub(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10123]),
[final] ).
cnf(i_0_17367,plain,
hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10513]),
[final] ).
cnf(i_0_17368,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10514]),
[final] ).
cnf(i_0_17369,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10235]),
[final] ).
cnf(i_0_17370,plain,
( c_Divides_Odivmod__int(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_5201]),
[final] ).
cnf(i_0_17371,plain,
( c_Divides_Odivmod__int(X2,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_5199]),
[final] ).
cnf(i_0_17372,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))
| ~ c_Nat__Transfer_Ois__nat(X1)
| ~ c_Nat__Transfer_Ois__nat(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10515]),
[final] ).
cnf(i_0_17373,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))
| ~ c_Nat__Transfer_Ois__nat(X1)
| ~ c_Nat__Transfer_Ois__nat(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10516]),
[final] ).
cnf(i_0_17374,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))
| ~ c_Nat__Transfer_Ois__nat(X1)
| ~ c_Nat__Transfer_Ois__nat(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10517]),
[final] ).
cnf(i_0_17375,plain,
( c_Divides_Odivmod__int(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_5201]),
[final] ).
cnf(i_0_17376,plain,
( c_Divides_Odivmod__int(X1,X2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_5199]),
[final] ).
cnf(i_0_17377,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10518]),
[final] ).
cnf(i_0_17378,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10518]),
[final] ).
cnf(i_0_17379,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10519]),
[final] ).
cnf(i_0_17380,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10520]),
[final] ).
cnf(i_0_17381,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OAss(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10521]),
[final] ).
cnf(i_0_17382,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10522]),
[final] ).
cnf(i_0_17383,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10523]),
[final] ).
cnf(i_0_17384,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OAss(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10524]),
[final] ).
cnf(i_0_17385,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10525]),
[final] ).
cnf(i_0_17386,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10526]),
[final] ).
cnf(i_0_17387,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OAss(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10527]),
[final] ).
cnf(i_0_17388,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OLocal(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10528]),
[final] ).
cnf(i_0_17389,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10529]),
[final] ).
cnf(i_0_17390,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OCall(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10530]),
[final] ).
cnf(i_0_17391,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OLocal(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10531]),
[final] ).
cnf(i_0_17392,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10532]),
[final] ).
cnf(i_0_17393,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OCall(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10533]),
[final] ).
cnf(i_0_17394,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OLocal(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10534]),
[final] ).
cnf(i_0_17395,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10535]),
[final] ).
cnf(i_0_17396,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OCall(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10536]),
[final] ).
cnf(i_0_17397,plain,
hAPP(c_Code__Numeral_Onat__of,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rw,[status(thm)],[i_0_10537,c_0_8844]),
[final] ).
cnf(i_0_17398,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10437]),
[final] ).
cnf(i_0_17399,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
inference(split_conjunct,[status(thm)],[i_0_10538]),
[final] ).
cnf(i_0_17400,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
inference(split_conjunct,[status(thm)],[i_0_10539]),
[final] ).
cnf(i_0_17401,plain,
c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2),
inference(split_conjunct,[status(thm)],[i_0_10540]),
[final] ).
cnf(i_0_17402,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10284]),
[final] ).
cnf(i_0_17403,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10285]),
[final] ).
cnf(i_0_17404,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10541]),
[final] ).
cnf(i_0_17405,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10542]),
[final] ).
cnf(i_0_17406,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10543]),
[final] ).
cnf(i_0_17407,plain,
c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_10544]),
[final] ).
cnf(i_0_17408,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10545]),
[final] ).
cnf(i_0_17409,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10546]),
[final] ).
cnf(i_0_17410,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10547]),
[final] ).
cnf(i_0_17411,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10548]),
[final] ).
cnf(i_0_17412,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != hAPP(c_Com_Ocom_OBODY,X4),
inference(split_conjunct,[status(thm)],[i_0_10549]),
[final] ).
cnf(i_0_17413,plain,
c_Com_Ocom_OCond(X1,X2,X3) != hAPP(c_Com_Ocom_OBODY,X4),
inference(split_conjunct,[status(thm)],[i_0_10550]),
[final] ).
cnf(i_0_17414,plain,
c_Com_Ocom_OCall(X1,X2,X3) != hAPP(c_Com_Ocom_OBODY,X4),
inference(split_conjunct,[status(thm)],[i_0_10551]),
[final] ).
cnf(i_0_17415,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OLocal(X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10552]),
[final] ).
cnf(i_0_17416,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OCond(X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10553]),
[final] ).
cnf(i_0_17417,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OCall(X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10554]),
[final] ).
cnf(i_0_17418,plain,
c_List_Olists(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10555]),
[final] ).
cnf(i_0_17419,plain,
hAPP(hAPP(c_List_Omap(X1,X1),c_COMBI(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10556]),
[final] ).
cnf(i_0_17420,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ c_Wellfounded_OwfP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10557]),
[final] ).
cnf(i_0_17421,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ c_Wellfounded_OwfP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10035]),
[final] ).
cnf(i_0_17422,plain,
( hBOOL(hAPP(hAPP(X2,X3),X3))
| ~ c_Predicate_Oreflp(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10558]),
[final] ).
cnf(i_0_17423,plain,
( hBOOL(hAPP(hAPP(X2,X3),X3))
| ~ c_Equiv__Relations_Oequivp(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10559]),
[final] ).
cnf(i_0_17424,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1) != X3
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10314]),
[final] ).
cnf(i_0_17425,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10315]),
[final] ).
cnf(i_0_17426,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10430]),
[final] ).
cnf(i_0_17427,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10431]),
[final] ).
cnf(i_0_17428,plain,
( hAPP(hAPP(c_List_Olist__update(X2,X1),X3),X4) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10302]),
[final] ).
cnf(i_0_17429,plain,
( hAPP(hAPP(c_Option_Omap(X2,X3),X4),X1) = c_Option_Ooption_ONone(X3)
| X1 != c_Option_Ooption_ONone(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10304]),
[final] ).
cnf(i_0_17430,plain,
( hAPP(hAPP(c_List_Omap(X2,X3),X4),X1) = c_List_Olist_ONil(X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10303]),
[final] ).
cnf(i_0_17431,plain,
( c_List_Olist_ONil(X3) = hAPP(hAPP(c_List_Omap(X2,X3),X4),X1)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10305]),
[final] ).
cnf(i_0_17432,plain,
c_List_Osublist(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10560]),
[final] ).
cnf(i_0_17433,plain,
( X2 = X3
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10561]),
[final] ).
cnf(i_0_17434,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orev(X1),X2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_10562]),
[final] ).
cnf(i_0_17435,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate1(X1),X2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_10563]),
[final] ).
cnf(i_0_17436,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,X2))
| X3 != c_Hilbert__Choice_OEps(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10564]),
[final] ).
cnf(i_0_17437,plain,
hAPP(hAPP(c_Nat_Ocompow(X1,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_Fun_Oid(X1),
inference(split_conjunct,[status(thm)],[i_0_10565]),
[final] ).
cnf(i_0_17438,plain,
hAPP(hAPP(c_Option_Omap(X1,X2),X3),c_Option_Ooption_ONone(X1)) = c_Option_Ooption_ONone(X2),
inference(split_conjunct,[status(thm)],[i_0_10566]),
[final] ).
cnf(i_0_17439,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
inference(split_conjunct,[status(thm)],[i_0_10567]),
[final] ).
cnf(i_0_17440,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10568]),
[final] ).
cnf(i_0_17441,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10569]),
[final] ).
cnf(i_0_17442,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10570]),
[final] ).
cnf(i_0_17443,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10571]),
[final] ).
cnf(i_0_17444,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X2 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
inference(split_conjunct,[status(thm)],[i_0_10572]),
[final] ).
cnf(i_0_17445,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X3) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice__bot(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10573]),
[final] ).
cnf(i_0_17446,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X3),X1) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice__bot(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10573]),
[final] ).
cnf(i_0_17447,plain,
( X1 = c_Orderings_Otop__class_Otop(X2)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X3) != c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice__top(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10574]),
[final] ).
cnf(i_0_17448,plain,
( X1 = c_Orderings_Otop__class_Otop(X2)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X3),X1) != c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice__top(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10574]),
[final] ).
cnf(i_0_17449,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10575]),
[final] ).
cnf(i_0_17450,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10576]),
[final] ).
cnf(i_0_17451,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10577]),
[final] ).
cnf(i_0_17452,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1))),
inference(split_conjunct,[status(thm)],[i_0_10578]),
[final] ).
cnf(i_0_17453,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1))),
inference(split_conjunct,[status(thm)],[i_0_10579]),
[final] ).
cnf(i_0_17454,plain,
( X1 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_9466]),
[final] ).
cnf(i_0_17455,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(rw,[status(thm)],[i_0_10580,c_0_8844]),
[final] ).
cnf(i_0_17456,plain,
( hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9699]),
[final] ).
cnf(i_0_17457,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[i_0_10581]),
[final] ).
cnf(i_0_17458,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10330]),
[final] ).
cnf(i_0_17459,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10331]),
[final] ).
cnf(i_0_17460,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10329]),
[final] ).
cnf(i_0_17461,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10582]),
[final] ).
cnf(i_0_17462,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10583]),
[final] ).
cnf(i_0_17463,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9705]),
[final] ).
cnf(i_0_17464,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_9705]),
[final] ).
cnf(i_0_17465,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9706]),
[final] ).
cnf(i_0_17466,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10584]),
[final] ).
cnf(i_0_17467,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10585]),
[final] ).
cnf(i_0_17468,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9935]),
[final] ).
cnf(i_0_17469,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9950]),
[final] ).
cnf(i_0_17470,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Otake(X1),X2),X3) != c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10586]),
[final] ).
cnf(i_0_17471,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10464]),
[final] ).
cnf(i_0_17472,plain,
( X1 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10572]),
[final] ).
cnf(i_0_17473,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10587]),
[final] ).
cnf(i_0_17474,plain,
( X1 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10572]),
[final] ).
cnf(i_0_17475,plain,
( X1 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10572]),
[final] ).
cnf(i_0_17476,plain,
( X1 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10572]),
[final] ).
cnf(i_0_17477,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10487]),
[final] ).
cnf(i_0_17478,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10588]),
[final] ).
cnf(i_0_17479,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Opdivmod(X2,X1) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10395]),
[final] ).
cnf(i_0_17480,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10589]),
[final] ).
cnf(i_0_17481,plain,
hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10590]),
[final] ).
cnf(i_0_17482,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10591]),
[final] ).
cnf(i_0_17483,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10592]),
[final] ).
cnf(i_0_17484,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[fact_bin__less__0__simps_I2_J]),
[final] ).
cnf(i_0_17485,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10593]),
[final] ).
cnf(i_0_17486,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10594]),
[final] ).
cnf(i_0_17487,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10595]),
[final] ).
cnf(i_0_17488,plain,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10596]),
[final] ).
cnf(i_0_17489,plain,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10597]),
[final] ).
cnf(i_0_17490,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10430]),
[final] ).
cnf(i_0_17491,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10430]),
[final] ).
cnf(i_0_17492,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10431]),
[final] ).
cnf(i_0_17493,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10431]),
[final] ).
cnf(i_0_17494,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),X1),X3) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10598]),
[final] ).
cnf(i_0_17495,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),X3),X1) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10598]),
[final] ).
cnf(i_0_17496,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10599]),
[final] ).
cnf(i_0_17497,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10599]),
[final] ).
cnf(i_0_17498,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(rw,[status(thm)],[i_0_10600,c_0_6016]),
[final] ).
cnf(i_0_17499,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(rw,[status(thm)],[i_0_10601,c_0_6169]),
[final] ).
cnf(i_0_17500,plain,
c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_List_Olist_ONil(tc_Nat_Onat),
inference(rw,[status(thm)],[i_0_10602,c_0_6135]),
[final] ).
cnf(i_0_17501,plain,
hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10603]),
[final] ).
cnf(i_0_17502,plain,
hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10604]),
[final] ).
cnf(i_0_17503,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_10605]),
[final] ).
cnf(i_0_17504,plain,
( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1)) = c_List_Olist_ONil(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_10606,c_0_6135]),
[final] ).
cnf(i_0_17505,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),
inference(split_conjunct,[status(thm)],[i_0_10607]),
[final] ).
cnf(i_0_17506,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_10608]),
[final] ).
cnf(i_0_17507,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_10609]),
[final] ).
cnf(i_0_17508,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_10610]),
[final] ).
cnf(i_0_17509,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_10611]),
[final] ).
cnf(i_0_17510,plain,
hAPP(hAPP(c_Nitpick_Ofrac(X1),X2),X3) = c_Nitpick_OAbs__Frac(X1,c_Nitpick_Onorm__frac(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_10612]),
[final] ).
cnf(i_0_17511,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10613]),
[final] ).
cnf(i_0_17512,plain,
hAPP(c_Nat_Osize__class_Osize(tc_String_Ochar),hAPP(hAPP(c_String_Ochar_OChar,X1),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10614]),
[final] ).
cnf(i_0_17513,plain,
( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10615]),
[final] ).
cnf(i_0_17514,plain,
( hBOOL(hAPP(X1,esk310_1(X1)))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10467]),
[final] ).
cnf(i_0_17515,plain,
( hBOOL(hAPP(X1,esk311_1(X1)))
| hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10468]),
[final] ).
cnf(i_0_17516,plain,
( X2 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_10616]),
[final] ).
cnf(i_0_17517,plain,
( X3 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10617]),
[final] ).
cnf(i_0_17518,plain,
( X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10618]),
[final] ).
cnf(i_0_17519,plain,
( X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10619]),
[final] ).
cnf(i_0_17520,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10620]),
[final] ).
cnf(i_0_17521,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10621]),
[final] ).
cnf(i_0_17522,plain,
c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_10622]),
[final] ).
cnf(i_0_17523,plain,
( hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10623]),
[final] ).
cnf(i_0_17524,plain,
hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_10624]),
[final] ).
cnf(i_0_17525,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10483]),
[final] ).
cnf(i_0_17526,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin),
inference(rw,[status(thm)],[i_0_10625,c_0_6169]),
[final] ).
cnf(i_0_17527,plain,
( hBOOL(hAPP(c_List_Odistinct(X2),X1))
| esk450_2(X1,X2) != esk451_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8201]),
[final] ).
cnf(i_0_17528,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10620]),
[final] ).
cnf(i_0_17529,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10626]),
[final] ).
cnf(i_0_17530,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10627]),
[final] ).
cnf(i_0_17531,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10628]),
[final] ).
cnf(i_0_17532,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10629]),
[final] ).
cnf(i_0_17533,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10630]),
[final] ).
cnf(i_0_17534,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10631]),
[final] ).
cnf(i_0_17535,plain,
c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10632]),
[final] ).
cnf(i_0_17536,plain,
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10633]),
[final] ).
cnf(i_0_17537,plain,
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10634]),
[final] ).
cnf(i_0_17538,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(c_List_Orev(X1),X2)) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10635]),
[final] ).
cnf(i_0_17539,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)) = hAPP(c_Groups_Oabs__class_Oabs(X1),X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10636]),
[final] ).
cnf(i_0_17540,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_Groups_Oabs__class_Oabs(X1),X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10637]),
[final] ).
cnf(i_0_17541,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10638]),
[final] ).
cnf(i_0_17542,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_rel__simps_I19_J]),
[final] ).
cnf(i_0_17543,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_rel__simps_I23_J]),
[final] ).
cnf(i_0_17544,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(split_conjunct,[status(thm)],[fact_rel__simps_I24_J]),
[final] ).
cnf(i_0_17545,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_rel__simps_I6_J]),
[final] ).
cnf(i_0_17546,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(split_conjunct,[status(thm)],[fact_neg__number__of__Min]),
[final] ).
cnf(i_0_17547,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)) ),
inference(split_conjunct,[status(thm)],[i_0_10639]),
[final] ).
cnf(i_0_17548,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10640]),
[final] ).
cnf(i_0_17549,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_10641]),
[final] ).
cnf(i_0_17550,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10642]),
[final] ).
cnf(i_0_17551,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10643]),
[final] ).
cnf(i_0_17552,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(split_conjunct,[status(thm)],[i_0_10644]),
[final] ).
cnf(i_0_17553,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(split_conjunct,[status(thm)],[i_0_10645]),
[final] ).
cnf(i_0_17554,plain,
c_Finite__Set_Ofun__left__comm__idem(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1)),
inference(split_conjunct,[status(thm)],[i_0_10646]),
[final] ).
cnf(i_0_17555,plain,
( hBOOL(hAPP(hAPP(c_fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10647]),
[final] ).
cnf(i_0_17556,plain,
( hBOOL(hAPP(hAPP(c_fdisj,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10648]),
[final] ).
cnf(i_0_17557,plain,
( hBOOL(hAPP(hAPP(c_fimplies,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10649]),
[final] ).
cnf(i_0_17558,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10650]),
[final] ).
cnf(i_0_17559,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10651]),
[final] ).
cnf(i_0_17560,plain,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,X1)),X3) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10652]),
[final] ).
cnf(i_0_17561,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_10653]),
[final] ).
cnf(i_0_17562,plain,
~ c_Option_Ois__none(X1,hAPP(c_Option_Ooption_OSome(X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10654]),
[final] ).
cnf(i_0_17563,plain,
( c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Otl(X1),X2))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10655]),
[final] ).
cnf(i_0_17564,plain,
( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10656]),
[final] ).
cnf(i_0_17565,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(c_List_Ohd(X2),X1) = hAPP(hAPP(c_List_Onth(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_10657]),
[final] ).
cnf(i_0_17566,plain,
( hBOOL(X1)
| hBOOL(hAPP(hAPP(c_fimplies,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10658]),
[final] ).
cnf(i_0_17567,plain,
c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10659]),
[final] ).
cnf(i_0_17568,plain,
c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10660]),
[final] ).
cnf(i_0_17569,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10661]),
[final] ).
cnf(i_0_17570,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10661]),
[final] ).
cnf(i_0_17571,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10662]),
[final] ).
cnf(i_0_17572,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10662]),
[final] ).
cnf(i_0_17573,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10663]),
[final] ).
cnf(i_0_17574,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10663]),
[final] ).
cnf(i_0_17575,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X3) = c_Orderings_Otop__class_Otop(X2)
| X1 != c_Orderings_Otop__class_Otop(X2)
| X3 != c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice__top(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10574]),
[final] ).
cnf(i_0_17576,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X3) = c_Orderings_Obot__class_Obot(X2)
| X1 != c_Orderings_Obot__class_Obot(X2)
| X3 != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice__bot(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10573]),
[final] ).
cnf(i_0_17577,plain,
( X2 = X3
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10664]),
[final] ).
cnf(i_0_17578,plain,
hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId__on(X1,X2)) = c_Relation_OId__on(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10665]),
[final] ).
cnf(i_0_17579,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10666]),
[final] ).
cnf(i_0_17580,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10667]),
[final] ).
cnf(i_0_17581,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10668]),
[final] ).
cnf(i_0_17582,plain,
( X2 = c_List_Olist_ONil(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_List_Oset(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10669]),
[final] ).
cnf(i_0_17583,plain,
( X2 = c_List_Olist_ONil(X1)
| hAPP(c_List_Oset(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10670]),
[final] ).
cnf(i_0_17584,plain,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_10671]),
[final] ).
cnf(i_0_17585,plain,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_10672]),
[final] ).
cnf(i_0_17586,plain,
( c_Wellfounded_Owf(X2,X1)
| esk351_2(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8093]),
[final] ).
cnf(i_0_17587,plain,
hAPP(c_List_Oset(X1),hAPP(c_List_Orev(X1),X2)) = hAPP(c_List_Oset(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_10673]),
[final] ).
cnf(i_0_17588,plain,
hAPP(c_List_Oset(X1),hAPP(c_List_Orotate1(X1),X2)) = hAPP(c_List_Oset(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_10674]),
[final] ).
cnf(i_0_17589,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10518]),
[final] ).
cnf(i_0_17590,plain,
( c_Power_Opower__class_Opower(X1) = c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1))
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10675]),
[final] ).
cnf(i_0_17591,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_10676]),
[final] ).
cnf(i_0_17592,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(c_List_Ohd(X2),hAPP(c_List_Orev(X2),X1)) = c_List_Olast(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10677]),
[final] ).
cnf(i_0_17593,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X2,hAPP(c_List_Orev(X2),X1)) = hAPP(c_List_Ohd(X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10678]),
[final] ).
cnf(i_0_17594,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X3) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10314]),
[final] ).
cnf(i_0_17595,plain,
( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X3)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10315]),
[final] ).
cnf(i_0_17596,plain,
( c_List_Olinorder__class_Osorted__list__of__set(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_List_Olist_ONil(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10679]),
[final] ).
cnf(i_0_17597,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10680]),
[final] ).
cnf(i_0_17598,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10681]),
[final] ).
cnf(i_0_17599,plain,
( c_Complete__Lattice_OInf__class_OInf(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10682]),
[final] ).
cnf(i_0_17600,plain,
( c_Complete__Lattice_OInf__class_OInf(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10683]),
[final] ).
cnf(i_0_17601,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X1,
inference(split_conjunct,[status(thm)],[i_0_10684]),
[final] ).
cnf(i_0_17602,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10685]),
[final] ).
cnf(i_0_17603,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10686]),
[final] ).
cnf(i_0_17604,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10687]),
[final] ).
cnf(i_0_17605,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10688]),
[final] ).
cnf(i_0_17606,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10689]),
[final] ).
cnf(i_0_17607,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10690]),
[final] ).
cnf(i_0_17608,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10691]),
[final] ).
cnf(i_0_17609,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10692]),
[final] ).
cnf(i_0_17610,plain,
( X2 = c_List_Olist_ONil(X1)
| c_List_Olinorder__class_Osorted(X1,c_List_Obutlast(X1,X2))
| ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10693]),
[final] ).
cnf(i_0_17611,plain,
( hBOOL(hAPP(c_Com_OWT,X2))
| ~ c_Com_OWT__bodies
| hAPP(c_Com_Obody,X1) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10694]),
[final] ).
cnf(i_0_17612,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10695]),
[final] ).
cnf(i_0_17613,plain,
hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10696]),
[final] ).
cnf(i_0_17614,plain,
( c_Int_OPls = X1
| c_Int_OPls != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) ),
inference(rw,[status(thm)],[i_0_10697,c_0_6015]),
[final] ).
cnf(i_0_17615,plain,
( X1 = c_Int_OPls
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != c_Int_OPls ),
inference(rw,[status(thm)],[i_0_10698,c_0_6015]),
[final] ).
cnf(i_0_17616,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10699]),
[final] ).
cnf(i_0_17617,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2)
| X3 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10598]),
[final] ).
cnf(i_0_17618,plain,
( c_List_Olist_ONil(X2) = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
| X1 != c_List_Olist_ONil(X2)
| X3 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10599]),
[final] ).
cnf(i_0_17619,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),hAPP(c_Option_Ooption_OSome(X1),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10700]),
[final] ).
cnf(i_0_17620,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_10701]),
[final] ).
cnf(i_0_17621,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != c_Int_OMin,
inference(rw,[status(thm)],[i_0_10702,c_0_6015]),
[final] ).
cnf(i_0_17622,plain,
c_Int_OMin != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
inference(rw,[status(thm)],[i_0_10703,c_0_6015]),
[final] ).
cnf(i_0_17623,plain,
( X2 = X3
| hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2) != hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10704]),
[final] ).
cnf(i_0_17624,plain,
( X2 = X3
| hAPP(c_SetInterval_Oord__class_OatMost(X1),X2) != hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10705]),
[final] ).
cnf(i_0_17625,plain,
( X2 = X3
| hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2) != hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10706]),
[final] ).
cnf(i_0_17626,plain,
( X2 = X3
| hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2) != hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10707]),
[final] ).
cnf(i_0_17627,plain,
( X2 = X3
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10708]),
[final] ).
cnf(i_0_17628,plain,
( X2 = X3
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10709]),
[final] ).
cnf(i_0_17629,plain,
( X2 = X3
| hAPP(c_Int_Oring__1__class_Oof__int(X1),X2) != hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10710]),
[final] ).
cnf(i_0_17630,plain,
( X2 = X3
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)
| ~ class_Nat_Osemiring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10711]),
[final] ).
cnf(i_0_17631,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10712]),
[final] ).
cnf(i_0_17632,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10713]),
[final] ).
cnf(i_0_17633,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10714]),
[final] ).
cnf(i_0_17634,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10715]),
[final] ).
cnf(i_0_17635,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10716]),
[final] ).
cnf(i_0_17636,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10717]),
[final] ).
cnf(i_0_17637,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10718]),
[final] ).
cnf(i_0_17638,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10719]),
[final] ).
cnf(i_0_17639,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X2) = c_Groups_Oone__class_Oone(X3)
| X2 = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(split_conjunct,[status(thm)],[i_0_10561]),
[final] ).
cnf(i_0_17640,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10720]),
[final] ).
cnf(i_0_17641,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10437]),
[final] ).
cnf(i_0_17642,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10543]),
[final] ).
cnf(i_0_17643,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10543]),
[final] ).
cnf(i_0_17644,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10576]),
[final] ).
cnf(i_0_17645,plain,
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10577]),
[final] ).
cnf(i_0_17646,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10721]),
[final] ).
cnf(i_0_17647,plain,
( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10722]),
[final] ).
cnf(i_0_17648,plain,
( X2 = c_Option_Ooption_ONone(X1)
| c_Option_Oset(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10723]),
[final] ).
cnf(i_0_17649,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10724]),
[final] ).
cnf(i_0_17650,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10725]),
[final] ).
cnf(i_0_17651,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10726]),
[final] ).
cnf(i_0_17652,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10727]),
[final] ).
cnf(i_0_17653,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10728]),
[final] ).
cnf(i_0_17654,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10729]),
[final] ).
cnf(i_0_17655,plain,
( c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olex(X1,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10730]),
[final] ).
cnf(i_0_17656,plain,
( c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olenlex(X1,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10731]),
[final] ).
cnf(i_0_17657,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10732]),
[final] ).
cnf(i_0_17658,plain,
( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10588]),
[final] ).
cnf(i_0_17659,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10720]),
[final] ).
cnf(i_0_17660,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10733]),
[final] ).
cnf(i_0_17661,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10734]),
[final] ).
cnf(i_0_17662,plain,
( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10735]),
[final] ).
cnf(i_0_17663,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_10736]),
[final] ).
cnf(i_0_17664,plain,
( c_Finite__Set_Ofun__left__comm(X1,X1,c_Groups_Otimes__class_Otimes(X1))
| ~ class_Groups_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10737]),
[final] ).
cnf(i_0_17665,plain,
( c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10738]),
[final] ).
cnf(i_0_17666,plain,
( c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10739]),
[final] ).
cnf(i_0_17667,plain,
( c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omax(X1))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10740]),
[final] ).
cnf(i_0_17668,plain,
( c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omin(X1))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10741]),
[final] ).
cnf(i_0_17669,plain,
( c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Groups_Otimes__class_Otimes(X1))
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10742]),
[final] ).
cnf(i_0_17670,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10483]),
[final] ).
cnf(i_0_17671,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2) = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Groups_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_10582]),
[final] ).
cnf(i_0_17672,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2) = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Groups_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_10583]),
[final] ).
cnf(i_0_17673,plain,
( hAPP(c_Finite__Set_Ocard(X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_10424]),
[final] ).
cnf(i_0_17674,plain,
hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10743]),
[final] ).
cnf(i_0_17675,plain,
hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10744]),
[final] ).
cnf(i_0_17676,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10745]),
[final] ).
cnf(i_0_17677,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10746]),
[final] ).
cnf(i_0_17678,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Otop__class_Otop(X1)) = X2
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10747]),
[final] ).
cnf(i_0_17679,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10748]),
[final] ).
cnf(i_0_17680,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10749]),
[final] ).
cnf(i_0_17681,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10750]),
[final] ).
cnf(i_0_17682,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10751]),
[final] ).
cnf(i_0_17683,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10752]),
[final] ).
cnf(i_0_17684,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10753]),
[final] ).
cnf(i_0_17685,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10754]),
[final] ).
cnf(i_0_17686,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10755]),
[final] ).
cnf(i_0_17687,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10756]),
[final] ).
cnf(i_0_17688,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10757]),
[final] ).
cnf(i_0_17689,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10758]),
[final] ).
cnf(i_0_17690,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10759]),
[final] ).
cnf(i_0_17691,plain,
hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),
inference(split_conjunct,[status(thm)],[i_0_10760]),
[final] ).
cnf(i_0_17692,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),
inference(split_conjunct,[status(thm)],[i_0_10761]),
[final] ).
cnf(i_0_17693,plain,
( c_Divides_Odiv__class_Omod(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10762]),
[final] ).
cnf(i_0_17694,plain,
( X2 = X3
| hAPP(c_List_Orev(X1),X2) != hAPP(c_List_Orev(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10763]),
[final] ).
cnf(i_0_17695,plain,
( X2 = X3
| hAPP(c_Option_Ooption_OSome(X1),X2) != hAPP(c_Option_Ooption_OSome(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10764]),
[final] ).
cnf(i_0_17696,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8160]),
[final] ).
cnf(i_0_17697,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10424]),
[final] ).
cnf(i_0_17698,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10765]),
[final] ).
cnf(i_0_17699,plain,
( X1 = X2
| c_Random_Oinc__shift(X1,X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ),
inference(split_conjunct,[status(thm)],[i_0_10766]),
[final] ).
cnf(i_0_17700,plain,
hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_card__UNIV__unit]),
[final] ).
cnf(i_0_17701,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10767]),
[final] ).
cnf(i_0_17702,plain,
( hAPP(hAPP(c_List_Otake(X2),X3),X1) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10586]),
[final] ).
cnf(i_0_17703,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(split_conjunct,[status(thm)],[i_0_10768]),
[final] ).
cnf(i_0_17704,plain,
c_List_Osublist(X1,c_List_Olist_ONil(X1),X2) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10769]),
[final] ).
cnf(i_0_17705,plain,
c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10770]),
[final] ).
cnf(i_0_17706,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10771]),
[final] ).
cnf(i_0_17707,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10772]),
[final] ).
cnf(i_0_17708,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10773]),
[final] ).
cnf(i_0_17709,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10774]),
[final] ).
cnf(i_0_17710,plain,
c_List_Olist_Olist__size(X1,X2,c_List_Olist_ONil(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10775]),
[final] ).
cnf(i_0_17711,plain,
c_Option_Ooption_Ooption__size(X1,X2,c_Option_Ooption_ONone(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10776]),
[final] ).
cnf(i_0_17712,plain,
hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10777]),
[final] ).
cnf(i_0_17713,plain,
hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10778]),
[final] ).
cnf(i_0_17714,plain,
hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10779]),
[final] ).
cnf(i_0_17715,plain,
( hAPP(hAPP(c_List_Otake(X2),X1),X3) = c_List_Olist_ONil(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10586]),
[final] ).
cnf(i_0_17716,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3) = X2
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10780]),
[final] ).
cnf(i_0_17717,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3) = X2
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10780]),
[final] ).
cnf(i_0_17718,plain,
( X3 = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10781]),
[final] ).
cnf(i_0_17719,plain,
( X3 = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10781]),
[final] ).
cnf(i_0_17720,plain,
( c_List_Onat__list(X1)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10782]),
[final] ).
cnf(i_0_17721,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10616]),
[final] ).
cnf(i_0_17722,plain,
( hAPP(hAPP(c_List_Oappend(X2),X3),X1) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10617]),
[final] ).
cnf(i_0_17723,plain,
( X3 = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10619]),
[final] ).
cnf(i_0_17724,plain,
( X3 = hAPP(hAPP(c_List_Oappend(X2),X3),X1)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10618]),
[final] ).
cnf(i_0_17725,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1)) = hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_10783]),
[final] ).
cnf(i_0_17726,plain,
hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_10784]),
[final] ).
cnf(i_0_17727,plain,
hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_10785]),
[final] ).
cnf(i_0_17728,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[i_0_10786]),
[final] ).
cnf(i_0_17729,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_10787]),
[final] ).
cnf(i_0_17730,plain,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Osgn__class_Osgn(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10788]),
[final] ).
cnf(i_0_17731,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10572]),
[final] ).
cnf(i_0_17732,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10661]),
[final] ).
cnf(i_0_17733,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10662]),
[final] ).
cnf(i_0_17734,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10663]),
[final] ).
cnf(i_0_17735,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10789]),
[final] ).
cnf(i_0_17736,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10790]),
[final] ).
cnf(i_0_17737,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10791]),
[final] ).
cnf(i_0_17738,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10792]),
[final] ).
cnf(i_0_17739,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10793]),
[final] ).
cnf(i_0_17740,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10794]),
[final] ).
cnf(i_0_17741,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10795]),
[final] ).
cnf(i_0_17742,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10796]),
[final] ).
cnf(i_0_17743,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10797]),
[final] ).
cnf(i_0_17744,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10798]),
[final] ).
cnf(i_0_17745,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10799]),
[final] ).
cnf(i_0_17746,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10800]),
[final] ).
cnf(i_0_17747,plain,
( X2 = c_List_Olist_ONil(X1)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10801]),
[final] ).
cnf(i_0_17748,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),
inference(split_conjunct,[status(thm)],[i_0_10802]),
[final] ).
cnf(i_0_17749,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_10803]),
[final] ).
cnf(i_0_17750,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| c_Nitpick_Ocard_H(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_6177]),
[final] ).
cnf(i_0_17751,plain,
hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10804]),
[final] ).
cnf(i_0_17752,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10805]),
[final] ).
cnf(i_0_17753,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10806]),
[final] ).
cnf(i_0_17754,plain,
hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10807]),
[final] ).
cnf(i_0_17755,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_10808]),
[final] ).
cnf(i_0_17756,plain,
( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10809]),
[final] ).
cnf(i_0_17757,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[fact_code__numeral__zero__minus__one]),
[final] ).
cnf(i_0_17758,plain,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_10810]),
[final] ).
cnf(i_0_17759,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_10811]),
[final] ).
cnf(i_0_17760,plain,
hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[i_0_10812]),
[final] ).
cnf(i_0_17761,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10813]),
[final] ).
cnf(i_0_17762,plain,
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10814]),
[final] ).
cnf(i_0_17763,plain,
hAPP(c_Option_Omap(X1,X1),c_Fun_Oid(X1)) = c_Fun_Oid(tc_Option_Ooption(X1)),
inference(split_conjunct,[status(thm)],[i_0_10815]),
[final] ).
cnf(i_0_17764,plain,
hAPP(c_Option_Omap(X1,X1),c_COMBI(X1)) = c_Fun_Oid(tc_Option_Ooption(X1)),
inference(split_conjunct,[status(thm)],[i_0_10816]),
[final] ).
cnf(i_0_17765,plain,
hAPP(c_List_Omap(X1,X1),c_Fun_Oid(X1)) = c_Fun_Oid(tc_List_Olist(X1)),
inference(split_conjunct,[status(thm)],[i_0_10817]),
[final] ).
cnf(i_0_17766,plain,
hAPP(c_List_Omap(X1,X1),c_COMBI(X1)) = c_Fun_Oid(tc_List_Olist(X1)),
inference(split_conjunct,[status(thm)],[i_0_10818]),
[final] ).
cnf(i_0_17767,plain,
( X1 = X2
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10819]),
[final] ).
cnf(i_0_17768,plain,
( X1 = X2
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10820]),
[final] ).
cnf(i_0_17769,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = hAPP(c_List_Oset(X2),X1)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10669]),
[final] ).
cnf(i_0_17770,plain,
( hAPP(c_List_Oset(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10670]),
[final] ).
cnf(i_0_17771,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_10821]),
[final] ).
cnf(i_0_17772,plain,
( hAPP(c_List_Orev(X2),X1) = X3
| X1 != hAPP(c_List_Orev(X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10822]),
[final] ).
cnf(i_0_17773,plain,
( X2 = hAPP(c_List_Orev(X1),X3)
| hAPP(c_List_Orev(X1),X2) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_10822]),
[final] ).
cnf(i_0_17774,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10823]),
[final] ).
cnf(i_0_17775,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10824]),
[final] ).
cnf(i_0_17776,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_10825]),
[final] ).
cnf(i_0_17777,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10826]),
[final] ).
cnf(i_0_17778,plain,
hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1))),
inference(split_conjunct,[status(thm)],[i_0_10827]),
[final] ).
cnf(i_0_17779,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_9451]),
[final] ).
cnf(i_0_17780,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_9489]),
[final] ).
cnf(i_0_17781,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8905]),
[final] ).
cnf(i_0_17782,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10643]),
[final] ).
cnf(i_0_17783,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10643]),
[final] ).
cnf(i_0_17784,plain,
hAPP(c_New__DSequence_Oneg__single(X1,X2),X3) = c_Lazy__Sequence_Ohb__single(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10828]),
[final] ).
cnf(i_0_17785,plain,
hAPP(c_New__DSequence_Opos__single(X1,X2),X3) = c_Lazy__Sequence_Osingle(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10829]),
[final] ).
cnf(i_0_17786,plain,
c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10830]),
[final] ).
cnf(i_0_17787,plain,
hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10831]),
[final] ).
cnf(i_0_17788,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_10832]),
[final] ).
cnf(i_0_17789,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_10833]),
[final] ).
cnf(i_0_17790,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_10834]),
[final] ).
cnf(i_0_17791,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_10835]),
[final] ).
cnf(i_0_17792,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_10836]),
[final] ).
cnf(i_0_17793,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_8991]),
[final] ).
cnf(i_0_17794,plain,
( c_List_Otranspose(X2,X1) = c_List_Olist_ONil(tc_List_Olist(X2))
| esk481_2(X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9134]),
[final] ).
cnf(i_0_17795,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_10837]),
[final] ).
cnf(i_0_17796,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_10838]),
[final] ).
cnf(i_0_17797,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X1) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10839]),
[final] ).
cnf(i_0_17798,plain,
( X1 = c_Option_Ooption_ONone(X2)
| X1 = hAPP(c_Option_Ooption_OSome(X2),esk27_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10840]),
[final] ).
cnf(i_0_17799,plain,
( X1 = hAPP(c_Option_Ooption_OSome(X2),esk24_2(X2,X1))
| X1 = c_Option_Ooption_ONone(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10841]),
[final] ).
cnf(i_0_17800,plain,
( X1 = c_Option_Ooption_ONone(X2)
| X1 = hAPP(c_Option_Ooption_OSome(X2),esk23_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10842]),
[final] ).
cnf(i_0_17801,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10843]),
[final] ).
cnf(i_0_17802,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10844]),
[final] ).
cnf(i_0_17803,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10845]),
[final] ).
cnf(i_0_17804,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_10813]),
[final] ).
cnf(i_0_17805,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10846]),
[final] ).
cnf(i_0_17806,plain,
( c_Groups_Ozero__class_Ozero(X1) = X2
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10847]),
[final] ).
cnf(i_0_17807,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Groups_Oabs__class_Oabs(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10848]),
[final] ).
cnf(i_0_17808,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10849]),
[final] ).
cnf(i_0_17809,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10850]),
[final] ).
cnf(i_0_17810,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10851]),
[final] ).
cnf(i_0_17811,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10852]),
[final] ).
cnf(i_0_17812,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10853]),
[final] ).
cnf(i_0_17813,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10854]),
[final] ).
cnf(i_0_17814,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10855]),
[final] ).
cnf(i_0_17815,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10856]),
[final] ).
cnf(i_0_17816,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10857]),
[final] ).
cnf(i_0_17817,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10858]),
[final] ).
cnf(i_0_17818,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J]),
[final] ).
cnf(i_0_17819,plain,
hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10859]),
[final] ).
cnf(i_0_17820,plain,
c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
inference(split_conjunct,[status(thm)],[fact_body__def]),
[final] ).
cnf(i_0_17821,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10860]),
[final] ).
cnf(i_0_17822,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10861]),
[final] ).
cnf(i_0_17823,plain,
( c_Option_Oset(X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X1 != c_Option_Ooption_ONone(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10723]),
[final] ).
cnf(i_0_17824,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10862]),
[final] ).
cnf(i_0_17825,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10863]),
[final] ).
cnf(i_0_17826,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
inference(split_conjunct,[status(thm)],[fact_eq__number__of__Pls__Min]),
[final] ).
cnf(i_0_17827,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) = c_Int_OPls
| X1 != c_Int_OPls ),
inference(rw,[status(thm)],[i_0_10864,c_0_6015]),
[final] ).
cnf(i_0_17828,plain,
( c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)
| c_Int_OPls != X1 ),
inference(rw,[status(thm)],[i_0_10865,c_0_6015]),
[final] ).
cnf(i_0_17829,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__Suc0__eq__1]),
[final] ).
cnf(i_0_17830,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10866]),
[final] ).
cnf(i_0_17831,plain,
( hAPP(c_Int_Onat,X2) = X1
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10116]),
[final] ).
cnf(i_0_17832,plain,
( X1 = hAPP(c_Int_Onat,X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10117]),
[final] ).
cnf(i_0_17833,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10867]),
[final] ).
cnf(i_0_17834,plain,
c_Option_Oset(X1,c_Option_Ooption_ONone(X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_10868]),
[final] ).
cnf(i_0_17835,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_10869]),
[final] ).
cnf(i_0_17836,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10869]),
[final] ).
cnf(i_0_17837,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_10870]),
[final] ).
cnf(i_0_17838,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10870]),
[final] ).
cnf(i_0_17839,plain,
( X1 = X2
| c_Com_Ocom_OAss(X1,X3) != c_Com_Ocom_OAss(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_10871]),
[final] ).
cnf(i_0_17840,plain,
( X1 = X2
| c_Com_Ocom_OAss(X3,X1) != c_Com_Ocom_OAss(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10871]),
[final] ).
cnf(i_0_17841,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != X2
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10872]),
[final] ).
cnf(i_0_17842,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10873]),
[final] ).
cnf(i_0_17843,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10874]),
[final] ).
cnf(i_0_17844,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[i_0_10875]),
[final] ).
cnf(i_0_17845,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[i_0_10876]),
[final] ).
cnf(i_0_17846,plain,
hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10877]),
[final] ).
cnf(i_0_17847,plain,
( class_Smallcheck_Osmall(tc_prod(X1,X2))
| ~ class_Smallcheck_Osmall(X1)
| ~ class_Smallcheck_Osmall(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10878]),
[final] ).
cnf(i_0_17848,plain,
( class_Finite__Set_Ofinite(tc_prod(X1,X2))
| ~ class_Finite__Set_Ofinite(X1)
| ~ class_Finite__Set_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10879]),
[final] ).
cnf(i_0_17849,plain,
( class_Finite__Set_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite(X1)
| ~ class_Finite__Set_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10880]),
[final] ).
cnf(i_0_17850,plain,
( class_Finite__Set_Ofinite(tc_sum(X1,X2))
| ~ class_Finite__Set_Ofinite(X1)
| ~ class_Finite__Set_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10881]),
[final] ).
cnf(i_0_17851,plain,
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X2))
| ~ c_Nat__Transfer_Ois__nat(X1)
| ~ c_Nat__Transfer_Ois__nat(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10882]),
[final] ).
cnf(i_0_17852,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSemi(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10883]),
[final] ).
cnf(i_0_17853,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OAss(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10884]),
[final] ).
cnf(i_0_17854,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OWhile(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10885]),
[final] ).
cnf(i_0_17855,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OWhile(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10886]),
[final] ).
cnf(i_0_17856,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OAss(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10887]),
[final] ).
cnf(i_0_17857,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OSemi(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10888]),
[final] ).
cnf(i_0_17858,plain,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[fact_atLeast__0]),
[final] ).
cnf(i_0_17859,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[fact_lessThan__0]),
[final] ).
cnf(i_0_17860,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_10889]),
[final] ).
cnf(i_0_17861,plain,
( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1))
| ~ c_List_Onat__list(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10782]),
[final] ).
cnf(i_0_17862,plain,
( X2 = c_List_Olist_ONil(X1)
| hAPP(c_List_Orev(X1),X2) != c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10890]),
[final] ).
cnf(i_0_17863,plain,
( X2 = c_List_Olist_ONil(X1)
| hAPP(c_List_Orotate1(X1),X2) != c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10891]),
[final] ).
cnf(i_0_17864,plain,
( X2 = c_List_Olist_ONil(X1)
| c_List_Olist_ONil(X1) != hAPP(c_List_Orev(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10892]),
[final] ).
cnf(i_0_17865,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10801]),
[final] ).
cnf(i_0_17866,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X1) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[i_0_10893]),
[final] ).
cnf(i_0_17867,plain,
c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)),
inference(split_conjunct,[status(thm)],[i_0_10894]),
[final] ).
cnf(i_0_17868,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10895]),
[final] ).
cnf(i_0_17869,plain,
c_List_Otranspose(X1,c_List_Olist_ONil(tc_List_Olist(X1))) = c_List_Olist_ONil(tc_List_Olist(X1)),
inference(split_conjunct,[status(thm)],[i_0_10896]),
[final] ).
cnf(i_0_17870,plain,
( X1 = hAPP(c_Int_Onat,X2)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10127]),
[final] ).
cnf(i_0_17871,plain,
( c_Nitpick_Owf_H(X1,X2)
| ~ c_Nitpick_Ounknown(tc_HOL_Obool)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9852]),
[final] ).
cnf(i_0_17872,plain,
( X1 != c_Option_Ooption_ONone(X2)
| X1 != hAPP(c_Option_Ooption_OSome(X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10841]),
[final] ).
cnf(i_0_17873,plain,
( X1 != hAPP(c_Option_Ooption_OSome(X2),X3)
| X1 != c_Option_Ooption_ONone(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10842]),
[final] ).
cnf(i_0_17874,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OWhile(X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10897]),
[final] ).
cnf(i_0_17875,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OSemi(X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10898]),
[final] ).
cnf(i_0_17876,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OAss(X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10899]),
[final] ).
cnf(i_0_17877,plain,
c_Com_Ocom_OWhile(X1,X2) != hAPP(c_Com_Ocom_OBODY,X3),
inference(split_conjunct,[status(thm)],[i_0_10900]),
[final] ).
cnf(i_0_17878,plain,
c_Com_Ocom_OSemi(X1,X2) != hAPP(c_Com_Ocom_OBODY,X3),
inference(split_conjunct,[status(thm)],[i_0_10901]),
[final] ).
cnf(i_0_17879,plain,
c_Com_Ocom_OAss(X1,X2) != hAPP(c_Com_Ocom_OBODY,X3),
inference(split_conjunct,[status(thm)],[i_0_10902]),
[final] ).
cnf(i_0_17880,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin) = c_Int_OPls,
inference(rw,[status(thm)],[i_0_10903,c_0_6016]),
[final] ).
cnf(i_0_17881,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls) = c_Int_OPls,
inference(rw,[status(thm)],[i_0_10904,c_0_6015]),
[final] ).
cnf(i_0_17882,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin) = c_Int_OMin,
inference(rw,[status(thm)],[i_0_10905,c_0_6169]),
[final] ).
cnf(i_0_17883,plain,
( X1 = X2
| hAPP(c_Int_ORep__Integ,X1) != hAPP(c_Int_ORep__Integ,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10906]),
[final] ).
cnf(i_0_17884,plain,
( X1 = X2
| hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10907]),
[final] ).
cnf(i_0_17885,plain,
( X1 = X2
| hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10908]),
[final] ).
cnf(i_0_17886,plain,
( X1 = X2
| hAPP(c_Code__Numeral_Oof__nat,X1) != hAPP(c_Code__Numeral_Oof__nat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10909]),
[final] ).
cnf(i_0_17887,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10910]),
[final] ).
cnf(i_0_17888,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10911]),
[final] ).
cnf(i_0_17889,plain,
( X1 = X2
| hAPP(c_Com_Ocom_OBODY,X1) != hAPP(c_Com_Ocom_OBODY,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10912]),
[final] ).
cnf(i_0_17890,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10913]),
[final] ).
cnf(i_0_17891,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olist_ONil(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10914]),
[final] ).
cnf(i_0_17892,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10915]),
[final] ).
cnf(i_0_17893,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X2),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10848]),
[final] ).
cnf(i_0_17894,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10849]),
[final] ).
cnf(i_0_17895,plain,
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| c_Groups_Ozero__class_Ozero(X1) != X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10847]),
[final] ).
cnf(i_0_17896,plain,
( ~ class_Rings_Osemiring__1(X1)
| ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10916]),
[final] ).
cnf(i_0_17897,plain,
c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10917]),
[final] ).
cnf(i_0_17898,plain,
hAPP(c_Option_Ooption_OSome(X1),X2) != c_Option_Ooption_ONone(X1),
inference(split_conjunct,[status(thm)],[i_0_10918]),
[final] ).
cnf(i_0_17899,plain,
c_Option_Ooption_ONone(X1) != hAPP(c_Option_Ooption_OSome(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_10919]),
[final] ).
cnf(i_0_17900,plain,
c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10920]),
[final] ).
cnf(i_0_17901,plain,
c_HOL_OThe(X1,hAPP(c_fequal,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10921]),
[final] ).
cnf(i_0_17902,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),c_List_Olist_ONil(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10922]),
[final] ).
cnf(i_0_17903,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10923]),
[final] ).
cnf(i_0_17904,plain,
( hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10924]),
[final] ).
cnf(i_0_17905,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10925]),
[final] ).
cnf(i_0_17906,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10926]),
[final] ).
cnf(i_0_17907,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10927]),
[final] ).
cnf(i_0_17908,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10928]),
[final] ).
cnf(i_0_17909,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10929]),
[final] ).
cnf(i_0_17910,plain,
( class_Lattices_Osemilattice__inf(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10930]),
[final] ).
cnf(i_0_17911,plain,
( class_Lattices_Obounded__lattice__bot(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10931]),
[final] ).
cnf(i_0_17912,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10932]),
[final] ).
cnf(i_0_17913,plain,
( class_Lattices_Obounded__lattice__top(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10933]),
[final] ).
cnf(i_0_17914,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10934]),
[final] ).
cnf(i_0_17915,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10935]),
[final] ).
cnf(i_0_17916,plain,
( class_Lattices_Osemilattice__sup(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10936]),
[final] ).
cnf(i_0_17917,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10937]),
[final] ).
cnf(i_0_17918,plain,
( class_Groups_Ominus(tc_fun(X2,X1))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10938]),
[final] ).
cnf(i_0_17919,plain,
( class_Groups_Ouminus(tc_fun(X2,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10939]),
[final] ).
cnf(i_0_17920,plain,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10940]),
[final] ).
cnf(i_0_17921,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10941]),
[final] ).
cnf(i_0_17922,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10942]),
[final] ).
cnf(i_0_17923,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10943]),
[final] ).
cnf(i_0_17924,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Int_Oring__char__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10862]),
[final] ).
cnf(i_0_17925,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5210]),
[final] ).
cnf(i_0_17926,plain,
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Int_Oring__char__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10863]),
[final] ).
cnf(i_0_17927,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Nitpick_Owf_H(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9852]),
[final] ).
cnf(i_0_17928,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10944]),
[final] ).
cnf(i_0_17929,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10872]),
[final] ).
cnf(i_0_17930,plain,
( X1 = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10873]),
[final] ).
cnf(i_0_17931,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[i_0_10945]),
[final] ).
cnf(i_0_17932,plain,
hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10946]),
[final] ).
cnf(i_0_17933,plain,
hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10947]),
[final] ).
cnf(i_0_17934,plain,
hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10948]),
[final] ).
cnf(i_0_17935,plain,
hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10949]),
[final] ).
cnf(i_0_17936,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Int_Oiszero(X1,X2)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10950]),
[final] ).
cnf(i_0_17937,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10951]),
[final] ).
cnf(i_0_17938,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10952]),
[final] ).
cnf(i_0_17939,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10953]),
[final] ).
cnf(i_0_17940,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10954]),
[final] ).
cnf(i_0_17941,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10955]),
[final] ).
cnf(i_0_17942,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1),
inference(split_conjunct,[status(thm)],[i_0_10956]),
[final] ).
cnf(i_0_17943,plain,
( c_Groups_Osgn__class_Osgn(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Osgn__if(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9967]),
[final] ).
cnf(i_0_17944,plain,
( c_Groups_Osgn__class_Osgn(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10913]),
[final] ).
cnf(i_0_17945,plain,
( hAPP(c_List_Orev(X2),X1) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10890]),
[final] ).
cnf(i_0_17946,plain,
( hAPP(c_List_Orotate1(X2),X1) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10891]),
[final] ).
cnf(i_0_17947,plain,
( c_List_Olist_ONil(X2) = hAPP(c_List_Orev(X2),X1)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10892]),
[final] ).
cnf(i_0_17948,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(split_conjunct,[status(thm)],[fact_wf__pair__less]),
[final] ).
cnf(i_0_17949,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(split_conjunct,[status(thm)],[fact_max__strict__def]),
[final] ).
cnf(i_0_17950,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(split_conjunct,[status(thm)],[fact_min__strict__def]),
[final] ).
cnf(i_0_17951,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10957]),
[final] ).
cnf(i_0_17952,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10958]),
[final] ).
cnf(i_0_17953,plain,
( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Osgn__if(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10959]),
[final] ).
cnf(i_0_17954,plain,
( c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord_Omax(X1,c_Orderings_Oord__class_Oless__eq(X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10960]),
[final] ).
cnf(i_0_17955,plain,
( c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord_Omin(X1,c_Orderings_Oord__class_Oless__eq(X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10961]),
[final] ).
cnf(i_0_17956,plain,
hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_nat__1]),
[final] ).
cnf(i_0_17957,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| esk447_1(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_9772]),
[final] ).
cnf(i_0_17958,plain,
hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10962]),
[final] ).
cnf(i_0_17959,plain,
hAPP(c_List_Otl(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10963]),
[final] ).
cnf(i_0_17960,plain,
hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_9750]),
[final] ).
cnf(i_0_17961,plain,
( c_Int_Oiszero(X2,X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Osemiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10950]),
[final] ).
cnf(i_0_17962,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10964]),
[final] ).
cnf(i_0_17963,plain,
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10965]),
[final] ).
cnf(i_0_17964,plain,
c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10966]),
[final] ).
cnf(i_0_17965,plain,
( X2 = c_Option_Ooption_ONone(X1)
| ~ c_Option_Ois__none(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10967]),
[final] ).
cnf(i_0_17966,plain,
( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10968]),
[final] ).
cnf(i_0_17967,plain,
( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10969]),
[final] ).
cnf(i_0_17968,plain,
( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10970]),
[final] ).
cnf(i_0_17969,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10971]),
[final] ).
cnf(i_0_17970,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10972]),
[final] ).
cnf(i_0_17971,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10951]),
[final] ).
cnf(i_0_17972,plain,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
inference(split_conjunct,[status(thm)],[fact_WT_OSkip]),
[final] ).
cnf(i_0_17973,plain,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
inference(split_conjunct,[status(thm)],[fact_WT_Oequations_I1_J]),
[final] ).
cnf(i_0_17974,plain,
hAPP(c_New__DSequence_Opos__empty(X1),X2) = c_Lazy__Sequence_Oempty(X1),
inference(split_conjunct,[status(thm)],[i_0_10973]),
[final] ).
cnf(i_0_17975,plain,
c_List_Obutlast(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10974]),
[final] ).
cnf(i_0_17976,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10975]),
[final] ).
cnf(i_0_17977,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10976]),
[final] ).
cnf(i_0_17978,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10977]),
[final] ).
cnf(i_0_17979,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_10978]),
[final] ).
cnf(i_0_17980,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_10979]),
[final] ).
cnf(i_0_17981,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_10980]),
[final] ).
cnf(i_0_17982,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,esk28_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10981]),
[final] ).
cnf(i_0_17983,plain,
( c_Option_Ois__none(X2,X1)
| X1 != c_Option_Ooption_ONone(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10967]),
[final] ).
cnf(i_0_17984,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_zminus__0]),
[final] ).
cnf(i_0_17985,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__1]),
[final] ).
cnf(i_0_17986,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__0]),
[final] ).
cnf(i_0_17987,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_code__numeral_Osize_I3_J]),
[final] ).
cnf(i_0_17988,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_nat_Osize_I3_J]),
[final] ).
cnf(i_0_17989,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]),
[final] ).
cnf(i_0_17990,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I1_J]),
[final] ).
cnf(i_0_17991,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10982]),
[final] ).
cnf(i_0_17992,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10983]),
[final] ).
cnf(i_0_17993,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10984]),
[final] ).
cnf(i_0_17994,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10985]),
[final] ).
cnf(i_0_17995,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10986]),
[final] ).
cnf(i_0_17996,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10987]),
[final] ).
cnf(i_0_17997,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Orderings_Oord__class_Omin(X1)
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10988]),
[final] ).
cnf(i_0_17998,plain,
( c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Orderings_Oord__class_Omax(X1)
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10989]),
[final] ).
cnf(i_0_17999,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_10990]),
[final] ).
cnf(i_0_18000,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_10991]),
[final] ).
cnf(i_0_18001,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10992]),
[final] ).
cnf(i_0_18002,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10993]),
[final] ).
cnf(i_0_18003,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10994]),
[final] ).
cnf(i_0_18004,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10995]),
[final] ).
cnf(i_0_18005,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_10205]),
[final] ).
cnf(i_0_18006,plain,
( hAPP(c_Code__Numeral_Oint__of,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(split_conjunct,[status(thm)],[i_0_5237]),
[final] ).
cnf(i_0_18007,plain,
( c_Nitpick_Onat__gcd(X2,X1) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10400]),
[final] ).
cnf(i_0_18008,plain,
c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_Int_OMin__def]),
[final] ).
cnf(i_0_18009,plain,
c_Option_Ois__none(X1,c_Option_Ooption_ONone(X1)),
inference(split_conjunct,[status(thm)],[i_0_10996]),
[final] ).
cnf(i_0_18010,plain,
( ~ class_Rings_Ozero__neq__one(X1)
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10997]),
[final] ).
cnf(i_0_18011,plain,
( ~ class_Rings_Ozero__neq__one(X1)
| c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10998]),
[final] ).
cnf(i_0_18012,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10999]),
[final] ).
cnf(i_0_18013,plain,
c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X1),
inference(split_conjunct,[status(thm)],[i_0_11000]),
[final] ).
cnf(i_0_18014,plain,
( c_Random_Oinc__shift(X1,X2) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10766]),
[final] ).
cnf(i_0_18015,plain,
hAPP(c_Nat_Osize__class_Osize(tc_String_Ochar),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_11001]),
[final] ).
cnf(i_0_18016,plain,
hAPP(c_Nat_Osize__class_Osize(tc_String_Oliteral),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_11002]),
[final] ).
cnf(i_0_18017,plain,
c_Quickcheck_Obeyond(X1,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[i_0_11003]),
[final] ).
cnf(i_0_18018,plain,
X1 = hAPP(c_Int_OAbs__Integ,esk335_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_8751]),
[final] ).
cnf(i_0_18019,plain,
c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1)),
inference(split_conjunct,[status(thm)],[i_0_11004]),
[final] ).
cnf(i_0_18020,plain,
c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1)),
inference(split_conjunct,[status(thm)],[i_0_11005]),
[final] ).
cnf(i_0_18021,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_nat__number__of__Pls]),
[final] ).
cnf(i_0_18022,plain,
hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_bool_Osize_I4_J]),
[final] ).
cnf(i_0_18023,plain,
hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_bool_Osize_I3_J]),
[final] ).
cnf(i_0_18024,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_com_Osize_I9_J]),
[final] ).
cnf(i_0_18025,plain,
hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_nat__0]),
[final] ).
cnf(i_0_18026,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_zero__code__numeral__code]),
[final] ).
cnf(i_0_18027,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_zero__is__num__zero]),
[final] ).
cnf(i_0_18028,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I113_J]),
[final] ).
cnf(i_0_18029,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_one__code__numeral__def]),
[final] ).
cnf(i_0_18030,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I2_J]),
[final] ).
cnf(i_0_18031,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_One__nat__def]),
[final] ).
cnf(i_0_18032,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_zero__code__numeral__def]),
[final] ).
cnf(i_0_18033,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]),
[final] ).
cnf(i_0_18034,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_11006]),
[final] ).
cnf(i_0_18035,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_11007]),
[final] ).
cnf(i_0_18036,negated_conjecture,
~ v_Q(esk493_0,esk495_0),
inference(split_conjunct,[status(thm)],[i_0_9846]),
[final] ).
cnf(i_0_18037,plain,
( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_11008]),
[final] ).
cnf(i_0_18038,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_minus__Pls]),
[final] ).
cnf(i_0_18039,plain,
( X1 = X2
| c_Com_Ovname_OGlb(X1) != c_Com_Ovname_OGlb(X2) ),
inference(split_conjunct,[status(thm)],[i_0_11009]),
[final] ).
cnf(i_0_18040,plain,
( X1 = X2
| c_Com_Ovname_OLoc(X1) != c_Com_Ovname_OLoc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_11010]),
[final] ).
cnf(i_0_18041,plain,
c_Com_Ovname_OGlb(X1) != c_Com_Ovname_OLoc(X2),
inference(split_conjunct,[status(thm)],[i_0_11011]),
[final] ).
cnf(i_0_18042,plain,
c_Com_Ovname_OLoc(X1) != c_Com_Ovname_OGlb(X2),
inference(split_conjunct,[status(thm)],[i_0_11012]),
[final] ).
cnf(i_0_18043,plain,
c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_11013]),
[final] ).
cnf(i_0_18044,plain,
c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_11014]),
[final] ).
cnf(i_0_18045,plain,
c_Equiv__Relations_Oequivp(X1,c_fequal),
inference(split_conjunct,[status(thm)],[i_0_11015]),
[final] ).
cnf(i_0_18046,negated_conjecture,
v_P(esk493_0,esk494_0),
inference(split_conjunct,[status(thm)],[i_0_9846]),
[final] ).
cnf(i_0_18047,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(split_conjunct,[status(thm)],[fact_wf__pred__nat]),
[final] ).
cnf(i_0_18048,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(split_conjunct,[status(thm)],[fact_wf__less__than]),
[final] ).
cnf(i_0_18049,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_code__numeral_Osize_I1_J]),
[final] ).
cnf(i_0_18050,plain,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_nat_Osize_I1_J]),
[final] ).
cnf(i_0_18051,plain,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__list__functions_I2_J]),
[final] ).
cnf(i_0_18052,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__0__neq__1]),
[final] ).
cnf(i_0_18053,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J]),
[final] ).
cnf(i_0_18054,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J]),
[final] ).
cnf(i_0_18055,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_of__int__eq__id]),
[final] ).
cnf(i_0_18056,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_inf__nat__def]),
[final] ).
cnf(i_0_18057,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_bot__nat__def]),
[final] ).
cnf(i_0_18058,plain,
c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_sup__nat__def]),
[final] ).
cnf(i_0_18059,plain,
c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_bool_Osize_I2_J]),
[final] ).
cnf(i_0_18060,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_bool_Osize_I1_J]),
[final] ).
cnf(i_0_18061,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_com_Osize_I1_J]),
[final] ).
cnf(i_0_18062,plain,
~ hBOOL(c_fFalse),
inference(split_conjunct,[status(thm)],[i_0_11016]),
[final] ).
cnf(i_0_18063,plain,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]),
[final] ).
cnf(i_0_18064,plain,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add]),
[final] ).
cnf(i_0_18065,plain,
class_Groups_Osemigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]),
[final] ).
cnf(i_0_18066,plain,
class_Groups_Osemigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]),
[final] ).
cnf(i_0_18067,plain,
class_Smallcheck_Osmall(tc_Product__Type_Ounit),
inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Smallcheck_Osmall]),
[final] ).
cnf(i_0_18068,plain,
class_Smallcheck_Osmall(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Smallcheck_Osmall]),
[final] ).
cnf(i_0_18069,plain,
class_Orderings_Owellorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]),
[final] ).
cnf(i_0_18070,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add]),
[final] ).
cnf(i_0_18071,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__semigroup__add]),
[final] ).
cnf(i_0_18072,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add]),
[final] ).
cnf(i_0_18073,plain,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]),
[final] ).
cnf(i_0_18074,plain,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]),
[final] ).
cnf(i_0_18075,plain,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]),
[final] ).
cnf(i_0_18076,plain,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_18077,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_18078,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_18079,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]),
[final] ).
cnf(i_0_18080,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]),
[final] ).
cnf(i_0_18081,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Obot]),
[final] ).
cnf(i_0_18082,plain,
class_Finite__Set_Ofinite(tc_String_Onibble),
inference(split_conjunct,[status(thm)],[arity_String__Onibble__Finite__Set_Ofinite]),
[final] ).
cnf(i_0_18083,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]),
[final] ).
cnf(i_0_18084,plain,
class_Finite__Set_Ofinite(tc_String_Ochar),
inference(split_conjunct,[status(thm)],[arity_String__Ochar__Finite__Set_Ofinite]),
[final] ).
cnf(i_0_18085,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
[final] ).
cnf(i_0_18086,plain,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]),
[final] ).
cnf(i_0_18087,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
[final] ).
cnf(i_0_18088,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice]),
[final] ).
cnf(i_0_18089,plain,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]),
[final] ).
cnf(i_0_18090,plain,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]),
[final] ).
cnf(i_0_18091,plain,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]),
[final] ).
cnf(i_0_18092,plain,
class_Lattices_Olattice(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Olattice]),
[final] ).
cnf(i_0_18093,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]),
[final] ).
cnf(i_0_18094,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]),
[final] ).
cnf(i_0_18095,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_18096,plain,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Odvd]),
[final] ).
cnf(i_0_18097,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Odvd]),
[final] ).
cnf(i_0_18098,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Odvd]),
[final] ).
cnf(i_0_18099,plain,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0]),
[final] ).
cnf(i_0_18100,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
[final] ).
cnf(i_0_18101,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
[final] ).
cnf(i_0_18102,plain,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Power_Opower]),
[final] ).
cnf(i_0_18103,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
[final] ).
cnf(i_0_18104,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
[final] ).
cnf(i_0_18105,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]),
[final] ).
cnf(i_0_18106,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]),
[final] ).
cnf(i_0_18107,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]),
[final] ).
cnf(i_0_18108,plain,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Int_Onumber]),
[final] ).
cnf(i_0_18109,plain,
class_Int_Onumber(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]),
[final] ).
cnf(i_0_18110,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]),
[final] ).
cnf(i_0_18111,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]),
[final] ).
cnf(i_0_18112,plain,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ominus]),
[final] ).
cnf(i_0_18113,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]),
[final] ).
cnf(i_0_18114,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
[final] ).
cnf(i_0_18115,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]),
[final] ).
cnf(i_0_18116,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
[final] ).
cnf(i_0_18117,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
[final] ).
cnf(i_0_18118,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]),
[final] ).
cnf(i_0_18119,plain,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div]),
[final] ).
cnf(i_0_18120,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
[final] ).
cnf(i_0_18121,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
[final] ).
cnf(i_0_18122,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
[final] ).
cnf(i_0_18123,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]),
[final] ).
cnf(i_0_18124,plain,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_18125,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_18126,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_18127,plain,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring]),
[final] ).
cnf(i_0_18128,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]),
[final] ).
cnf(i_0_18129,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]),
[final] ).
cnf(i_0_18130,plain,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_18131,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_18132,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_18133,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
[final] ).
cnf(i_0_18134,plain,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring]),
[final] ).
cnf(i_0_18135,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]),
[final] ).
cnf(i_0_18136,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]),
[final] ).
cnf(i_0_18137,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add]),
[final] ).
cnf(i_0_18138,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]),
[final] ).
cnf(i_0_18139,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]),
[final] ).
cnf(i_0_18140,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]),
[final] ).
cnf(i_0_18141,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]),
[final] ).
cnf(i_0_18142,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_18143,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_18144,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_18145,plain,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_18146,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_18147,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_18148,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]),
[final] ).
cnf(i_0_18149,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_18150,plain,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_18151,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_18152,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_18153,plain,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring]),
[final] ).
cnf(i_0_18154,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
[final] ).
cnf(i_0_18155,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
[final] ).
cnf(i_0_18156,plain,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_18157,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_18158,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_18159,plain,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_18160,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_18161,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_18162,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]),
[final] ).
cnf(i_0_18163,plain,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero]),
[final] ).
cnf(i_0_18164,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
[final] ).
cnf(i_0_18165,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
[final] ).
cnf(i_0_18166,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]),
[final] ).
cnf(i_0_18167,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]),
[final] ).
cnf(i_0_18168,plain,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_18169,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_18170,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_18171,plain,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oone]),
[final] ).
cnf(i_0_18172,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
[final] ).
cnf(i_0_18173,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_18174,plain,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_18175,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_18176,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_18177,plain,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_18178,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_18179,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_18180,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
[final] ).
cnf(i_0_18181,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]),
[final] ).
cnf(i_0_18182,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]),
[final] ).
cnf(i_0_18183,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
[final] ).
cnf(i_0_18184,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
[final] ).
cnf(i_0_18185,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]),
[final] ).
cnf(i_0_18186,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
[final] ).
cnf(i_0_18187,plain,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oord]),
[final] ).
cnf(i_0_18188,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
[final] ).
cnf(i_0_18189,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_18190,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_18191,plain,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder]),
[final] ).
cnf(i_0_18192,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
[final] ).
cnf(i_0_18193,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_18194,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_18195,plain,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder]),
[final] ).
cnf(i_0_18196,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
[final] ).
cnf(i_0_18197,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_18198,plain,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oorder]),
[final] ).
cnf(i_0_18199,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
[final] ).
cnf(i_0_18200,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_18201,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_18202,plain,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0]),
[final] ).
cnf(i_0_18203,plain,
class_Nat_Osemiring__char__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]),
[final] ).
cnf(i_0_18204,plain,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]),
[final] ).
cnf(i_0_18205,plain,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_18206,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_18207,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_18208,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_18209,plain,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_18210,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_18211,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_18212,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_18213,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_18214,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_18215,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_18216,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_18217,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_18218,plain,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1]),
[final] ).
cnf(i_0_18219,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]),
[final] ).
cnf(i_0_18220,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]),
[final] ).
cnf(i_0_18221,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
[final] ).
cnf(i_0_18222,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
[final] ).
cnf(i_0_18223,plain,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_18224,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_18225,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_18226,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]),
[final] ).
cnf(i_0_18227,plain,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_18228,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_18229,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_18230,plain,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add]),
[final] ).
cnf(i_0_18231,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
[final] ).
cnf(i_0_18232,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_18233,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_18234,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_18235,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_18236,plain,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_18237,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_18238,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_18239,plain,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_18240,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_18241,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_18242,plain,
hBOOL(c_fTrue),
inference(split_conjunct,[status(thm)],[help_c__fTrue__1]),
[final] ).
cnf(i_0_18243,plain,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ozero]),
[final] ).
cnf(i_0_18244,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
[final] ).
cnf(i_0_18245,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_18246,plain,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[fact_Code__Numeral_Oof__nat__code]),
[final] ).
cnf(i_0_18247,plain,
c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(split_conjunct,[status(thm)],[fact_subtract__code__numeral__def]),
[final] ).
cnf(i_0_18248,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]),
[final] ).
cnf(i_0_18249,plain,
c_Int_OPls != c_Int_OMin,
inference(split_conjunct,[status(thm)],[fact_rel__simps_I37_J]),
[final] ).
cnf(i_0_18250,plain,
c_Int_OMin != c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_rel__simps_I40_J]),
[final] ).
cnf(i_0_18251,axiom,
X1 = X1 ).
cnf(i_0_18252,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_18253,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_18254,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_18255,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_18256,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X1,X3,X4) = c_Com_Ocom_OCond(X2,X3,X4) ) ).
cnf(i_0_18257,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X3,X1,X4) = c_Com_Ocom_OCond(X3,X2,X4) ) ).
cnf(i_0_18258,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X3,X4,X1) = c_Com_Ocom_OCond(X3,X4,X2) ) ).
cnf(i_0_18259,axiom,
( X1 != X2
| c_Map_Omap__upds(X1,X3,X4,X5,X6) = c_Map_Omap__upds(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18260,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X1,X4,X5,X6) = c_Map_Omap__upds(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18261,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X4,X1,X5,X6) = c_Map_Omap__upds(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18262,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X4,X5,X1,X6) = c_Map_Omap__upds(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18263,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X4,X5,X6,X1) = c_Map_Omap__upds(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18264,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).
cnf(i_0_18265,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).
cnf(i_0_18266,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).
cnf(i_0_18267,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).
cnf(i_0_18268,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).
cnf(i_0_18269,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).
cnf(i_0_18270,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X1,X3,X4,X5) = c_Option_Ooption_Ooption__case(X2,X3,X4,X5) ) ).
cnf(i_0_18271,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X3,X1,X4,X5) = c_Option_Ooption_Ooption__case(X3,X2,X4,X5) ) ).
cnf(i_0_18272,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X3,X4,X1,X5) = c_Option_Ooption_Ooption__case(X3,X4,X2,X5) ) ).
cnf(i_0_18273,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X3,X4,X5,X1) = c_Option_Ooption_Ooption__case(X3,X4,X5,X2) ) ).
cnf(i_0_18274,axiom,
( X1 != X2
| c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).
cnf(i_0_18275,axiom,
( X1 != X2
| c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).
cnf(i_0_18276,axiom,
( X1 != X2
| c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).
cnf(i_0_18277,axiom,
( X1 != X2
| c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).
cnf(i_0_18278,axiom,
( X1 != X2
| c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).
cnf(i_0_18279,axiom,
( X1 != X2
| c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).
cnf(i_0_18280,axiom,
( X1 != X2
| c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).
cnf(i_0_18281,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).
cnf(i_0_18282,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).
cnf(i_0_18283,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).
cnf(i_0_18284,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).
cnf(i_0_18285,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_18286,axiom,
( X1 != X2
| c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).
cnf(i_0_18287,axiom,
( X1 != X2
| c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).
cnf(i_0_18288,axiom,
( X1 != X2
| c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).
cnf(i_0_18289,axiom,
( X1 != X2
| c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).
cnf(i_0_18290,axiom,
( X1 != X2
| c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).
cnf(i_0_18291,axiom,
( X1 != X2
| c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).
cnf(i_0_18292,axiom,
( X1 != X2
| c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).
cnf(i_0_18293,axiom,
( X1 != X2
| c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).
cnf(i_0_18294,axiom,
( X1 != X2
| c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).
cnf(i_0_18295,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).
cnf(i_0_18296,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).
cnf(i_0_18297,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).
cnf(i_0_18298,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).
cnf(i_0_18299,axiom,
( X1 != X2
| c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).
cnf(i_0_18300,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).
cnf(i_0_18301,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).
cnf(i_0_18302,axiom,
( X1 != X2
| c_List_Olinorder__class_Osorted__list__of__set(X1,X3) = c_List_Olinorder__class_Osorted__list__of__set(X2,X3) ) ).
cnf(i_0_18303,axiom,
( X1 != X2
| c_List_Olinorder__class_Osorted__list__of__set(X3,X1) = c_List_Olinorder__class_Osorted__list__of__set(X3,X2) ) ).
cnf(i_0_18304,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).
cnf(i_0_18305,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).
cnf(i_0_18306,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).
cnf(i_0_18307,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).
cnf(i_0_18308,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).
cnf(i_0_18309,axiom,
( X1 != X2
| c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).
cnf(i_0_18310,axiom,
( X1 != X2
| c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).
cnf(i_0_18311,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_18312,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_18313,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_18314,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_18315,axiom,
( X1 != X2
| c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).
cnf(i_0_18316,axiom,
( X1 != X2
| c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).
cnf(i_0_18317,axiom,
( X1 != X2
| c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).
cnf(i_0_18318,axiom,
( X1 != X2
| c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).
cnf(i_0_18319,axiom,
( X1 != X2
| c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).
cnf(i_0_18320,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X1,X3,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X2,X3,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18321,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X1,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X2,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18322,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X1,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X2,X5,X6,X7,X8) ) ).
cnf(i_0_18323,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X1,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X2,X6,X7,X8) ) ).
cnf(i_0_18324,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X1,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X2,X7,X8) ) ).
cnf(i_0_18325,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X1,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X2,X8) ) ).
cnf(i_0_18326,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X8,X1) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X8,X2) ) ).
cnf(i_0_18327,axiom,
( X1 != X2
| c_New__DSequence_Oneg__decr__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18328,axiom,
( X1 != X2
| c_New__DSequence_Oneg__decr__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__decr__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18329,axiom,
( X1 != X2
| c_New__DSequence_Oneg__decr__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__decr__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18330,axiom,
( X1 != X2
| c_New__DSequence_Oneg__decr__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__decr__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18331,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).
cnf(i_0_18332,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X1,X3,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X2,X3,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18333,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X1,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X2,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18334,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X4,X1,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X2,X5,X6,X7,X8) ) ).
cnf(i_0_18335,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X1,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X2,X6,X7,X8) ) ).
cnf(i_0_18336,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X1,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X2,X7,X8) ) ).
cnf(i_0_18337,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X1,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X2,X8) ) ).
cnf(i_0_18338,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X8,X1) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X8,X2) ) ).
cnf(i_0_18339,axiom,
( X1 != X2
| c_New__DSequence_Opos__decr__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__decr__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18340,axiom,
( X1 != X2
| c_New__DSequence_Opos__decr__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__decr__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18341,axiom,
( X1 != X2
| c_New__DSequence_Opos__decr__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__decr__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18342,axiom,
( X1 != X2
| c_New__DSequence_Opos__decr__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__decr__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18343,axiom,
( X1 != X2
| c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).
cnf(i_0_18344,axiom,
( X1 != X2
| c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).
cnf(i_0_18345,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).
cnf(i_0_18346,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).
cnf(i_0_18347,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__bind(X1,X3,X4,X5) = c_New__Random__Sequence_Oneg__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18348,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__bind(X3,X1,X4,X5) = c_New__Random__Sequence_Oneg__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18349,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__bind(X3,X4,X1,X5) = c_New__Random__Sequence_Oneg__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18350,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__bind(X3,X4,X5,X1) = c_New__Random__Sequence_Oneg__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18351,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18352,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18353,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18354,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18355,axiom,
( X1 != X2
| esk381_5(X1,X3,X4,X5,X6) = esk381_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18356,axiom,
( X1 != X2
| esk381_5(X3,X1,X4,X5,X6) = esk381_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18357,axiom,
( X1 != X2
| esk381_5(X3,X4,X1,X5,X6) = esk381_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18358,axiom,
( X1 != X2
| esk381_5(X3,X4,X5,X1,X6) = esk381_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18359,axiom,
( X1 != X2
| esk381_5(X3,X4,X5,X6,X1) = esk381_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18360,axiom,
( X1 != X2
| esk382_5(X1,X3,X4,X5,X6) = esk382_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18361,axiom,
( X1 != X2
| esk382_5(X3,X1,X4,X5,X6) = esk382_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18362,axiom,
( X1 != X2
| esk382_5(X3,X4,X1,X5,X6) = esk382_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18363,axiom,
( X1 != X2
| esk382_5(X3,X4,X5,X1,X6) = esk382_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18364,axiom,
( X1 != X2
| esk382_5(X3,X4,X5,X6,X1) = esk382_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18365,axiom,
( X1 != X2
| esk377_5(X1,X3,X4,X5,X6) = esk377_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18366,axiom,
( X1 != X2
| esk377_5(X3,X1,X4,X5,X6) = esk377_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18367,axiom,
( X1 != X2
| esk377_5(X3,X4,X1,X5,X6) = esk377_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18368,axiom,
( X1 != X2
| esk377_5(X3,X4,X5,X1,X6) = esk377_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18369,axiom,
( X1 != X2
| esk377_5(X3,X4,X5,X6,X1) = esk377_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18370,axiom,
( X1 != X2
| esk376_5(X1,X3,X4,X5,X6) = esk376_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18371,axiom,
( X1 != X2
| esk376_5(X3,X1,X4,X5,X6) = esk376_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18372,axiom,
( X1 != X2
| esk376_5(X3,X4,X1,X5,X6) = esk376_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18373,axiom,
( X1 != X2
| esk376_5(X3,X4,X5,X1,X6) = esk376_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18374,axiom,
( X1 != X2
| esk376_5(X3,X4,X5,X6,X1) = esk376_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18375,axiom,
( X1 != X2
| c_Option_Ooption_ONone(X1) = c_Option_Ooption_ONone(X2) ) ).
cnf(i_0_18376,axiom,
( X1 != X2
| c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).
cnf(i_0_18377,axiom,
( X1 != X2
| c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).
cnf(i_0_18378,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__bind(X1,X3,X4,X5) = c_New__Random__Sequence_Opos__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18379,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__bind(X3,X1,X4,X5) = c_New__Random__Sequence_Opos__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18380,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__bind(X3,X4,X1,X5) = c_New__Random__Sequence_Opos__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18381,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__bind(X3,X4,X5,X1) = c_New__Random__Sequence_Opos__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18382,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18383,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18384,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18385,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18386,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18387,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18388,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18389,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18390,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18391,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18392,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18393,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18394,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18395,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18396,axiom,
( X1 != X2
| c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).
cnf(i_0_18397,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).
cnf(i_0_18398,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).
cnf(i_0_18399,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).
cnf(i_0_18400,axiom,
( X1 != X2
| esk241_6(X1,X3,X4,X5,X6,X7) = esk241_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18401,axiom,
( X1 != X2
| esk241_6(X3,X1,X4,X5,X6,X7) = esk241_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18402,axiom,
( X1 != X2
| esk241_6(X3,X4,X1,X5,X6,X7) = esk241_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18403,axiom,
( X1 != X2
| esk241_6(X3,X4,X5,X1,X6,X7) = esk241_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18404,axiom,
( X1 != X2
| esk241_6(X3,X4,X5,X6,X1,X7) = esk241_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18405,axiom,
( X1 != X2
| esk241_6(X3,X4,X5,X6,X7,X1) = esk241_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18406,axiom,
( X1 != X2
| esk240_6(X1,X3,X4,X5,X6,X7) = esk240_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18407,axiom,
( X1 != X2
| esk240_6(X3,X1,X4,X5,X6,X7) = esk240_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18408,axiom,
( X1 != X2
| esk240_6(X3,X4,X1,X5,X6,X7) = esk240_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18409,axiom,
( X1 != X2
| esk240_6(X3,X4,X5,X1,X6,X7) = esk240_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18410,axiom,
( X1 != X2
| esk240_6(X3,X4,X5,X6,X1,X7) = esk240_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18411,axiom,
( X1 != X2
| esk240_6(X3,X4,X5,X6,X7,X1) = esk240_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18412,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).
cnf(i_0_18413,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_18414,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).
cnf(i_0_18415,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).
cnf(i_0_18416,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).
cnf(i_0_18417,axiom,
( X1 != X2
| c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).
cnf(i_0_18418,axiom,
( X1 != X2
| c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).
cnf(i_0_18419,axiom,
( X1 != X2
| c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).
cnf(i_0_18420,axiom,
( X1 != X2
| c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).
cnf(i_0_18421,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).
cnf(i_0_18422,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).
cnf(i_0_18423,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).
cnf(i_0_18424,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).
cnf(i_0_18425,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).
cnf(i_0_18426,axiom,
( X1 != X2
| c_List_Omap__filter(X1,X3,X4,X5) = c_List_Omap__filter(X2,X3,X4,X5) ) ).
cnf(i_0_18427,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X1,X4,X5) = c_List_Omap__filter(X3,X2,X4,X5) ) ).
cnf(i_0_18428,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X4,X1,X5) = c_List_Omap__filter(X3,X4,X2,X5) ) ).
cnf(i_0_18429,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X4,X5,X1) = c_List_Omap__filter(X3,X4,X5,X2) ) ).
cnf(i_0_18430,axiom,
( X1 != X2
| c_Map_Odom(X1,X3,X4) = c_Map_Odom(X2,X3,X4) ) ).
cnf(i_0_18431,axiom,
( X1 != X2
| c_Map_Odom(X3,X1,X4) = c_Map_Odom(X3,X2,X4) ) ).
cnf(i_0_18432,axiom,
( X1 != X2
| c_Map_Odom(X3,X4,X1) = c_Map_Odom(X3,X4,X2) ) ).
cnf(i_0_18433,axiom,
( X1 != X2
| c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).
cnf(i_0_18434,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X1,X3,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X2,X3,X4,X5) ) ).
cnf(i_0_18435,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X1,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X2,X4,X5) ) ).
cnf(i_0_18436,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X1,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X2,X5) ) ).
cnf(i_0_18437,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X2) ) ).
cnf(i_0_18438,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_18439,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_18440,axiom,
( X1 != X2
| c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).
cnf(i_0_18441,axiom,
( X1 != X2
| c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).
cnf(i_0_18442,axiom,
( X1 != X2
| c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).
cnf(i_0_18443,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).
cnf(i_0_18444,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).
cnf(i_0_18445,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).
cnf(i_0_18446,axiom,
( X1 != X2
| c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).
cnf(i_0_18447,axiom,
( X1 != X2
| c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).
cnf(i_0_18448,axiom,
( X1 != X2
| c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).
cnf(i_0_18449,axiom,
( X1 != X2
| c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).
cnf(i_0_18450,axiom,
( X1 != X2
| esk473_4(X1,X3,X4,X5) = esk473_4(X2,X3,X4,X5) ) ).
cnf(i_0_18451,axiom,
( X1 != X2
| esk473_4(X3,X1,X4,X5) = esk473_4(X3,X2,X4,X5) ) ).
cnf(i_0_18452,axiom,
( X1 != X2
| esk473_4(X3,X4,X1,X5) = esk473_4(X3,X4,X2,X5) ) ).
cnf(i_0_18453,axiom,
( X1 != X2
| esk473_4(X3,X4,X5,X1) = esk473_4(X3,X4,X5,X2) ) ).
cnf(i_0_18454,axiom,
( X1 != X2
| esk472_4(X1,X3,X4,X5) = esk472_4(X2,X3,X4,X5) ) ).
cnf(i_0_18455,axiom,
( X1 != X2
| esk472_4(X3,X1,X4,X5) = esk472_4(X3,X2,X4,X5) ) ).
cnf(i_0_18456,axiom,
( X1 != X2
| esk472_4(X3,X4,X1,X5) = esk472_4(X3,X4,X2,X5) ) ).
cnf(i_0_18457,axiom,
( X1 != X2
| esk472_4(X3,X4,X5,X1) = esk472_4(X3,X4,X5,X2) ) ).
cnf(i_0_18458,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X1,X3,X4,X5,X6) = c_Fun_Ooverride__on(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18459,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X1,X4,X5,X6) = c_Fun_Ooverride__on(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18460,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X1,X5,X6) = c_Fun_Ooverride__on(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18461,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X5,X1,X6) = c_Fun_Ooverride__on(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18462,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X5,X6,X1) = c_Fun_Ooverride__on(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18463,axiom,
( X1 != X2
| c_Map_Oran(X1,X3,X4) = c_Map_Oran(X2,X3,X4) ) ).
cnf(i_0_18464,axiom,
( X1 != X2
| c_Map_Oran(X3,X1,X4) = c_Map_Oran(X3,X2,X4) ) ).
cnf(i_0_18465,axiom,
( X1 != X2
| c_Map_Oran(X3,X4,X1) = c_Map_Oran(X3,X4,X2) ) ).
cnf(i_0_18466,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_18467,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_18468,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_18469,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_18470,axiom,
( X1 != X2
| c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).
cnf(i_0_18471,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).
cnf(i_0_18472,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).
cnf(i_0_18473,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).
cnf(i_0_18474,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_18475,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).
cnf(i_0_18476,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).
cnf(i_0_18477,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).
cnf(i_0_18478,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).
cnf(i_0_18479,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).
cnf(i_0_18480,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).
cnf(i_0_18481,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).
cnf(i_0_18482,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).
cnf(i_0_18483,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).
cnf(i_0_18484,axiom,
( X1 != X2
| c_Map_Orestrict__map(X1,X3,X4,X5) = c_Map_Orestrict__map(X2,X3,X4,X5) ) ).
cnf(i_0_18485,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X1,X4,X5) = c_Map_Orestrict__map(X3,X2,X4,X5) ) ).
cnf(i_0_18486,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X4,X1,X5) = c_Map_Orestrict__map(X3,X4,X2,X5) ) ).
cnf(i_0_18487,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X4,X5,X1) = c_Map_Orestrict__map(X3,X4,X5,X2) ) ).
cnf(i_0_18488,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).
cnf(i_0_18489,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).
cnf(i_0_18490,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).
cnf(i_0_18491,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OInf__fin(X1,X3,X4) = c_Big__Operators_Olattice_OInf__fin(X2,X3,X4) ) ).
cnf(i_0_18492,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OInf__fin(X3,X1,X4) = c_Big__Operators_Olattice_OInf__fin(X3,X2,X4) ) ).
cnf(i_0_18493,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OInf__fin(X3,X4,X1) = c_Big__Operators_Olattice_OInf__fin(X3,X4,X2) ) ).
cnf(i_0_18494,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).
cnf(i_0_18495,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).
cnf(i_0_18496,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).
cnf(i_0_18497,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).
cnf(i_0_18498,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OSup__fin(X1,X3,X4) = c_Big__Operators_Olattice_OSup__fin(X2,X3,X4) ) ).
cnf(i_0_18499,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OSup__fin(X3,X1,X4) = c_Big__Operators_Olattice_OSup__fin(X3,X2,X4) ) ).
cnf(i_0_18500,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OSup__fin(X3,X4,X1) = c_Big__Operators_Olattice_OSup__fin(X3,X4,X2) ) ).
cnf(i_0_18501,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).
cnf(i_0_18502,axiom,
( X1 != X2
| c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).
cnf(i_0_18503,axiom,
( X1 != X2
| c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).
cnf(i_0_18504,axiom,
( X1 != X2
| c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).
cnf(i_0_18505,axiom,
( X1 != X2
| c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).
cnf(i_0_18506,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__case(X1,X3,X4,X5,X6) = c_Sum__Type_Osum_Osum__case(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18507,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__case(X3,X1,X4,X5,X6) = c_Sum__Type_Osum_Osum__case(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18508,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__case(X3,X4,X1,X5,X6) = c_Sum__Type_Osum_Osum__case(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18509,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__case(X3,X4,X5,X1,X6) = c_Sum__Type_Osum_Osum__case(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18510,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__case(X3,X4,X5,X6,X1) = c_Sum__Type_Osum_Osum__case(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18511,axiom,
( X1 != X2
| c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).
cnf(i_0_18512,axiom,
( X1 != X2
| c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).
cnf(i_0_18513,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).
cnf(i_0_18514,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).
cnf(i_0_18515,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).
cnf(i_0_18516,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OSup__fin(X1,X3) = c_Big__Operators_Olattice__class_OSup__fin(X2,X3) ) ).
cnf(i_0_18517,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OSup__fin(X3,X1) = c_Big__Operators_Olattice__class_OSup__fin(X3,X2) ) ).
cnf(i_0_18518,axiom,
( X1 != X2
| c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).
cnf(i_0_18519,axiom,
( X1 != X2
| c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).
cnf(i_0_18520,axiom,
( X1 != X2
| c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).
cnf(i_0_18521,axiom,
( X1 != X2
| c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).
cnf(i_0_18522,axiom,
( X1 != X2
| c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).
cnf(i_0_18523,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X1,X3,X4,X5,X6,X7) = c_Sum__Type_Osum_Osum__rec(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18524,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X3,X1,X4,X5,X6,X7) = c_Sum__Type_Osum_Osum__rec(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18525,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X3,X4,X1,X5,X6,X7) = c_Sum__Type_Osum_Osum__rec(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18526,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X1,X6,X7) = c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18527,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X6,X1,X7) = c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18528,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X6,X7,X1) = c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18529,axiom,
( X1 != X2
| c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).
cnf(i_0_18530,axiom,
( X1 != X2
| esk370_3(X1,X3,X4) = esk370_3(X2,X3,X4) ) ).
cnf(i_0_18531,axiom,
( X1 != X2
| esk370_3(X3,X1,X4) = esk370_3(X3,X2,X4) ) ).
cnf(i_0_18532,axiom,
( X1 != X2
| esk370_3(X3,X4,X1) = esk370_3(X3,X4,X2) ) ).
cnf(i_0_18533,axiom,
( X1 != X2
| esk369_3(X1,X3,X4) = esk369_3(X2,X3,X4) ) ).
cnf(i_0_18534,axiom,
( X1 != X2
| esk369_3(X3,X1,X4) = esk369_3(X3,X2,X4) ) ).
cnf(i_0_18535,axiom,
( X1 != X2
| esk369_3(X3,X4,X1) = esk369_3(X3,X4,X2) ) ).
cnf(i_0_18536,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X1,X3,X4) = c_Smallcheck_Osmall_H(X2,X3,X4) ) ).
cnf(i_0_18537,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X3,X1,X4) = c_Smallcheck_Osmall_H(X3,X2,X4) ) ).
cnf(i_0_18538,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X3,X4,X1) = c_Smallcheck_Osmall_H(X3,X4,X2) ) ).
cnf(i_0_18539,axiom,
( X1 != X2
| c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).
cnf(i_0_18540,axiom,
( X1 != X2
| c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).
cnf(i_0_18541,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5) ) ).
cnf(i_0_18542,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X1,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X2,X4,X5) ) ).
cnf(i_0_18543,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X4,X1,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X2,X5) ) ).
cnf(i_0_18544,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X2) ) ).
cnf(i_0_18545,axiom,
( X1 != X2
| c_List_Olinorder__class_Oinsort__insert__key(X1,X3,X4,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18546,axiom,
( X1 != X2
| c_List_Olinorder__class_Oinsort__insert__key(X3,X1,X4,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18547,axiom,
( X1 != X2
| c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X1,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18548,axiom,
( X1 != X2
| c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X1,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18549,axiom,
( X1 != X2
| c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X6,X1) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18550,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OInf__fin(X1,X3) = c_Big__Operators_Olattice__class_OInf__fin(X2,X3) ) ).
cnf(i_0_18551,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OInf__fin(X3,X1) = c_Big__Operators_Olattice__class_OInf__fin(X3,X2) ) ).
cnf(i_0_18552,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X1,X3,X4) = c_Com_Ocom_OLocal(X2,X3,X4) ) ).
cnf(i_0_18553,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X3,X1,X4) = c_Com_Ocom_OLocal(X3,X2,X4) ) ).
cnf(i_0_18554,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X3,X4,X1) = c_Com_Ocom_OLocal(X3,X4,X2) ) ).
cnf(i_0_18555,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).
cnf(i_0_18556,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).
cnf(i_0_18557,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__map(X1,X3,X4,X5) = c_New__Random__Sequence_Oneg__map(X2,X3,X4,X5) ) ).
cnf(i_0_18558,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__map(X3,X1,X4,X5) = c_New__Random__Sequence_Oneg__map(X3,X2,X4,X5) ) ).
cnf(i_0_18559,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__map(X3,X4,X1,X5) = c_New__Random__Sequence_Oneg__map(X3,X4,X2,X5) ) ).
cnf(i_0_18560,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__map(X3,X4,X5,X1) = c_New__Random__Sequence_Oneg__map(X3,X4,X5,X2) ) ).
cnf(i_0_18561,axiom,
( X1 != X2
| c_Com_Ocom_OWhile(X1,X3) = c_Com_Ocom_OWhile(X2,X3) ) ).
cnf(i_0_18562,axiom,
( X1 != X2
| c_Com_Ocom_OWhile(X3,X1) = c_Com_Ocom_OWhile(X3,X2) ) ).
cnf(i_0_18563,axiom,
( X1 != X2
| c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).
cnf(i_0_18564,axiom,
( X1 != X2
| c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).
cnf(i_0_18565,axiom,
( X1 != X2
| c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).
cnf(i_0_18566,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__map(X1,X3,X4,X5) = c_New__Random__Sequence_Opos__map(X2,X3,X4,X5) ) ).
cnf(i_0_18567,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__map(X3,X1,X4,X5) = c_New__Random__Sequence_Opos__map(X3,X2,X4,X5) ) ).
cnf(i_0_18568,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__map(X3,X4,X1,X5) = c_New__Random__Sequence_Opos__map(X3,X4,X2,X5) ) ).
cnf(i_0_18569,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__map(X3,X4,X5,X1) = c_New__Random__Sequence_Opos__map(X3,X4,X5,X2) ) ).
cnf(i_0_18570,axiom,
( X1 != X2
| esk266_5(X1,X3,X4,X5,X6) = esk266_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18571,axiom,
( X1 != X2
| esk266_5(X3,X1,X4,X5,X6) = esk266_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18572,axiom,
( X1 != X2
| esk266_5(X3,X4,X1,X5,X6) = esk266_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18573,axiom,
( X1 != X2
| esk266_5(X3,X4,X5,X1,X6) = esk266_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18574,axiom,
( X1 != X2
| esk266_5(X3,X4,X5,X6,X1) = esk266_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18575,axiom,
( X1 != X2
| esk380_3(X1,X3,X4) = esk380_3(X2,X3,X4) ) ).
cnf(i_0_18576,axiom,
( X1 != X2
| esk380_3(X3,X1,X4) = esk380_3(X3,X2,X4) ) ).
cnf(i_0_18577,axiom,
( X1 != X2
| esk380_3(X3,X4,X1) = esk380_3(X3,X4,X2) ) ).
cnf(i_0_18578,axiom,
( X1 != X2
| esk379_3(X1,X3,X4) = esk379_3(X2,X3,X4) ) ).
cnf(i_0_18579,axiom,
( X1 != X2
| esk379_3(X3,X1,X4) = esk379_3(X3,X2,X4) ) ).
cnf(i_0_18580,axiom,
( X1 != X2
| esk379_3(X3,X4,X1) = esk379_3(X3,X4,X2) ) ).
cnf(i_0_18581,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__size(X1,X3,X4,X5,X6) = c_Product__Type_Oprod_Oprod__size(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18582,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__size(X3,X1,X4,X5,X6) = c_Product__Type_Oprod_Oprod__size(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18583,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__size(X3,X4,X1,X5,X6) = c_Product__Type_Oprod_Oprod__size(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18584,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X1,X6) = c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18585,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X6,X1) = c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18586,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).
cnf(i_0_18587,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).
cnf(i_0_18588,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).
cnf(i_0_18589,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).
cnf(i_0_18590,axiom,
( X1 != X2
| c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).
cnf(i_0_18591,axiom,
( X1 != X2
| c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).
cnf(i_0_18592,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X1,X3,X4,X5,X6,X7) = c_Product__Type_Omap__pair(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18593,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X3,X1,X4,X5,X6,X7) = c_Product__Type_Omap__pair(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18594,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X3,X4,X1,X5,X6,X7) = c_Product__Type_Omap__pair(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18595,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X3,X4,X5,X1,X6,X7) = c_Product__Type_Omap__pair(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18596,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X3,X4,X5,X6,X1,X7) = c_Product__Type_Omap__pair(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18597,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X3,X4,X5,X6,X7,X1) = c_Product__Type_Omap__pair(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18598,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).
cnf(i_0_18599,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).
cnf(i_0_18600,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).
cnf(i_0_18601,axiom,
( X1 != X2
| c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).
cnf(i_0_18602,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).
cnf(i_0_18603,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).
cnf(i_0_18604,axiom,
( X1 != X2
| c_Com_Ovname_OLoc(X1) = c_Com_Ovname_OLoc(X2) ) ).
cnf(i_0_18605,axiom,
( X1 != X2
| esk91_3(X1,X3,X4) = esk91_3(X2,X3,X4) ) ).
cnf(i_0_18606,axiom,
( X1 != X2
| esk91_3(X3,X1,X4) = esk91_3(X3,X2,X4) ) ).
cnf(i_0_18607,axiom,
( X1 != X2
| esk91_3(X3,X4,X1) = esk91_3(X3,X4,X2) ) ).
cnf(i_0_18608,axiom,
( X1 != X2
| esk158_4(X1,X3,X4,X5) = esk158_4(X2,X3,X4,X5) ) ).
cnf(i_0_18609,axiom,
( X1 != X2
| esk158_4(X3,X1,X4,X5) = esk158_4(X3,X2,X4,X5) ) ).
cnf(i_0_18610,axiom,
( X1 != X2
| esk158_4(X3,X4,X1,X5) = esk158_4(X3,X4,X2,X5) ) ).
cnf(i_0_18611,axiom,
( X1 != X2
| esk158_4(X3,X4,X5,X1) = esk158_4(X3,X4,X5,X2) ) ).
cnf(i_0_18612,axiom,
( X1 != X2
| esk160_4(X1,X3,X4,X5) = esk160_4(X2,X3,X4,X5) ) ).
cnf(i_0_18613,axiom,
( X1 != X2
| esk160_4(X3,X1,X4,X5) = esk160_4(X3,X2,X4,X5) ) ).
cnf(i_0_18614,axiom,
( X1 != X2
| esk160_4(X3,X4,X1,X5) = esk160_4(X3,X4,X2,X5) ) ).
cnf(i_0_18615,axiom,
( X1 != X2
| esk160_4(X3,X4,X5,X1) = esk160_4(X3,X4,X5,X2) ) ).
cnf(i_0_18616,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X1,X3,X4) = c_Com_Ocom_OCall(X2,X3,X4) ) ).
cnf(i_0_18617,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X3,X1,X4) = c_Com_Ocom_OCall(X3,X2,X4) ) ).
cnf(i_0_18618,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X3,X4,X1) = c_Com_Ocom_OCall(X3,X4,X2) ) ).
cnf(i_0_18619,axiom,
( X1 != X2
| esk264_4(X1,X3,X4,X5) = esk264_4(X2,X3,X4,X5) ) ).
cnf(i_0_18620,axiom,
( X1 != X2
| esk264_4(X3,X1,X4,X5) = esk264_4(X3,X2,X4,X5) ) ).
cnf(i_0_18621,axiom,
( X1 != X2
| esk264_4(X3,X4,X1,X5) = esk264_4(X3,X4,X2,X5) ) ).
cnf(i_0_18622,axiom,
( X1 != X2
| esk264_4(X3,X4,X5,X1) = esk264_4(X3,X4,X5,X2) ) ).
cnf(i_0_18623,axiom,
( X1 != X2
| esk263_4(X1,X3,X4,X5) = esk263_4(X2,X3,X4,X5) ) ).
cnf(i_0_18624,axiom,
( X1 != X2
| esk263_4(X3,X1,X4,X5) = esk263_4(X3,X2,X4,X5) ) ).
cnf(i_0_18625,axiom,
( X1 != X2
| esk263_4(X3,X4,X1,X5) = esk263_4(X3,X4,X2,X5) ) ).
cnf(i_0_18626,axiom,
( X1 != X2
| esk263_4(X3,X4,X5,X1) = esk263_4(X3,X4,X5,X2) ) ).
cnf(i_0_18627,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__size(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18628,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__size(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18629,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__size(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18630,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18631,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18632,axiom,
( X1 != X2
| c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).
cnf(i_0_18633,axiom,
( X1 != X2
| c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).
cnf(i_0_18634,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X1,X3,X4,X5) = c_Nitpick_Opair__box_OPairBox(X2,X3,X4,X5) ) ).
cnf(i_0_18635,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X3,X1,X4,X5) = c_Nitpick_Opair__box_OPairBox(X3,X2,X4,X5) ) ).
cnf(i_0_18636,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) = c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X5) ) ).
cnf(i_0_18637,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) = c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X2) ) ).
cnf(i_0_18638,axiom,
( X1 != X2
| esk405_3(X1,X3,X4) = esk405_3(X2,X3,X4) ) ).
cnf(i_0_18639,axiom,
( X1 != X2
| esk405_3(X3,X1,X4) = esk405_3(X3,X2,X4) ) ).
cnf(i_0_18640,axiom,
( X1 != X2
| esk405_3(X3,X4,X1) = esk405_3(X3,X4,X2) ) ).
cnf(i_0_18641,axiom,
( X1 != X2
| esk406_3(X1,X3,X4) = esk406_3(X2,X3,X4) ) ).
cnf(i_0_18642,axiom,
( X1 != X2
| esk406_3(X3,X1,X4) = esk406_3(X3,X2,X4) ) ).
cnf(i_0_18643,axiom,
( X1 != X2
| esk406_3(X3,X4,X1) = esk406_3(X3,X4,X2) ) ).
cnf(i_0_18644,axiom,
( X1 != X2
| esk265_4(X1,X3,X4,X5) = esk265_4(X2,X3,X4,X5) ) ).
cnf(i_0_18645,axiom,
( X1 != X2
| esk265_4(X3,X1,X4,X5) = esk265_4(X3,X2,X4,X5) ) ).
cnf(i_0_18646,axiom,
( X1 != X2
| esk265_4(X3,X4,X1,X5) = esk265_4(X3,X4,X2,X5) ) ).
cnf(i_0_18647,axiom,
( X1 != X2
| esk265_4(X3,X4,X5,X1) = esk265_4(X3,X4,X5,X2) ) ).
cnf(i_0_18648,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_18649,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_18650,axiom,
( X1 != X2
| esk409_3(X1,X3,X4) = esk409_3(X2,X3,X4) ) ).
cnf(i_0_18651,axiom,
( X1 != X2
| esk409_3(X3,X1,X4) = esk409_3(X3,X2,X4) ) ).
cnf(i_0_18652,axiom,
( X1 != X2
| esk409_3(X3,X4,X1) = esk409_3(X3,X4,X2) ) ).
cnf(i_0_18653,axiom,
( X1 != X2
| esk408_3(X1,X3,X4) = esk408_3(X2,X3,X4) ) ).
cnf(i_0_18654,axiom,
( X1 != X2
| esk408_3(X3,X1,X4) = esk408_3(X3,X2,X4) ) ).
cnf(i_0_18655,axiom,
( X1 != X2
| esk408_3(X3,X4,X1) = esk408_3(X3,X4,X2) ) ).
cnf(i_0_18656,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__rec(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18657,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__rec(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18658,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18659,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18660,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18661,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__case(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18662,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__case(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18663,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__case(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18664,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18665,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18666,axiom,
( X1 != X2
| c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).
cnf(i_0_18667,axiom,
( X1 != X2
| c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).
cnf(i_0_18668,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X1,X3,X4,X5) = c_Lazy__Sequence_Ohb__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18669,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X3,X1,X4,X5) = c_Lazy__Sequence_Ohb__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18670,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X3,X4,X1,X5) = c_Lazy__Sequence_Ohb__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18671,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X1) = c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18672,axiom,
( X1 != X2
| c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).
cnf(i_0_18673,axiom,
( X1 != X2
| c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).
cnf(i_0_18674,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X1,X3,X4,X5) = c_Lazy__Sequence_Obind(X2,X3,X4,X5) ) ).
cnf(i_0_18675,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X1,X4,X5) = c_Lazy__Sequence_Obind(X3,X2,X4,X5) ) ).
cnf(i_0_18676,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X4,X1,X5) = c_Lazy__Sequence_Obind(X3,X4,X2,X5) ) ).
cnf(i_0_18677,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X4,X5,X1) = c_Lazy__Sequence_Obind(X3,X4,X5,X2) ) ).
cnf(i_0_18678,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X1,X3,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18679,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X1,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18680,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X1,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18681,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X1,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18682,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X1) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18683,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__size(X1,X3,X4,X5,X6) = c_Sum__Type_Osum_Osum__size(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18684,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__size(X3,X1,X4,X5,X6) = c_Sum__Type_Osum_Osum__size(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18685,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__size(X3,X4,X1,X5,X6) = c_Sum__Type_Osum_Osum__size(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18686,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__size(X3,X4,X5,X1,X6) = c_Sum__Type_Osum_Osum__size(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18687,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__size(X3,X4,X5,X6,X1) = c_Sum__Type_Osum_Osum__size(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18688,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__rec(X1,X3,X4,X5,X6) = c_Option_Ooption_Ooption__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18689,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__rec(X3,X1,X4,X5,X6) = c_Option_Ooption_Ooption__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18690,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__rec(X3,X4,X1,X5,X6) = c_Option_Ooption_Ooption__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18691,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__rec(X3,X4,X5,X1,X6) = c_Option_Ooption_Ooption__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18692,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__rec(X3,X4,X5,X6,X1) = c_Option_Ooption_Ooption__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18693,axiom,
( X1 != X2
| esk191_3(X1,X3,X4) = esk191_3(X2,X3,X4) ) ).
cnf(i_0_18694,axiom,
( X1 != X2
| esk191_3(X3,X1,X4) = esk191_3(X3,X2,X4) ) ).
cnf(i_0_18695,axiom,
( X1 != X2
| esk191_3(X3,X4,X1) = esk191_3(X3,X4,X2) ) ).
cnf(i_0_18696,axiom,
( X1 != X2
| c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).
cnf(i_0_18697,axiom,
( X1 != X2
| c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).
cnf(i_0_18698,axiom,
( X1 != X2
| esk351_2(X1,X3) = esk351_2(X2,X3) ) ).
cnf(i_0_18699,axiom,
( X1 != X2
| esk351_2(X3,X1) = esk351_2(X3,X2) ) ).
cnf(i_0_18700,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X1,X3,X4,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X2,X3,X4,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18701,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X1,X4,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X2,X4,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18702,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X1,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X2,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18703,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X1,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X2,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18704,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X1,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X2,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18705,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X1,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X2,X8,X9,X10,X11) ) ).
cnf(i_0_18706,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X1,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X2,X9,X10,X11) ) ).
cnf(i_0_18707,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X1,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X2,X10,X11) ) ).
cnf(i_0_18708,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X10,X1,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X10,X2,X11) ) ).
cnf(i_0_18709,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X10,X11,X1) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X10,X11,X2) ) ).
cnf(i_0_18710,axiom,
( X1 != X2
| esk490_2(X1,X3) = esk490_2(X2,X3) ) ).
cnf(i_0_18711,axiom,
( X1 != X2
| esk490_2(X3,X1) = esk490_2(X3,X2) ) ).
cnf(i_0_18712,axiom,
( X1 != X2
| esk489_2(X1,X3) = esk489_2(X2,X3) ) ).
cnf(i_0_18713,axiom,
( X1 != X2
| esk489_2(X3,X1) = esk489_2(X3,X2) ) ).
cnf(i_0_18714,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X3,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X2,X3,X4,X5) ) ).
cnf(i_0_18715,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X1,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X2,X4,X5) ) ).
cnf(i_0_18716,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X1,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X2,X5) ) ).
cnf(i_0_18717,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X5,X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X5,X2) ) ).
cnf(i_0_18718,axiom,
( X1 != X2
| c_Com_Ocom_OAss(X1,X3) = c_Com_Ocom_OAss(X2,X3) ) ).
cnf(i_0_18719,axiom,
( X1 != X2
| c_Com_Ocom_OAss(X3,X1) = c_Com_Ocom_OAss(X3,X2) ) ).
cnf(i_0_18720,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).
cnf(i_0_18721,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).
cnf(i_0_18722,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).
cnf(i_0_18723,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).
cnf(i_0_18724,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).
cnf(i_0_18725,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).
cnf(i_0_18726,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X3,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,X4,X5) ) ).
cnf(i_0_18727,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X1,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X2,X4,X5) ) ).
cnf(i_0_18728,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X1,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X2,X5) ) ).
cnf(i_0_18729,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X2) ) ).
cnf(i_0_18730,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_18731,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_18732,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_18733,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X1,X3,X4,X5) = c_Sum__Type_OSumr(X2,X3,X4,X5) ) ).
cnf(i_0_18734,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X1,X4,X5) = c_Sum__Type_OSumr(X3,X2,X4,X5) ) ).
cnf(i_0_18735,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X4,X1,X5) = c_Sum__Type_OSumr(X3,X4,X2,X5) ) ).
cnf(i_0_18736,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X4,X5,X1) = c_Sum__Type_OSumr(X3,X4,X5,X2) ) ).
cnf(i_0_18737,axiom,
( X1 != X2
| c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).
cnf(i_0_18738,axiom,
( X1 != X2
| c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).
cnf(i_0_18739,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X1,X3,X4,X5) = c_Sum__Type_OSuml(X2,X3,X4,X5) ) ).
cnf(i_0_18740,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X1,X4,X5) = c_Sum__Type_OSuml(X3,X2,X4,X5) ) ).
cnf(i_0_18741,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X4,X1,X5) = c_Sum__Type_OSuml(X3,X4,X2,X5) ) ).
cnf(i_0_18742,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X4,X5,X1) = c_Sum__Type_OSuml(X3,X4,X5,X2) ) ).
cnf(i_0_18743,axiom,
( X1 != X2
| esk467_2(X1,X3) = esk467_2(X2,X3) ) ).
cnf(i_0_18744,axiom,
( X1 != X2
| esk467_2(X3,X1) = esk467_2(X3,X2) ) ).
cnf(i_0_18745,axiom,
( X1 != X2
| esk157_3(X1,X3,X4) = esk157_3(X2,X3,X4) ) ).
cnf(i_0_18746,axiom,
( X1 != X2
| esk157_3(X3,X1,X4) = esk157_3(X3,X2,X4) ) ).
cnf(i_0_18747,axiom,
( X1 != X2
| esk157_3(X3,X4,X1) = esk157_3(X3,X4,X2) ) ).
cnf(i_0_18748,axiom,
( X1 != X2
| esk159_3(X1,X3,X4) = esk159_3(X2,X3,X4) ) ).
cnf(i_0_18749,axiom,
( X1 != X2
| esk159_3(X3,X1,X4) = esk159_3(X3,X2,X4) ) ).
cnf(i_0_18750,axiom,
( X1 != X2
| esk159_3(X3,X4,X1) = esk159_3(X3,X4,X2) ) ).
cnf(i_0_18751,axiom,
( X1 != X2
| esk244_3(X1,X3,X4) = esk244_3(X2,X3,X4) ) ).
cnf(i_0_18752,axiom,
( X1 != X2
| esk244_3(X3,X1,X4) = esk244_3(X3,X2,X4) ) ).
cnf(i_0_18753,axiom,
( X1 != X2
| esk244_3(X3,X4,X1) = esk244_3(X3,X4,X2) ) ).
cnf(i_0_18754,axiom,
( X1 != X2
| esk243_3(X1,X3,X4) = esk243_3(X2,X3,X4) ) ).
cnf(i_0_18755,axiom,
( X1 != X2
| esk243_3(X3,X1,X4) = esk243_3(X3,X2,X4) ) ).
cnf(i_0_18756,axiom,
( X1 != X2
| esk243_3(X3,X4,X1) = esk243_3(X3,X4,X2) ) ).
cnf(i_0_18757,axiom,
( X1 != X2
| c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).
cnf(i_0_18758,axiom,
( X1 != X2
| c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).
cnf(i_0_18759,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).
cnf(i_0_18760,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).
cnf(i_0_18761,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).
cnf(i_0_18762,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__case(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X2,X3,X4,X5) ) ).
cnf(i_0_18763,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X2,X4,X5) ) ).
cnf(i_0_18764,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X2,X5) ) ).
cnf(i_0_18765,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X2) ) ).
cnf(i_0_18766,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X2,X3,X4,X5) ) ).
cnf(i_0_18767,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X2,X4,X5) ) ).
cnf(i_0_18768,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X2,X5) ) ).
cnf(i_0_18769,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X2) ) ).
cnf(i_0_18770,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).
cnf(i_0_18771,axiom,
( X1 != X2
| c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).
cnf(i_0_18772,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_18773,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_18774,axiom,
( X1 != X2
| c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).
cnf(i_0_18775,axiom,
( X1 != X2
| c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).
cnf(i_0_18776,axiom,
( X1 != X2
| c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).
cnf(i_0_18777,axiom,
( X1 != X2
| c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).
cnf(i_0_18778,axiom,
( X1 != X2
| c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).
cnf(i_0_18779,axiom,
( X1 != X2
| c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).
cnf(i_0_18780,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__size(X1) = c_Com_Ocom_Ocom__size(X2) ) ).
cnf(i_0_18781,axiom,
( X1 != X2
| c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).
cnf(i_0_18782,axiom,
( X1 != X2
| c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).
cnf(i_0_18783,axiom,
( X1 != X2
| c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).
cnf(i_0_18784,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).
cnf(i_0_18785,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).
cnf(i_0_18786,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).
cnf(i_0_18787,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X3,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X2,X3,X4,X5) ) ).
cnf(i_0_18788,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X1,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X2,X4,X5) ) ).
cnf(i_0_18789,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X1,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X2,X5) ) ).
cnf(i_0_18790,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X5,X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X5,X2) ) ).
cnf(i_0_18791,axiom,
( X1 != X2
| esk481_2(X1,X3) = esk481_2(X2,X3) ) ).
cnf(i_0_18792,axiom,
( X1 != X2
| esk481_2(X3,X1) = esk481_2(X3,X2) ) ).
cnf(i_0_18793,axiom,
( X1 != X2
| c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).
cnf(i_0_18794,axiom,
( X1 != X2
| c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).
cnf(i_0_18795,axiom,
( X1 != X2
| c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).
cnf(i_0_18796,axiom,
( X1 != X2
| c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).
cnf(i_0_18797,axiom,
( X1 != X2
| c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).
cnf(i_0_18798,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).
cnf(i_0_18799,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).
cnf(i_0_18800,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).
cnf(i_0_18801,axiom,
( X1 != X2
| esk451_2(X1,X3) = esk451_2(X2,X3) ) ).
cnf(i_0_18802,axiom,
( X1 != X2
| esk451_2(X3,X1) = esk451_2(X3,X2) ) ).
cnf(i_0_18803,axiom,
( X1 != X2
| esk450_2(X1,X3) = esk450_2(X2,X3) ) ).
cnf(i_0_18804,axiom,
( X1 != X2
| esk450_2(X3,X1) = esk450_2(X3,X2) ) ).
cnf(i_0_18805,axiom,
( X1 != X2
| c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).
cnf(i_0_18806,axiom,
( X1 != X2
| c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).
cnf(i_0_18807,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X3,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X2,X3,X4) ) ).
cnf(i_0_18808,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X1,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X2,X4) ) ).
cnf(i_0_18809,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X1) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X2) ) ).
cnf(i_0_18810,axiom,
( X1 != X2
| c_Orderings_Oord_Omax(X1,X3) = c_Orderings_Oord_Omax(X2,X3) ) ).
cnf(i_0_18811,axiom,
( X1 != X2
| c_Orderings_Oord_Omax(X3,X1) = c_Orderings_Oord_Omax(X3,X2) ) ).
cnf(i_0_18812,axiom,
( X1 != X2
| c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).
cnf(i_0_18813,axiom,
( X1 != X2
| c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).
cnf(i_0_18814,axiom,
( X1 != X2
| c_Option_Oset(X1,X3) = c_Option_Oset(X2,X3) ) ).
cnf(i_0_18815,axiom,
( X1 != X2
| c_Option_Oset(X3,X1) = c_Option_Oset(X3,X2) ) ).
cnf(i_0_18816,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X1,X3,X4,X5) = c_Com_Ovname_Ovname__rec(X2,X3,X4,X5) ) ).
cnf(i_0_18817,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X3,X1,X4,X5) = c_Com_Ovname_Ovname__rec(X3,X2,X4,X5) ) ).
cnf(i_0_18818,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X3,X4,X1,X5) = c_Com_Ovname_Ovname__rec(X3,X4,X2,X5) ) ).
cnf(i_0_18819,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X3,X4,X5,X1) = c_Com_Ovname_Ovname__rec(X3,X4,X5,X2) ) ).
cnf(i_0_18820,axiom,
( X1 != X2
| c_Com_Ovname_OGlb(X1) = c_Com_Ovname_OGlb(X2) ) ).
cnf(i_0_18821,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X1,X3,X4,X5) = c_Com_Ovname_Ovname__case(X2,X3,X4,X5) ) ).
cnf(i_0_18822,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X3,X1,X4,X5) = c_Com_Ovname_Ovname__case(X3,X2,X4,X5) ) ).
cnf(i_0_18823,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X3,X4,X1,X5) = c_Com_Ovname_Ovname__case(X3,X4,X2,X5) ) ).
cnf(i_0_18824,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X3,X4,X5,X1) = c_Com_Ovname_Ovname__case(X3,X4,X5,X2) ) ).
cnf(i_0_18825,axiom,
( X1 != X2
| c_New__DSequence_Oneg__single(X1,X3) = c_New__DSequence_Oneg__single(X2,X3) ) ).
cnf(i_0_18826,axiom,
( X1 != X2
| c_New__DSequence_Oneg__single(X3,X1) = c_New__DSequence_Oneg__single(X3,X2) ) ).
cnf(i_0_18827,axiom,
( X1 != X2
| c_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).
cnf(i_0_18828,axiom,
( X1 != X2
| c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(X3,X2) ) ).
cnf(i_0_18829,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X2) ) ).
cnf(i_0_18830,axiom,
( X1 != X2
| c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).
cnf(i_0_18831,axiom,
( X1 != X2
| c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).
cnf(i_0_18832,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X1,X3,X4) = c_Option_Ooption_Ooption__size(X2,X3,X4) ) ).
cnf(i_0_18833,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X3,X1,X4) = c_Option_Ooption_Ooption__size(X3,X2,X4) ) ).
cnf(i_0_18834,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X3,X4,X1) = c_Option_Ooption_Ooption__size(X3,X4,X2) ) ).
cnf(i_0_18835,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small__class_Ofull__small(X1,X3,X4) = c_Smallcheck_Ofull__small__class_Ofull__small(X2,X3,X4) ) ).
cnf(i_0_18836,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small__class_Ofull__small(X3,X1,X4) = c_Smallcheck_Ofull__small__class_Ofull__small(X3,X2,X4) ) ).
cnf(i_0_18837,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small__class_Ofull__small(X3,X4,X1) = c_Smallcheck_Ofull__small__class_Ofull__small(X3,X4,X2) ) ).
cnf(i_0_18838,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X1,X3,X4) = c_Smallcheck_Ofull__small_H(X2,X3,X4) ) ).
cnf(i_0_18839,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X3,X1,X4) = c_Smallcheck_Ofull__small_H(X3,X2,X4) ) ).
cnf(i_0_18840,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X3,X4,X1) = c_Smallcheck_Ofull__small_H(X3,X4,X2) ) ).
cnf(i_0_18841,axiom,
( X1 != X2
| esk447_1(X1) = esk447_1(X2) ) ).
cnf(i_0_18842,axiom,
( X1 != X2
| c_String_Ochar_Ochar__case(X1,X3,X4) = c_String_Ochar_Ochar__case(X2,X3,X4) ) ).
cnf(i_0_18843,axiom,
( X1 != X2
| c_String_Ochar_Ochar__case(X3,X1,X4) = c_String_Ochar_Ochar__case(X3,X2,X4) ) ).
cnf(i_0_18844,axiom,
( X1 != X2
| c_String_Ochar_Ochar__case(X3,X4,X1) = c_String_Ochar_Ochar__case(X3,X4,X2) ) ).
cnf(i_0_18845,axiom,
( X1 != X2
| c_String_Ochar_Ochar__rec(X1,X3,X4) = c_String_Ochar_Ochar__rec(X2,X3,X4) ) ).
cnf(i_0_18846,axiom,
( X1 != X2
| c_String_Ochar_Ochar__rec(X3,X1,X4) = c_String_Ochar_Ochar__rec(X3,X2,X4) ) ).
cnf(i_0_18847,axiom,
( X1 != X2
| c_String_Ochar_Ochar__rec(X3,X4,X1) = c_String_Ochar_Ochar__rec(X3,X4,X2) ) ).
cnf(i_0_18848,axiom,
( X1 != X2
| c_Quickcheck_Obeyond(X1,X3) = c_Quickcheck_Obeyond(X2,X3) ) ).
cnf(i_0_18849,axiom,
( X1 != X2
| c_Quickcheck_Obeyond(X3,X1) = c_Quickcheck_Obeyond(X3,X2) ) ).
cnf(i_0_18850,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X1,X3,X4) = c_Sum__Type_OProjr(X2,X3,X4) ) ).
cnf(i_0_18851,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X3,X1,X4) = c_Sum__Type_OProjr(X3,X2,X4) ) ).
cnf(i_0_18852,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X3,X4,X1) = c_Sum__Type_OProjr(X3,X4,X2) ) ).
cnf(i_0_18853,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X1,X3,X4) = c_Sum__Type_OProjl(X2,X3,X4) ) ).
cnf(i_0_18854,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X3,X1,X4) = c_Sum__Type_OProjl(X3,X2,X4) ) ).
cnf(i_0_18855,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X3,X4,X1) = c_Sum__Type_OProjl(X3,X4,X2) ) ).
cnf(i_0_18856,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_18857,axiom,
( X1 != X2
| c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).
cnf(i_0_18858,axiom,
( X1 != X2
| c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).
cnf(i_0_18859,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).
cnf(i_0_18860,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).
cnf(i_0_18861,axiom,
( X1 != X2
| c_Lazy__Sequence_Osingle(X1,X3) = c_Lazy__Sequence_Osingle(X2,X3) ) ).
cnf(i_0_18862,axiom,
( X1 != X2
| c_Lazy__Sequence_Osingle(X3,X1) = c_Lazy__Sequence_Osingle(X3,X2) ) ).
cnf(i_0_18863,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_18864,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__size(X1) = c_Com_Ovname_Ovname__size(X2) ) ).
cnf(i_0_18865,axiom,
( X1 != X2
| c_List_Oreturn__list(X1) = c_List_Oreturn__list(X2) ) ).
cnf(i_0_18866,axiom,
( X1 != X2
| c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).
cnf(i_0_18867,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_18868,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_18869,axiom,
( X1 != X2
| c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).
cnf(i_0_18870,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X1,X3,X4,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X2,X3,X4,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18871,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X1,X4,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X2,X4,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18872,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X1,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X2,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18873,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X1,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X2,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18874,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X1,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X2,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18875,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X1,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X2,X8,X9,X10,X11) ) ).
cnf(i_0_18876,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X1,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X2,X9,X10,X11) ) ).
cnf(i_0_18877,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X1,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X2,X10,X11) ) ).
cnf(i_0_18878,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X10,X1,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X10,X2,X11) ) ).
cnf(i_0_18879,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X10,X11,X1) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X10,X11,X2) ) ).
cnf(i_0_18880,axiom,
( X1 != X2
| c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).
cnf(i_0_18881,axiom,
( X1 != X2
| c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).
cnf(i_0_18882,axiom,
( X1 != X2
| c_Map_Omap__add(X1,X3,X4,X5) = c_Map_Omap__add(X2,X3,X4,X5) ) ).
cnf(i_0_18883,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X1,X4,X5) = c_Map_Omap__add(X3,X2,X4,X5) ) ).
cnf(i_0_18884,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X4,X1,X5) = c_Map_Omap__add(X3,X4,X2,X5) ) ).
cnf(i_0_18885,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X4,X5,X1) = c_Map_Omap__add(X3,X4,X5,X2) ) ).
cnf(i_0_18886,axiom,
( X1 != X2
| c_Map_Omap__of(X1,X3,X4) = c_Map_Omap__of(X2,X3,X4) ) ).
cnf(i_0_18887,axiom,
( X1 != X2
| c_Map_Omap__of(X3,X1,X4) = c_Map_Omap__of(X3,X2,X4) ) ).
cnf(i_0_18888,axiom,
( X1 != X2
| c_Map_Omap__of(X3,X4,X1) = c_Map_Omap__of(X3,X4,X2) ) ).
cnf(i_0_18889,axiom,
( X1 != X2
| c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).
cnf(i_0_18890,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).
cnf(i_0_18891,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).
cnf(i_0_18892,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).
cnf(i_0_18893,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_18894,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_18895,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_18896,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_18897,axiom,
( X1 != X2
| ~ c_Predicate_Oreflp(X1,X3)
| c_Predicate_Oreflp(X2,X3) ) ).
cnf(i_0_18898,axiom,
( X1 != X2
| ~ c_Predicate_Oreflp(X3,X1)
| c_Predicate_Oreflp(X3,X2) ) ).
cnf(i_0_18899,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_18900,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_18901,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_18902,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_18903,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_18904,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_18905,axiom,
( X1 != X2
| ~ class_Orderings_Owellorder(X1)
| class_Orderings_Owellorder(X2) ) ).
cnf(i_0_18906,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_18907,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_18908,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_18909,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_18910,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_18911,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_18912,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_18913,axiom,
( X1 != X2
| ~ c_Groups_Osemigroup(X1,X3)
| c_Groups_Osemigroup(X2,X3) ) ).
cnf(i_0_18914,axiom,
( X1 != X2
| ~ c_Groups_Osemigroup(X3,X1)
| c_Groups_Osemigroup(X3,X2) ) ).
cnf(i_0_18915,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_18916,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
| c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).
cnf(i_0_18917,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
| c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).
cnf(i_0_18918,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
| c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).
cnf(i_0_18919,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
| c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).
cnf(i_0_18920,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_18921,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_18922,axiom,
( X1 != X2
| ~ c_Nitpick_Owf_H(X1,X3)
| c_Nitpick_Owf_H(X2,X3) ) ).
cnf(i_0_18923,axiom,
( X1 != X2
| ~ c_Nitpick_Owf_H(X3,X1)
| c_Nitpick_Owf_H(X3,X2) ) ).
cnf(i_0_18924,axiom,
( X1 != X2
| ~ class_Groups_Osgn__if(X1)
| class_Groups_Osgn__if(X2) ) ).
cnf(i_0_18925,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_18926,axiom,
( X1 != X2
| ~ class_Groups_Oabs__if(X1)
| class_Groups_Oabs__if(X2) ) ).
cnf(i_0_18927,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_18928,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
| c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).
cnf(i_0_18929,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
| c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).
cnf(i_0_18930,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
| c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).
cnf(i_0_18931,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_18932,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_18933,axiom,
( X1 != X2
| ~ c_Nitpick_Ounknown(X1)
| c_Nitpick_Ounknown(X2) ) ).
cnf(i_0_18934,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_18935,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_18936,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_18937,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X1,X3,X4)
| c_Groups_Ocomm__monoid(X2,X3,X4) ) ).
cnf(i_0_18938,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X3,X1,X4)
| c_Groups_Ocomm__monoid(X3,X2,X4) ) ).
cnf(i_0_18939,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X3,X4,X1)
| c_Groups_Ocomm__monoid(X3,X4,X2) ) ).
cnf(i_0_18940,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_18941,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_18942,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_18943,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_18944,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__bot(X1)
| class_Lattices_Obounded__lattice__bot(X2) ) ).
cnf(i_0_18945,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__top(X1)
| class_Lattices_Obounded__lattice__top(X2) ) ).
cnf(i_0_18946,axiom,
( X1 != X2
| ~ c_Option_Ois__none(X1,X3)
| c_Option_Ois__none(X2,X3) ) ).
cnf(i_0_18947,axiom,
( X1 != X2
| ~ c_Option_Ois__none(X3,X1)
| c_Option_Ois__none(X3,X2) ) ).
cnf(i_0_18948,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_18949,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__semigroup__add(X1)
| class_Groups_Olinordered__ab__semigroup__add(X2) ) ).
cnf(i_0_18950,axiom,
( X1 != X2
| ~ c_List_Onat__list(X1)
| c_List_Onat__list(X2) ) ).
cnf(i_0_18951,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_18952,axiom,
( X1 != X2
| ~ v_Q(X1,X3)
| v_Q(X2,X3) ) ).
cnf(i_0_18953,axiom,
( X1 != X2
| ~ v_Q(X3,X1)
| v_Q(X3,X2) ) ).
cnf(i_0_18954,axiom,
( X1 != X2
| ~ v_P(X1,X3)
| v_P(X2,X3) ) ).
cnf(i_0_18955,axiom,
( X1 != X2
| ~ v_P(X3,X1)
| v_P(X3,X2) ) ).
cnf(i_0_18956,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_18957,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_18958,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18959,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X1,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18960,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X1,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18961,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X1,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18962,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X1,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18963,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X1)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18964,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_18965,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X1,X3,X4,X5,X6,X7,X8)
| c_Predicate_Opred__comp(X2,X3,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18966,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X1,X4,X5,X6,X7,X8)
| c_Predicate_Opred__comp(X3,X2,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18967,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X4,X1,X5,X6,X7,X8)
| c_Predicate_Opred__comp(X3,X4,X2,X5,X6,X7,X8) ) ).
cnf(i_0_18968,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X4,X5,X1,X6,X7,X8)
| c_Predicate_Opred__comp(X3,X4,X5,X2,X6,X7,X8) ) ).
cnf(i_0_18969,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X4,X5,X6,X1,X7,X8)
| c_Predicate_Opred__comp(X3,X4,X5,X6,X2,X7,X8) ) ).
cnf(i_0_18970,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X4,X5,X6,X7,X1,X8)
| c_Predicate_Opred__comp(X3,X4,X5,X6,X7,X2,X8) ) ).
cnf(i_0_18971,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X4,X5,X6,X7,X8,X1)
| c_Predicate_Opred__comp(X3,X4,X5,X6,X7,X8,X2) ) ).
cnf(i_0_18972,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X1,X3,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18973,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X1,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18974,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X1,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18975,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X1,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18976,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X1,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18977,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X1)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18978,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X1,X3,X4,X5)
| c_Natural_Oevaln(X2,X3,X4,X5) ) ).
cnf(i_0_18979,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X1,X4,X5)
| c_Natural_Oevaln(X3,X2,X4,X5) ) ).
cnf(i_0_18980,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X4,X1,X5)
| c_Natural_Oevaln(X3,X4,X2,X5) ) ).
cnf(i_0_18981,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X4,X5,X1)
| c_Natural_Oevaln(X3,X4,X5,X2) ) ).
cnf(i_0_18982,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X1,X3,X4,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18983,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X1,X4,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18984,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X1,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18985,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X1,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18986,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X1,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18987,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X1)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18988,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_18989,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_18990,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_18991,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_18992,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_18993,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
| c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).
cnf(i_0_18994,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
| c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).
cnf(i_0_18995,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
| c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).
cnf(i_0_18996,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
| c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).
cnf(i_0_18997,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X1,X3,X4,X5)
| c_List_Olistrelp(X2,X3,X4,X5) ) ).
cnf(i_0_18998,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X1,X4,X5)
| c_List_Olistrelp(X3,X2,X4,X5) ) ).
cnf(i_0_18999,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X1,X5)
| c_List_Olistrelp(X3,X4,X2,X5) ) ).
cnf(i_0_19000,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X5,X1)
| c_List_Olistrelp(X3,X4,X5,X2) ) ).
cnf(i_0_19001,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequivp(X1,X3)
| c_Equiv__Relations_Oequivp(X2,X3) ) ).
cnf(i_0_19002,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequivp(X3,X1)
| c_Equiv__Relations_Oequivp(X3,X2) ) ).
cnf(i_0_19003,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(X2,X3) ) ).
cnf(i_0_19004,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X3,X1)
| c_Wellfounded_Owf(X3,X2) ) ).
cnf(i_0_19005,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X1,X3)
| c_Wellfounded_OwfP(X2,X3) ) ).
cnf(i_0_19006,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X3,X1)
| c_Wellfounded_OwfP(X3,X2) ) ).
cnf(i_0_19007,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
| c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).
cnf(i_0_19008,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
| c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).
cnf(i_0_19009,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
| c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).
cnf(i_0_19010,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_19011,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
| c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).
cnf(i_0_19012,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
| c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).
cnf(i_0_19013,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
| c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).
cnf(i_0_19014,axiom,
( X1 != X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(X2) ) ).
cnf(i_0_19015,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_19016,axiom,
( X1 != X2
| ~ class_Smallcheck_Osmall(X1)
| class_Smallcheck_Osmall(X2) ) ).
cnf(i_0_19017,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_19018,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X1,X3,X4,X5)
| c_Orderings_Oorder_Ostrict__mono(X2,X3,X4,X5) ) ).
cnf(i_0_19019,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X1,X4,X5)
| c_Orderings_Oorder_Ostrict__mono(X3,X2,X4,X5) ) ).
cnf(i_0_19020,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X1,X5)
| c_Orderings_Oorder_Ostrict__mono(X3,X4,X2,X5) ) ).
cnf(i_0_19021,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X1)
| c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X2) ) ).
cnf(i_0_19022,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X1,X3,X4,X5)
| c_Orderings_Oorder_Omono(X2,X3,X4,X5) ) ).
cnf(i_0_19023,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X1,X4,X5)
| c_Orderings_Oorder_Omono(X3,X2,X4,X5) ) ).
cnf(i_0_19024,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X4,X1,X5)
| c_Orderings_Oorder_Omono(X3,X4,X2,X5) ) ).
cnf(i_0_19025,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X4,X5,X1)
| c_Orderings_Oorder_Omono(X3,X4,X5,X2) ) ).
cnf(i_0_19026,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_19027,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_19028,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_19029,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_19030,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_19031,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_19032,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
| c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).
cnf(i_0_19033,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
| c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).
cnf(i_0_19034,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
| c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).
cnf(i_0_19035,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__1(X1)
| class_Rings_Osemiring__1(X2) ) ).
cnf(i_0_19036,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
| c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).
cnf(i_0_19037,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
| c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).
cnf(i_0_19038,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
| c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).
cnf(i_0_19039,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_19040,axiom,
( X1 != X2
| ~ c_FunDef_Oreduction__pair(X1,X3)
| c_FunDef_Oreduction__pair(X2,X3) ) ).
cnf(i_0_19041,axiom,
( X1 != X2
| ~ c_FunDef_Oreduction__pair(X3,X1)
| c_FunDef_Oreduction__pair(X3,X2) ) ).
cnf(i_0_19042,axiom,
( X1 != X2
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| c_List_Olinorder__class_Osorted(X2,X3) ) ).
cnf(i_0_19043,axiom,
( X1 != X2
| ~ c_List_Olinorder__class_Osorted(X3,X1)
| c_List_Olinorder__class_Osorted(X3,X2) ) ).
cnf(i_0_19044,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Ois__nat(X1)
| c_Nat__Transfer_Ois__nat(X2) ) ).
cnf(i_0_19045,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
| c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).
cnf(i_0_19046,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
| c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).
cnf(i_0_19047,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
| c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).
cnf(i_0_19048,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X1,X3,X4)
| c_Nitpick_Oless__frac(X2,X3,X4) ) ).
cnf(i_0_19049,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X3,X1,X4)
| c_Nitpick_Oless__frac(X3,X2,X4) ) ).
cnf(i_0_19050,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X3,X4,X1)
| c_Nitpick_Oless__frac(X3,X4,X2) ) ).
cnf(i_0_19051,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_19052,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_19053,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_19054,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_19055,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_19056,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_19057,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_19058,axiom,
( X1 != X2
| ~ class_Rings_Oinverse(X1)
| class_Rings_Oinverse(X2) ) ).
cnf(i_0_19059,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_19060,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X3,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_19061,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X1,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_19062,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X1,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_19063,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X1,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_19064,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X1,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_19065,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X1)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_19066,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_19067,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image(X1,X3,X4,X5,X6)
| c_Finite__Set_Ofolding__image(X2,X3,X4,X5,X6) ) ).
cnf(i_0_19068,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image(X3,X1,X4,X5,X6)
| c_Finite__Set_Ofolding__image(X3,X2,X4,X5,X6) ) ).
cnf(i_0_19069,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image(X3,X4,X1,X5,X6)
| c_Finite__Set_Ofolding__image(X3,X4,X2,X5,X6) ) ).
cnf(i_0_19070,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image(X3,X4,X5,X1,X6)
| c_Finite__Set_Ofolding__image(X3,X4,X5,X2,X6) ) ).
cnf(i_0_19071,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image(X3,X4,X5,X6,X1)
| c_Finite__Set_Ofolding__image(X3,X4,X5,X6,X2) ) ).
cnf(i_0_19072,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_19073,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Onat__set(X1)
| c_Nat__Transfer_Onat__set(X2) ) ).
cnf(i_0_19074,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_19075,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_19076,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X3,X4)
| c_Finite__Set_Ofun__left__comm__idem(X2,X3,X4) ) ).
cnf(i_0_19077,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm__idem(X3,X1,X4)
| c_Finite__Set_Ofun__left__comm__idem(X3,X2,X4) ) ).
cnf(i_0_19078,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm__idem(X3,X4,X1)
| c_Finite__Set_Ofun__left__comm__idem(X3,X4,X2) ) ).
cnf(i_0_19079,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__sup(X1)
| class_Lattices_Osemilattice__sup(X2) ) ).
cnf(i_0_19080,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X1,X3)
| c_Int_Oiszero(X2,X3) ) ).
cnf(i_0_19081,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X3,X1)
| c_Int_Oiszero(X3,X2) ) ).
cnf(i_0_19082,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_19083,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_19084,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_19085,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_19086,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_19087,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_19088,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_19089,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,X3,X4)
| c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4) ) ).
cnf(i_0_19090,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X3,X1,X4)
| c_Hoare__Mirabelle_Otriple__valid(X3,X2,X4) ) ).
cnf(i_0_19091,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X3,X4,X1)
| c_Hoare__Mirabelle_Otriple__valid(X3,X4,X2) ) ).
cnf(i_0_19092,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_19093,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_19094,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_19095,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_19096,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_19097,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_19098,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_19099,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
| c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).
cnf(i_0_19100,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
| c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).
cnf(i_0_19101,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
| c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).
cnf(i_0_19102,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
| c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).
cnf(i_0_19103,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_19104,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_19105,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__inf(X1)
| class_Lattices_Osemilattice__inf(X2) ) ).
cnf(i_0_19106,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_19107,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_19108,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_19109,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).
cnf(i_0_19110,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).
cnf(i_0_19111,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).
cnf(i_0_19112,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_19113,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_19114,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_19115,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
| c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).
cnf(i_0_19116,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
| c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).
cnf(i_0_19117,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
| c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).
cnf(i_0_19118,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
| c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).
cnf(i_0_19119,axiom,
( X1 != X2
| ~ c_Big__Operators_Ocomm__monoid__big(X1,X3,X4,X5,X6)
| c_Big__Operators_Ocomm__monoid__big(X2,X3,X4,X5,X6) ) ).
cnf(i_0_19120,axiom,
( X1 != X2
| ~ c_Big__Operators_Ocomm__monoid__big(X3,X1,X4,X5,X6)
| c_Big__Operators_Ocomm__monoid__big(X3,X2,X4,X5,X6) ) ).
cnf(i_0_19121,axiom,
( X1 != X2
| ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X1,X5,X6)
| c_Big__Operators_Ocomm__monoid__big(X3,X4,X2,X5,X6) ) ).
cnf(i_0_19122,axiom,
( X1 != X2
| ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X1,X6)
| c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X2,X6) ) ).
cnf(i_0_19123,axiom,
( X1 != X2
| ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X6,X1)
| c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X6,X2) ) ).
cnf(i_0_19124,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
| c_Hoare__Mirabelle_Ohoare__valids(X2,X3,X4) ) ).
cnf(i_0_19125,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X1,X4)
| c_Hoare__Mirabelle_Ohoare__valids(X3,X2,X4) ) ).
cnf(i_0_19126,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X1)
| c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X2) ) ).
cnf(i_0_19127,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_19128,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
| c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).
cnf(i_0_19129,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
| c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).
cnf(i_0_19130,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
| c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).
cnf(i_0_19131,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
| c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).
cnf(i_0_19132,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
| c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).
cnf(i_0_19133,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_19134,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_19135,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
| c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).
cnf(i_0_19136,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
| c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).
cnf(i_0_19137,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
| c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).
cnf(i_0_19138,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
| c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).
cnf(i_0_19139,axiom,
( X1 != X2
| ~ class_Groups_Osemigroup__add(X1)
| class_Groups_Osemigroup__add(X2) ) ).
cnf(i_0_19140,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_19141,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_19142,axiom,
( X1 != X2
| ~ epred2_3(X1,X3,X4)
| epred2_3(X2,X3,X4) ) ).
cnf(i_0_19143,axiom,
( X1 != X2
| ~ epred2_3(X3,X1,X4)
| epred2_3(X3,X2,X4) ) ).
cnf(i_0_19144,axiom,
( X1 != X2
| ~ epred2_3(X3,X4,X1)
| epred2_3(X3,X4,X2) ) ).
cnf(i_0_19145,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_19146,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_19147,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_19148,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_19149,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_19150,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_19151,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_19152,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_19153,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_18251_001,axiom,
X1 = X1 ).
cnf(i_0_18252_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_18253_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_18254_004,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_18255_005,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_18256_006,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X1,X3,X4) = c_Com_Ocom_OCond(X2,X3,X4) ) ).
cnf(i_0_18257_007,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X3,X1,X4) = c_Com_Ocom_OCond(X3,X2,X4) ) ).
cnf(i_0_18258_008,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X3,X4,X1) = c_Com_Ocom_OCond(X3,X4,X2) ) ).
cnf(i_0_18259_009,axiom,
( X1 != X2
| c_Map_Omap__upds(X1,X3,X4,X5,X6) = c_Map_Omap__upds(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18260_010,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X1,X4,X5,X6) = c_Map_Omap__upds(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18261_011,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X4,X1,X5,X6) = c_Map_Omap__upds(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18262_012,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X4,X5,X1,X6) = c_Map_Omap__upds(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18263_013,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X4,X5,X6,X1) = c_Map_Omap__upds(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18264_014,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).
cnf(i_0_18265_015,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).
cnf(i_0_18266_016,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).
cnf(i_0_18267_017,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).
cnf(i_0_18268_018,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).
cnf(i_0_18269_019,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).
cnf(i_0_18270_020,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X1,X3,X4,X5) = c_Option_Ooption_Ooption__case(X2,X3,X4,X5) ) ).
cnf(i_0_18271_021,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X3,X1,X4,X5) = c_Option_Ooption_Ooption__case(X3,X2,X4,X5) ) ).
cnf(i_0_18272_022,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X3,X4,X1,X5) = c_Option_Ooption_Ooption__case(X3,X4,X2,X5) ) ).
cnf(i_0_18273_023,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X3,X4,X5,X1) = c_Option_Ooption_Ooption__case(X3,X4,X5,X2) ) ).
cnf(i_0_18274_024,axiom,
( X1 != X2
| c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).
cnf(i_0_18275_025,axiom,
( X1 != X2
| c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).
cnf(i_0_18276_026,axiom,
( X1 != X2
| c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).
cnf(i_0_18277_027,axiom,
( X1 != X2
| c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).
cnf(i_0_18278_028,axiom,
( X1 != X2
| c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).
cnf(i_0_18279_029,axiom,
( X1 != X2
| c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).
cnf(i_0_18280_030,axiom,
( X1 != X2
| c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).
cnf(i_0_18281_031,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).
cnf(i_0_18282_032,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).
cnf(i_0_18283_033,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).
cnf(i_0_18284_034,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).
cnf(i_0_18285_035,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_18286_036,axiom,
( X1 != X2
| c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).
cnf(i_0_18287_037,axiom,
( X1 != X2
| c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).
cnf(i_0_18288_038,axiom,
( X1 != X2
| c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).
cnf(i_0_18289_039,axiom,
( X1 != X2
| c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).
cnf(i_0_18290_040,axiom,
( X1 != X2
| c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).
cnf(i_0_18291_041,axiom,
( X1 != X2
| c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).
cnf(i_0_18292_042,axiom,
( X1 != X2
| c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).
cnf(i_0_18293_043,axiom,
( X1 != X2
| c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).
cnf(i_0_18294_044,axiom,
( X1 != X2
| c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).
cnf(i_0_18295_045,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).
cnf(i_0_18296_046,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).
cnf(i_0_18297_047,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).
cnf(i_0_18298_048,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).
cnf(i_0_18299_049,axiom,
( X1 != X2
| c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).
cnf(i_0_18300_050,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).
cnf(i_0_18301_051,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).
cnf(i_0_18302_052,axiom,
( X1 != X2
| c_List_Olinorder__class_Osorted__list__of__set(X1,X3) = c_List_Olinorder__class_Osorted__list__of__set(X2,X3) ) ).
cnf(i_0_18303_053,axiom,
( X1 != X2
| c_List_Olinorder__class_Osorted__list__of__set(X3,X1) = c_List_Olinorder__class_Osorted__list__of__set(X3,X2) ) ).
cnf(i_0_18304_054,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).
cnf(i_0_18305_055,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).
cnf(i_0_18306_056,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).
cnf(i_0_18307_057,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).
cnf(i_0_18308_058,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).
cnf(i_0_18309_059,axiom,
( X1 != X2
| c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).
cnf(i_0_18310_060,axiom,
( X1 != X2
| c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).
cnf(i_0_18311_061,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_18312_062,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_18313_063,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_18314_064,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_18315_065,axiom,
( X1 != X2
| c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).
cnf(i_0_18316_066,axiom,
( X1 != X2
| c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).
cnf(i_0_18317_067,axiom,
( X1 != X2
| c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).
cnf(i_0_18318_068,axiom,
( X1 != X2
| c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).
cnf(i_0_18319_069,axiom,
( X1 != X2
| c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).
cnf(i_0_18320_070,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X1,X3,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X2,X3,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18321_071,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X1,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X2,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18322_072,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X1,X5,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X2,X5,X6,X7,X8) ) ).
cnf(i_0_18323_073,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X1,X6,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X2,X6,X7,X8) ) ).
cnf(i_0_18324_074,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X1,X7,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X2,X7,X8) ) ).
cnf(i_0_18325_075,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X1,X8) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X2,X8) ) ).
cnf(i_0_18326_076,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X8,X1) = c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X5,X6,X7,X8,X2) ) ).
cnf(i_0_18327_077,axiom,
( X1 != X2
| c_New__DSequence_Oneg__decr__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18328_078,axiom,
( X1 != X2
| c_New__DSequence_Oneg__decr__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__decr__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18329_079,axiom,
( X1 != X2
| c_New__DSequence_Oneg__decr__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__decr__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18330_080,axiom,
( X1 != X2
| c_New__DSequence_Oneg__decr__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__decr__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18331_081,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).
cnf(i_0_18332_082,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X1,X3,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X2,X3,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18333_083,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X1,X4,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X2,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18334_084,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X4,X1,X5,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X2,X5,X6,X7,X8) ) ).
cnf(i_0_18335_085,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X1,X6,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X2,X6,X7,X8) ) ).
cnf(i_0_18336_086,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X1,X7,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X2,X7,X8) ) ).
cnf(i_0_18337_087,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X1,X8) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X2,X8) ) ).
cnf(i_0_18338_088,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X8,X1) = c_New__Random__Sequence_Opos__decr__bind(X3,X4,X5,X6,X7,X8,X2) ) ).
cnf(i_0_18339_089,axiom,
( X1 != X2
| c_New__DSequence_Opos__decr__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__decr__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18340_090,axiom,
( X1 != X2
| c_New__DSequence_Opos__decr__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__decr__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18341_091,axiom,
( X1 != X2
| c_New__DSequence_Opos__decr__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__decr__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18342_092,axiom,
( X1 != X2
| c_New__DSequence_Opos__decr__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__decr__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18343_093,axiom,
( X1 != X2
| c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).
cnf(i_0_18344_094,axiom,
( X1 != X2
| c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).
cnf(i_0_18345_095,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).
cnf(i_0_18346_096,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).
cnf(i_0_18347_097,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__bind(X1,X3,X4,X5) = c_New__Random__Sequence_Oneg__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18348_098,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__bind(X3,X1,X4,X5) = c_New__Random__Sequence_Oneg__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18349_099,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__bind(X3,X4,X1,X5) = c_New__Random__Sequence_Oneg__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18350_100,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__bind(X3,X4,X5,X1) = c_New__Random__Sequence_Oneg__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18351_101,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18352_102,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18353_103,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18354_104,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18355_105,axiom,
( X1 != X2
| esk381_5(X1,X3,X4,X5,X6) = esk381_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18356_106,axiom,
( X1 != X2
| esk381_5(X3,X1,X4,X5,X6) = esk381_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18357_107,axiom,
( X1 != X2
| esk381_5(X3,X4,X1,X5,X6) = esk381_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18358_108,axiom,
( X1 != X2
| esk381_5(X3,X4,X5,X1,X6) = esk381_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18359_109,axiom,
( X1 != X2
| esk381_5(X3,X4,X5,X6,X1) = esk381_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18360_110,axiom,
( X1 != X2
| esk382_5(X1,X3,X4,X5,X6) = esk382_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18361_111,axiom,
( X1 != X2
| esk382_5(X3,X1,X4,X5,X6) = esk382_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18362_112,axiom,
( X1 != X2
| esk382_5(X3,X4,X1,X5,X6) = esk382_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18363_113,axiom,
( X1 != X2
| esk382_5(X3,X4,X5,X1,X6) = esk382_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18364_114,axiom,
( X1 != X2
| esk382_5(X3,X4,X5,X6,X1) = esk382_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18365_115,axiom,
( X1 != X2
| esk377_5(X1,X3,X4,X5,X6) = esk377_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18366_116,axiom,
( X1 != X2
| esk377_5(X3,X1,X4,X5,X6) = esk377_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18367_117,axiom,
( X1 != X2
| esk377_5(X3,X4,X1,X5,X6) = esk377_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18368_118,axiom,
( X1 != X2
| esk377_5(X3,X4,X5,X1,X6) = esk377_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18369_119,axiom,
( X1 != X2
| esk377_5(X3,X4,X5,X6,X1) = esk377_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18370_120,axiom,
( X1 != X2
| esk376_5(X1,X3,X4,X5,X6) = esk376_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18371_121,axiom,
( X1 != X2
| esk376_5(X3,X1,X4,X5,X6) = esk376_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18372_122,axiom,
( X1 != X2
| esk376_5(X3,X4,X1,X5,X6) = esk376_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18373_123,axiom,
( X1 != X2
| esk376_5(X3,X4,X5,X1,X6) = esk376_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18374_124,axiom,
( X1 != X2
| esk376_5(X3,X4,X5,X6,X1) = esk376_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18375_125,axiom,
( X1 != X2
| c_Option_Ooption_ONone(X1) = c_Option_Ooption_ONone(X2) ) ).
cnf(i_0_18376_126,axiom,
( X1 != X2
| c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).
cnf(i_0_18377_127,axiom,
( X1 != X2
| c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).
cnf(i_0_18378_128,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__bind(X1,X3,X4,X5) = c_New__Random__Sequence_Opos__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18379_129,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__bind(X3,X1,X4,X5) = c_New__Random__Sequence_Opos__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18380_130,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__bind(X3,X4,X1,X5) = c_New__Random__Sequence_Opos__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18381_131,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__bind(X3,X4,X5,X1) = c_New__Random__Sequence_Opos__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18382_132,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18383_133,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18384_134,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18385_135,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18386_136,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18387_137,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18388_138,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18389_139,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18390_140,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18391_141,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18392_142,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18393_143,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18394_144,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18395_145,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18396_146,axiom,
( X1 != X2
| c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).
cnf(i_0_18397_147,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).
cnf(i_0_18398_148,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).
cnf(i_0_18399_149,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).
cnf(i_0_18400_150,axiom,
( X1 != X2
| esk241_6(X1,X3,X4,X5,X6,X7) = esk241_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18401_151,axiom,
( X1 != X2
| esk241_6(X3,X1,X4,X5,X6,X7) = esk241_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18402_152,axiom,
( X1 != X2
| esk241_6(X3,X4,X1,X5,X6,X7) = esk241_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18403_153,axiom,
( X1 != X2
| esk241_6(X3,X4,X5,X1,X6,X7) = esk241_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18404_154,axiom,
( X1 != X2
| esk241_6(X3,X4,X5,X6,X1,X7) = esk241_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18405_155,axiom,
( X1 != X2
| esk241_6(X3,X4,X5,X6,X7,X1) = esk241_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18406_156,axiom,
( X1 != X2
| esk240_6(X1,X3,X4,X5,X6,X7) = esk240_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18407_157,axiom,
( X1 != X2
| esk240_6(X3,X1,X4,X5,X6,X7) = esk240_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18408_158,axiom,
( X1 != X2
| esk240_6(X3,X4,X1,X5,X6,X7) = esk240_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18409_159,axiom,
( X1 != X2
| esk240_6(X3,X4,X5,X1,X6,X7) = esk240_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18410_160,axiom,
( X1 != X2
| esk240_6(X3,X4,X5,X6,X1,X7) = esk240_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18411_161,axiom,
( X1 != X2
| esk240_6(X3,X4,X5,X6,X7,X1) = esk240_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18412_162,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).
cnf(i_0_18413_163,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_18414_164,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).
cnf(i_0_18415_165,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).
cnf(i_0_18416_166,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).
cnf(i_0_18417_167,axiom,
( X1 != X2
| c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).
cnf(i_0_18418_168,axiom,
( X1 != X2
| c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).
cnf(i_0_18419_169,axiom,
( X1 != X2
| c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).
cnf(i_0_18420_170,axiom,
( X1 != X2
| c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).
cnf(i_0_18421_171,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).
cnf(i_0_18422_172,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).
cnf(i_0_18423_173,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).
cnf(i_0_18424_174,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).
cnf(i_0_18425_175,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).
cnf(i_0_18426_176,axiom,
( X1 != X2
| c_List_Omap__filter(X1,X3,X4,X5) = c_List_Omap__filter(X2,X3,X4,X5) ) ).
cnf(i_0_18427_177,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X1,X4,X5) = c_List_Omap__filter(X3,X2,X4,X5) ) ).
cnf(i_0_18428_178,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X4,X1,X5) = c_List_Omap__filter(X3,X4,X2,X5) ) ).
cnf(i_0_18429_179,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X4,X5,X1) = c_List_Omap__filter(X3,X4,X5,X2) ) ).
cnf(i_0_18430_180,axiom,
( X1 != X2
| c_Map_Odom(X1,X3,X4) = c_Map_Odom(X2,X3,X4) ) ).
cnf(i_0_18431_181,axiom,
( X1 != X2
| c_Map_Odom(X3,X1,X4) = c_Map_Odom(X3,X2,X4) ) ).
cnf(i_0_18432_182,axiom,
( X1 != X2
| c_Map_Odom(X3,X4,X1) = c_Map_Odom(X3,X4,X2) ) ).
cnf(i_0_18433_183,axiom,
( X1 != X2
| c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).
cnf(i_0_18434_184,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X1,X3,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X2,X3,X4,X5) ) ).
cnf(i_0_18435_185,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X1,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X2,X4,X5) ) ).
cnf(i_0_18436_186,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X1,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X2,X5) ) ).
cnf(i_0_18437_187,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X2) ) ).
cnf(i_0_18438_188,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_18439_189,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_18440_190,axiom,
( X1 != X2
| c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).
cnf(i_0_18441_191,axiom,
( X1 != X2
| c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).
cnf(i_0_18442_192,axiom,
( X1 != X2
| c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).
cnf(i_0_18443_193,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).
cnf(i_0_18444_194,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).
cnf(i_0_18445_195,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).
cnf(i_0_18446_196,axiom,
( X1 != X2
| c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).
cnf(i_0_18447_197,axiom,
( X1 != X2
| c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).
cnf(i_0_18448_198,axiom,
( X1 != X2
| c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).
cnf(i_0_18449_199,axiom,
( X1 != X2
| c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).
cnf(i_0_18450_200,axiom,
( X1 != X2
| esk473_4(X1,X3,X4,X5) = esk473_4(X2,X3,X4,X5) ) ).
cnf(i_0_18451_201,axiom,
( X1 != X2
| esk473_4(X3,X1,X4,X5) = esk473_4(X3,X2,X4,X5) ) ).
cnf(i_0_18452_202,axiom,
( X1 != X2
| esk473_4(X3,X4,X1,X5) = esk473_4(X3,X4,X2,X5) ) ).
cnf(i_0_18453_203,axiom,
( X1 != X2
| esk473_4(X3,X4,X5,X1) = esk473_4(X3,X4,X5,X2) ) ).
cnf(i_0_18454_204,axiom,
( X1 != X2
| esk472_4(X1,X3,X4,X5) = esk472_4(X2,X3,X4,X5) ) ).
cnf(i_0_18455_205,axiom,
( X1 != X2
| esk472_4(X3,X1,X4,X5) = esk472_4(X3,X2,X4,X5) ) ).
cnf(i_0_18456_206,axiom,
( X1 != X2
| esk472_4(X3,X4,X1,X5) = esk472_4(X3,X4,X2,X5) ) ).
cnf(i_0_18457_207,axiom,
( X1 != X2
| esk472_4(X3,X4,X5,X1) = esk472_4(X3,X4,X5,X2) ) ).
cnf(i_0_18458_208,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X1,X3,X4,X5,X6) = c_Fun_Ooverride__on(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18459_209,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X1,X4,X5,X6) = c_Fun_Ooverride__on(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18460_210,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X1,X5,X6) = c_Fun_Ooverride__on(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18461_211,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X5,X1,X6) = c_Fun_Ooverride__on(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18462_212,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X5,X6,X1) = c_Fun_Ooverride__on(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18463_213,axiom,
( X1 != X2
| c_Map_Oran(X1,X3,X4) = c_Map_Oran(X2,X3,X4) ) ).
cnf(i_0_18464_214,axiom,
( X1 != X2
| c_Map_Oran(X3,X1,X4) = c_Map_Oran(X3,X2,X4) ) ).
cnf(i_0_18465_215,axiom,
( X1 != X2
| c_Map_Oran(X3,X4,X1) = c_Map_Oran(X3,X4,X2) ) ).
cnf(i_0_18466_216,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_18467_217,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_18468_218,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_18469_219,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_18470_220,axiom,
( X1 != X2
| c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).
cnf(i_0_18471_221,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).
cnf(i_0_18472_222,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).
cnf(i_0_18473_223,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).
cnf(i_0_18474_224,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_18475_225,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).
cnf(i_0_18476_226,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).
cnf(i_0_18477_227,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).
cnf(i_0_18478_228,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).
cnf(i_0_18479_229,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).
cnf(i_0_18480_230,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).
cnf(i_0_18481_231,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).
cnf(i_0_18482_232,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).
cnf(i_0_18483_233,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).
cnf(i_0_18484_234,axiom,
( X1 != X2
| c_Map_Orestrict__map(X1,X3,X4,X5) = c_Map_Orestrict__map(X2,X3,X4,X5) ) ).
cnf(i_0_18485_235,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X1,X4,X5) = c_Map_Orestrict__map(X3,X2,X4,X5) ) ).
cnf(i_0_18486_236,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X4,X1,X5) = c_Map_Orestrict__map(X3,X4,X2,X5) ) ).
cnf(i_0_18487_237,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X4,X5,X1) = c_Map_Orestrict__map(X3,X4,X5,X2) ) ).
cnf(i_0_18488_238,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).
cnf(i_0_18489_239,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).
cnf(i_0_18490_240,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).
cnf(i_0_18491_241,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OInf__fin(X1,X3,X4) = c_Big__Operators_Olattice_OInf__fin(X2,X3,X4) ) ).
cnf(i_0_18492_242,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OInf__fin(X3,X1,X4) = c_Big__Operators_Olattice_OInf__fin(X3,X2,X4) ) ).
cnf(i_0_18493_243,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OInf__fin(X3,X4,X1) = c_Big__Operators_Olattice_OInf__fin(X3,X4,X2) ) ).
cnf(i_0_18494_244,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).
cnf(i_0_18495_245,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).
cnf(i_0_18496_246,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).
cnf(i_0_18497_247,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).
cnf(i_0_18498_248,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OSup__fin(X1,X3,X4) = c_Big__Operators_Olattice_OSup__fin(X2,X3,X4) ) ).
cnf(i_0_18499_249,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OSup__fin(X3,X1,X4) = c_Big__Operators_Olattice_OSup__fin(X3,X2,X4) ) ).
cnf(i_0_18500_250,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OSup__fin(X3,X4,X1) = c_Big__Operators_Olattice_OSup__fin(X3,X4,X2) ) ).
cnf(i_0_18501_251,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).
cnf(i_0_18502_252,axiom,
( X1 != X2
| c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).
cnf(i_0_18503_253,axiom,
( X1 != X2
| c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).
cnf(i_0_18504_254,axiom,
( X1 != X2
| c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).
cnf(i_0_18505_255,axiom,
( X1 != X2
| c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).
cnf(i_0_18506_256,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__case(X1,X3,X4,X5,X6) = c_Sum__Type_Osum_Osum__case(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18507_257,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__case(X3,X1,X4,X5,X6) = c_Sum__Type_Osum_Osum__case(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18508_258,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__case(X3,X4,X1,X5,X6) = c_Sum__Type_Osum_Osum__case(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18509_259,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__case(X3,X4,X5,X1,X6) = c_Sum__Type_Osum_Osum__case(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18510_260,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__case(X3,X4,X5,X6,X1) = c_Sum__Type_Osum_Osum__case(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18511_261,axiom,
( X1 != X2
| c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).
cnf(i_0_18512_262,axiom,
( X1 != X2
| c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).
cnf(i_0_18513_263,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).
cnf(i_0_18514_264,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).
cnf(i_0_18515_265,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).
cnf(i_0_18516_266,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OSup__fin(X1,X3) = c_Big__Operators_Olattice__class_OSup__fin(X2,X3) ) ).
cnf(i_0_18517_267,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OSup__fin(X3,X1) = c_Big__Operators_Olattice__class_OSup__fin(X3,X2) ) ).
cnf(i_0_18518_268,axiom,
( X1 != X2
| c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).
cnf(i_0_18519_269,axiom,
( X1 != X2
| c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).
cnf(i_0_18520_270,axiom,
( X1 != X2
| c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).
cnf(i_0_18521_271,axiom,
( X1 != X2
| c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).
cnf(i_0_18522_272,axiom,
( X1 != X2
| c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).
cnf(i_0_18523_273,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X1,X3,X4,X5,X6,X7) = c_Sum__Type_Osum_Osum__rec(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18524_274,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X3,X1,X4,X5,X6,X7) = c_Sum__Type_Osum_Osum__rec(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18525_275,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X3,X4,X1,X5,X6,X7) = c_Sum__Type_Osum_Osum__rec(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18526_276,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X1,X6,X7) = c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18527_277,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X6,X1,X7) = c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18528_278,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X6,X7,X1) = c_Sum__Type_Osum_Osum__rec(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18529_279,axiom,
( X1 != X2
| c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).
cnf(i_0_18530_280,axiom,
( X1 != X2
| esk370_3(X1,X3,X4) = esk370_3(X2,X3,X4) ) ).
cnf(i_0_18531_281,axiom,
( X1 != X2
| esk370_3(X3,X1,X4) = esk370_3(X3,X2,X4) ) ).
cnf(i_0_18532_282,axiom,
( X1 != X2
| esk370_3(X3,X4,X1) = esk370_3(X3,X4,X2) ) ).
cnf(i_0_18533_283,axiom,
( X1 != X2
| esk369_3(X1,X3,X4) = esk369_3(X2,X3,X4) ) ).
cnf(i_0_18534_284,axiom,
( X1 != X2
| esk369_3(X3,X1,X4) = esk369_3(X3,X2,X4) ) ).
cnf(i_0_18535_285,axiom,
( X1 != X2
| esk369_3(X3,X4,X1) = esk369_3(X3,X4,X2) ) ).
cnf(i_0_18536_286,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X1,X3,X4) = c_Smallcheck_Osmall_H(X2,X3,X4) ) ).
cnf(i_0_18537_287,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X3,X1,X4) = c_Smallcheck_Osmall_H(X3,X2,X4) ) ).
cnf(i_0_18538_288,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X3,X4,X1) = c_Smallcheck_Osmall_H(X3,X4,X2) ) ).
cnf(i_0_18539_289,axiom,
( X1 != X2
| c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).
cnf(i_0_18540_290,axiom,
( X1 != X2
| c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).
cnf(i_0_18541_291,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5) ) ).
cnf(i_0_18542_292,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X1,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X2,X4,X5) ) ).
cnf(i_0_18543_293,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X4,X1,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X2,X5) ) ).
cnf(i_0_18544_294,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X2) ) ).
cnf(i_0_18545_295,axiom,
( X1 != X2
| c_List_Olinorder__class_Oinsort__insert__key(X1,X3,X4,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18546_296,axiom,
( X1 != X2
| c_List_Olinorder__class_Oinsort__insert__key(X3,X1,X4,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18547_297,axiom,
( X1 != X2
| c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X1,X5,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18548_298,axiom,
( X1 != X2
| c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X1,X6) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18549_299,axiom,
( X1 != X2
| c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X6,X1) = c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18550_300,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OInf__fin(X1,X3) = c_Big__Operators_Olattice__class_OInf__fin(X2,X3) ) ).
cnf(i_0_18551_301,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OInf__fin(X3,X1) = c_Big__Operators_Olattice__class_OInf__fin(X3,X2) ) ).
cnf(i_0_18552_302,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X1,X3,X4) = c_Com_Ocom_OLocal(X2,X3,X4) ) ).
cnf(i_0_18553_303,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X3,X1,X4) = c_Com_Ocom_OLocal(X3,X2,X4) ) ).
cnf(i_0_18554_304,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X3,X4,X1) = c_Com_Ocom_OLocal(X3,X4,X2) ) ).
cnf(i_0_18555_305,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).
cnf(i_0_18556_306,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).
cnf(i_0_18557_307,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__map(X1,X3,X4,X5) = c_New__Random__Sequence_Oneg__map(X2,X3,X4,X5) ) ).
cnf(i_0_18558_308,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__map(X3,X1,X4,X5) = c_New__Random__Sequence_Oneg__map(X3,X2,X4,X5) ) ).
cnf(i_0_18559_309,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__map(X3,X4,X1,X5) = c_New__Random__Sequence_Oneg__map(X3,X4,X2,X5) ) ).
cnf(i_0_18560_310,axiom,
( X1 != X2
| c_New__Random__Sequence_Oneg__map(X3,X4,X5,X1) = c_New__Random__Sequence_Oneg__map(X3,X4,X5,X2) ) ).
cnf(i_0_18561_311,axiom,
( X1 != X2
| c_Com_Ocom_OWhile(X1,X3) = c_Com_Ocom_OWhile(X2,X3) ) ).
cnf(i_0_18562_312,axiom,
( X1 != X2
| c_Com_Ocom_OWhile(X3,X1) = c_Com_Ocom_OWhile(X3,X2) ) ).
cnf(i_0_18563_313,axiom,
( X1 != X2
| c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).
cnf(i_0_18564_314,axiom,
( X1 != X2
| c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).
cnf(i_0_18565_315,axiom,
( X1 != X2
| c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).
cnf(i_0_18566_316,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__map(X1,X3,X4,X5) = c_New__Random__Sequence_Opos__map(X2,X3,X4,X5) ) ).
cnf(i_0_18567_317,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__map(X3,X1,X4,X5) = c_New__Random__Sequence_Opos__map(X3,X2,X4,X5) ) ).
cnf(i_0_18568_318,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__map(X3,X4,X1,X5) = c_New__Random__Sequence_Opos__map(X3,X4,X2,X5) ) ).
cnf(i_0_18569_319,axiom,
( X1 != X2
| c_New__Random__Sequence_Opos__map(X3,X4,X5,X1) = c_New__Random__Sequence_Opos__map(X3,X4,X5,X2) ) ).
cnf(i_0_18570_320,axiom,
( X1 != X2
| esk266_5(X1,X3,X4,X5,X6) = esk266_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18571_321,axiom,
( X1 != X2
| esk266_5(X3,X1,X4,X5,X6) = esk266_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18572_322,axiom,
( X1 != X2
| esk266_5(X3,X4,X1,X5,X6) = esk266_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18573_323,axiom,
( X1 != X2
| esk266_5(X3,X4,X5,X1,X6) = esk266_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18574_324,axiom,
( X1 != X2
| esk266_5(X3,X4,X5,X6,X1) = esk266_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18575_325,axiom,
( X1 != X2
| esk380_3(X1,X3,X4) = esk380_3(X2,X3,X4) ) ).
cnf(i_0_18576_326,axiom,
( X1 != X2
| esk380_3(X3,X1,X4) = esk380_3(X3,X2,X4) ) ).
cnf(i_0_18577_327,axiom,
( X1 != X2
| esk380_3(X3,X4,X1) = esk380_3(X3,X4,X2) ) ).
cnf(i_0_18578_328,axiom,
( X1 != X2
| esk379_3(X1,X3,X4) = esk379_3(X2,X3,X4) ) ).
cnf(i_0_18579_329,axiom,
( X1 != X2
| esk379_3(X3,X1,X4) = esk379_3(X3,X2,X4) ) ).
cnf(i_0_18580_330,axiom,
( X1 != X2
| esk379_3(X3,X4,X1) = esk379_3(X3,X4,X2) ) ).
cnf(i_0_18581_331,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__size(X1,X3,X4,X5,X6) = c_Product__Type_Oprod_Oprod__size(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18582_332,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__size(X3,X1,X4,X5,X6) = c_Product__Type_Oprod_Oprod__size(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18583_333,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__size(X3,X4,X1,X5,X6) = c_Product__Type_Oprod_Oprod__size(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18584_334,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X1,X6) = c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18585_335,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X6,X1) = c_Product__Type_Oprod_Oprod__size(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18586_336,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).
cnf(i_0_18587_337,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).
cnf(i_0_18588_338,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).
cnf(i_0_18589_339,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).
cnf(i_0_18590_340,axiom,
( X1 != X2
| c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).
cnf(i_0_18591_341,axiom,
( X1 != X2
| c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).
cnf(i_0_18592_342,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X1,X3,X4,X5,X6,X7) = c_Product__Type_Omap__pair(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18593_343,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X3,X1,X4,X5,X6,X7) = c_Product__Type_Omap__pair(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18594_344,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X3,X4,X1,X5,X6,X7) = c_Product__Type_Omap__pair(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18595_345,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X3,X4,X5,X1,X6,X7) = c_Product__Type_Omap__pair(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18596_346,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X3,X4,X5,X6,X1,X7) = c_Product__Type_Omap__pair(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18597_347,axiom,
( X1 != X2
| c_Product__Type_Omap__pair(X3,X4,X5,X6,X7,X1) = c_Product__Type_Omap__pair(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18598_348,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).
cnf(i_0_18599_349,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).
cnf(i_0_18600_350,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).
cnf(i_0_18601_351,axiom,
( X1 != X2
| c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).
cnf(i_0_18602_352,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).
cnf(i_0_18603_353,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).
cnf(i_0_18604_354,axiom,
( X1 != X2
| c_Com_Ovname_OLoc(X1) = c_Com_Ovname_OLoc(X2) ) ).
cnf(i_0_18605_355,axiom,
( X1 != X2
| esk91_3(X1,X3,X4) = esk91_3(X2,X3,X4) ) ).
cnf(i_0_18606_356,axiom,
( X1 != X2
| esk91_3(X3,X1,X4) = esk91_3(X3,X2,X4) ) ).
cnf(i_0_18607_357,axiom,
( X1 != X2
| esk91_3(X3,X4,X1) = esk91_3(X3,X4,X2) ) ).
cnf(i_0_18608_358,axiom,
( X1 != X2
| esk158_4(X1,X3,X4,X5) = esk158_4(X2,X3,X4,X5) ) ).
cnf(i_0_18609_359,axiom,
( X1 != X2
| esk158_4(X3,X1,X4,X5) = esk158_4(X3,X2,X4,X5) ) ).
cnf(i_0_18610_360,axiom,
( X1 != X2
| esk158_4(X3,X4,X1,X5) = esk158_4(X3,X4,X2,X5) ) ).
cnf(i_0_18611_361,axiom,
( X1 != X2
| esk158_4(X3,X4,X5,X1) = esk158_4(X3,X4,X5,X2) ) ).
cnf(i_0_18612_362,axiom,
( X1 != X2
| esk160_4(X1,X3,X4,X5) = esk160_4(X2,X3,X4,X5) ) ).
cnf(i_0_18613_363,axiom,
( X1 != X2
| esk160_4(X3,X1,X4,X5) = esk160_4(X3,X2,X4,X5) ) ).
cnf(i_0_18614_364,axiom,
( X1 != X2
| esk160_4(X3,X4,X1,X5) = esk160_4(X3,X4,X2,X5) ) ).
cnf(i_0_18615_365,axiom,
( X1 != X2
| esk160_4(X3,X4,X5,X1) = esk160_4(X3,X4,X5,X2) ) ).
cnf(i_0_18616_366,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X1,X3,X4) = c_Com_Ocom_OCall(X2,X3,X4) ) ).
cnf(i_0_18617_367,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X3,X1,X4) = c_Com_Ocom_OCall(X3,X2,X4) ) ).
cnf(i_0_18618_368,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X3,X4,X1) = c_Com_Ocom_OCall(X3,X4,X2) ) ).
cnf(i_0_18619_369,axiom,
( X1 != X2
| esk264_4(X1,X3,X4,X5) = esk264_4(X2,X3,X4,X5) ) ).
cnf(i_0_18620_370,axiom,
( X1 != X2
| esk264_4(X3,X1,X4,X5) = esk264_4(X3,X2,X4,X5) ) ).
cnf(i_0_18621_371,axiom,
( X1 != X2
| esk264_4(X3,X4,X1,X5) = esk264_4(X3,X4,X2,X5) ) ).
cnf(i_0_18622_372,axiom,
( X1 != X2
| esk264_4(X3,X4,X5,X1) = esk264_4(X3,X4,X5,X2) ) ).
cnf(i_0_18623_373,axiom,
( X1 != X2
| esk263_4(X1,X3,X4,X5) = esk263_4(X2,X3,X4,X5) ) ).
cnf(i_0_18624_374,axiom,
( X1 != X2
| esk263_4(X3,X1,X4,X5) = esk263_4(X3,X2,X4,X5) ) ).
cnf(i_0_18625_375,axiom,
( X1 != X2
| esk263_4(X3,X4,X1,X5) = esk263_4(X3,X4,X2,X5) ) ).
cnf(i_0_18626_376,axiom,
( X1 != X2
| esk263_4(X3,X4,X5,X1) = esk263_4(X3,X4,X5,X2) ) ).
cnf(i_0_18627_377,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__size(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18628_378,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__size(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18629_379,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__size(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18630_380,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18631_381,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__size(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18632_382,axiom,
( X1 != X2
| c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).
cnf(i_0_18633_383,axiom,
( X1 != X2
| c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).
cnf(i_0_18634_384,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X1,X3,X4,X5) = c_Nitpick_Opair__box_OPairBox(X2,X3,X4,X5) ) ).
cnf(i_0_18635_385,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X3,X1,X4,X5) = c_Nitpick_Opair__box_OPairBox(X3,X2,X4,X5) ) ).
cnf(i_0_18636_386,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) = c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X5) ) ).
cnf(i_0_18637_387,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) = c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X2) ) ).
cnf(i_0_18638_388,axiom,
( X1 != X2
| esk405_3(X1,X3,X4) = esk405_3(X2,X3,X4) ) ).
cnf(i_0_18639_389,axiom,
( X1 != X2
| esk405_3(X3,X1,X4) = esk405_3(X3,X2,X4) ) ).
cnf(i_0_18640_390,axiom,
( X1 != X2
| esk405_3(X3,X4,X1) = esk405_3(X3,X4,X2) ) ).
cnf(i_0_18641_391,axiom,
( X1 != X2
| esk406_3(X1,X3,X4) = esk406_3(X2,X3,X4) ) ).
cnf(i_0_18642_392,axiom,
( X1 != X2
| esk406_3(X3,X1,X4) = esk406_3(X3,X2,X4) ) ).
cnf(i_0_18643_393,axiom,
( X1 != X2
| esk406_3(X3,X4,X1) = esk406_3(X3,X4,X2) ) ).
cnf(i_0_18644_394,axiom,
( X1 != X2
| esk265_4(X1,X3,X4,X5) = esk265_4(X2,X3,X4,X5) ) ).
cnf(i_0_18645_395,axiom,
( X1 != X2
| esk265_4(X3,X1,X4,X5) = esk265_4(X3,X2,X4,X5) ) ).
cnf(i_0_18646_396,axiom,
( X1 != X2
| esk265_4(X3,X4,X1,X5) = esk265_4(X3,X4,X2,X5) ) ).
cnf(i_0_18647_397,axiom,
( X1 != X2
| esk265_4(X3,X4,X5,X1) = esk265_4(X3,X4,X5,X2) ) ).
cnf(i_0_18648_398,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_18649_399,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_18650_400,axiom,
( X1 != X2
| esk409_3(X1,X3,X4) = esk409_3(X2,X3,X4) ) ).
cnf(i_0_18651_401,axiom,
( X1 != X2
| esk409_3(X3,X1,X4) = esk409_3(X3,X2,X4) ) ).
cnf(i_0_18652_402,axiom,
( X1 != X2
| esk409_3(X3,X4,X1) = esk409_3(X3,X4,X2) ) ).
cnf(i_0_18653_403,axiom,
( X1 != X2
| esk408_3(X1,X3,X4) = esk408_3(X2,X3,X4) ) ).
cnf(i_0_18654_404,axiom,
( X1 != X2
| esk408_3(X3,X1,X4) = esk408_3(X3,X2,X4) ) ).
cnf(i_0_18655_405,axiom,
( X1 != X2
| esk408_3(X3,X4,X1) = esk408_3(X3,X4,X2) ) ).
cnf(i_0_18656_406,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__rec(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18657_407,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__rec(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18658_408,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18659_409,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18660_410,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18661_411,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__case(X1,X3,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18662_412,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__case(X3,X1,X4,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18663_413,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__case(X3,X4,X1,X5,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18664_414,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X1,X6) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18665_415,axiom,
( X1 != X2
| c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X6,X1) = c_Nitpick_Opair__box_Opair__box__case(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18666_416,axiom,
( X1 != X2
| c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).
cnf(i_0_18667_417,axiom,
( X1 != X2
| c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).
cnf(i_0_18668_418,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X1,X3,X4,X5) = c_Lazy__Sequence_Ohb__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18669_419,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X3,X1,X4,X5) = c_Lazy__Sequence_Ohb__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18670_420,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X3,X4,X1,X5) = c_Lazy__Sequence_Ohb__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18671_421,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X1) = c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18672_422,axiom,
( X1 != X2
| c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).
cnf(i_0_18673_423,axiom,
( X1 != X2
| c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).
cnf(i_0_18674_424,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X1,X3,X4,X5) = c_Lazy__Sequence_Obind(X2,X3,X4,X5) ) ).
cnf(i_0_18675_425,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X1,X4,X5) = c_Lazy__Sequence_Obind(X3,X2,X4,X5) ) ).
cnf(i_0_18676_426,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X4,X1,X5) = c_Lazy__Sequence_Obind(X3,X4,X2,X5) ) ).
cnf(i_0_18677_427,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X4,X5,X1) = c_Lazy__Sequence_Obind(X3,X4,X5,X2) ) ).
cnf(i_0_18678_428,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X1,X3,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18679_429,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X1,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18680_430,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X1,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18681_431,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X1,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18682_432,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X1) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18683_433,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__size(X1,X3,X4,X5,X6) = c_Sum__Type_Osum_Osum__size(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18684_434,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__size(X3,X1,X4,X5,X6) = c_Sum__Type_Osum_Osum__size(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18685_435,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__size(X3,X4,X1,X5,X6) = c_Sum__Type_Osum_Osum__size(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18686_436,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__size(X3,X4,X5,X1,X6) = c_Sum__Type_Osum_Osum__size(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18687_437,axiom,
( X1 != X2
| c_Sum__Type_Osum_Osum__size(X3,X4,X5,X6,X1) = c_Sum__Type_Osum_Osum__size(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18688_438,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__rec(X1,X3,X4,X5,X6) = c_Option_Ooption_Ooption__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18689_439,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__rec(X3,X1,X4,X5,X6) = c_Option_Ooption_Ooption__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18690_440,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__rec(X3,X4,X1,X5,X6) = c_Option_Ooption_Ooption__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18691_441,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__rec(X3,X4,X5,X1,X6) = c_Option_Ooption_Ooption__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18692_442,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__rec(X3,X4,X5,X6,X1) = c_Option_Ooption_Ooption__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18693_443,axiom,
( X1 != X2
| esk191_3(X1,X3,X4) = esk191_3(X2,X3,X4) ) ).
cnf(i_0_18694_444,axiom,
( X1 != X2
| esk191_3(X3,X1,X4) = esk191_3(X3,X2,X4) ) ).
cnf(i_0_18695_445,axiom,
( X1 != X2
| esk191_3(X3,X4,X1) = esk191_3(X3,X4,X2) ) ).
cnf(i_0_18696_446,axiom,
( X1 != X2
| c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).
cnf(i_0_18697_447,axiom,
( X1 != X2
| c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).
cnf(i_0_18698_448,axiom,
( X1 != X2
| esk351_2(X1,X3) = esk351_2(X2,X3) ) ).
cnf(i_0_18699_449,axiom,
( X1 != X2
| esk351_2(X3,X1) = esk351_2(X3,X2) ) ).
cnf(i_0_18700_450,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X1,X3,X4,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X2,X3,X4,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18701_451,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X1,X4,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X2,X4,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18702_452,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X1,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X2,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18703_453,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X1,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X2,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18704_454,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X1,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X2,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18705_455,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X1,X8,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X2,X8,X9,X10,X11) ) ).
cnf(i_0_18706_456,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X1,X9,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X2,X9,X10,X11) ) ).
cnf(i_0_18707_457,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X1,X10,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X2,X10,X11) ) ).
cnf(i_0_18708_458,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X10,X1,X11) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X10,X2,X11) ) ).
cnf(i_0_18709_459,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X10,X11,X1) = c_Com_Ocom_Ocom__case(X3,X4,X5,X6,X7,X8,X9,X10,X11,X2) ) ).
cnf(i_0_18710_460,axiom,
( X1 != X2
| esk490_2(X1,X3) = esk490_2(X2,X3) ) ).
cnf(i_0_18711_461,axiom,
( X1 != X2
| esk490_2(X3,X1) = esk490_2(X3,X2) ) ).
cnf(i_0_18712_462,axiom,
( X1 != X2
| esk489_2(X1,X3) = esk489_2(X2,X3) ) ).
cnf(i_0_18713_463,axiom,
( X1 != X2
| esk489_2(X3,X1) = esk489_2(X3,X2) ) ).
cnf(i_0_18714_464,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X3,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X2,X3,X4,X5) ) ).
cnf(i_0_18715_465,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X1,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X2,X4,X5) ) ).
cnf(i_0_18716_466,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X1,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X2,X5) ) ).
cnf(i_0_18717_467,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X5,X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X3,X4,X5,X2) ) ).
cnf(i_0_18718_468,axiom,
( X1 != X2
| c_Com_Ocom_OAss(X1,X3) = c_Com_Ocom_OAss(X2,X3) ) ).
cnf(i_0_18719_469,axiom,
( X1 != X2
| c_Com_Ocom_OAss(X3,X1) = c_Com_Ocom_OAss(X3,X2) ) ).
cnf(i_0_18720_470,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).
cnf(i_0_18721_471,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).
cnf(i_0_18722_472,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).
cnf(i_0_18723_473,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).
cnf(i_0_18724_474,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).
cnf(i_0_18725_475,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).
cnf(i_0_18726_476,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X3,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,X4,X5) ) ).
cnf(i_0_18727_477,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X1,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X2,X4,X5) ) ).
cnf(i_0_18728_478,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X1,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X2,X5) ) ).
cnf(i_0_18729_479,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X2) ) ).
cnf(i_0_18730_480,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_18731_481,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_18732_482,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_18733_483,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X1,X3,X4,X5) = c_Sum__Type_OSumr(X2,X3,X4,X5) ) ).
cnf(i_0_18734_484,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X1,X4,X5) = c_Sum__Type_OSumr(X3,X2,X4,X5) ) ).
cnf(i_0_18735_485,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X4,X1,X5) = c_Sum__Type_OSumr(X3,X4,X2,X5) ) ).
cnf(i_0_18736_486,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X4,X5,X1) = c_Sum__Type_OSumr(X3,X4,X5,X2) ) ).
cnf(i_0_18737_487,axiom,
( X1 != X2
| c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).
cnf(i_0_18738_488,axiom,
( X1 != X2
| c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).
cnf(i_0_18739_489,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X1,X3,X4,X5) = c_Sum__Type_OSuml(X2,X3,X4,X5) ) ).
cnf(i_0_18740_490,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X1,X4,X5) = c_Sum__Type_OSuml(X3,X2,X4,X5) ) ).
cnf(i_0_18741_491,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X4,X1,X5) = c_Sum__Type_OSuml(X3,X4,X2,X5) ) ).
cnf(i_0_18742_492,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X4,X5,X1) = c_Sum__Type_OSuml(X3,X4,X5,X2) ) ).
cnf(i_0_18743_493,axiom,
( X1 != X2
| esk467_2(X1,X3) = esk467_2(X2,X3) ) ).
cnf(i_0_18744_494,axiom,
( X1 != X2
| esk467_2(X3,X1) = esk467_2(X3,X2) ) ).
cnf(i_0_18745_495,axiom,
( X1 != X2
| esk157_3(X1,X3,X4) = esk157_3(X2,X3,X4) ) ).
cnf(i_0_18746_496,axiom,
( X1 != X2
| esk157_3(X3,X1,X4) = esk157_3(X3,X2,X4) ) ).
cnf(i_0_18747_497,axiom,
( X1 != X2
| esk157_3(X3,X4,X1) = esk157_3(X3,X4,X2) ) ).
cnf(i_0_18748_498,axiom,
( X1 != X2
| esk159_3(X1,X3,X4) = esk159_3(X2,X3,X4) ) ).
cnf(i_0_18749_499,axiom,
( X1 != X2
| esk159_3(X3,X1,X4) = esk159_3(X3,X2,X4) ) ).
cnf(i_0_18750_500,axiom,
( X1 != X2
| esk159_3(X3,X4,X1) = esk159_3(X3,X4,X2) ) ).
cnf(i_0_18751_501,axiom,
( X1 != X2
| esk244_3(X1,X3,X4) = esk244_3(X2,X3,X4) ) ).
cnf(i_0_18752_502,axiom,
( X1 != X2
| esk244_3(X3,X1,X4) = esk244_3(X3,X2,X4) ) ).
cnf(i_0_18753_503,axiom,
( X1 != X2
| esk244_3(X3,X4,X1) = esk244_3(X3,X4,X2) ) ).
cnf(i_0_18754_504,axiom,
( X1 != X2
| esk243_3(X1,X3,X4) = esk243_3(X2,X3,X4) ) ).
cnf(i_0_18755_505,axiom,
( X1 != X2
| esk243_3(X3,X1,X4) = esk243_3(X3,X2,X4) ) ).
cnf(i_0_18756_506,axiom,
( X1 != X2
| esk243_3(X3,X4,X1) = esk243_3(X3,X4,X2) ) ).
cnf(i_0_18757_507,axiom,
( X1 != X2
| c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).
cnf(i_0_18758_508,axiom,
( X1 != X2
| c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).
cnf(i_0_18759_509,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).
cnf(i_0_18760_510,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).
cnf(i_0_18761_511,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).
cnf(i_0_18762_512,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__case(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X2,X3,X4,X5) ) ).
cnf(i_0_18763_513,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X2,X4,X5) ) ).
cnf(i_0_18764_514,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X2,X5) ) ).
cnf(i_0_18765_515,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X2) ) ).
cnf(i_0_18766_516,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X2,X3,X4,X5) ) ).
cnf(i_0_18767_517,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X2,X4,X5) ) ).
cnf(i_0_18768_518,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X2,X5) ) ).
cnf(i_0_18769_519,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X2) ) ).
cnf(i_0_18770_520,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).
cnf(i_0_18771_521,axiom,
( X1 != X2
| c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).
cnf(i_0_18772_522,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_18773_523,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_18774_524,axiom,
( X1 != X2
| c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).
cnf(i_0_18775_525,axiom,
( X1 != X2
| c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).
cnf(i_0_18776_526,axiom,
( X1 != X2
| c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).
cnf(i_0_18777_527,axiom,
( X1 != X2
| c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).
cnf(i_0_18778_528,axiom,
( X1 != X2
| c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).
cnf(i_0_18779_529,axiom,
( X1 != X2
| c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).
cnf(i_0_18780_530,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__size(X1) = c_Com_Ocom_Ocom__size(X2) ) ).
cnf(i_0_18781_531,axiom,
( X1 != X2
| c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).
cnf(i_0_18782_532,axiom,
( X1 != X2
| c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).
cnf(i_0_18783_533,axiom,
( X1 != X2
| c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).
cnf(i_0_18784_534,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).
cnf(i_0_18785_535,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).
cnf(i_0_18786_536,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).
cnf(i_0_18787_537,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X3,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X2,X3,X4,X5) ) ).
cnf(i_0_18788_538,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X1,X4,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X2,X4,X5) ) ).
cnf(i_0_18789_539,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X1,X5) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X2,X5) ) ).
cnf(i_0_18790_540,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X5,X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X5,X2) ) ).
cnf(i_0_18791_541,axiom,
( X1 != X2
| esk481_2(X1,X3) = esk481_2(X2,X3) ) ).
cnf(i_0_18792_542,axiom,
( X1 != X2
| esk481_2(X3,X1) = esk481_2(X3,X2) ) ).
cnf(i_0_18793_543,axiom,
( X1 != X2
| c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).
cnf(i_0_18794_544,axiom,
( X1 != X2
| c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).
cnf(i_0_18795_545,axiom,
( X1 != X2
| c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).
cnf(i_0_18796_546,axiom,
( X1 != X2
| c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).
cnf(i_0_18797_547,axiom,
( X1 != X2
| c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).
cnf(i_0_18798_548,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).
cnf(i_0_18799_549,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).
cnf(i_0_18800_550,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).
cnf(i_0_18801_551,axiom,
( X1 != X2
| esk451_2(X1,X3) = esk451_2(X2,X3) ) ).
cnf(i_0_18802_552,axiom,
( X1 != X2
| esk451_2(X3,X1) = esk451_2(X3,X2) ) ).
cnf(i_0_18803_553,axiom,
( X1 != X2
| esk450_2(X1,X3) = esk450_2(X2,X3) ) ).
cnf(i_0_18804_554,axiom,
( X1 != X2
| esk450_2(X3,X1) = esk450_2(X3,X2) ) ).
cnf(i_0_18805_555,axiom,
( X1 != X2
| c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).
cnf(i_0_18806_556,axiom,
( X1 != X2
| c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).
cnf(i_0_18807_557,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X3,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X2,X3,X4) ) ).
cnf(i_0_18808_558,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X1,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X2,X4) ) ).
cnf(i_0_18809_559,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X1) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X2) ) ).
cnf(i_0_18810_560,axiom,
( X1 != X2
| c_Orderings_Oord_Omax(X1,X3) = c_Orderings_Oord_Omax(X2,X3) ) ).
cnf(i_0_18811_561,axiom,
( X1 != X2
| c_Orderings_Oord_Omax(X3,X1) = c_Orderings_Oord_Omax(X3,X2) ) ).
cnf(i_0_18812_562,axiom,
( X1 != X2
| c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).
cnf(i_0_18813_563,axiom,
( X1 != X2
| c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).
cnf(i_0_18814_564,axiom,
( X1 != X2
| c_Option_Oset(X1,X3) = c_Option_Oset(X2,X3) ) ).
cnf(i_0_18815_565,axiom,
( X1 != X2
| c_Option_Oset(X3,X1) = c_Option_Oset(X3,X2) ) ).
cnf(i_0_18816_566,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X1,X3,X4,X5) = c_Com_Ovname_Ovname__rec(X2,X3,X4,X5) ) ).
cnf(i_0_18817_567,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X3,X1,X4,X5) = c_Com_Ovname_Ovname__rec(X3,X2,X4,X5) ) ).
cnf(i_0_18818_568,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X3,X4,X1,X5) = c_Com_Ovname_Ovname__rec(X3,X4,X2,X5) ) ).
cnf(i_0_18819_569,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X3,X4,X5,X1) = c_Com_Ovname_Ovname__rec(X3,X4,X5,X2) ) ).
cnf(i_0_18820_570,axiom,
( X1 != X2
| c_Com_Ovname_OGlb(X1) = c_Com_Ovname_OGlb(X2) ) ).
cnf(i_0_18821_571,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X1,X3,X4,X5) = c_Com_Ovname_Ovname__case(X2,X3,X4,X5) ) ).
cnf(i_0_18822_572,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X3,X1,X4,X5) = c_Com_Ovname_Ovname__case(X3,X2,X4,X5) ) ).
cnf(i_0_18823_573,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X3,X4,X1,X5) = c_Com_Ovname_Ovname__case(X3,X4,X2,X5) ) ).
cnf(i_0_18824_574,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X3,X4,X5,X1) = c_Com_Ovname_Ovname__case(X3,X4,X5,X2) ) ).
cnf(i_0_18825_575,axiom,
( X1 != X2
| c_New__DSequence_Oneg__single(X1,X3) = c_New__DSequence_Oneg__single(X2,X3) ) ).
cnf(i_0_18826_576,axiom,
( X1 != X2
| c_New__DSequence_Oneg__single(X3,X1) = c_New__DSequence_Oneg__single(X3,X2) ) ).
cnf(i_0_18827_577,axiom,
( X1 != X2
| c_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).
cnf(i_0_18828_578,axiom,
( X1 != X2
| c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(X3,X2) ) ).
cnf(i_0_18829_579,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X2) ) ).
cnf(i_0_18830_580,axiom,
( X1 != X2
| c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).
cnf(i_0_18831_581,axiom,
( X1 != X2
| c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).
cnf(i_0_18832_582,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X1,X3,X4) = c_Option_Ooption_Ooption__size(X2,X3,X4) ) ).
cnf(i_0_18833_583,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X3,X1,X4) = c_Option_Ooption_Ooption__size(X3,X2,X4) ) ).
cnf(i_0_18834_584,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X3,X4,X1) = c_Option_Ooption_Ooption__size(X3,X4,X2) ) ).
cnf(i_0_18835_585,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small__class_Ofull__small(X1,X3,X4) = c_Smallcheck_Ofull__small__class_Ofull__small(X2,X3,X4) ) ).
cnf(i_0_18836_586,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small__class_Ofull__small(X3,X1,X4) = c_Smallcheck_Ofull__small__class_Ofull__small(X3,X2,X4) ) ).
cnf(i_0_18837_587,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small__class_Ofull__small(X3,X4,X1) = c_Smallcheck_Ofull__small__class_Ofull__small(X3,X4,X2) ) ).
cnf(i_0_18838_588,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X1,X3,X4) = c_Smallcheck_Ofull__small_H(X2,X3,X4) ) ).
cnf(i_0_18839_589,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X3,X1,X4) = c_Smallcheck_Ofull__small_H(X3,X2,X4) ) ).
cnf(i_0_18840_590,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X3,X4,X1) = c_Smallcheck_Ofull__small_H(X3,X4,X2) ) ).
cnf(i_0_18841_591,axiom,
( X1 != X2
| esk447_1(X1) = esk447_1(X2) ) ).
cnf(i_0_18842_592,axiom,
( X1 != X2
| c_String_Ochar_Ochar__case(X1,X3,X4) = c_String_Ochar_Ochar__case(X2,X3,X4) ) ).
cnf(i_0_18843_593,axiom,
( X1 != X2
| c_String_Ochar_Ochar__case(X3,X1,X4) = c_String_Ochar_Ochar__case(X3,X2,X4) ) ).
cnf(i_0_18844_594,axiom,
( X1 != X2
| c_String_Ochar_Ochar__case(X3,X4,X1) = c_String_Ochar_Ochar__case(X3,X4,X2) ) ).
cnf(i_0_18845_595,axiom,
( X1 != X2
| c_String_Ochar_Ochar__rec(X1,X3,X4) = c_String_Ochar_Ochar__rec(X2,X3,X4) ) ).
cnf(i_0_18846_596,axiom,
( X1 != X2
| c_String_Ochar_Ochar__rec(X3,X1,X4) = c_String_Ochar_Ochar__rec(X3,X2,X4) ) ).
cnf(i_0_18847_597,axiom,
( X1 != X2
| c_String_Ochar_Ochar__rec(X3,X4,X1) = c_String_Ochar_Ochar__rec(X3,X4,X2) ) ).
cnf(i_0_18848_598,axiom,
( X1 != X2
| c_Quickcheck_Obeyond(X1,X3) = c_Quickcheck_Obeyond(X2,X3) ) ).
cnf(i_0_18849_599,axiom,
( X1 != X2
| c_Quickcheck_Obeyond(X3,X1) = c_Quickcheck_Obeyond(X3,X2) ) ).
cnf(i_0_18850_600,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X1,X3,X4) = c_Sum__Type_OProjr(X2,X3,X4) ) ).
cnf(i_0_18851_601,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X3,X1,X4) = c_Sum__Type_OProjr(X3,X2,X4) ) ).
cnf(i_0_18852_602,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X3,X4,X1) = c_Sum__Type_OProjr(X3,X4,X2) ) ).
cnf(i_0_18853_603,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X1,X3,X4) = c_Sum__Type_OProjl(X2,X3,X4) ) ).
cnf(i_0_18854_604,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X3,X1,X4) = c_Sum__Type_OProjl(X3,X2,X4) ) ).
cnf(i_0_18855_605,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X3,X4,X1) = c_Sum__Type_OProjl(X3,X4,X2) ) ).
cnf(i_0_18856_606,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_18857_607,axiom,
( X1 != X2
| c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).
cnf(i_0_18858_608,axiom,
( X1 != X2
| c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).
cnf(i_0_18859_609,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).
cnf(i_0_18860_610,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).
cnf(i_0_18861_611,axiom,
( X1 != X2
| c_Lazy__Sequence_Osingle(X1,X3) = c_Lazy__Sequence_Osingle(X2,X3) ) ).
cnf(i_0_18862_612,axiom,
( X1 != X2
| c_Lazy__Sequence_Osingle(X3,X1) = c_Lazy__Sequence_Osingle(X3,X2) ) ).
cnf(i_0_18863_613,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_18864_614,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__size(X1) = c_Com_Ovname_Ovname__size(X2) ) ).
cnf(i_0_18865_615,axiom,
( X1 != X2
| c_List_Oreturn__list(X1) = c_List_Oreturn__list(X2) ) ).
cnf(i_0_18866_616,axiom,
( X1 != X2
| c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).
cnf(i_0_18867_617,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_18868_618,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_18869_619,axiom,
( X1 != X2
| c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).
cnf(i_0_18870_620,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X1,X3,X4,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X2,X3,X4,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18871_621,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X1,X4,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X2,X4,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18872_622,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X1,X5,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X2,X5,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18873_623,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X1,X6,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X2,X6,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18874_624,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X1,X7,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X2,X7,X8,X9,X10,X11) ) ).
cnf(i_0_18875_625,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X1,X8,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X2,X8,X9,X10,X11) ) ).
cnf(i_0_18876_626,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X1,X9,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X2,X9,X10,X11) ) ).
cnf(i_0_18877_627,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X1,X10,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X2,X10,X11) ) ).
cnf(i_0_18878_628,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X10,X1,X11) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X10,X2,X11) ) ).
cnf(i_0_18879_629,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X10,X11,X1) = c_Com_Ocom_Ocom__rec(X3,X4,X5,X6,X7,X8,X9,X10,X11,X2) ) ).
cnf(i_0_18880_630,axiom,
( X1 != X2
| c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).
cnf(i_0_18881_631,axiom,
( X1 != X2
| c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).
cnf(i_0_18882_632,axiom,
( X1 != X2
| c_Map_Omap__add(X1,X3,X4,X5) = c_Map_Omap__add(X2,X3,X4,X5) ) ).
cnf(i_0_18883_633,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X1,X4,X5) = c_Map_Omap__add(X3,X2,X4,X5) ) ).
cnf(i_0_18884_634,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X4,X1,X5) = c_Map_Omap__add(X3,X4,X2,X5) ) ).
cnf(i_0_18885_635,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X4,X5,X1) = c_Map_Omap__add(X3,X4,X5,X2) ) ).
cnf(i_0_18886_636,axiom,
( X1 != X2
| c_Map_Omap__of(X1,X3,X4) = c_Map_Omap__of(X2,X3,X4) ) ).
cnf(i_0_18887_637,axiom,
( X1 != X2
| c_Map_Omap__of(X3,X1,X4) = c_Map_Omap__of(X3,X2,X4) ) ).
cnf(i_0_18888_638,axiom,
( X1 != X2
| c_Map_Omap__of(X3,X4,X1) = c_Map_Omap__of(X3,X4,X2) ) ).
cnf(i_0_18889_639,axiom,
( X1 != X2
| c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).
cnf(i_0_18890_640,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).
cnf(i_0_18891_641,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).
cnf(i_0_18892_642,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).
cnf(i_0_18893_643,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_18894_644,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_18895_645,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_18896_646,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_18897_647,axiom,
( X1 != X2
| ~ c_Predicate_Oreflp(X1,X3)
| c_Predicate_Oreflp(X2,X3) ) ).
cnf(i_0_18898_648,axiom,
( X1 != X2
| ~ c_Predicate_Oreflp(X3,X1)
| c_Predicate_Oreflp(X3,X2) ) ).
cnf(i_0_18899_649,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_18900_650,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_18901_651,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_18902_652,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_18903_653,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_18904_654,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_18905_655,axiom,
( X1 != X2
| ~ class_Orderings_Owellorder(X1)
| class_Orderings_Owellorder(X2) ) ).
cnf(i_0_18906_656,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_18907_657,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_18908_658,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_18909_659,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_18910_660,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_18911_661,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_18912_662,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_18913_663,axiom,
( X1 != X2
| ~ c_Groups_Osemigroup(X1,X3)
| c_Groups_Osemigroup(X2,X3) ) ).
cnf(i_0_18914_664,axiom,
( X1 != X2
| ~ c_Groups_Osemigroup(X3,X1)
| c_Groups_Osemigroup(X3,X2) ) ).
cnf(i_0_18915_665,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_18916_666,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
| c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).
cnf(i_0_18917_667,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
| c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).
cnf(i_0_18918_668,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
| c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).
cnf(i_0_18919_669,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
| c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).
cnf(i_0_18920_670,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_18921_671,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_18922_672,axiom,
( X1 != X2
| ~ c_Nitpick_Owf_H(X1,X3)
| c_Nitpick_Owf_H(X2,X3) ) ).
cnf(i_0_18923_673,axiom,
( X1 != X2
| ~ c_Nitpick_Owf_H(X3,X1)
| c_Nitpick_Owf_H(X3,X2) ) ).
cnf(i_0_18924_674,axiom,
( X1 != X2
| ~ class_Groups_Osgn__if(X1)
| class_Groups_Osgn__if(X2) ) ).
cnf(i_0_18925_675,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_18926_676,axiom,
( X1 != X2
| ~ class_Groups_Oabs__if(X1)
| class_Groups_Oabs__if(X2) ) ).
cnf(i_0_18927_677,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_18928_678,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
| c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).
cnf(i_0_18929_679,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
| c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).
cnf(i_0_18930_680,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
| c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).
cnf(i_0_18931_681,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_18932_682,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_18933_683,axiom,
( X1 != X2
| ~ c_Nitpick_Ounknown(X1)
| c_Nitpick_Ounknown(X2) ) ).
cnf(i_0_18934_684,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_18935_685,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_18936_686,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_18937_687,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X1,X3,X4)
| c_Groups_Ocomm__monoid(X2,X3,X4) ) ).
cnf(i_0_18938_688,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X3,X1,X4)
| c_Groups_Ocomm__monoid(X3,X2,X4) ) ).
cnf(i_0_18939_689,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X3,X4,X1)
| c_Groups_Ocomm__monoid(X3,X4,X2) ) ).
cnf(i_0_18940_690,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_18941_691,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_18942_692,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_18943_693,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_18944_694,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__bot(X1)
| class_Lattices_Obounded__lattice__bot(X2) ) ).
cnf(i_0_18945_695,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__top(X1)
| class_Lattices_Obounded__lattice__top(X2) ) ).
cnf(i_0_18946_696,axiom,
( X1 != X2
| ~ c_Option_Ois__none(X1,X3)
| c_Option_Ois__none(X2,X3) ) ).
cnf(i_0_18947_697,axiom,
( X1 != X2
| ~ c_Option_Ois__none(X3,X1)
| c_Option_Ois__none(X3,X2) ) ).
cnf(i_0_18948_698,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_18949_699,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__semigroup__add(X1)
| class_Groups_Olinordered__ab__semigroup__add(X2) ) ).
cnf(i_0_18950_700,axiom,
( X1 != X2
| ~ c_List_Onat__list(X1)
| c_List_Onat__list(X2) ) ).
cnf(i_0_18951_701,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_18952_702,axiom,
( X1 != X2
| ~ v_Q(X1,X3)
| v_Q(X2,X3) ) ).
cnf(i_0_18953_703,axiom,
( X1 != X2
| ~ v_Q(X3,X1)
| v_Q(X3,X2) ) ).
cnf(i_0_18954_704,axiom,
( X1 != X2
| ~ v_P(X1,X3)
| v_P(X2,X3) ) ).
cnf(i_0_18955_705,axiom,
( X1 != X2
| ~ v_P(X3,X1)
| v_P(X3,X2) ) ).
cnf(i_0_18956_706,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_18957_707,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_18958_708,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18959_709,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X1,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18960_710,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X1,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18961_711,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X1,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18962_712,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X1,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18963_713,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X1)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18964_714,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_18965_715,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X1,X3,X4,X5,X6,X7,X8)
| c_Predicate_Opred__comp(X2,X3,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18966_716,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X1,X4,X5,X6,X7,X8)
| c_Predicate_Opred__comp(X3,X2,X4,X5,X6,X7,X8) ) ).
cnf(i_0_18967_717,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X4,X1,X5,X6,X7,X8)
| c_Predicate_Opred__comp(X3,X4,X2,X5,X6,X7,X8) ) ).
cnf(i_0_18968_718,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X4,X5,X1,X6,X7,X8)
| c_Predicate_Opred__comp(X3,X4,X5,X2,X6,X7,X8) ) ).
cnf(i_0_18969_719,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X4,X5,X6,X1,X7,X8)
| c_Predicate_Opred__comp(X3,X4,X5,X6,X2,X7,X8) ) ).
cnf(i_0_18970_720,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X4,X5,X6,X7,X1,X8)
| c_Predicate_Opred__comp(X3,X4,X5,X6,X7,X2,X8) ) ).
cnf(i_0_18971_721,axiom,
( X1 != X2
| ~ c_Predicate_Opred__comp(X3,X4,X5,X6,X7,X8,X1)
| c_Predicate_Opred__comp(X3,X4,X5,X6,X7,X8,X2) ) ).
cnf(i_0_18972_722,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X1,X3,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18973_723,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X1,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18974_724,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X1,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18975_725,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X1,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18976_726,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X1,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18977_727,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X1)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18978_728,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X1,X3,X4,X5)
| c_Natural_Oevaln(X2,X3,X4,X5) ) ).
cnf(i_0_18979_729,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X1,X4,X5)
| c_Natural_Oevaln(X3,X2,X4,X5) ) ).
cnf(i_0_18980_730,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X4,X1,X5)
| c_Natural_Oevaln(X3,X4,X2,X5) ) ).
cnf(i_0_18981_731,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X4,X5,X1)
| c_Natural_Oevaln(X3,X4,X5,X2) ) ).
cnf(i_0_18982_732,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X1,X3,X4,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18983_733,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X1,X4,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18984_734,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X1,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18985_735,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X1,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18986_736,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X1,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18987_737,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X1)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18988_738,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_18989_739,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_18990_740,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_18991_741,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_18992_742,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_18993_743,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
| c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).
cnf(i_0_18994_744,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
| c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).
cnf(i_0_18995_745,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
| c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).
cnf(i_0_18996_746,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
| c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).
cnf(i_0_18997_747,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X1,X3,X4,X5)
| c_List_Olistrelp(X2,X3,X4,X5) ) ).
cnf(i_0_18998_748,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X1,X4,X5)
| c_List_Olistrelp(X3,X2,X4,X5) ) ).
cnf(i_0_18999_749,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X1,X5)
| c_List_Olistrelp(X3,X4,X2,X5) ) ).
cnf(i_0_19000_750,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X5,X1)
| c_List_Olistrelp(X3,X4,X5,X2) ) ).
cnf(i_0_19001_751,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequivp(X1,X3)
| c_Equiv__Relations_Oequivp(X2,X3) ) ).
cnf(i_0_19002_752,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequivp(X3,X1)
| c_Equiv__Relations_Oequivp(X3,X2) ) ).
cnf(i_0_19003_753,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(X2,X3) ) ).
cnf(i_0_19004_754,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X3,X1)
| c_Wellfounded_Owf(X3,X2) ) ).
cnf(i_0_19005_755,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X1,X3)
| c_Wellfounded_OwfP(X2,X3) ) ).
cnf(i_0_19006_756,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X3,X1)
| c_Wellfounded_OwfP(X3,X2) ) ).
cnf(i_0_19007_757,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
| c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).
cnf(i_0_19008_758,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
| c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).
cnf(i_0_19009_759,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
| c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).
cnf(i_0_19010_760,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_19011_761,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
| c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).
cnf(i_0_19012_762,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
| c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).
cnf(i_0_19013_763,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
| c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).
cnf(i_0_19014_764,axiom,
( X1 != X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(X2) ) ).
cnf(i_0_19015_765,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_19016_766,axiom,
( X1 != X2
| ~ class_Smallcheck_Osmall(X1)
| class_Smallcheck_Osmall(X2) ) ).
cnf(i_0_19017_767,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_19018_768,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X1,X3,X4,X5)
| c_Orderings_Oorder_Ostrict__mono(X2,X3,X4,X5) ) ).
cnf(i_0_19019_769,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X1,X4,X5)
| c_Orderings_Oorder_Ostrict__mono(X3,X2,X4,X5) ) ).
cnf(i_0_19020_770,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X1,X5)
| c_Orderings_Oorder_Ostrict__mono(X3,X4,X2,X5) ) ).
cnf(i_0_19021_771,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X1)
| c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X2) ) ).
cnf(i_0_19022_772,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X1,X3,X4,X5)
| c_Orderings_Oorder_Omono(X2,X3,X4,X5) ) ).
cnf(i_0_19023_773,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X1,X4,X5)
| c_Orderings_Oorder_Omono(X3,X2,X4,X5) ) ).
cnf(i_0_19024_774,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X4,X1,X5)
| c_Orderings_Oorder_Omono(X3,X4,X2,X5) ) ).
cnf(i_0_19025_775,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X4,X5,X1)
| c_Orderings_Oorder_Omono(X3,X4,X5,X2) ) ).
cnf(i_0_19026_776,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_19027_777,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_19028_778,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_19029_779,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_19030_780,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_19031_781,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_19032_782,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
| c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).
cnf(i_0_19033_783,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
| c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).
cnf(i_0_19034_784,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
| c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).
cnf(i_0_19035_785,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__1(X1)
| class_Rings_Osemiring__1(X2) ) ).
cnf(i_0_19036_786,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
| c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).
cnf(i_0_19037_787,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
| c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).
cnf(i_0_19038_788,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
| c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).
cnf(i_0_19039_789,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_19040_790,axiom,
( X1 != X2
| ~ c_FunDef_Oreduction__pair(X1,X3)
| c_FunDef_Oreduction__pair(X2,X3) ) ).
cnf(i_0_19041_791,axiom,
( X1 != X2
| ~ c_FunDef_Oreduction__pair(X3,X1)
| c_FunDef_Oreduction__pair(X3,X2) ) ).
cnf(i_0_19042_792,axiom,
( X1 != X2
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| c_List_Olinorder__class_Osorted(X2,X3) ) ).
cnf(i_0_19043_793,axiom,
( X1 != X2
| ~ c_List_Olinorder__class_Osorted(X3,X1)
| c_List_Olinorder__class_Osorted(X3,X2) ) ).
cnf(i_0_19044_794,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Ois__nat(X1)
| c_Nat__Transfer_Ois__nat(X2) ) ).
cnf(i_0_19045_795,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
| c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).
cnf(i_0_19046_796,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
| c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).
cnf(i_0_19047_797,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
| c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).
cnf(i_0_19048_798,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X1,X3,X4)
| c_Nitpick_Oless__frac(X2,X3,X4) ) ).
cnf(i_0_19049_799,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X3,X1,X4)
| c_Nitpick_Oless__frac(X3,X2,X4) ) ).
cnf(i_0_19050_800,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X3,X4,X1)
| c_Nitpick_Oless__frac(X3,X4,X2) ) ).
cnf(i_0_19051_801,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_19052_802,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_19053_803,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_19054_804,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_19055_805,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_19056_806,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_19057_807,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_19058_808,axiom,
( X1 != X2
| ~ class_Rings_Oinverse(X1)
| class_Rings_Oinverse(X2) ) ).
cnf(i_0_19059_809,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_19060_810,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X3,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_19061_811,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X1,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_19062_812,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X1,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_19063_813,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X1,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_19064_814,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X1,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_19065_815,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X1)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_19066_816,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_19067_817,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image(X1,X3,X4,X5,X6)
| c_Finite__Set_Ofolding__image(X2,X3,X4,X5,X6) ) ).
cnf(i_0_19068_818,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image(X3,X1,X4,X5,X6)
| c_Finite__Set_Ofolding__image(X3,X2,X4,X5,X6) ) ).
cnf(i_0_19069_819,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image(X3,X4,X1,X5,X6)
| c_Finite__Set_Ofolding__image(X3,X4,X2,X5,X6) ) ).
cnf(i_0_19070_820,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image(X3,X4,X5,X1,X6)
| c_Finite__Set_Ofolding__image(X3,X4,X5,X2,X6) ) ).
cnf(i_0_19071_821,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image(X3,X4,X5,X6,X1)
| c_Finite__Set_Ofolding__image(X3,X4,X5,X6,X2) ) ).
cnf(i_0_19072_822,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_19073_823,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Onat__set(X1)
| c_Nat__Transfer_Onat__set(X2) ) ).
cnf(i_0_19074_824,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_19075_825,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_19076_826,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X3,X4)
| c_Finite__Set_Ofun__left__comm__idem(X2,X3,X4) ) ).
cnf(i_0_19077_827,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm__idem(X3,X1,X4)
| c_Finite__Set_Ofun__left__comm__idem(X3,X2,X4) ) ).
cnf(i_0_19078_828,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm__idem(X3,X4,X1)
| c_Finite__Set_Ofun__left__comm__idem(X3,X4,X2) ) ).
cnf(i_0_19079_829,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__sup(X1)
| class_Lattices_Osemilattice__sup(X2) ) ).
cnf(i_0_19080_830,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X1,X3)
| c_Int_Oiszero(X2,X3) ) ).
cnf(i_0_19081_831,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X3,X1)
| c_Int_Oiszero(X3,X2) ) ).
cnf(i_0_19082_832,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_19083_833,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_19084_834,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_19085_835,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_19086_836,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_19087_837,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_19088_838,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_19089_839,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,X3,X4)
| c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4) ) ).
cnf(i_0_19090_840,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X3,X1,X4)
| c_Hoare__Mirabelle_Otriple__valid(X3,X2,X4) ) ).
cnf(i_0_19091_841,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X3,X4,X1)
| c_Hoare__Mirabelle_Otriple__valid(X3,X4,X2) ) ).
cnf(i_0_19092_842,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_19093_843,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_19094_844,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_19095_845,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_19096_846,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_19097_847,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_19098_848,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_19099_849,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
| c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).
cnf(i_0_19100_850,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
| c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).
cnf(i_0_19101_851,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
| c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).
cnf(i_0_19102_852,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
| c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).
cnf(i_0_19103_853,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_19104_854,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_19105_855,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__inf(X1)
| class_Lattices_Osemilattice__inf(X2) ) ).
cnf(i_0_19106_856,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_19107_857,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_19108_858,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_19109_859,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).
cnf(i_0_19110_860,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).
cnf(i_0_19111_861,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).
cnf(i_0_19112_862,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_19113_863,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_19114_864,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_19115_865,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
| c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).
cnf(i_0_19116_866,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
| c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).
cnf(i_0_19117_867,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
| c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).
cnf(i_0_19118_868,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
| c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).
cnf(i_0_19119_869,axiom,
( X1 != X2
| ~ c_Big__Operators_Ocomm__monoid__big(X1,X3,X4,X5,X6)
| c_Big__Operators_Ocomm__monoid__big(X2,X3,X4,X5,X6) ) ).
cnf(i_0_19120_870,axiom,
( X1 != X2
| ~ c_Big__Operators_Ocomm__monoid__big(X3,X1,X4,X5,X6)
| c_Big__Operators_Ocomm__monoid__big(X3,X2,X4,X5,X6) ) ).
cnf(i_0_19121_871,axiom,
( X1 != X2
| ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X1,X5,X6)
| c_Big__Operators_Ocomm__monoid__big(X3,X4,X2,X5,X6) ) ).
cnf(i_0_19122_872,axiom,
( X1 != X2
| ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X1,X6)
| c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X2,X6) ) ).
cnf(i_0_19123_873,axiom,
( X1 != X2
| ~ c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X6,X1)
| c_Big__Operators_Ocomm__monoid__big(X3,X4,X5,X6,X2) ) ).
cnf(i_0_19124_874,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
| c_Hoare__Mirabelle_Ohoare__valids(X2,X3,X4) ) ).
cnf(i_0_19125_875,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X1,X4)
| c_Hoare__Mirabelle_Ohoare__valids(X3,X2,X4) ) ).
cnf(i_0_19126_876,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X1)
| c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X2) ) ).
cnf(i_0_19127_877,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_19128_878,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
| c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).
cnf(i_0_19129_879,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
| c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).
cnf(i_0_19130_880,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
| c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).
cnf(i_0_19131_881,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
| c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).
cnf(i_0_19132_882,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
| c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).
cnf(i_0_19133_883,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_19134_884,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_19135_885,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
| c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).
cnf(i_0_19136_886,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
| c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).
cnf(i_0_19137_887,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
| c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).
cnf(i_0_19138_888,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
| c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).
cnf(i_0_19139_889,axiom,
( X1 != X2
| ~ class_Groups_Osemigroup__add(X1)
| class_Groups_Osemigroup__add(X2) ) ).
cnf(i_0_19140_890,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_19141_891,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_19142_892,axiom,
( X1 != X2
| ~ epred2_3(X1,X3,X4)
| epred2_3(X2,X3,X4) ) ).
cnf(i_0_19143_893,axiom,
( X1 != X2
| ~ epred2_3(X3,X1,X4)
| epred2_3(X3,X2,X4) ) ).
cnf(i_0_19144_894,axiom,
( X1 != X2
| ~ epred2_3(X3,X4,X1)
| epred2_3(X3,X4,X2) ) ).
cnf(i_0_19145_895,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_19146_896,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_19147_897,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_19148_898,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_19149_899,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_19150_900,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_19151_901,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_19152_902,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_19153_903,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_19154,plain,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X4
| ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X3,X6)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk245_7(X4,X4,X6,X5,X3,X2,X1)),esk246_7(X4,X4,X6,X5,X3,X2,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))) ),
inference(equality_inference,[],[11058]) ).
cnf(i_0_19155,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ class_Groups_Ocomm__monoid__mult(X5)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X5),X6),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X7),X4)
| hBOOL(hAPP(hAPP(c_member(X1),esk272_8(X6,X7,hAPP(c_Set_Oimage(X1,X2,X3),X4),X4,X3,X2,X1,X5)),X4)) ),
inference(equality_inference,[],[11071]) ).
cnf(i_0_19156,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ class_Groups_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X5),X6),hAPP(c_Set_Oimage(X1,X2,X3),X4)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X7),X4)
| hBOOL(hAPP(hAPP(c_member(X1),esk364_8(X6,X7,hAPP(c_Set_Oimage(X1,X2,X3),X4),X4,X3,X2,X1,X5)),X4)) ),
inference(equality_inference,[],[11072]) ).
cnf(i_0_19157,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olistrel(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X3)),esk442_4(X3,X2,X2,X1))) ),
inference(equality_inference,[],[11094]) ).
cnf(i_0_19158,plain,
( X1 = X1
| ~ c_Equiv__Relations_Oequiv(X2,X3,X4)
| ~ c_Equiv__Relations_Ocongruent(X2,tc_fun(X5,tc_HOL_Obool),X4,X6)
| hBOOL(hAPP(hAPP(c_member(X2),esk246_7(X1,X1,X6,X5,X4,X3,X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4))) ),
inference(equality_inference,[],[11143]) ).
cnf(i_0_19159,plain,
( X1 = X1
| ~ c_Equiv__Relations_Oequiv(X2,X3,X4)
| ~ c_Equiv__Relations_Ocongruent(X2,tc_fun(X5,tc_HOL_Obool),X4,X6)
| hBOOL(hAPP(hAPP(c_member(X2),esk245_7(X1,X1,X6,X5,X4,X3,X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4))) ),
inference(equality_inference,[],[11144]) ).
cnf(i_0_19160,plain,
X1 = X1,
inference(equality_inference,[],[11183]) ).
cnf(i_0_19161,plain,
( X1 = X1
| ~ c_Equiv__Relations_Oequiv(X2,X3,X4)
| ~ c_Equiv__Relations_Ocongruent(X2,tc_fun(X5,tc_HOL_Obool),X4,X6)
| hAPP(X6,esk245_7(X1,X1,X6,X5,X4,X3,X2)) = hAPP(X6,esk246_7(X1,X1,X6,X5,X4,X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X3),X4))) ),
inference(equality_inference,[],[11196]) ).
cnf(i_0_19162,plain,
( ~ class_Groups_Oordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X5,esk209_6(X4,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3),X5,X3,X2,X1))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3))) ),
inference(equality_inference,[],[11247]) ).
cnf(i_0_19163,plain,
( ~ class_Groups_Oordered__ab__group__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X4,X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X3))
| hBOOL(hAPP(hAPP(c_member(X2),esk209_6(X5,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3),X4,X3,X2,X1)),X3)) ),
inference(equality_inference,[],[11317]) ).
cnf(i_0_19164,plain,
( c_List_Otranspose(X1,X2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk488_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))) ),
inference(equality_inference,[],[11327]) ).
cnf(i_0_19165,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olistrel(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk454_4(X3,X2,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk454_4(X3,X2,X2,X1)))),X3)) ),
inference(equality_inference,[],[11338]) ).
cnf(i_0_19166,plain,
( ~ class_Groups_Oab__semigroup__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),X5),X3) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),X5),X3) ),
inference(equality_inference,[],[11380]) ).
cnf(i_0_19167,plain,
hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)),
inference(equality_inference,[],[11387]) ).
cnf(i_0_19168,plain,
hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)),
inference(equality_inference,[],[11388]) ).
cnf(i_0_19169,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
inference(equality_inference,[],[11417]) ).
cnf(i_0_19170,plain,
hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X4),X5) = hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X4),X5),
inference(equality_inference,[],[11470]) ).
cnf(i_0_19171,plain,
hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),X5) = hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),X5),
inference(equality_inference,[],[11471]) ).
cnf(i_0_19172,plain,
( c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X6),X7))
| ~ c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X7)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5)) ),
inference(equality_inference,[],[11545]) ).
cnf(i_0_19173,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(equality_inference,[],[11548]) ).
cnf(i_0_19174,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X5))) ),
inference(equality_inference,[],[11641]) ).
cnf(i_0_19175,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X5)) ),
inference(equality_inference,[],[11667]) ).
cnf(i_0_19176,plain,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X3,X2))),X4))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X5,X1,X3)),X2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X4),hAPP(c_Natural_Ogetlocs,X2))),X5),hAPP(hAPP(c_Natural_Ogetlocs,X4),c_Com_ORes)))) ),
inference(equality_inference,[],[11691]) ).
cnf(i_0_19177,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5))),c_Wellfounded_Olex__prod(X1,X2,X6,X7)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X5)),X7)) ),
inference(equality_inference,[],[11706]) ).
cnf(i_0_19178,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk457_5(X2,X3,X2,X3,X1)),X2) = X2
| X2 = hAPP(hAPP(c_List_Oappend(X1),esk458_5(X2,X3,X2,X3,X1)),X2) ),
inference(equality_inference,[],[11741]) ).
cnf(i_0_19179,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),X4) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk268_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),X4))),X4)) ),
inference(equality_inference,[],[11758]) ).
cnf(i_0_19180,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olexord(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X4)),hAPP(hAPP(c_List_Onth(X1),X2),X4))),X3)) ),
inference(equality_inference,[],[11788]) ).
cnf(i_0_19181,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,X3,X4),X5))
| hBOOL(hAPP(hAPP(c_member(X1),X3),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5)) ),
inference(equality_inference,[],[11803]) ).
cnf(i_0_19182,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X3)),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[11805]) ).
cnf(i_0_19183,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X3)),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[11806]) ).
cnf(i_0_19184,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X3)),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[11807]) ).
cnf(i_0_19185,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) = hAPP(hAPP(c_List_Omap(X1,X2),X3),X4),
inference(equality_inference,[],[11841]) ).
cnf(i_0_19186,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),esk458_5(X3,X2,X3,X2,X1)) = X2
| hAPP(hAPP(c_List_Oappend(X1),esk457_5(X3,X2,X3,X2,X1)),X3) = X3 ),
inference(equality_inference,[],[11864]) ).
cnf(i_0_19187,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk457_5(X3,X1,X3,X1,X2))
| X3 = hAPP(hAPP(c_List_Oappend(X2),esk458_5(X3,X1,X3,X1,X2)),X3) ),
inference(equality_inference,[],[11865]) ).
cnf(i_0_19188,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2))),c_Int_Ointrel)),
inference(equality_inference,[],[11896]) ).
cnf(i_0_19189,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X4),X3))),c_List_Olistrel1(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X5))) ),
inference(equality_inference,[],[11900]) ).
cnf(i_0_19190,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X2),X4))),c_List_Olistrel1(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel1(X1,X5))) ),
inference(equality_inference,[],[11901]) ).
cnf(i_0_19191,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olistrel1(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel1(X1,X5))) ),
inference(equality_inference,[],[11902]) ).
cnf(i_0_19192,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olexord(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olexord(X1,X5))) ),
inference(equality_inference,[],[11903]) ).
cnf(i_0_19193,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olex(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olex(X1,X5))) ),
inference(equality_inference,[],[11904]) ).
cnf(i_0_19194,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),c_List_Olistrel1(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),X4)),X5)) ),
inference(equality_inference,[],[11924]) ).
cnf(i_0_19195,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olex(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X5)) ),
inference(equality_inference,[],[11967]) ).
cnf(i_0_19196,plain,
( c_Map_Orestrict__map(X1,X1,c_Map_Omap__upds(X1,X1,X2,X3,X3),X4) = c_Map_Omap__upds(X1,X1,c_Map_Orestrict__map(X1,X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_List_Oset(X1),X3))),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),X4)) ),
inference(equality_inference,[],[11968]) ).
cnf(i_0_19197,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel1(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X5)) ),
inference(equality_inference,[],[11974]) ).
cnf(i_0_19198,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[12032]) ).
cnf(i_0_19199,plain,
( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X3,X2)),X4,X5)
| c_Natural_Oevaln(c_Com_Ocom_OCall(X6,X1,X3),X2,X4,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X5),hAPP(c_Natural_Ogetlocs,X2))),X6),hAPP(hAPP(c_Natural_Ogetlocs,X5),c_Com_ORes))) ),
inference(equality_inference,[],[12041]) ).
cnf(i_0_19200,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Wellfounded_Omax__ext(X1,X3))),
inference(equality_inference,[],[12043]) ).
cnf(i_0_19201,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[12048]) ).
cnf(i_0_19202,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[12049]) ).
cnf(i_0_19203,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X1)),c_Int_Ointrel)),
inference(equality_inference,[],[12050]) ).
cnf(i_0_19204,plain,
( ~ c_Nat__Transfer_Onat__set(X1)
| ~ class_Groups_Ocomm__monoid__add(X2)
| ~ class_Groups_Ocomm__monoid__mult(X2)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X2),X3),X1) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X2),X4),X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk236_5(X4,X3,X1,X1,X2))) ),
inference(equality_inference,[],[12061]) ).
cnf(i_0_19205,plain,
( ~ c_Nat__Transfer_Onat__set(X1)
| ~ class_Groups_Ocomm__monoid__add(X2)
| ~ class_Groups_Ocomm__monoid__mult(X2)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X2),X3),X1) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X2),X4),X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk131_5(X4,X3,X1,X1,X2))) ),
inference(equality_inference,[],[12062]) ).
cnf(i_0_19206,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk457_5(X3,X1,X3,X1,X2))
| hAPP(hAPP(c_List_Oappend(X2),X1),esk458_5(X3,X1,X3,X1,X2)) = X1 ),
inference(equality_inference,[],[12066]) ).
cnf(i_0_19207,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olistrel(X1,X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk442_4(X3,X2,X2,X1)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)))) ),
inference(equality_inference,[],[12069]) ).
cnf(i_0_19208,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X2)) ),
inference(equality_inference,[],[12152]) ).
cnf(i_0_19209,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olexord(X1,X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olex(X1,X3))) ),
inference(equality_inference,[],[12155]) ).
cnf(i_0_19210,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olistrel(X1,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk454_4(X3,X2,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(equality_inference,[],[12191]) ).
cnf(i_0_19211,plain,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),hAPP(hAPP(hAPP(c_Natural_Oupdate,X2),c_Com_Ovname_OLoc(X3)),hAPP(X4,X2))),X5))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X3,X4,X1)),X2),hAPP(hAPP(hAPP(c_Natural_Oupdate,X5),c_Com_Ovname_OLoc(X3)),hAPP(hAPP(c_Natural_Ogetlocs,X2),X3)))) ),
inference(equality_inference,[],[12196]) ).
cnf(i_0_19212,plain,
X1 = X1,
inference(equality_inference,[],[12214]) ).
cnf(i_0_19213,plain,
X1 = X1,
inference(equality_inference,[],[12215]) ).
cnf(i_0_19214,plain,
( c_Map_Omap__of(X1,X2,X3) = c_Map_Omap__of(X1,X2,X3)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
inference(equality_inference,[],[12254]) ).
cnf(i_0_19215,plain,
( hAPP(c_List_Oset(tc_prod(X1,X2)),X3) = hAPP(c_List_Oset(tc_prod(X1,X2)),X3)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
inference(equality_inference,[],[12257]) ).
cnf(i_0_19216,plain,
( hAPP(c_Map_Omap__of(X1,X1,hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)),X3) = hAPP(c_Option_Ooption_OSome(X1),esk441_5(X3,X2,X1,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))) ),
inference(equality_inference,[],[12323]) ).
cnf(i_0_19217,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)) ),
inference(equality_inference,[],[12340]) ).
cnf(i_0_19218,plain,
( X1 = X1
| ~ class_Orderings_Olinorder(X2)
| ~ c_Fun_Oinj__on(X3,X2,X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(c_List_Oset(X3),X1)),hAPP(c_List_Oset(X3),X1)))
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Omap(X3,X2),X4),X1))
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Omap(X3,X2),X4),X1))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Omap(X3,X2),X4),X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Omap(X3,X2),X4),X1))) ),
inference(equality_inference,[],[12349]) ).
cnf(i_0_19219,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X1))) ),
inference(equality_inference,[],[12394]) ).
cnf(i_0_19220,plain,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X6),X4)),X3)) ),
inference(equality_inference,[],[12395]) ).
cnf(i_0_19221,plain,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X3)) ),
inference(equality_inference,[],[12421]) ).
cnf(i_0_19222,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk184_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2))) ),
inference(equality_inference,[],[12544]) ).
cnf(i_0_19223,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk182_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2))) ),
inference(equality_inference,[],[12545]) ).
cnf(i_0_19224,plain,
c_Map_Omap__upds(X1,X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4),X3) = c_Map_Omap__upds(X1,X1,X2,X3,X3),
inference(equality_inference,[],[12574]) ).
cnf(i_0_19225,plain,
c_Map_Omap__upds(X1,X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = c_Map_Omap__upds(X1,X1,X2,X3,X3),
inference(equality_inference,[],[12575]) ).
cnf(i_0_19226,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))),c_List_Olexord(X1,X5))),
inference(equality_inference,[],[12582]) ).
cnf(i_0_19227,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3)))) ),
inference(equality_inference,[],[12584]) ).
cnf(i_0_19228,plain,
( hAPP(hAPP(c_List_Otake(X1),X2),X3) = hAPP(hAPP(c_List_Otake(X1),X2),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
inference(equality_inference,[],[12617]) ).
cnf(i_0_19229,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)) ),
inference(equality_inference,[],[12628]) ).
cnf(i_0_19230,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),c_Nat_OSuc),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),esk158_4(c_Nat_OSuc,X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
inference(equality_inference,[],[12630]) ).
cnf(i_0_19231,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk185_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
inference(equality_inference,[],[12632]) ).
cnf(i_0_19232,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk183_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
inference(equality_inference,[],[12633]) ).
cnf(i_0_19233,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3)))) ),
inference(equality_inference,[],[12673]) ).
cnf(i_0_19234,plain,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X3)) ),
inference(equality_inference,[],[12685]) ).
cnf(i_0_19235,plain,
( X1 = X1
| ~ c_Typedef_Otype__definition(X2,X3,X4,X5,X6)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X6)) ),
inference(equality_inference,[],[12709]) ).
cnf(i_0_19236,plain,
hAPP(c_Map_Omap__of(X1,X2,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)),X3) = hAPP(c_Option_Ooption_OSome(X2),X4),
inference(equality_inference,[],[12735]) ).
cnf(i_0_19237,plain,
( ~ class_Rings_Oring(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)) ),
inference(equality_inference,[],[12744]) ).
cnf(i_0_19238,plain,
( ~ class_Rings_Oring(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X2)),X3)),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5) ),
inference(equality_inference,[],[12745]) ).
cnf(i_0_19239,plain,
hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(c_Fun_Ocomp(X7,X2,X8,X4),X5),X6),
inference(equality_inference,[],[12755]) ).
cnf(i_0_19240,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)) ),
inference(equality_inference,[],[12798]) ).
cnf(i_0_19241,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)),X2)),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)) ),
inference(equality_inference,[],[12799]) ).
cnf(i_0_19242,plain,
( ~ c_Natural_Oevaln(X1,hAPP(hAPP(hAPP(c_Natural_Oupdate,X2),c_Com_Ovname_OLoc(X3)),hAPP(X4,X2)),X5,X6)
| c_Natural_Oevaln(c_Com_Ocom_OLocal(X3,X4,X1),X2,X5,hAPP(hAPP(hAPP(c_Natural_Oupdate,X6),c_Com_Ovname_OLoc(X3)),hAPP(hAPP(c_Natural_Ogetlocs,X2),X3))) ),
inference(equality_inference,[],[12861]) ).
cnf(i_0_19243,plain,
( X1 = esk265_4(hAPP(X2,X1),X2,X3,X4)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),hAPP(c_Set_Oimage(X4,X3,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))) ),
inference(equality_inference,[],[12867]) ).
cnf(i_0_19244,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3)),X4)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4)) ),
inference(equality_inference,[],[12898]) ).
cnf(i_0_19245,plain,
( X1 = X1
| ~ c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ),
inference(equality_inference,[],[12905]) ).
cnf(i_0_19246,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3)),X4)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3)) ),
inference(equality_inference,[],[12909]) ).
cnf(i_0_19247,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)
| X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk183_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),esk182_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3)) ),
inference(equality_inference,[],[12914]) ).
cnf(i_0_19248,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)
| X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk185_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),esk184_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3)) ),
inference(equality_inference,[],[12915]) ).
cnf(i_0_19249,plain,
( ~ class_Rings_Oring(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2)),X3)),X4) = X4 ),
inference(equality_inference,[],[12930]) ).
cnf(i_0_19250,plain,
( ~ class_Rings_Oring(X1)
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X3)),X4)),X2) ),
inference(equality_inference,[],[12931]) ).
cnf(i_0_19251,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))),c_List_Olexord(X1,X4))),
inference(equality_inference,[],[12939]) ).
cnf(i_0_19252,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),esk440_3(X2,X1,X1)),hAPP(c_List_Oset(tc_prod(X2,X2)),hAPP(hAPP(c_List_Ozip(X2,X2),X1),X1)))) ),
inference(equality_inference,[],[12941]) ).
cnf(i_0_19253,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1)),X2)),X3) = X3 ),
inference(equality_inference,[],[12982]) ).
cnf(i_0_19254,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1)),X3)),X2) ),
inference(equality_inference,[],[12983]) ).
cnf(i_0_19255,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(tc_Nat_Onat,X1,X2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X3))))),
inference(equality_inference,[],[13000]) ).
cnf(i_0_19256,plain,
hAPP(X1,hAPP(X2,X3)) = hAPP(X1,hAPP(X2,X3)),
inference(equality_inference,[],[13081]) ).
cnf(i_0_19257,plain,
hAPP(c_Fun_Oid(X1),hAPP(X2,X3)) = hAPP(X2,X3),
inference(equality_inference,[],[13086]) ).
cnf(i_0_19258,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X3)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(equality_inference,[],[13094]) ).
cnf(i_0_19259,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3)),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[13115]) ).
cnf(i_0_19260,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3)),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[13116]) ).
cnf(i_0_19261,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3)),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[13117]) ).
cnf(i_0_19262,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_List_Oset(X2),X1)),hAPP(c_List_Oset(X2),X1))) ),
inference(equality_inference,[],[13248]) ).
cnf(i_0_19263,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Ovimage(X1,X3,X4),hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X4,X2)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))),
inference(equality_inference,[],[13305]) ).
cnf(i_0_19264,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5)) ),
inference(equality_inference,[],[13328]) ).
cnf(i_0_19265,plain,
( hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X2)),X3) = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(equality_inference,[],[13347]) ).
cnf(i_0_19266,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X1))) ),
inference(equality_inference,[],[13367]) ).
cnf(i_0_19267,plain,
c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),hAPP(c_Option_Ooption_OSome(X2),X4))) = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(equality_inference,[],[13440]) ).
cnf(i_0_19268,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X3)),X4)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[13469]) ).
cnf(i_0_19269,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Relation_OId__on(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(equality_inference,[],[13495]) ).
cnf(i_0_19270,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),X2),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))) ),
inference(equality_inference,[],[13550]) ).
cnf(i_0_19271,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X1)) ),
inference(equality_inference,[],[13571]) ).
cnf(i_0_19272,plain,
( X1 = X1
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),c_fequal),esk440_3(X2,X1,X1))) ),
inference(equality_inference,[],[13586]) ).
cnf(i_0_19273,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X1))) ),
inference(equality_inference,[],[13646]) ).
cnf(i_0_19274,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4),
inference(equality_inference,[],[13649]) ).
cnf(i_0_19275,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)))
| hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Orderings_Oord__class_Omax(X1)),X2),hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1))) = X2 ),
inference(equality_inference,[],[13669]) ).
cnf(i_0_19276,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X3
| X4 = X4 ),
inference(equality_inference,[],[13692]) ).
cnf(i_0_19277,plain,
c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(equality_inference,[],[13732]) ).
cnf(i_0_19278,plain,
X1 = X1,
inference(equality_inference,[],[13743]) ).
cnf(i_0_19279,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Ortrancl(X1,X3))),
inference(equality_inference,[],[13765]) ).
cnf(i_0_19280,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,c_List_Olist_ONil(tc_List_Olist(X1)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1))))) ),
inference(equality_inference,[],[13785]) ).
cnf(i_0_19281,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(equality_inference,[],[13787]) ).
cnf(i_0_19282,plain,
( X1 = hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
inference(equality_inference,[],[13813]) ).
cnf(i_0_19283,plain,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)),
inference(equality_inference,[],[13830]) ).
cnf(i_0_19284,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1) = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)) ),
inference(equality_inference,[],[13891]) ).
cnf(i_0_19285,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)) ),
inference(equality_inference,[],[13899]) ).
cnf(i_0_19286,plain,
( X1 = X1
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4)) ),
inference(equality_inference,[],[13943]) ).
cnf(i_0_19287,plain,
( c_Fun_Oinj__on(X1,X2,esk268_4(X3,X2,X1,hAPP(c_Set_Oimage(X2,X1,X4),X3)),hAPP(c_Set_Oimage(X2,X1,X4),X3))
| hAPP(c_Set_Oimage(X2,X1,X4),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(equality_inference,[],[13996]) ).
cnf(i_0_19288,plain,
( ~ epred1_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2)) ),
inference(equality_inference,[],[13999]) ).
cnf(i_0_19289,plain,
( ~ epred2_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2)) ),
inference(equality_inference,[],[14000]) ).
cnf(i_0_19290,plain,
( ~ epred1_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ),
inference(equality_inference,[],[14046]) ).
cnf(i_0_19291,plain,
( ~ epred2_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ),
inference(equality_inference,[],[14047]) ).
cnf(i_0_19292,plain,
( X1 = X1
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
inference(equality_inference,[],[14111]) ).
cnf(i_0_19293,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3)),X4) = X4,
inference(equality_inference,[],[14121]) ).
cnf(i_0_19294,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3)),X4) = X4,
inference(equality_inference,[],[14122]) ).
cnf(i_0_19295,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X1)) ),
inference(equality_inference,[],[14136]) ).
cnf(i_0_19296,plain,
hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)) = hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)),
inference(equality_inference,[],[14159]) ).
cnf(i_0_19297,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1) = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)) ),
inference(equality_inference,[],[14164]) ).
cnf(i_0_19298,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)) ),
inference(equality_inference,[],[14192]) ).
cnf(i_0_19299,plain,
X1 = X1,
inference(equality_inference,[],[14195]) ).
cnf(i_0_19300,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X1))
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),X1))) ),
inference(equality_inference,[],[14232]) ).
cnf(i_0_19301,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1))) ),
inference(equality_inference,[],[14248]) ).
cnf(i_0_19302,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[14280]) ).
cnf(i_0_19303,plain,
hAPP(X1,hAPP(X2,X3)) = hAPP(hAPP(c_Fun_Ocomp(X4,X5,X6,X1),X2),X3),
inference(equality_inference,[],[14284]) ).
cnf(i_0_19304,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),X2)),
inference(equality_inference,[],[14328]) ).
cnf(i_0_19305,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1) = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)) ),
inference(equality_inference,[],[14334]) ).
cnf(i_0_19306,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),
inference(equality_inference,[],[14352]) ).
cnf(i_0_19307,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)) ),
inference(equality_inference,[],[14353]) ).
cnf(i_0_19308,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(equality_inference,[],[14366]) ).
cnf(i_0_19309,plain,
hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[14368]) ).
cnf(i_0_19310,plain,
hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(equality_inference,[],[14369]) ).
cnf(i_0_19311,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[14370]) ).
cnf(i_0_19312,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[14371]) ).
cnf(i_0_19313,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[14372]) ).
cnf(i_0_19314,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[14373]) ).
cnf(i_0_19315,plain,
( hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X2) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(equality_inference,[],[14377]) ).
cnf(i_0_19316,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_List_Olists(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(equality_inference,[],[14440]) ).
cnf(i_0_19317,plain,
X1 = X1,
inference(equality_inference,[],[14487]) ).
cnf(i_0_19318,plain,
X1 = X1,
inference(equality_inference,[],[14488]) ).
cnf(i_0_19319,plain,
X1 = X1,
inference(equality_inference,[],[14489]) ).
cnf(i_0_19320,plain,
X1 = X1,
inference(equality_inference,[],[14490]) ).
cnf(i_0_19321,plain,
( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk467_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1))) ),
inference(equality_inference,[],[14493]) ).
cnf(i_0_19322,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4))
| hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_Set_Ovimage(X5,X1,X2),X4))) ),
inference(equality_inference,[],[14494]) ).
cnf(i_0_19323,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
inference(equality_inference,[],[14497]) ).
cnf(i_0_19324,plain,
( hAPP(c_Map_Omap__of(X1,X1,hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)),X3) = c_Option_Ooption_ONone(X1)
| hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))) ),
inference(equality_inference,[],[14506]) ).
cnf(i_0_19325,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X5)) ),
inference(equality_inference,[],[14510]) ).
cnf(i_0_19326,plain,
( hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X3) = X4
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(equality_inference,[],[14515]) ).
cnf(i_0_19327,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[14525]) ).
cnf(i_0_19328,plain,
( X1 = X1
| ~ class_Rings_Olinordered__semidom(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(equality_inference,[],[14561]) ).
cnf(i_0_19329,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_3(X2,X1,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
inference(equality_inference,[],[14569]) ).
cnf(i_0_19330,plain,
( ~ class_Rings_Oidom(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X3))) ),
inference(equality_inference,[],[14621]) ).
cnf(i_0_19331,plain,
( ~ class_Rings_Oidom(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),c_Groups_Ozero__class_Ozero(X1)))) ),
inference(equality_inference,[],[14622]) ).
cnf(i_0_19332,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(equality_inference,[],[14642]) ).
cnf(i_0_19333,plain,
( ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
| c_Map_Odom(X1,X1,c_Map_Omap__of(X1,X1,hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2))) = hAPP(c_List_Oset(X1),X2) ),
inference(equality_inference,[],[14680]) ).
cnf(i_0_19334,plain,
X1 = X1,
inference(equality_inference,[],[14696]) ).
cnf(i_0_19335,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))),X2)) ),
inference(equality_inference,[],[14717]) ).
cnf(i_0_19336,plain,
hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3)),hAPP(c_Set_OPow(X1),X4)) = hAPP(c_Set_OPow(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4)),
inference(equality_inference,[],[14787]) ).
cnf(i_0_19337,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk70_3(X1,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)) ),
inference(equality_inference,[],[14815]) ).
cnf(i_0_19338,plain,
( X1 = X1
| ~ class_Rings_Olinordered__semidom(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ),
inference(equality_inference,[],[14841]) ).
cnf(i_0_19339,plain,
( X1 = X2
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),c_Option_Ooption_OSome(X4)),X2),hAPP(c_Option_Ooption_OSome(X4),X5)),X1) = hAPP(c_Option_Ooption_OSome(X4),X1) ),
inference(equality_inference,[],[14858]) ).
cnf(i_0_19340,plain,
hAPP(c_Lazy__Sequence_Oanamorph(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X4) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),X1),c_List_Olist_ONil(X2)),X4),
inference(equality_inference,[],[14891]) ).
cnf(i_0_19341,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))),
inference(equality_inference,[],[14893]) ).
cnf(i_0_19342,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)),X1)) ),
inference(equality_inference,[],[14922]) ).
cnf(i_0_19343,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)) ),
inference(equality_inference,[],[14923]) ).
cnf(i_0_19344,plain,
hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),X3),hAPP(c_Option_Ooption_OSome(X2),X4)) = hAPP(X3,X4),
inference(equality_inference,[],[14940]) ).
cnf(i_0_19345,plain,
( ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X3) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X3)) ),
inference(equality_inference,[],[14967]) ).
cnf(i_0_19346,plain,
( ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(equality_inference,[],[14968]) ).
cnf(i_0_19347,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(c_List_Oset(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(equality_inference,[],[14996]) ).
cnf(i_0_19348,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))) ),
inference(equality_inference,[],[15006]) ).
cnf(i_0_19349,plain,
( hAPP(X1,X2) = hAPP(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))) ),
inference(equality_inference,[],[15011]) ).
cnf(i_0_19350,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(equality_inference,[],[15063]) ).
cnf(i_0_19351,plain,
hAPP(c_Map_Omap__add(X1,X2,X3,c_Option_Ooption_OSome(X2)),X4) = hAPP(c_Option_Ooption_OSome(X2),X4),
inference(equality_inference,[],[15111]) ).
cnf(i_0_19352,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(equality_inference,[],[15153]) ).
cnf(i_0_19353,plain,
hAPP(hAPP(c_List_Ozip(X1,X1),hAPP(c_List_Orev(X1),X2)),hAPP(c_List_Orev(X1),X2)) = hAPP(c_List_Orev(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)),
inference(equality_inference,[],[15158]) ).
cnf(i_0_19354,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4)) = X2,
inference(equality_inference,[],[15172]) ).
cnf(i_0_19355,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4)) = X2,
inference(equality_inference,[],[15173]) ).
cnf(i_0_19356,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4)) = X2,
inference(equality_inference,[],[15174]) ).
cnf(i_0_19357,plain,
hAPP(c_Random_Oiterate(X1,X2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),X3),X4) = hAPP(c_Product__Type_OPair(X1,X2),X4),
inference(equality_inference,[],[15179]) ).
cnf(i_0_19358,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(equality_inference,[],[15192]) ).
cnf(i_0_19359,plain,
hAPP(hAPP(c_List_Omap(tc_prod(X1,X1),X1),c_Product__Type_Ofst(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)) = X2,
inference(equality_inference,[],[15286]) ).
cnf(i_0_19360,plain,
hAPP(hAPP(c_List_Omap(tc_prod(X1,X1),X1),c_Product__Type_Osnd(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)) = X2,
inference(equality_inference,[],[15287]) ).
cnf(i_0_19361,plain,
X1 = X1,
inference(equality_inference,[],[15304]) ).
cnf(i_0_19362,plain,
X1 = X1,
inference(equality_inference,[],[15305]) ).
cnf(i_0_19363,plain,
( hAPP(hAPP(c_List_Olist__update(X1,X2),X3),hAPP(hAPP(c_List_Onth(X1),X2),X3)) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(equality_inference,[],[15322]) ).
cnf(i_0_19364,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[15347]) ).
cnf(i_0_19365,plain,
hAPP(c_New__DSequence_Oneg__decr__bind(X1,X2,X3,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Lazy__Sequence_Ohit__bound(X2),
inference(equality_inference,[],[15349]) ).
cnf(i_0_19366,plain,
hAPP(c_New__DSequence_Opos__decr__bind(X1,X2,X3,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Lazy__Sequence_Oempty(X2),
inference(equality_inference,[],[15350]) ).
cnf(i_0_19367,plain,
c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)) = c_List_Obutlast(X1,X2),
inference(equality_inference,[],[15460]) ).
cnf(i_0_19368,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X2,hAPP(hAPP(c_List_Olist__update(X2,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)) = X3 ),
inference(equality_inference,[],[15484]) ).
cnf(i_0_19369,plain,
( X1 = X1
| ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X3)) ),
inference(equality_inference,[],[15508]) ).
cnf(i_0_19370,plain,
( X1 = X1
| ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X1)) ),
inference(equality_inference,[],[15509]) ).
cnf(i_0_19371,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[15551]) ).
cnf(i_0_19372,plain,
hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2),
inference(equality_inference,[],[15564]) ).
cnf(i_0_19373,plain,
( X1 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(equality_inference,[],[15605]) ).
cnf(i_0_19374,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_inference,[],[15615]) ).
cnf(i_0_19375,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X2))),
inference(equality_inference,[],[15616]) ).
cnf(i_0_19376,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)),X3))) ),
inference(equality_inference,[],[15632]) ).
cnf(i_0_19377,plain,
~ c_Wellfounded_Omax__extp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(equality_inference,[],[15650]) ).
cnf(i_0_19378,plain,
( ~ class_Int_Onumber__ring(X1)
| c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))) ),
inference(equality_inference,[],[15660]) ).
cnf(i_0_19379,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)),
inference(equality_inference,[],[15687]) ).
cnf(i_0_19380,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(equality_inference,[],[15699]) ).
cnf(i_0_19381,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[15708]) ).
cnf(i_0_19382,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[15709]) ).
cnf(i_0_19383,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_inference,[],[15786]) ).
cnf(i_0_19384,plain,
hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X4) = X5,
inference(equality_inference,[],[15794]) ).
cnf(i_0_19385,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
inference(equality_inference,[],[15819]) ).
cnf(i_0_19386,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),
inference(equality_inference,[],[15882]) ).
cnf(i_0_19387,plain,
hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),
inference(equality_inference,[],[15883]) ).
cnf(i_0_19388,plain,
X1 = X1,
inference(equality_inference,[],[15892]) ).
cnf(i_0_19389,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(equality_inference,[],[15903]) ).
cnf(i_0_19390,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X3)) ),
inference(equality_inference,[],[15904]) ).
cnf(i_0_19391,plain,
( ~ class_Divides_Osemiring__div(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[15906]) ).
cnf(i_0_19392,plain,
( X1 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(equality_inference,[],[15918]) ).
cnf(i_0_19393,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Oran(X3,X1,c_Option_Ooption_OSome(X1)))),
inference(equality_inference,[],[15927]) ).
cnf(i_0_19394,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,c_Option_Ooption_OSome(X3)))),
inference(equality_inference,[],[15928]) ).
cnf(i_0_19395,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_inference,[],[15935]) ).
cnf(i_0_19396,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olist_ONil(X1)))),
inference(equality_inference,[],[15936]) ).
cnf(i_0_19397,plain,
( ~ c_Nat__Transfer_Onat__set(X1)
| ~ c_Nat__Transfer_Onat__set(X1)
| X1 = X1 ),
inference(equality_inference,[],[15948]) ).
cnf(i_0_19398,plain,
X1 = X1,
inference(equality_inference,[],[15949]) ).
cnf(i_0_19399,plain,
X1 = X1,
inference(equality_inference,[],[15950]) ).
cnf(i_0_19400,plain,
X1 = X1,
inference(equality_inference,[],[15951]) ).
cnf(i_0_19401,plain,
( ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3) ),
inference(equality_inference,[],[15969]) ).
cnf(i_0_19402,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2),
inference(equality_inference,[],[16019]) ).
cnf(i_0_19403,plain,
X1 = hAPP(c_Product__Type_Ofst(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X1),X4)),
inference(equality_inference,[],[16023]) ).
cnf(i_0_19404,plain,
X1 = hAPP(c_Product__Type_Osnd(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X1)),
inference(equality_inference,[],[16024]) ).
cnf(i_0_19405,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X2)) ),
inference(equality_inference,[],[16031]) ).
cnf(i_0_19406,plain,
c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X1) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(equality_inference,[],[16056]) ).
cnf(i_0_19407,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1)))) ),
inference(equality_inference,[],[16072]) ).
cnf(i_0_19408,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(equality_inference,[],[16098]) ).
cnf(i_0_19409,plain,
X1 = X1,
inference(equality_inference,[],[16112]) ).
cnf(i_0_19410,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2))) ),
inference(equality_inference,[],[16123]) ).
cnf(i_0_19411,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[16128]) ).
cnf(i_0_19412,plain,
hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[16154]) ).
cnf(i_0_19413,plain,
( ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))) ),
inference(equality_inference,[],[16156]) ).
cnf(i_0_19414,plain,
( ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(equality_inference,[],[16157]) ).
cnf(i_0_19415,plain,
( X1 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(equality_inference,[],[16179]) ).
cnf(i_0_19416,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
inference(equality_inference,[],[16183]) ).
cnf(i_0_19417,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(equality_inference,[],[16202]) ).
cnf(i_0_19418,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(equality_inference,[],[16207]) ).
cnf(i_0_19419,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X3,X4,X3)
| hBOOL(hAPP(X1,X3)) ),
inference(equality_inference,[],[16214]) ).
cnf(i_0_19420,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(equality_inference,[],[16263]) ).
cnf(i_0_19421,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[16291]) ).
cnf(i_0_19422,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[16292]) ).
cnf(i_0_19423,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(equality_inference,[],[16293]) ).
cnf(i_0_19424,plain,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_inference,[],[16298]) ).
cnf(i_0_19425,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X2))))),
inference(equality_inference,[],[16299]) ).
cnf(i_0_19426,plain,
X1 = X1,
inference(equality_inference,[],[16300]) ).
cnf(i_0_19427,plain,
X1 = X1,
inference(equality_inference,[],[16302]) ).
cnf(i_0_19428,plain,
X1 = X1,
inference(equality_inference,[],[16304]) ).
cnf(i_0_19429,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(equality_inference,[],[16308]) ).
cnf(i_0_19430,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))),c_Groups_Ozero__class_Ozero(X1))) ),
inference(equality_inference,[],[16329]) ).
cnf(i_0_19431,plain,
( ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) ),
inference(equality_inference,[],[16331]) ).
cnf(i_0_19432,plain,
( ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) ),
inference(equality_inference,[],[16332]) ).
cnf(i_0_19433,plain,
c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = X2,
inference(equality_inference,[],[16395]) ).
cnf(i_0_19434,plain,
c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = X3,
inference(equality_inference,[],[16396]) ).
cnf(i_0_19435,plain,
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_inference,[],[16429]) ).
cnf(i_0_19436,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ),
inference(equality_inference,[],[16451]) ).
cnf(i_0_19437,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(equality_inference,[],[16452]) ).
cnf(i_0_19438,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Map_Odom(X1,X3,c_Option_Ooption_OSome(X3))) = c_Map_Odom(X1,X3,c_Option_Ooption_OSome(X3)),
inference(equality_inference,[],[16461]) ).
cnf(i_0_19439,plain,
hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(equality_inference,[],[16478]) ).
cnf(i_0_19440,plain,
X1 = hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(hAPP(c_List_Oappend(X2),X3),X1)),
inference(equality_inference,[],[16490]) ).
cnf(i_0_19441,plain,
X1 = hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),hAPP(hAPP(c_List_Oappend(X2),X1),X3)),
inference(equality_inference,[],[16491]) ).
cnf(i_0_19442,plain,
( ~ class_Int_Oring__char__0(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1))) ),
inference(equality_inference,[],[16508]) ).
cnf(i_0_19443,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
inference(equality_inference,[],[16522]) ).
cnf(i_0_19444,plain,
X1 = X1,
inference(equality_inference,[],[16523]) ).
cnf(i_0_19445,plain,
( ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| X2 = X2
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(equality_inference,[],[16536]) ).
cnf(i_0_19446,plain,
hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X3,
inference(equality_inference,[],[16573]) ).
cnf(i_0_19447,plain,
( X1 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(equality_inference,[],[16598]) ).
cnf(i_0_19448,plain,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
inference(equality_inference,[],[16605]) ).
cnf(i_0_19449,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(equality_inference,[],[16627]) ).
cnf(i_0_19450,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(equality_inference,[],[16628]) ).
cnf(i_0_19451,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),c_Int_OMin) = c_Int_OMin,
inference(equality_inference,[],[16680]) ).
cnf(i_0_19452,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),c_Int_OMin),
inference(equality_inference,[],[16681]) ).
cnf(i_0_19453,plain,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
inference(equality_inference,[],[16699]) ).
cnf(i_0_19454,plain,
hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),hAPP(X3,X4)) = X3,
inference(equality_inference,[],[16732]) ).
cnf(i_0_19455,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))),
inference(equality_inference,[],[16742]) ).
cnf(i_0_19456,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
inference(equality_inference,[],[16761]) ).
cnf(i_0_19457,plain,
hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(equality_inference,[],[16783]) ).
cnf(i_0_19458,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(equality_inference,[],[16786]) ).
cnf(i_0_19459,plain,
( hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))) ),
inference(equality_inference,[],[16795]) ).
cnf(i_0_19460,plain,
( X1 = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))) ),
inference(equality_inference,[],[16796]) ).
cnf(i_0_19461,plain,
( c_Nitpick_Onorm__frac(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(equality_inference,[],[16797]) ).
cnf(i_0_19462,plain,
( c_Nitpick_Onorm__frac(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(equality_inference,[],[16798]) ).
cnf(i_0_19463,plain,
X1 = X1,
inference(equality_inference,[],[16799]) ).
cnf(i_0_19464,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1)) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(equality_inference,[],[16808]) ).
cnf(i_0_19465,plain,
( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(equality_inference,[],[16809]) ).
cnf(i_0_19466,plain,
( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(equality_inference,[],[16810]) ).
cnf(i_0_19467,plain,
( ~ class_Rings_Odvd(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))) ),
inference(equality_inference,[],[16863]) ).
cnf(i_0_19468,plain,
( ~ class_Rings_Oidom(X1)
| X2 = X2
| X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) ),
inference(equality_inference,[],[16884]) ).
cnf(i_0_19469,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(equality_inference,[],[16888]) ).
cnf(i_0_19470,plain,
hAPP(c_Relation_ODomain(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(equality_inference,[],[16889]) ).
cnf(i_0_19471,plain,
hAPP(c_Relation_ORange(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[16890]) ).
cnf(i_0_19472,plain,
hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[16893]) ).
cnf(i_0_19473,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(equality_inference,[],[16894]) ).
cnf(i_0_19474,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X2)))),
inference(equality_inference,[],[16896]) ).
cnf(i_0_19475,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))) ),
inference(equality_inference,[],[16950]) ).
cnf(i_0_19476,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[16954]) ).
cnf(i_0_19477,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[16955]) ).
cnf(i_0_19478,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[16956]) ).
cnf(i_0_19479,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[16958]) ).
cnf(i_0_19480,plain,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X2)) ),
inference(equality_inference,[],[16964]) ).
cnf(i_0_19481,plain,
c_Map_Odom(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(equality_inference,[],[16973]) ).
cnf(i_0_19482,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[16979]) ).
cnf(i_0_19483,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[16980]) ).
cnf(i_0_19484,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[16982]) ).
cnf(i_0_19485,plain,
X1 = X1,
inference(equality_inference,[],[16983]) ).
cnf(i_0_19486,plain,
X1 = X1,
inference(equality_inference,[],[16984]) ).
cnf(i_0_19487,plain,
X1 = X1,
inference(equality_inference,[],[16985]) ).
cnf(i_0_19488,plain,
X1 = X1,
inference(equality_inference,[],[16986]) ).
cnf(i_0_19489,plain,
X1 = X1,
inference(equality_inference,[],[16987]) ).
cnf(i_0_19490,plain,
X1 = X1,
inference(equality_inference,[],[16988]) ).
cnf(i_0_19491,plain,
X1 = X1,
inference(equality_inference,[],[16989]) ).
cnf(i_0_19492,plain,
X1 = X1,
inference(equality_inference,[],[16990]) ).
cnf(i_0_19493,plain,
X1 = X1,
inference(equality_inference,[],[16991]) ).
cnf(i_0_19494,plain,
( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(equality_inference,[],[16997]) ).
cnf(i_0_19495,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)) = hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))),
inference(equality_inference,[],[16998]) ).
cnf(i_0_19496,plain,
hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)),
inference(equality_inference,[],[16999]) ).
cnf(i_0_19497,plain,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(equality_inference,[],[17017]) ).
cnf(i_0_19498,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2),
inference(equality_inference,[],[17018]) ).
cnf(i_0_19499,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(equality_inference,[],[17019]) ).
cnf(i_0_19500,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(equality_inference,[],[17021]) ).
cnf(i_0_19501,plain,
X1 = X1,
inference(equality_inference,[],[17028]) ).
cnf(i_0_19502,plain,
X1 = X1,
inference(equality_inference,[],[17029]) ).
cnf(i_0_19503,plain,
X1 = X1,
inference(equality_inference,[],[17030]) ).
cnf(i_0_19504,plain,
X1 = X1,
inference(equality_inference,[],[17031]) ).
cnf(i_0_19505,plain,
c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
inference(equality_inference,[],[17056]) ).
cnf(i_0_19506,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[17081]) ).
cnf(i_0_19507,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[17088]) ).
cnf(i_0_19508,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)),
inference(equality_inference,[],[17098]) ).
cnf(i_0_19509,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[17102]) ).
cnf(i_0_19510,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[17103]) ).
cnf(i_0_19511,plain,
c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(equality_inference,[],[17112]) ).
cnf(i_0_19512,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[17114]) ).
cnf(i_0_19513,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[17116]) ).
cnf(i_0_19514,plain,
hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)) = hAPP(c_List_Ohd(X1),X2),
inference(equality_inference,[],[17117]) ).
cnf(i_0_19515,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) = X3 ),
inference(equality_inference,[],[17128]) ).
cnf(i_0_19516,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X2) = X3 ),
inference(equality_inference,[],[17129]) ).
cnf(i_0_19517,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) = X3 ),
inference(equality_inference,[],[17131]) ).
cnf(i_0_19518,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X2) = X3 ),
inference(equality_inference,[],[17132]) ).
cnf(i_0_19519,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) ),
inference(equality_inference,[],[17133]) ).
cnf(i_0_19520,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X2) ),
inference(equality_inference,[],[17134]) ).
cnf(i_0_19521,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) ),
inference(equality_inference,[],[17136]) ).
cnf(i_0_19522,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X2) ),
inference(equality_inference,[],[17137]) ).
cnf(i_0_19523,plain,
( ~ c_Equiv__Relations_Oequivp(X1,X2)
| hBOOL(hAPP(hAPP(X2,X3),X3)) ),
inference(equality_inference,[],[17144]) ).
cnf(i_0_19524,plain,
X1 = X1,
inference(equality_inference,[],[17154]) ).
cnf(i_0_19525,plain,
X1 = X1,
inference(equality_inference,[],[17155]) ).
cnf(i_0_19526,plain,
X1 = X1,
inference(equality_inference,[],[17156]) ).
cnf(i_0_19527,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[17162]) ).
cnf(i_0_19528,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) ),
inference(equality_inference,[],[17170]) ).
cnf(i_0_19529,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[17179]) ).
cnf(i_0_19530,plain,
c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1))) = c_List_Obutlast(X1,X2),
inference(equality_inference,[],[17193]) ).
cnf(i_0_19531,plain,
c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1))) = c_List_Olast(X1,X2),
inference(equality_inference,[],[17195]) ).
cnf(i_0_19532,plain,
c_Divides_Opdivmod(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),
inference(equality_inference,[],[17201]) ).
cnf(i_0_19533,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
inference(equality_inference,[],[17209]) ).
cnf(i_0_19534,plain,
( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(equality_inference,[],[17228]) ).
cnf(i_0_19535,plain,
( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(equality_inference,[],[17229]) ).
cnf(i_0_19536,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(equality_inference,[],[17250]) ).
cnf(i_0_19537,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[17251]) ).
cnf(i_0_19538,plain,
( ~ epred2_3(X1,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(equality_inference,[],[17253]) ).
cnf(i_0_19539,plain,
c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[17254]) ).
cnf(i_0_19540,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[17257]) ).
cnf(i_0_19541,plain,
X1 = X1,
inference(equality_inference,[],[17259]) ).
cnf(i_0_19542,plain,
X1 = X1,
inference(equality_inference,[],[17261]) ).
cnf(i_0_19543,plain,
X1 = X1,
inference(equality_inference,[],[17262]) ).
cnf(i_0_19544,plain,
( hAPP(c_Int_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(equality_inference,[],[17267]) ).
cnf(i_0_19545,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(equality_inference,[],[17268]) ).
cnf(i_0_19546,plain,
c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = X2,
inference(equality_inference,[],[17276]) ).
cnf(i_0_19547,plain,
( ~ epred1_3(X1,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(X1,X2)) ),
inference(equality_inference,[],[17292]) ).
cnf(i_0_19548,plain,
X1 = X1,
inference(equality_inference,[],[17311]) ).
cnf(i_0_19549,plain,
X1 = X1,
inference(equality_inference,[],[17312]) ).
cnf(i_0_19550,plain,
( ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
inference(equality_inference,[],[17324]) ).
cnf(i_0_19551,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
inference(equality_inference,[],[17326]) ).
cnf(i_0_19552,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
inference(equality_inference,[],[17327]) ).
cnf(i_0_19553,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) ),
inference(equality_inference,[],[17371]) ).
cnf(i_0_19554,plain,
c_Divides_Odivmod__int(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(equality_inference,[],[17376]) ).
cnf(i_0_19555,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[17398]) ).
cnf(i_0_19556,plain,
hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[17428]) ).
cnf(i_0_19557,plain,
hAPP(hAPP(c_Option_Omap(X1,X2),X3),c_Option_Ooption_ONone(X1)) = c_Option_Ooption_ONone(X2),
inference(equality_inference,[],[17429]) ).
cnf(i_0_19558,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
inference(equality_inference,[],[17430]) ).
cnf(i_0_19559,plain,
c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olist_ONil(X2)),
inference(equality_inference,[],[17431]) ).
cnf(i_0_19560,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(equality_inference,[],[17436]) ).
cnf(i_0_19561,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),X1) = X1,
inference(equality_inference,[],[17455]) ).
cnf(i_0_19562,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),
inference(equality_inference,[],[17459]) ).
cnf(i_0_19563,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[17460]) ).
cnf(i_0_19564,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[17464]) ).
cnf(i_0_19565,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[17466]) ).
cnf(i_0_19566,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[17469]) ).
cnf(i_0_19567,plain,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17471]) ).
cnf(i_0_19568,plain,
( ~ class_Groups_Ogroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17477]) ).
cnf(i_0_19569,plain,
c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_List_Olist_ONil(tc_Nat_Onat),
inference(equality_inference,[],[17504]) ).
cnf(i_0_19570,plain,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[17520]) ).
cnf(i_0_19571,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[17525]) ).
cnf(i_0_19572,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 = X2 ),
inference(equality_inference,[],[17577]) ).
cnf(i_0_19573,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[17579]) ).
cnf(i_0_19574,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 = X2 ),
inference(equality_inference,[],[17623]) ).
cnf(i_0_19575,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 = X2 ),
inference(equality_inference,[],[17624]) ).
cnf(i_0_19576,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 = X2 ),
inference(equality_inference,[],[17625]) ).
cnf(i_0_19577,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 = X2 ),
inference(equality_inference,[],[17626]) ).
cnf(i_0_19578,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| X2 = X2 ),
inference(equality_inference,[],[17627]) ).
cnf(i_0_19579,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[17628]) ).
cnf(i_0_19580,plain,
( ~ class_Int_Oring__char__0(X1)
| X2 = X2 ),
inference(equality_inference,[],[17629]) ).
cnf(i_0_19581,plain,
( ~ class_Nat_Osemiring__char__0(X1)
| X2 = X2 ),
inference(equality_inference,[],[17630]) ).
cnf(i_0_19582,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[17639]) ).
cnf(i_0_19583,plain,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17640]) ).
cnf(i_0_19584,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[17641]) ).
cnf(i_0_19585,plain,
( ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17642]) ).
cnf(i_0_19586,plain,
( ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17643]) ).
cnf(i_0_19587,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17644]) ).
cnf(i_0_19588,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[17645]) ).
cnf(i_0_19589,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
inference(equality_inference,[],[17657]) ).
cnf(i_0_19590,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[17658]) ).
cnf(i_0_19591,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[17670]) ).
cnf(i_0_19592,plain,
( ~ class_Groups_Oab__group__add(X1)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17671]) ).
cnf(i_0_19593,plain,
( ~ class_Groups_Ogroup__add(X1)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17672]) ).
cnf(i_0_19594,plain,
hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[17673]) ).
cnf(i_0_19595,plain,
X1 = X1,
inference(equality_inference,[],[17694]) ).
cnf(i_0_19596,plain,
X1 = X1,
inference(equality_inference,[],[17695]) ).
cnf(i_0_19597,plain,
hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[17702]) ).
cnf(i_0_19598,plain,
hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[17715]) ).
cnf(i_0_19599,plain,
( ~ class_Groups_Ogroup__add(X1)
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = X2 ),
inference(equality_inference,[],[17717]) ).
cnf(i_0_19600,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) ),
inference(equality_inference,[],[17719]) ).
cnf(i_0_19601,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
inference(equality_inference,[],[17721]) ).
cnf(i_0_19602,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(equality_inference,[],[17722]) ).
cnf(i_0_19603,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
inference(equality_inference,[],[17723]) ).
cnf(i_0_19604,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Olist_ONil(X2)),
inference(equality_inference,[],[17724]) ).
cnf(i_0_19605,plain,
X1 = X1,
inference(equality_inference,[],[17768]) ).
cnf(i_0_19606,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1)),
inference(equality_inference,[],[17769]) ).
cnf(i_0_19607,plain,
hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(equality_inference,[],[17770]) ).
cnf(i_0_19608,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(equality_inference,[],[17772]) ).
cnf(i_0_19609,plain,
X1 = hAPP(c_List_Orev(X2),hAPP(c_List_Orev(X2),X1)),
inference(equality_inference,[],[17773]) ).
cnf(i_0_19610,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(equality_inference,[],[17779]) ).
cnf(i_0_19611,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(equality_inference,[],[17780]) ).
cnf(i_0_19612,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[17782]) ).
cnf(i_0_19613,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[17783]) ).
cnf(i_0_19614,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
inference(equality_inference,[],[17793]) ).
cnf(i_0_19615,plain,
c_Option_Oset(X1,c_Option_Ooption_ONone(X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(equality_inference,[],[17823]) ).
cnf(i_0_19616,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls) = c_Int_OPls,
inference(equality_inference,[],[17827]) ).
cnf(i_0_19617,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls),
inference(equality_inference,[],[17828]) ).
cnf(i_0_19618,plain,
X1 = X1,
inference(equality_inference,[],[17835]) ).
cnf(i_0_19619,plain,
X1 = X1,
inference(equality_inference,[],[17836]) ).
cnf(i_0_19620,plain,
X1 = X1,
inference(equality_inference,[],[17837]) ).
cnf(i_0_19621,plain,
X1 = X1,
inference(equality_inference,[],[17838]) ).
cnf(i_0_19622,plain,
X1 = X1,
inference(equality_inference,[],[17839]) ).
cnf(i_0_19623,plain,
X1 = X1,
inference(equality_inference,[],[17840]) ).
cnf(i_0_19624,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olist_ONil(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[17865]) ).
cnf(i_0_19625,plain,
X1 = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
inference(equality_inference,[],[17870]) ).
cnf(i_0_19626,plain,
X1 = X1,
inference(equality_inference,[],[17883]) ).
cnf(i_0_19627,plain,
X1 = X1,
inference(equality_inference,[],[17885]) ).
cnf(i_0_19628,plain,
X1 = X1,
inference(equality_inference,[],[17886]) ).
cnf(i_0_19629,plain,
X1 = X1,
inference(equality_inference,[],[17888]) ).
cnf(i_0_19630,plain,
X1 = X1,
inference(equality_inference,[],[17889]) ).
cnf(i_0_19631,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17893]) ).
cnf(i_0_19632,plain,
( ~ class_Groups_Ogroup__add(X1)
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17894]) ).
cnf(i_0_19633,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[17895]) ).
cnf(i_0_19634,plain,
( ~ class_Int_Oring__char__0(X1)
| hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17924]) ).
cnf(i_0_19635,plain,
( ~ class_Rings_Oring__1(X1)
| hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17925]) ).
cnf(i_0_19636,plain,
( ~ class_Int_Oring__char__0(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(equality_inference,[],[17926]) ).
cnf(i_0_19637,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17929]) ).
cnf(i_0_19638,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[17930]) ).
cnf(i_0_19639,plain,
( ~ class_Groups_Osgn__if(X1)
| c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17943]) ).
cnf(i_0_19640,plain,
( ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[17944]) ).
cnf(i_0_19641,plain,
hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[17945]) ).
cnf(i_0_19642,plain,
hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[17946]) ).
cnf(i_0_19643,plain,
c_List_Olist_ONil(X1) = hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)),
inference(equality_inference,[],[17947]) ).
cnf(i_0_19644,plain,
( ~ class_Rings_Osemiring__1(X1)
| c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[17961]) ).
cnf(i_0_19645,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(equality_inference,[],[17971]) ).
cnf(i_0_19646,plain,
c_Option_Ois__none(X1,c_Option_Ooption_ONone(X1)),
inference(equality_inference,[],[17983]) ).
cnf(i_0_19647,plain,
c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(equality_inference,[],[18005]) ).
cnf(i_0_19648,plain,
hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(equality_inference,[],[18006]) ).
cnf(i_0_19649,plain,
c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(equality_inference,[],[18007]) ).
cnf(i_0_19650,plain,
c_Random_Oinc__shift(X1,X1) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),
inference(equality_inference,[],[18014]) ).
cnf(i_0_19651,plain,
X1 = X1,
inference(equality_inference,[],[18039]) ).
cnf(i_0_19652,plain,
X1 = X1,
inference(equality_inference,[],[18040]) ).
cnf(i_0_19653,plain,
$false,
inference(scs_inference,[],[i_0_17981,i_0_16455,i_0_14058]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW294+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n015.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 06:34:32 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 33.31/18.22 % Version : CSE_E---1.7
% 33.31/18.22 % Problem : theBenchmark.p
% 33.31/18.22 % SZS status Theorem for theBenchmark.p
% 33.31/18.22 % SZS output start CNFRefutation
% See solution above
% 33.60/18.58 % Total time : 17.854s
%------------------------------------------------------------------------------